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OPEN READING FRAME COMPOSITION AND
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OPEN READING FRAME COMPOSITION AND ORGANIZATION AS INDICATORS OF
PHENOTYPIC DIVERSITY IN BACTERIA AND ARCHAEA

By
SCOTT HENRY HARRISON

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Microbiology and Molecular Genetics

2006

ABSTRACT
OPEN READING FRAME COMPOSITION AND ORGANIZATION AS INDICATORS OF
PHENOTYPIC DIVERSITY IN BACTERIA AND ARCHAEA
By
SCOTT HENRY HARRISON
Phenotypically, intragenomic recombination enables prokaryotic organisms to respond to
dramatic changes in environmental conditions by restructuring the genome. The relationship
between adaptation and alterations to genome structure over time impacts phylogeny and
relates to factors regarding the optimal physiological conﬁguration of genome structure. This
study provides a quantitative treatment of open reading frame (ORF) organization based on
aspects of functional conservation and DNA mobility. An analytical software system was
built to facilitate randomizations, subsamplings, and comparative treatments of calculated
and organized measures of open reading frame (ORF) attributes encompassing 447,551
annotated ORFs from 155 fully sequenced prokaryotic genomes. An operational subset of
ORFS (O—ORFS) of putative phenotypic importance was selected based on a simple heuristic
of similar length and content in comparison to ﬁve or more other ORFs. The proportion of
total, annotated ORFs represented by O-ORFS strongly correlated with a predicted 3:1
signal-to—noise ratio of O-ORFs, likely associated with some phenotype, to putatively silent
ORFs (S-ORFs) of unknown and undeﬁned phenotype. The O-ORF subset had a signiﬁcant
degree of clustered chromosomal organization across a broad phylogenetic range. Additional
study of ORF organization was conducted by developing quantitative measures of ORF
clustering based on segmentation of the chromosomal sequence into consecutive regions of
speciﬁed scalings. Properties associated with performance of non-parametric measures were
partly characterized by simulation using an extended model of an abstract expansion
modiﬁcation system. Measures of ORF organization were evaluated as potential signatures of
the recombinational history of an organism. As predicted by a postulated relationship
between genomic organization and phylogenetic relatedness, the measurements had
signiﬁcant correspondence with times of divergence from last common ancestors. The
presence of mobile elements predictably correlated with greater deviations from

organizational symmetries of ORFs.

Copyright by
SCOTT HENRY HARRISON
2006

In Memory of Richard John Harrison

iv

ACKNOWLEDGEMENTS

I would foremostly like to acknowledge the many in my family, especially my brothers,
Richard and Timothy, who for me have always set an example of conscientious ethic and
genuine dialogue whatever the season or circumstance. I am grateful to my wife, Tara, and
my children for their love, good humor, and kindness. My beloved wife Tara provided an
extraordinary degree of comforting support, especially when I was working at greatest
intensity.

Special thanks goes to my mentor, Julius H. Jackson, for the many thoughtful
conversations we have shared over the years, and his openness and encouragment of
innovative effort. Both in terms of magnitude and consistency, Dr. Jackson’s assessments of
the literature, mentoring of students, demands for rigor with systems-based approaches, and
extensive knowledge concerning microbial biochemistry, physiology, and dynamic analysis,
reﬂect the type of scholarly devotion I most hope to emulate in the years ahead. I deeply
valued the opportunity to work with and assist the many undergraduate students who were
members of Dr. Jackson’s laboratory. On both a personal and professional level, Dr.
Jackson’s efforts towards me, a student and aspiring scholar, will always be for me an
example of Socratic virtue in its ﬁnest form.

I am grateful to my committee for demanding detail and excellence, for being pithy
when I was being protracted, and for their strong, unmitigating sense of scholarship when I
was a beginning student of research and science. They are Brian Feeny, Michele Fluck,
Patricia Herring, Richard Lenski, and Larry Snyder.

There are also colleagues, friends and faculty to whom I am indebted for their
encouragement and demonstrations of professionalism. They include Janet Batzli, Cedric
Buckley, James Cole, Tony D’Angelo, Les Dethlefsen, Diane Ebert-May, George Garrity,
Feng Han, Helen Keefe, Gerd Kortemeyer, Niels Larsen, Douglas Luckie, Desmond Stephens,
and Bill Uicker. I am a better person for having known them. I would like to also make
special mention of my high school biology teacher, Phil Browne, who always made biology an
exciting and intriguing subject of study.

There are not the words nor the pages to fully describe the contributions of scholars and

others who have played an invaluable role in my development as an aspiring researcher of the
natural sciences. I am especially grateful to those, such as Harvey and Pagel (1991) and
Torretti (1984), who have each put together illuminating texts on how to assess pattern in
the natural world. Also, the bioinformatics aspect to my effort greatly beneﬁtted from the
availability of powerful, reliable and highly ﬂexible free and open source software tools.

I am deeply grateful to those who have invested and sacriﬁced their time, energies, lives
and fortunes to safeguard and champion how it is that ongoing generations of persons can so
freely and openly pursue the discovery and advancement of knowledge in a democratic
society. I would be sorely remiss if I were not to thank my parents for all of their many
unheralded acts of love that I believe deﬁne the essence of such a profoundly meaningful

purpose. Thanks, mom and dad, for emphasizing integrity and giving me a start in life.

vi

TABLE OF CONTENTS

LIST OF TABLES ix
LIST OF FIGURES xi
1 Introduction 1
1.1 Overview ....................................... 1
1.2 Genomic Variation and Phylogeny ......................... 3
1.3 Genomic Mobility .................................. 13
1.4 Annotated Open Reading Frames ......................... 20
1.5 Summary and Objectives .............................. 26
2 Methods and Developed Methodology 29
2.1 Analytical Design .................................. 29
2.2 Data Assembly ................................... 31
2.2.1 Collection of Genome Data ......................... 31
2.2.2 Management of ORF Data ......................... 35
2.2.3 Taxonomic and Phylogenetic Categorizations ............... 38
2.2.4 External ORF—Based Data Sets ...................... 41
2.2.5 Mobile Elements .............................. 41
2.3 Dot Matrix Evaluation of Conserved Chromosomal Organization ........ 42
2.4 Measuring Mutual Information .......................... 42
2.5 Speciﬁcation of Operational ORF Subset ..................... 45
2.6 Running Tally .................................... 45
2.7 Simulation of Informational Expansion and Modiﬁcation ............ 46
2.8 Measures of Internal Physical Clustering ..................... 50
2.8.1 ORF Density Calculation and Randomization .............. 50
2.8.2 Lag k Autocorrelation ........................... 51
2.8.3 Scalar Residue Measures of Internal Clustering .............. 52
2.8.4 Bootstrapping ................................ 53

2.8.5 Harmonic Symmetry of ORF Density and the Windowed Asymmetric
Deviation .................................. 54
3 Diversity and Stability of Chromosomal Organization and Content 56
3.1 Taxonomy of Chromosomal Data ......................... 56
3.1.1 Patchiness of Taxonomic Representation ................. 56
3.1.2 Evolutionary Times of Divergence ..................... 58
3.1.3 Comparative Power of Data Set ...................... 58
3.1.4 Replicon Topology, Size, and Composition ................ 61
3.2 Structural Constraints of Chromosomal Organization and Content ....... 65
3.2.1 Open Reading Frames ........................... 65
3.2.2 ORF Arrangement ............................. 69
3.2.3 Chromosome Size .............................. 92
3.3 Discussion ...................................... 96
4 Subsets of Open Reading Frames 104
4.1 Comparative Parameters of Sequence Conservation ............... 104

vii

4.2 Paralogous ORFs .................................. 106

4.3 Findings for an Operational ORF Subset ..................... 113
4.3.1 Differences in Length and Similarity Cluster Size ............ 113

4.3.2 Composition of Phyla within ORF Similarity Clusters .......... 128

4.3.3 Expressional, Phenotypic, and Functional Aspects of the ORF Subsets 128

4.4 Non-Stochastic Clustering of O-ORFs ....................... 140
4.5 Discussion ...................................... 140

5 Measures of Internal Physical O-ORF Clustering 147
5.1 Lagged Autocorrelations of O-ORF Densities ................... 147
5.2 Scalar Residue Measures .............................. 149
5.2.1 Sum of Squared Differences on Lagged Autocorrelation Series ..... 149

5.2.2 Frequency of Changes in Angular Variation on the O-ORF Density Series 153

5.2.3 Taxonomic Correspondence ........................ 155

5.3 Simulation of Informational Change ........................ 156
5.3.1 Development and Characterization of Simulation Model ......... 156

5.3.2 Scalar and Spectral Measures of Model Output ............. 161

5.4 Investigating Phylogeny .............................. 167
5.5 Discussion ...................................... 172

6 Summary and Conclusion 176
BIBLIOGRAPHY 180

viii

LIST OF TABLES

1 Introduction 1
2 Methods and Developed Methodology 29
1 Descriptions of four NCBI ﬁle formats. ...................... 32
2 Abbreviated labels for chromosomal accession numbers .............. 36
3 Diversity and Stability of Chromosomal Organization and Content 56
3 Conservation of total genome size for various genera. .............. 63
4 Conservation of total genome size for various species. .............. 64
5 Diverging set of phylogenetic comparisons. .................... 72
6 Correlation of APMI with time of divergence. .................. 74
7 Relationship of time of divergence to quantitative indicators of conserved ORF
organization for pairwise comparisons of archaeal chromosomes. ........ 87
8 Relationship of time of divergence to visual and quantitative indicators of
conserved ORF organization for pairwise comparisons of bacterial chromosomes. 88
9 Normalized ranges of polarity tallies. ....................... 89
4 Subsets of Open Reading names 104
10 Names and descriptions of open reading frame subsets. ............. 107
11 O-ORF and S-ORF comparison of ORF length norms for 6 taxonomic
groupings. ...................................... 1 14
12 ORF subset comparisons of ORF counts for 6 taxonomic groupings ....... 115
13 Phenotypic inactivation associated with Bacillus subtilis O-ORFS and S-ORFS. 132
14 ORF counts from Bacillus subtilis for single and multiple phenotypes based on
COG and O-ORF categorizations .......................... 132
15 S—ORF percentages of ORF counts for various functional COG categories . . . 137
16 Percent O-ORF representation for groups of COG categories based on
bacterial genomes and genome size indicators of organism lifestyle ........ 139
17 Threshold parameters of sequence conservation for the operational ORF subset

(O-ORFS) and the COG membership subset (C-ORFS) .............. 142

5 Measures of Internal Physical O-ORF Clustering 147

18

19

20

Cross-correlations 1" among sets of three chromosomes (c1, c2, c3) between series
of Q(ci, 6) values for segmentation-based symmetries of O-ORF densities
where 6 = 10, 20,30, ..., 150 kb ............................ 152

Average mutual information of lagged series for Q(c,-. 6) values of the
symmetry score where segmentation size 6 = 10, 20, 30, ..., 150 kb. ....... 152

Average mutual information of lagged series for P(c,~. 6) values of symmetric
shape for segmentation sizes 6 = 10, 20, 30, 150 kb. .............. 155

LIST OF FIGURES

Images in this dissertation are presented in color.

1 Introduction 1
2 Methods and Developed Methodology 29
1 Resampling strategies and randomization design .................. 30
2 Calculation of regional ORF counts ......................... 31

3 Selecting ORF attributes for retrieval from the online MYCROW information
retrieval web page. ................................. 39

4 Selecting a set of chromosomes or organisms from the online MYCROW
information retrieval web page. .......................... 40

5 Calculating the pointwise mutual information on a dot. matrix of conserved

ORF organization. ................................. 44
6 My method for counting up a running tally for original and randomized ORF
annotations ...................................... 47
7 Illustration of the windowed asymmetric deviation measure. .......... 55
3 Diversity and Stability of Chromosomal Organization and Content 56
8 Taxonomic scope of 155 fully sequenced genomes. ................ 57
9 Times of divergence for 15 Archaea ......................... 59
10 Times of divergence for 12 Gammaproteobacteria ................. 60
11 Times of divergence for 8 Bacilli. ......................... 60
12 Times of divergence for 4 Actinobacteria ...................... 61

13 Comparative scope of available chromosomes and genome-sequenced strains

over time. ...................................... 62
14 Number of annotated ORFs versus genome size for 155 genomes ......... 65
15 Distribution of 447,551 ORF lengths for 155 genomes ............... 66
16 Subsampled distributions of ORF lengths. .................... 68
17 ORF length frequency distributions among 5 taxonomic subgroupings ...... 70
18 Log-transformed distribution of ORF lengths for 155 genomes .......... 71

xi

19 Comparisons of ORF organization for two M. tuberculosis strains and two E.
coli strains. ..................................... 71

20 Comparisons of ORF organization for two Mycobacterium species and two
species from the Enterobacteriales ......................... 72

21 APMI values on dot matrix plots for various taxonomy-based comparisons of
chromosomes. .................................... 73

22 APMI values on dot matrix plots for various times of divergence ......... 7o

23 Taxonomy-based differences in average pointwise mutual information for
various segmentation sizes .............................. 76

24 Difference between averaged W-values of lineage and species—genus comparisons. 77
25 Comparisons of conserved ORF organization among three Pyrococcus strains. . 78

26 Comparisons of conserved ORF organization among two M ethanosarcina
strains with A. fulgidus. .............................. 79

27 Comparisons of conserved ORF organization among three Crenarchaeota strains. 80

28 Comparisons of conserved ORF organization among two Mycobocterium
tuberculosis strains and Corynebacterium glutamicum ............... 81

29 Comparisons of conserved ORF organization among Nostoc sp. PCC 7120,
Synechocystis sp. PCC 6803, and Therrnosynechococcus elongatus BP-l. . . . . 82

30 Comparisons of conserved ORF organization among S. pyogenes, S.
pneumoniae, and L. lactis. ............................. 83

31 Comparisons of conserved ORF organization among three Mycoplasma strains. 84

32 Comparisons of conserved ORF organization among two Rickettsia strains and
Caulobocter crescentus ................................ 85

33 Comparisons of conserved ORF organization among two X anthomonas strains

and Xylella fastidiosa Temeculal. ......................... 86
34 Running tally graphs of polarity along four chromosomes ............. 90
35 Running tally graphs of COG membership along four chromosomes. . . . . . . 91
36 Histogram of 165 chromosome sizes. Bin size is 500,000 base pairs ........ 93
37 Relationship of divergence time from a last common ancestor to changes in

chromosome size and pointwise mutual information ................ 95
Subsets of Open Reading Frames 104

38 Frequency of distances between related paralogs for four strains of Escherichia
coli. ......................................... 109

xii

39 Frequency of distances between related paralogs for three strains of
Pseudomonas species .................................

40 Frequency of distances between related paralogs for four strains of
Streptococcous pyogenes. ..............................

41 Frequency of distances between related paralogs for three strains of
Staphylococcus aureus. ...............................

42 Relative frequency distributions of S-ORF. O-ORF. and U-ORF lengths for
155 genomes. ....................................

43 Frequency distributions of logarithut-transformed ORF lengths for various
samplings of genomes. ...............................

44 Number of ORFs associated with various ranges of similarity cluster sizes.
45 Relationship between ORF length and ORF similarity. .............
46 Relationship between ORF length and ORF similarity. .............

47 Log-log frequency distributions of number of ORFs for similarity cluster size
limits. ........................................

48 Normality of log-transformed ORF lengths .....................
49 Normality of log-transformed S-ORF lengths. ..................
50 Normality of log-transformed O-ORF lengths. ..................
51 Membership within phyla for similarity clusters ..................
52 Membership within four other phyla for similarity clusters. ...........
53 ORF membership subset comparisons with total ORF counts ..........
54 ORF membership intersecting subset comparisons with total ORF counts.

55 Number of ORFs, O-ORFs, and S-ORFs for various COG-based categories of
function ........................................

56 Running tally graphs of O-ORF membership along four chromosomes ......

Measures of Internal Physical O-ORF Clustering

57 Lag k autocorrelation values calculated on ORF density series built. with
segmentation size 6 = 40 kb .............................

58 The Q(cz-, 6) measure of segmentation-based symmetries of O-ORF densities
among three Crenarchaeota strains and three Actinobacteria strains for
6 = 10, 20, 30, ..., 150 kb. ..............................

59 The P(c,-, 6) measure of symmetric shape among three Crenarchaeota strains
and three Actinobacteria strains for 6 = 10, 20, 30, 150 kb. ..........

xiii

110

125

129
130
134
135

136
141

147

148

150

154

60
61

62

63

64

66

67

68

69

70

71

72

Q-based symmetry scores of O-ORF densities on 9 archaeal chromosomes.

Q-based symmetry scores of O-ORF densities on the chromosomes of 3
Actinobacteria, 3 Cyanobacteria, and 3 Lactobacillales. .............

Q-based symmetry scores of O—ORF densities on the chromosomes of 3
Mollicutes and 6 Proteobacteria ...........................

Examples of the abstract simulation for structural duplications and
translocations on a symbolic sequence. ......................

Scorings of segmentation-based symmetries for simulations of informational
expansion and modiﬁcation. ............................

Scorings of segmentation-based symmetries for simulations of informational
expansion and modiﬁcation. ............................

Changes to FFT on the Q series based on adjusting the simulation model T
value. ........................................

Changes to F FT on the Q series based on adjusting the simulation model S
and N values .....................................

KS distances of Q and kr'lod(fft(Q))-based measures of simulated
rearrangements ....................................

Differences of windowed asymmetric deviations between S. pyogenes strains
based on a 25 kb window of segmentation sizes. .................

Frequency of differences between windowed asymmetric deviations among
closely related strains of the same species. ....................

Relationship of divergence time from a last common ancestor to differences in
chromosomal structure and organization. .....................

Relationship of windowed asymmetric deviation to IS element density. . . . . .

xiv

157

158

159

162

163

165

166

170

171

Chapter 1: Introduction

1.1 Overview

Recombinations are one of two major forms of heritable change in prokaryotic genomes,
and the consequence of a recombination event is to restructure the organization and
composition of genomic elements such as open reading frames (ORFs) (Brown, 2002). The
other form of heritable change, sequence-level mutations, has been well studied in terms of
evolutionary models and comparative treatments (Zuckerkandl & Pauling, 1965; Woese, 1987;
Ochman et al., 1999). There exists a database of functionally grouped clusters of orthologous
genes that characterizes those genes with conserved sequences implicating a directly vertical
last common ancestor (Tatusov et al., 1997a, 2003). There is not however a database with a
function-based cataloguing of the formations and disruptions of genomic structure.
Characterizing prokaryotic diversity in terms of the functional aspects of recombinative
change may help develop current proposals as to how expansions and modiﬁcations of
genomic structure relate to speciﬁc phenotypes of an organism (Bentley & Parkhill, 2004;
Cohan, 2004; Moran & Plague, 2004; Ochman & Davalos, 2006).

Signiﬁcant phenotypic change does not necessarily correspond with conventional
evaluations of conserved sequence and genomic structure. Mycobacterium avium subspecies
avium is frequently encountered in the environment and causes infections in certain animals
and immunocompromised patients. Mycobacterium avium subspecies paratuberculosis has
signiﬁcantly different behavior than M. avium in terms of a much slower growth rate and
different pathogenicity. Yet, when M. avium subspecies paratuberculosis is compared to M.
avium subspecies auium, it is almost identical for 168 rRNA sequence, conserved genomic
organization, and the region surrounding oriC (Bannantine et al., 2003). Furthermore, it is a
complex question to consider how phenotypic categorizations of diversity may efﬁciently
account for the variable lifestyles, ecologies, ancestral lineages, appearances and behaviors of
prokaryotic organisms. Taxonomically, for prokaryotes, there is not yet “a consensus for
deﬁning the fundamental unit of biological diversity, the species” (Cohan, 2002).

Reconstructions of the prokaryotic phylogeny have often been based upon patterns of

sequence similarity as a primary means for asserting homology (inferred origin of DNA
sequence from the same ancestral sequence) (Morell, 1997; Zhaxybayeva et al., 2004;
Patterson, 1988). Differences between sequences help reveal branch points in the phylogeny
(Pearson & Lipman, 1988) as well as the rates at which mutating random events occur from
various branch points to the present (Ochman & Wilson, 1987; Ochman et al., 1999).
Sequence-level changes themselves do not fully resolve how surrounding changes in
evolutionary rate may occur. For higher taxa, it is especially difficult to see how a procession
of changes in ribosomal sequence may closely follow signiﬁcant alterations in proteomic
content. ﬁ-proteobacteria differ from a-proteobacteria not just by ribosomal sequence but
also by photoreaction centers, cytochrome c type, and having cytochromes of the small type
compared to the medium-large type (Woese, 1987). More comprehensive assays of genome
structure and content may provide the empirical information needed to directly characterize
the emergence of such properties within the proteome.

Inspection of synteny (conserved arrangement of genome structure) (Horimoto et al.,
2001; Kalrnan et al., 1999; Rocap et al., 2003) can be a means for inferring branch points
based on lineages experiencing different series of rearranging recombinations. This has been
especially the case when comparing closely-related strains (Naas et al., 1994; Dalevi et al.,
2002; Rocap et al., 2003). While ancestral genome structure may partially dissipate due to
both horizontal transfer events (Doolittle, 1999a; Xie et al., 2004) and a high level of
intragenomic recombination (Wolf et al., 2001), patterns of vertical ancestry are not
completely removed. There are various cases of vertically inherited recombinations being
stable despite presumed competition from ongoing emergent recombinants. For example,
pulsed-ﬁeld gel electrophoresis measurements have identiﬁed stable recombinant strains of
Campylobacter jejuni coming from poultry processing batches (Wassenaar et al., 1998). The
stability in C. jejuni genome structure cannot be attributed to horizontal gene transfer
because natural transformation between Campylobacter jejuni strains does not occur in vivo
(Wassenaar et al., 1998). Higher clade investigation in the Enterobacteriaceae family presents
another case of tractable vertical evolution. Free and random intragenomic shuffling and
horizontal replication of genomic structure between species does not occur (Sanderson, 1976;

Souza & Eguiarte, 1997). There may also be gross structural conservation between members

from differing phyla or from each of the two domains, Archaea and Bacteria. Horimoto et al.
(2001) ﬁnds a statistically signiﬁcant portion of orthologs to be constrained in chromosomal
position across a phylogenetic span represented by nineteen archaeal and bacterial genomes.
While a comprehensive, functional decomposition cannot yet be accomplished by
analysis of a fully sequenced genome, genome sequences do help to delineate practical
distinctions between prokaryotic organisms. Genomovars has been a term coined to
characterize the capability of genome sequence to chart taxonomic boundaries independent of
direct biochemical assessments of phenotype (Ursing et al., 1995). A variety of studies have
illustrated how genomovars work to help categorize diverse sets of strains from the genera
Pseudomonas (Cladera et al., 2004), Burkholderia (Vandamme, 2001), and Sinorhizobium
(Young, 2003). In terms of chromosomal organization, functional accountings of non-random
symmetries or periodicities have been proposed to involve past duplications of the
chromosome (Kunisawa & Otsuka, 1988), the effects of supercoiling (Jeong et al., 2004), and
aspects of gene dosage (Jurka & Savageau, 1985). There is mounting empirical and
comparative evidence as to how the physical organization of proteins as they are encoded by
open reading frames on the physical length of a chromosome corresponds with both
expression (Deng et al., 2005; Higgins et al., 1990) and function (Li et al., 2005; Wolf et al.,
2001). This evidence suggests that an analysis of chromosomal ORF organization on the
expanding data set of fully sequenced genomes may aid in a greater characterization of the

functional and phylogenetic nature of prokaryotic genomes.

1.2 Genomic Variation and Phylogeny

A major goal in biology has been to determine the “universal tree of life” (Philipe 85
Forterre, 1999; Doolittle, 1999b; Kennedy & Norman, 2005) where various lineages of
organisms generate progeny that either survive and reproduce, or do not. Survival and
reproduction is inﬂuenced by competition with other organisms, ecological conditions, the
inherited genetics of the organism, and chance events (Darwin, 1859; Kutschera & Niklas,
2004). For a time period of over several billion years (Schidlowski, 1988), organisms have

been affected by many large-scale ecological changes (Nisbet & Sleep, 2001; Battistuzzi et al.,

2004), so it is difﬁcult to re-enact in vivo the entire formation of life’s history. Yet, the
evolutionary history of known organisms can be inferred from comparisons of data to produce
a phylogeny, a tree of life based on ancestral lineages (Harvey & Pagel, 1991). Comparisons
between different ancestral lineages involves measurement of difference, and attempting to
characterize when and why differences emerge. On a phylogenetic tree, there are large
branches from which smaller branches emerge, eventually leading to known contemporary
organisms which are placed at the leaves of the tree. The Woesian tree’s largest branches
represent three superkingdoms: Archaea, Bacteria, and Eukarya (Woese et al., 1990). Two of
these superkingdoms, Archaea and Bacteria, are prokaryotic; they contain unicellular
organisms lacking organelles. The asexual form of prokaryotic reproduction is advantageous
for evolutionary studies due to the non-reticulating pattern of vertical ancestry associated
with asexual reproduction.

Although prokaryotes reproduce asexually, not all heritable characteristics follow a
tree-shaped vertical ancestry. Through a variety of mechanisms, different strains can share
genetic material with one another through a process called lateral, or horizontal, gene
transfer (LGT or HGT) (Doolittle, 1999a; Battistuzzi et al., 2004). Evidence for LGT
challenges the idea of an immutably core set of monophyletic genes; LGT appears to have
been a process that extends back billions of years (Rivera & Lake, 2004) with an effect
ranging across most, if not all, functional categories of genes (Battistuzzi et al., 2004).
Currently, available data and the number of putatively conserved core genes is small enough
so as to preclude estimation of the last common ancestor branchpoint (Battistuzzi et al.,
2004). Other phenomena that contravene or confound tests for vertical ancestry among the
prokaryotes include paralogous origination of new genes (Patterson, 1988) and phenotypic
switching (Balaban et al., 2004).

To meaningfully predict behavior as a result of phylogenetic history, changes in the
environment must be evaluated in addition to vertical (or horizontal) changes to the genome
(Rjdley, 1993; Lande, 1985, 1982). Calibrating an inferred history of mutational events
against historical changes in the environment enables inferrence of an evolutionary 'clock’s
relationship to physical time (Ochman et al., 1999; Battistuzzi et al., 2004). Informationally,

such a strategy of analysis has theoretical justiﬁcation (Zuckerkandl & Pauling, 1965; Woese,

1987). When such calibration has occurred for sequence-level phylogenetic reconstructions
however, there is signiﬁcant variability of molecular clock rates between lineages.
Contemporary efforts have sought resolution with either explicitly parametric models
(Gillooly et al., 2005), or semiparametric methods that help compensate for the complex
“interplay between estimates of divergence times and rates” (Sanderson, 2002). To approach
a molecular clock characterization of the dynamics between recombination events and
phylogenetic branch points, there may be additional sources of complexity to the available
information. Lineage-related diversity of recombinative mechanisms is extensive (Craig et al.,
2002). Furthermore, in the DNA sequence, historical evidence of DNA mobility gradually
disappears through amelioration (Campbell, 2002). Visualizing and comparing different sets
of recombinative events necessarily would involve a degree of inference for reconstructions of
past history, especially as might be applicable to the testing of hypotheses involving
historical changes in the environment.

While the theory underpinning a molecular clock is informational (Zuckerkandl &
Pauling, 1965), hypothesis testing to characterize how lifestyle (evolutionary mode) causes
variation in neutral changes (evolutionary tempo) requires identiﬁcation of the “molecular
counterpart of that ill-deﬁned quality, evolutionary mode” (Woese, 1987). Recent
observations of recombinative systems under experimental conditions have been consistent
with recombinative behavior producing mutations under selective conditions that “cannot
readily be produced by point mutations” (Schneider & Lenski, 2004). Treatment of
recombinative changes in addition to sequence-level changes may therefore increase the
amount of molecular data that can characterize evolutionary tempo and mode. With
additional molecular data, wide-ranging credibility intervals for times of divergence in
prokaryotic phylogeny (Battistuzzi et al., 2004) may be to some degree shortened. An
alternate possibility is that changes in lifestyle may be characterized more in terms of how
environmental factors intersect with altered functional compositions produced by
recombination (Konstantinidis & Tiedje, 2004).

Evolutionary mode and tempo have been characterized as being quasi-independent
(Woese, 1987). Contrasting the effects of mode and tempo would require distinguishing these

dynamics of change based on concepts corresponding to nature. Woese (1987) proposes three

distinguishing characteristics for evolutionary tempo: chronic ongoing change (“clocklike
behavior”), action over a long period of time (“range”), and “loosely coupled domains” over
which chronic changes are averaged (or, as called by Woese: “size”). Recombinations are
being associated with an increased number of functional consequences (Schneider & Lenski,
2004). The increasing number of different functional consequences may elevate the possibility
of there being “loosely coupled domains” as to how and where different recombinations occur
throughout the genome. As would correspond to the chronic-like property of evolutionary
tempo, recombinative activity has also been observed to be ongoing throughout both stressful
and non-stressful conditions.

In general, gene order is poorly conserved in bacteria, even among closely related
bacteria such as Escherichia coli and Pseudomonas aeruginosa (Nolling et al., 2001). While
gene order is more strongly conserved for other lineages such as the Clostridia, there is still
prevalent disruption of low-level structures such as operons. Yet, although recombination can
greatly disrupt genomic structure and, correspondingly, open reading frame (ORF)
arrangement (Suerbaum et al., 1998), comparisons of regions larger than operons show
remarkably wide-ranging proximal similarity between orthologous pairings among genomes
across phylogeny (Horimoto et al., 2001). Such a ﬁnding suggests that strong forces of
conservation prohibit dissipation of large scale ancestral ORF arrangement. If the pattern of
ORF arrangement is retained over lengthy evolutionary ranges, and if changes occur in a
chronic ongoing process that each independently inﬂuence disparate parts of the genome,
then there is theoretical support for some of the variation in ORF structure to reﬂect
evolutionary tempo. Testing of a proposed molecular clock can compare branch lengths so as
to evaluate likelihood ratios (Shimodaira & Hasegawa, 1999). Furthermore, to independently
compare the robustness of how recombinational history covaries with ribosomal phylogeny,
different subtrees in the phylogeny can be identiﬁed and a nested analysis, such as that
described by Bell (1989), performed.

The process of robustly measured ORF arrangement for clocklike properties may also
facilitate baseline comparisons for how supercoiling arrangements contrast with optimal
adaptation to variation in the environment. Water, virulence, salt and temperature have all

been proposed as environmental factors associated with supercoiling (Higgins et al., 1990;

Luttinger, 1995; Mojica et al., 1994). The absence of a formula to precisely model the
biochemistry between supercoiling and an external environment makes comparative tests of
optimality implicit in that they rest upon preliminary expectations of maximized levels of
“Darwinian ﬁtness” (Harvey & Pagel, 1991). The construction of more explicit assessments
could foreseeably involve dynamics of how the regulatory role of supercoiling controls DNA
condensation and the transcriptional availability of genomic regions (Worcel & Burgi, 1972;
Aki & Adhya, 1997; Reznikoff et al., 1985). Based on current knowledge, there is difficulty
with arriving at an explicit assessment. For example, there are varying estimates of nucleoid
structure with supercoiling domains being conﬂictingly characterized as 10 kb per domain
(Postow et al., 2004) versus 50 kb - 100 kb per domain (Miller & Simons, 1993).
Informational analyses may still help elucidate general evolutionary dynamics such as
selection against deleterious mutants (Kimura, 1983). While initial characterization of various
evolutionary consequences to recombinative change may be implicit for environment-based
optima, implicit functional assessments are “a reasonable ﬁrst step” (Harvey & Pagel, 1991).
While the ﬁtness of genomic restructuring cannot yet be accounted for by an explicit
formula, evolutionary comparisons can infer aspects of ﬁtness and their phylogenetic range.
A variety of “functional barriers” have been proposed to the ﬁtness consequences of
recombination (Mahan et al., 1990). For example, a phenomenon of “replichore balancing”
occurs where evolutionary ﬁt recombinations act to keep the origin of replication at a position
halfway (180°) from the termini. This phylogenetically widespread phenomenon can be
inferred from various comparisons of closely related genomes belonging to different lineages
(Dalevi et al., 2002; Ren et al., 2003; Andersson, 2000; Leblond & Decaris, 1998; Deng et al.,
2002). Replichore balancing has also been conﬁrmed experimentally in both Gram negative
(Hill & Gray, 1988) and Gram positive bacteria (Campo et al., 2004). The presence of
functional barriers such as replichore balancing implies possibilities where selection against
deﬁnitively deleterious mutants would occur, consistent with neutral theory (Kimura, 1983).
Yet, replichore balancing is not mandatory. The high frequency of IS—element recombinations
in Bordetella spp. appears to overwhelm any selective pressure associated with replichore
balancing (Preston et al., 2004). Also, Chlamydophila pneumoniae strains J 138 and CWL029

have 16 kb hot spots of rearrangements that are not near the chromosomal origin or terminus

(Shirai et al., 2000). In controlled experiments, recombinational events have been observed to
cause a wide range of variation without necessarily lethal effect (Mahan et al., 1990). Other
proposed “functional barriers” to recombination have included gene dosage effects, and
conservation of structure around chromosomal termini (Mahan et al., 1990). Shigella fleameri
is thought to deviate signiﬁcantly from Escherichia coli based on reoptimized placement of
its transcriptional units in respect to the gene dosage gradient relative to oriC (Jin et al.,
2002). Further evaluation as to the strength of selection, measurement of ﬁtness, and
long-term competitiveness of recombinants may be helpful to characterize the evolutionary
dynamics of recombinative events.

For purposes of inference, the amount of divergence associated with recombinative
change between lineages must be considered. While “most sequence evolution is
predominantly divergent” (Harvey & Pagel, 1991), several aspects of recombination confound
a scenario of divergent heritable changes. Phenomena include reciprocal events occurring to
balance the replichore (Deng et al., 2002), balanced inﬂux and loss of genome segments
through horizontal transfer (Lawrence et al., 2001; Parkhill et al., 2001a), biphasic
rearrangements (Barbour, 2002; Nanassy & Hughes, 2003), and duplication ampliﬁcations
(Sonti & Roth, 1989; Read at al., 2000). Promisingly, recombination does not appear to be
convergent in scenarios where that might otherwise be expected (Schneider et al., 2000).
Recombinative divergence per se can be essential for driving rapid evolution of new traits
(Sanderson & Liu, 1998). An overall divergent phenomenon of interest is where there is
extensive gross-level conservation of genome structure compared to mosaic-like differences in
smaller-scale structures. An instance of this phenomena can be observed with the 3 species of
Mycobacterium: M. leprae, M. tuberculosis, and M. bovis (Philipp et al., 1998).

The available genomes and their ORFs, having arised from various evolutionary lineages,
may present challenges with causal and population inferences. Whether concerning
sequence-level changes, non-vertical inheritance, or recombinative changes (Gillooly et al.,
2005; Zhaxybayeva et al., 2004; Craig et al., 2002), each lineage considered as a treatment is
not a random allocation, so causal inference is not directly achievable (Lunneborg, 2000).
Population inference requires random sampling (Lunneborg, 2000). The

Gammaproteobacteria are likely to be over-represented as evident from larger compilations

structured from rRNA analyses (Garrity et al., 2004). Additionally, beyond just the
population of genomes, the ORF population is over-annotated and contains many false
positives (Snyder & Gerstein, 2003). Beyond considerations of randomized treatments and
randomized samples (or a rich, well-curated data set from which random resampling could be
extensively performed), further difﬁculty with an analysis may come from the imperfectly
resolved phylogeny (Kennedy & Norman, 2005) as well as the inavailability of explicit models
to relate recombinative change to ﬁtness and speciation. These aspects of observational noise
(e.g., hypothetical ORFs), estimation error (e.g., over-representation of certain taxa), and
dynamic noise (e.g., the consequences of a given recombination in an organismal population
and the surrounding environment) are real-world complexities that make it difficult to
characterize system dynamics (Casdagli et al., 1991). A comparative method requires an
evolutionary model (Harvey & Pagel, 1991), and a model would ideally have one data point
per uniform taxon (Grafen & Ridley, 1997). Aspects of recombinative constancy to the
genome is not something yet established for uniform taxonomic classiﬁcations.

It may be practically signiﬁcant to address notions that explore populations of genes
from a paradigm of behavioral ecology (Kurland, 2005; Dawkins, 1976). ORFs, mobile
elements, and chromosomes have each been characterized as interdependent “populations”
with aspects of competitive growth, ﬁtness, and function (Lawrence & Roth, 1996; Schneider
& Lenski, 2004; Terzaghi & O’Hara, 1990). Improved measures of associated patterns may
better quantify both the observed population of ORFs and the consequences of different
rearrangements. There have recently been advances that address the distribution of ORFs as
informational units (Azad et al., 2002), as well as advances in how informational signatures
of interactions between populations can be detected (Sandvik et al., 2004).

Azad et al. (2002) presents an investigation for ORF traits and their relationship to
coding sequence versus non-coding sequence. By looking at dynamics of information, Azad
et al. (2002) claim to “go beyond an analysis of the functional parts of the DNA.” The
informational analysis of Azad et al. (2002) proceeds with measuring information present
inside various segments (successive regions of genomic DNA of a speciﬁc length in base
pairs). Segmentation studies of genomic DNA serve to “break up a complex object into its

’constituent’ parts...to understand how the organization comes about in the ﬁrst place”

(Azad et al., 2002). Azad et al. (2002) abstractly evaluate region lengths of potential coding
space against a breakage process also known as the Kolmogorov theory of physical
fragmentation. Essentially, the breakage of units at random points along their length leads to
a log-normal distribution (Li, 1991; Azad et al., 2002). Such a mode of ORF fragmentation
could be attributable to nonsense codon mutations; in a study that separates actual genes
from annotated genes, the length-based effects of randomly occurring start-stop codon pairs
is utilized as a chief and phylogenetically widespread criterion to separate “real” from
“non-real” ORFs (Skovgaard et al., 2001).

The diversity and cryptic evidence of past recombinative histories (Campbell, 2002;
Craig et al., 2002) makes an exact parameteric model difficult to achieve since such noise
must be evaluated to defensibly reconstruct changes in state (Casdagli et al., 1991). Linear
relationships cannot be fully assumed for how recombinative changes pass from ancestor to
progeny. Ongoing debate and dialogue concerns, for example, the reticulating role of
horizontal transfer and paralogous duplication (Kurland, 2000) and the implication of
circular evolutionary pathways (Rivera & Lake, 2004). Strategies for direct manipulation of
the interactions, parameterization of mechanical models, or direct simplifying assumptions
that help characterize “linear relationships between response and predictor values” (Sandvik
et al., 2004) may all be signiﬁcantly limited by current inferrence when applied to charting
recombinational history. The ﬁeld of ecology is producing new approaches that “do not make
any a priori assumptions about dynamic properties” (Sandvik et al., 2004). Sandvik et al.
(2004) measures robust signatures of ecological interaction between multiple populations.
Sandvik et al. (2004) demonstrate the usage of an approach for rigorously characterizing
signals of interaction “that avoids these [mechanical models and linear relationships]
difficulties.”

Aside from bibliographic references to the literature item(s) characterizing particular
submitted genome sequences, ecological and phenotypic information is generally absent from
submitted genome sequence data ﬁles. A curatorial challenge has been to comparatively
qualify the different lifestyles and ecologies associated with each genome-sequenced strain.
Distinctions implicating varying schemes of genomic expansions, modiﬁcations, and

contractions can involve the organism’s intracellular or extracellular setting as well as

10

metabolic activity (Bentley & Parkhill, 2004; Ochman & Davalos, 2006). A limiting aspect to
the analysis that may bias the set of 155 genomes, is that only 1% of all estimated microbes
can be cultivated in artiﬁcial laboratory conditions, and the biochemical and metabolic
properties of culturable organisms become, by default, “key characteristics” (Santos &
Ochman, 2004). Conventional morphological and nutritional criteria used to describe
microbes do not lead to a natural taxonomy (Pace, 1997).

A full characterization of phenotypic diversity across the phylogenetic range represented
by fully sequenced prokaryotic genomes is a signiﬁcant enterprise involving hereditary
information in addition to the behavior and environments inhabited by prokaryotic strains.
The current phylogenetic estimates are quite variable. As calculated from nucleotide
sequence changes, the divergence of Yersinia from E. coli is estimated to be 375 Ma 3145
Ma (Deng et al., 2002). Even the comparably richer historical record concerning Y. pestis
and Y. pseudotuberculosis leads to an estimated time of divergence 1,500—20,000 years ago
(Achtman et al., 1999). For time spans involving billions of years, the range of variation for
credibility intervals is approximately :1: 10—20% (Battistuzzi et al., 2004).

At minimum, for most of the fully sequenced prokaryotes, the genomic DNA is present
in the form of at least one distinct chromosome. Variation between species can extend to
multiple copies of the same chromosome, multiple different chromosomes, and other replicons
such as plasmids. A functional deﬁnition of a plasmid is that it is unnecessary for the
viability of a particular organism (Bentley & Parkhill, 2004). Yet, such a distinction may not
be perfect for current classiﬁcations of replicons. Larger plasmids may have especially high
maintenance costs and there would need to be some offsetting selective advantage to promote
their presence within a prokaryotic organism. Halobacterium has a 200 kb plasmid, pNRCIOO,
that has “properties of resistance to curing suggest that this replicon may be evolving into a
new chromosome” (N g at al., 1998). Other large plasmids associated with fully sequenced
genomes include a 2 million base pair plasmid in Ralstonia solanacearum, and a 1.6 million
base pair plasmid in Sinorhizobium meliloti. Conversely, there are various chromosomes that,
based on size and horizontal ancestry, might otherwise be considered plasmids except for
having some degree of “essentiality” to the life of the organism. Vibrio cholerae has a

chromosome that appears to be a captured megaplasmid from a non-Proteobacterial origin

11

(Heidelberg et al., 2000). It has also been suggested that unknown, novel chromosomal
structures may yet be identiﬁed. For instance, the conventional PFGE approach misses what
new methods, such as optical mapping, can ﬁnd (Lin et al., 1999; Zhou & Schwartz, 2004).

The number of distinct chromosomes is not necessarily ﬁxed between closely related
strains. Different biovars in Brucella suis can have either a single 3.3 Mb chromosome, or 2
chromosomes of smaller sizes (Jumas-Bilak et al., 1998; Paulsen et al., 2002). In the sense of
a cellular stoichiometry, there can be multiple copies of the same chromosome per cell.
Stoichiometric measurements have some relationship to growth, but do not follow an exact
formula across all taxa. Methanocaldococcus jannaschii has an incremental L-shaped
distribution from 1 to 5 chromosome equivalents for stationary growth, and an L—shaped
curve ranging from 1 to 15 chromosome equivalents for exponential growth (Malandrin et al.,
1999). This is in contrast to the “multiple of 2” distribution of chromosome copy numbers in
Escherichia coli where the copy numbers of chromosome equivalents ascend in the sequence:
1,2,4,8 (Malandrin et al., 1999). At what may be an upper extreme, Buchnera can have 100
genomic copies per cell (Shigenobu et al., 2000).

Association with metabolism and lifestyle is sometimes explicable from recombinative
dynamics and conservation. For example, a recombination deletion event can be inferred
when observing that Buchnera aphidicola has many fli and ﬁg orthologs to Escherichia coli,
yet it is missing a ﬂiC gene (Tamas et al., 2002). This is evidence for non-motile behavior
and corresponds to how the endosymbiotic lifestyle of B. aphidicola contrasts with the
free-living Escherichia coli (Tamas et al., 2002). Intracellular bacteria such as B. aphidicola
generally represent strains with stable genomes where deletions of repeated sequences are
irreversible and mobility has been reduced (Andersson & Kurland, 1998). By contrast,
non—intracellular pathogens and commensals that face greater competition and more
ﬂuctuation of available resources in their host environments rely on genomic rearrangement
to facilitate frequent and revertible phenotypic changes (Ballet, 2001).

In whatever degree of detail the data set is evaluated, there remain additional obstacles
to inferring exact molecular changes over a lengthy periods of time. Both the amelioration of
DNA composition (Campbell, 2002) and the highly composite, dynamic interaction between

interleaving IS elements (Campbell, 2002; Gray, 2000) introduce substantial complexity as to

12

how the history of the internal genomic structure may be retrospectively untangled. The
challenge for a comparative analysis is to identify, measure, and account for the variance of
common properties across the phylogenetic range being evaluated. There is not yet however a
broadly prescribed method for inferring a historical series of recombinative events so as to
evaluate diverse hypotheses about how recombinative changes impact ﬁtness. Explanations
as to how strategies of recombinative expansions and modiﬁcations relate to ecological
adaptation are presently anecdotal (Bentley & Parkhill, 2004). It is difficult to envisage an
explicitly parametric model that can directly evaluate how recombinative change relates to
the correspondence of phenotypic diversity with genomic structure. The fact that an
informational approach does not rely on assuming the constraints of one particular model
versus another may be advantageous, especially given the uncertainty as to how
recombinative changes in genomic structure relate to changes in ﬁtness for an organism and

its lineage.

1 .3 Genomic Mobility

W’ithin sets of closely related strains, change in chromosome size is largely due to
recombination events. Evolutionary experiments by Bergthorsson & Ochman (1999) show
that such changes in the size of chromosomes occur more often than base pair mutations
altering restriction sites. Recombination also alters the internal structure of a replicon such
as a chromosome (Andersson, 2000). Chromosomal variation is often measured in terms of
length differences between ribosomal sequences as assayed by restrictive digests (Ge &
Taylor, 1998; Ralyea et al., 1998). This variation is called “ribotype diversity”, and is
generally attributed to recombinations between rrn operons. In strains of Salmonella typhi,
ribotype diversity is much greater than corresponding base pair diversity (Ng et al., 1999).

Recombinations can cause deletions, duplications, inversions, and translocations
(Andersson, 2000), and recombination frequently involves double strand separation of the
double helix to reveal single strands. These strands can either interact with macromolecules
to facilitate recombinative mechanisms or, by homology, complementarily bind directly to a

single strand of DNA at another site on the double-stranded DNA molecule (Brown, 2002).

13

Recombinations can sometimes be attributed to mechanisms of replication slippage at the
replication fork and duplication events (Li?) et al., 1996; Tillier & Collins, 2000). Mechanisms
of recombination can be categorized as follows: site-speciﬁc, homologous, and illegitimate
(Brown, 2002; Ikeda et al., 1982; Bachellier et al., 1996; Nair et al., 2004). The frequency of a
recombination event can be dependent on the mobilized length of DNA (Bi & Liu, 1994), and
there are also “hot spots” of recombinative activity as well as highly conserved regions
(Watanabe et al., 1997).

Recombination frequency is signiﬁcantly dependent on the mechanism.
RecA-independent recombination between large repeats (> 100 base pairs) happens at a rate
of 10‘5 to 10‘4 recombinations per large repeat per generation; when occurring due to a
slippage mechanism, this requires that repeats be less than 10 kb apart (Lovett, 2004).
RecA—dependent tandem duplications between IS elements occurs at a frequency from 10‘4 to
10‘2 per IS element per generation (Haack & Roth, 1995). Per hour, this rate has been
observed experimentally per IS element as being 2 * 10‘6 to 9 no: 10"6 per cell per hour.
(Schneider & Lenski, 2004). Estimates of sequence-level mutational rates range from 10‘8
(Lovett, 2004) to 10‘11 (Ochman et al., 1999) changes per genomic base pair per generation.
With an estimated 100—300 successful generations per year, Ochman et al. (1999) calculate
there to be 0.0045 mutations per genome base pair per million years. For a 3 million base
pair genome, this corresponds to 1,350 mutations per genome per million years.
Contrastingly, without negative selection or reversible changes, tandem duplications
attributable to IS element-based changes would be expected to introduce a staggering
number of about 200,000 changes per genome per million years.

DNA mobility may relate to evolutionary dynamics in a number of ways. Mobile
elements may either be conserved in a mutualistic sense to promote heterogeneous offspring
or, alternatively, persist based on their own “selﬁsh” parasite—like behavior (Schneider &
Lenski, 2004). The frequency of DNA mobility may impact general diversity of a species-like
taxa. Staphylococcus aureus has a recombination rate 3 times lower than mutation compared
to Neisseria meningitidis which has a recombination rate 3.6 times more frequent than
mutation (Cohan, 2004). Staphylococcus aureus may be thus expected to exhibit greater

population clonality in comparison to N eisseria meningitidis, where clonality is the stable

14

transmission of multiple sets of alleles (Wisplinghoff et al., 2003). Intriguingly, Neisseria
meningitidis can still be very clonal in nature due to a few highly successful strains (Souza &
Eguiarte, 1997). In this sense, externally-inﬂuenced dynamics of selection can act to ﬁlter the
retrospectively calculated stochastic dynamics of occurrence.

Recombinant changes between generations may be evolutionarily unstable. Stable,
vertically divergent recombinations may be a different type of evolutionary dynamic than
genomic plasticity, a variation-producing feature of frequently generated, unstable changes.
Genomic plasticity can involve reciprocating changes that occur in response to alternating
environmental conditions. One example of genomic plasticity involves the amplifying
expression of the his operon in the Salmonella genome. RecA dependent tandem duplications
of this operon occur at a frequency of 0.01 to 1 percent of progeny and can be preserved
under selected conditions (Haack & Roth, 1995). The rate of deletion that removes these
duplicated operons is 1 to 30 percent of progeny. Tandem duplications are often deleted since
their duplication produces direct repeats that can subsequently undergo a D—shaped
recombination event (Romero & Palacios, 1997). Another example of genomic plasticity
involves a site-speciﬁc inversion system in Salmonella (Nanassy & Hughes, 2003). A hin
recombinase mediates inversion of 1,000 bp in order to biphasically vary an antigen protein so
as to “outsmart” the immune system. None of these examples, however, suggest a basis for
the type of long-term trajectory of divergent, conserved change that could correspond to the
recombinative dynamics proposed by Lathe et al. (2000) or Horimoto et al. (2001).

One way to estimate the inﬂuence of stable recombinations, is to assess the rules that
may apply to how recombinations proceed in nature. There are a variety of parsimonious
criteria that, if applicable, can act to compile and summarize the most likely phylogenetic
tree (Harvey & Pagel, 1991). Dollo’s law “states that complex characters will not have
evolved more than once” (Harvey & Pagel, 1991). Yet, since recombinations are frequently
produced by speciﬁc recombinations involving IS elements on the genome, it is possible that
evolution may be somewhat parallel. In the case of 18 replicate populations that were each
separately propagated for 1,000 generations, patterns of both parallel and divergent evolution
were observed for conditions related to 2,4 dichlorophenoxyacetic acid as a sole carbon source

(Nakatsu et al., 1998). Multiple composite recombinations can lead to a wide range of

15

combinations (Gray, 2000) so, over time, it is plausible that many steps of recombination
would be divergent enough to produce distinct signatures for various lineages. Some
additional, alternative parsimonious criteria to consider are: “the smallest number of
character trait transitions,” and “derived characters being lost on fewest occasions” (Harvey
& Pagel, 1991). Yet, recombinations can readily violate some of the above assumptions
governing vertical ancestry (Patterson, 1988; Snel et al., 2002), so it is difﬁcult to know if
there are consistent levels at which rules of vertical ancestry can be considered reliable versus
relaxed.

An alternative to parsimonious reconstruction is to approach efforts at phylogenetic
reconstruction as a statistical problem. In a parametric fashion however, degrees of freedom
may be difﬁcult to characterize in more sophisticated statistical models related to DNA
mobility. As mobile DNA and other changes act to both expand and otherwise alter a
genome, it is comparable to the, albeit simpler, expansion-modiﬁcation systems proposed by
Li (1991). These systems are a type of “probabilistic context—free Lindenmayer systems”
that, as open dynamical systems, have changing degrees of freedom. The fact that these
changes occur on a nested hierarchical phylogeny also leads to variable precision as to how
degrees of freedom might be characterized (Harvey & Pagel, 1991). Species belonging to the
same genus generally have fewer degrees of freedom than species coming from different genera
(Harvey & Pagel, 1991). In a biological sense, a hierarchy of recombinational differences may
be variable in how they constitute adaptive differences, and such a distinction may be
difﬁcult to model (Harvey & Pagel, 1991).

There is also natural variation in how DNA mobility does not fully reﬂect an
intragenomic dynamic proceeding along a vertical hierarchy. The estimated fraction of a
genome that has been laterally transferred from other species is 5-10‘70 (Cohan, 2004).
Lateral transfer does not always readily occur between species though, and bacterial
“sexuality” can be limited to closely related strains within a species such as for
Sinorhizobium meliloti or occur with signiﬁcantly fewer constraints of close relationship such
as for Neisseria gonorrhoeae (Souza & Eguiarte, 1997). Overall, the non-vertical dynamic of
intraspecies genomic exchange can be quite frequent. Lawrence (2002) estimate that less

than 10 LGT events successfully occur per million years with Escherichia coli. Zhaxybayeva

16

et al. (2004) estimate that “several hundred [genes] every four million years” are transferred
among some sets of closely related strains.

A further complication for modelling recombinative change involves the dynamic of
illegitimate recombination. At the lower end of recombination frequencies (10‘12 to 10’15 per
genome base pair per generation), illegitimate recombinations were ﬁrst proposed to involve
12 base pairs or less in the asymmetric pairing of complementary sequence (Franklin, 1971).
As is the case with bacteriophage A, these can be site-speciﬁc and require extra factors and
enzymes like the integration host factor (IHF) and viral integrase (int) in order to facilitate
the illegitimate recombination (Franklin, 1971). These can also, rather than requiring extra
factors, be facilitated directly by hairpin structures (palindromic repeats) surrounded by
direct repeats. Hairpin structures like these have been seen in a recombining 96bp Borrelia
segment that generates genomic diversity in such a way as “to avoid host immune
elimination” (Wang et al., 1997). A more updated deﬁnition of illegitimate recombination is
that it “involves junctions of nonhomologous or very short homologous DNA sequences (often
less than 3 bp) which are not recognized by site-speciﬁc enzymes” (Nair et al., 2004).

Despite their regulatory importance, operon structures are not conserved and are widely
disrupted across various lineages by both intragenomic and intergenomic dynamics
(Watanabe et al., 1997; Nolling et al., 2001). Yet, in the form of positive selection, operons
can be selected targets of duplication such as can be seen with the multiple copies of
ammonia monooxygenase (amo) operons in ammonia-oxidizing autotrophic bacteria (Klotz &
Norton, 1998). Such a duplicated operon corresponds to an analysis from Snel et al. (2002)
suggesting that gene addition is under positive selection. Despite disruption at a localized
operon level, there appear to be larger “uber-operonic” aspects to conserved ORF location
(Horimoto et al., 2001; Lathe et al., 2000). The fact that laterally transferred, functionally
related genes do not reassociate with a corresponding uber-operonic functional complex
suggests some limitation as to the frequency or ﬁtness characteristics associated with
localized rearrangement events (Lathe et al., 2000).

From the standpoint of altered expression and host immune evasion, DNA
rearrangement has been equated to the network motif of a noise ampliﬁer—contributing to

population heterogeneity and antigenic variation (Wolf & Arkin, 2003). This noise is

17

proposed as a way to spread risk over multiple phenotypes and, in abstract engineering
terms, may also enhance signal by “stochastic resonance” (Wolf & Arkin, 2003) where
possible negative side-effects of an otherwise successful change are balanced out. The
spreading of risk may correspond to a lottery model described by (Smith, 1975). In this case
of augmented population heterogeneity, those strains with a greater chance of introducing
diverse progeny are more likely to hit a metaphorical “jackpot.” Another related scenario is
the “arms race.” This scenario involves those species that can react more quickly to the
environment by adaptively changing ﬁrst with respect to ﬁtness, thereby succeeding over
those who are diversifying without direct relationship to ﬁtness (Williams, 1971).

Recombinations associated with speciation do not necessarily relate solely to
considerations of stochastic frequency and external conditions. The evolutionarily stable
changes may possibly be those that best conserve characteristics of expression or regulation
associated with the large scale topology of the entire supercoiled prokaryotic genome (Deng
et al., 2005). In addition to speciﬁc hot spots on a chromosome inﬂuencing the incidence and
impact of recombinations such as oriC, there may also be other aspects governing the overall
genomic distribution on a replicon’s topology. A more sophisticated molecular model may be
proposed that characterizes how the superstructure to the genome may inﬂuence regulation
based on topology. The location of functional promoter domains near HU-mediated
supercoiling (Tanaka et al., 1993) sterically hinders expression (Kohno et al., 1994). Yet, if
ORFs are positioned far away from HU-sites, the degree of expression, looking at 14 different
sigma factors, is independent of which supercoiled loop a regulated open reading frame is
present upon (Reznikoff et al., 1985). This independence of location is conﬁrmed in a broader
survey of other prokaryotes (Wolffe & Drew, 1995). Regulatory dynamics occur between
distant chromosomal regions. For example, xylene/ toluene metabolism can have four
different operon/ transcriptional control regions with interactive regulation (Ramos et al.,
1997). If recombination repositioned an open reading frame near an HU-site, this could have
an impact that may cascade across large functional networks such as described by Ramos
et al. (1997) and Li et al. (2005).

Mechanistically, RecA and H U are some of the many macromolecules that bind to DNA

that may potentially effect genomic structure and subsequent expression. Macromolecular

18

binding is sequence—dependent, frequently involving DNA recognition of a speciﬁc sequence
by proteins with the helix-turn-helix motif (Harrison & Aggarwal, 1990). In the case of
DNase I, these sequences have been found to be about 8 nucleotides, corresponding to groove
width and stiffness associated with the helically wound double-stranded DNA (Lahm & Suck,
1991). Another mechanism involves illegitimate recombinations that are facilitated by DNA
gyrase (Ikeda et al., 1982). If gyrase-stimulated recombinations correspond to producing
functionally competitive progeny, the archaealogy of genome structure would show how
locations of gyrase activity correspond to optimal characteristics of genome organization.
Indeed, DNA gyrase activity correlates positionally with restraints on spatial patterns of
transcriptional activity (Jeong et al., 2004). It is conceivable that there is a framework of
recombinational mechanisms and consequences in ﬁtness that may be corroborated by
measures of optimal genome arrangement. It is unknown, however, as to how precisely an
analysis of recombinational mechanisms and ﬁtness dynamics will map to the many different
possibilities for such a framework. It is also unknown as to how complex the framework
would have to be to account for a wide view of both Archaea and Bacteria.

ORF arrangement and clustering may exhibit some invariance based on patterns of
content, size, and distances of ORFs as they occur between diiffering chromosomal regions.
While genome structure may change to some extent, various assays provide a basis for
relating measures of ORF clustering to evolutionary range. Sequence similarity among ORFs
is abundant; “50% of prokaryotic genes emerge from duplication” (Li et al., 2005) where
duplicate sequence pattern has been produced from past gene duplications and conserved
amongst various domain rearrangements. There is also evidence that the evolutionary
heritage of a DNA segment containing multiple ORFs relates to the evolutionary heritage of
encoded ORFs. In Thermoplasma acidophilum, 32% (484) of the ORFs are found in 139
conserved gene clusters (Ruepp et al., 2000). Cluster-related conservation is ascertained by
comparison with 13 other prokaryotic genomes where pairs of potentially orthologous ORF
sets were separated by at most three other ORFs (Ruepp et al., 2000). In another approach
of conserved orthologous proximity, Horimoto et al. (2001) ﬁnd that, while ORFs may wind
up on separate locations between two circular replicons from two different species, the ORFs

signiﬁcantly trend to remaining within a 20° (e.g., 600 kb on a 3 Mb chromosome) region on

19

a chromosomal circle relative in position to to other ORFs. Horimoto et al. (2001) note that
regional constraints of an ORF are inﬂuenced by the functional role of the ORF as evident
from functional categories for COG. These inferred regional constraints suggest some
interdependence between content of a chromosomal segment and dynamics of alteration to
ORF clustering. From the standpoint of function, the Escherichia coli K-12 genome may
possibly include a 600 kb “supercluster” periodicity that appears to associate with
coordinated gene expression (Allen et al., 2003). (Kunisawa & Otsuka, 1988) claim to have
found a “7 minute periodicity” (i.e., 350 kb) on the E. coli K-12 genome to the clustering
arrangement of ORFs. A more recent evaluation characterizes E. coli K-12’s large-scale
periodicity as being “weak” and, in summary, Koonin et al. (1996) offer two explanations for
large-scale periodic arrangement of ORFs: 1) duplication of large segments of the
chromosome early in evolution; and 2) “the periodicity relates to nucleoid superstructure.”
Yet, a well-parameterized model that makes a defensible account of causative dynamics for

large-scale periodicity has not yet been proposed.

1.4 Annotated Open Reading ﬂames

“Many genomes are over-annotated” in the sense that real genes are not discriminated
from random ORFs (Larsen & Krogh, 2003). There exist false positives in the form of
annotated ORFs that are not transcribed into functional units such as enzymes (Frishman
et al., 1998). A variety of studies have either indicated or predicted that the fraction of
annotated ORFs with low, “unreal”, or non-functional importance to the organism is z 25%
of the total set of annotated ORFs for a given genome (Williamson et al., 1993; Jackson
et al., 2002; Skovgaard et al., 2001; Tatusov et al., 2003). An exact, prescribed
characterization of every ORF has not yet been achieved (Roberts et al., 2004) and “the
boundary between living and dead genes is often not sharp” (Snyder & Gerstein, 2003). This
may in part be due to a complex diversity of characteristics and categorizations that may be
used to consider each ORF. One set of groupings for ORFs (originally proposed for yeast)
has been proposed as: “eORF (essential ORF), kORF (known ORF with a well-characterized
function), hORF (ORF validated by homology only), shORF (short ORF), tORF

20

(transposon identiﬁed ORF), qORF (questionable ORF), and dORF (disabled ORF or
pseudogene)” (Snyder & Gerstein, 2003).

Analytical criteria that help weigh “the likelihood that a gene encodes a functional
product” are: sequence features, evidence for transcription, sequence conservation, patterns of
gene inactivation, and functional genomics information (Snyder & Gerstein, 2003). Sequence
conservation analyses work to compare an individual DNA sequence from one organism to
the sequences of other known sequences, and is “an excellent method to gauge the
importance of the gene product” (Snyder & Gerstein, 2003). Sequence features can involve
detailed measurement of mutational effects such as codon bias, since there are dynamics
underyling the nonrandom use of codons compared to non-coding regions and distinguishng
associations between genes involving aspects of expression (Duret & Mouchiroud, 1999), gene
length (Eyre-Walker, 1996), and horizontal gene transfer (Garcia-Valivé et al., 2000).

A sequence conservation approach is, however, strongly inﬂuenced by the phylogenetic
proxirnities of relationship between the associated organisms (Snyder & Gerstein, 2003).
Strains that are phylogenetically close have had, over time, less opportunity for phenotypic
deviation due to a recent shared ancestry (Harvey & Pagel, 1991). Strains that are
phylogenetically far apart may have conserved sequences due to LGT, or strong evolutionary
forces of conservation. In order to utilize sequence conservation as a criterion for separating
“real” ORFs from ORFs of little functional or evolutionary importance, there must be some
account for phyletic pattern (Glazko & Mushegian, 2004). A monophyletic distribution of
similar ORFs saturates a phylogenetic subtree where a last common ancestor can be inferred
as having vertically transferred speciﬁc ORFs to its descendants. Other phyletic distributions
include polyphyletic (occurring among various disparate lineages in a way to suggest
non-vertical evolution) and paraphyletic (a subtree with a sub-subtree removed) distributions.
As modelled by Snel et al. (2002), LGT may account for polyphyletic distributions of ORFs
among prokaryotic organisms, and gene loss may account for paraphyletic distributions.

Sequence conservation is often used as a basis for making functional annotations to
ORFs whose activity and function have not been directly assayed. Yet, functional genomics
information, as recorded in ORF annotations, is signiﬁcantly incomplete: “all prokaryotic

genomes sequenced to date have a fairly high fraction (between 20 and 40%) of genes for

21

which no function has been assigned” (Van Sluys et al., 2002). Furthermore, 5-10% of
functional annotations are wrong (Roberts et al., 2004). The present situation with
prokaryotic genomes is that curatorial efforts for improved annotations of ORFs have been
“sluggish”, and the blurry boundary between living and dead genes may be partly a function
of insufﬁcient curatorial effort as well as a lack of more exacting assays of the transcriptome
and proteome (Roberts et al., 2004).

Evidence for transcription involves measurement of RNA or protein expression that
comes from a given DNA sequence. Rom the vantage point of transcriptional evidence, a
“conceptually straightforward” approach may be to utilize a whole-genome DNA microarray
designed to study a fully sequenced microbe (Cummings & Relrnan, 2000). In Escherichia
coli, the number of annotated genes to express above background levels is 3,496 (81%) out of
a total possible 4,290 ORFs (Tao et al., 1999). Assessments of DNA expression can be
unreliable however due to the frequency at which a probe for a falsely annotated gene may
associate with an untranslated region of an expressed gene (Skovgaard et al., 2001).

Gene inactivation assays involve measuring the effect of how artiﬁcially-induced
mutations have a phenotypic consequence due to an inactivated, though still expressed, gene
or set of genes. There are currently limits to the availability of data. For Bacillus subtilis
(Biaudet et al., 1997), only 13% of annotated ORFs have been assessed for patterns of
phenotypic inactivation. In general, experimental assessments of annotated ORF operation
and function have not been comprehensively performed for the larger set of publicly
available, fully sequenced genomes.

Over—annotated false positives (random, “unreal” ORF S) occur predominantly for ORFs
that trend toward shortness in length (Larsen & Krogh, 2003; Skovgaard et al., 2001). Such a
trend may occur by truncating nonsense mutations (Skovgaard et al., 2001), although there
may also be physiological differences to ORF lengths that are accounted for by the
multidomain structures of the encoded proteins (Liang et al., 2002). A direct structural
classiﬁcation of evolutionarily divergent proteins and their internal modules is not easily
performed. Within the Structural Classiﬁcation of Proteins database (SCOP) (Murzin et al.,
1995), folds (structural similarities) from divergent sequences of common origin lead to

superfamily predictions that are only 29% accurate (Lindahl & Elofsson, 2000). Assessment

22

of sequence similarity on conserved domains, with divergent sequence, are on the level of 75%
accuracy (Lindahl & Elofsson, 2000). There are other approaches, such as BLASTCLUST,
that address the issue of common evolutionary origins with a variety of default choices for
percent identical residues, comparison of length, and BLAST score density which is the
proportional amount of length covered by a high scoring segment pair (Altschul et al., 1990).
Additional reﬁnements to a sequence conservation analyses can ﬁlter out common motifs,
such as coiled coil regions, which by themselves do not add much evolutionary signal
(Tatusov et al., 1997b). Any comprehensive handling of structural protein features and data
involves some “curatorial pain” (Chung & Yona, 2004), and more automated reﬁnements,
such as practical adjustment of the expectation score in terms of repetitive low complexity
protein structure—especially for smaller proteins (Birkland et al., 2005)—are still not fully
usable. Whatever the proﬁle (domain structure) diversity of an ORF, it is generally
recommended to evaluate as many sequence homologs as possible to assert meaningful
ancestral membership within a protein family (Sadreyev & Grishin, 2004). For example, the
detection of remote homologies is three times more likely when more than 2 sequences are
used to assess for homology (Park et al., 1998), and there are sequences with less than 30%
pairwise identities to other sequences that, when analyzed in groups of several or more,
signiﬁcantly cluster together as homologs. Overall, for purposes of asserting some vertical
origin, e-value cutoffs appear to range from 10’2 (Altschul & Koonin) to 10‘8 (Pagni &
Jongeneel, 2001; Sadreyev, 2003). Even for strict expectation score cutoffs like 10‘”, false
positives have still been observed (Sadreyev, 2003). For the purposes of evaluating a sampling
of ORFs, there is a way to estimate the number of false positive hits based on a given
expectation score cutoff. Expectation scores less than 0.01 are equivalent to the expected
percentage of random (false positive) hits within a population of sequences (Koonin &
Galperin, 2003). In this regard, surveying 10,000 sequences for a match to a sequence based
on an expectation score threshold of 10‘3 would amount to approximately 10 random hits.
Evolutionary dynamics other than stop codon truncations can also be inferred from
ORF length characteristics. For example, Teichmann et al. (1998) report, beyond the
approximate quarter of Mycoplasma genitolium ORFs that contain just one conserved

domain, that the “large majority of proteins in the MG genome have involved rearrangement

23

of domains.” This qualiﬁcation is based on a characteristic distribution of ORFs with
distinct composite domains. Wheelan et al. (2000), however, ﬁnd that, whatever the
underlying dynamics of gene rearrangements are, the domain size distributions lead to
discontinuous frequencies of various ORF lengths. Savageau (1986) makes a case for proteins
in Escherichia coli generally occurring in structural subunits of 14 kDa which is about 127
amino acids (aa). While E. coli protein modules (single domains) have an average length of
219 aa, the normative “bulk” of evaluated modules range in length from 100 to 150 aa (Liang
et al., 2002). In an informational sense then, based on relationships between distributions,
the impact of recombinative processes of change can be sometimes revealed. Future
resolution may involve case-by-case assessments of proteomic structure and function. This is
however dependent upon a mixture of curatorial effort and biochemical detail that may be
difficult to uniformly apply to each fully sequenced genome.

For operons, a predictive genome-wide algorithm and database was recently established
for Staphylococcus aureus Mu50 (Wang et al., 2004) which represents a signiﬁcant innovation
beyond databases that have been limited to evaluating Escherichia coli K-12 (Huerta et al.,
1997). Predictive algorithms are important; even in the well-studied E. coli K-12 genome,
the RegulonDB database shows that just 869 operons are known compared to 2325 operons
that are predicted (Huerta et al., 1997). Operons vary in the number of ORFs that they
transcriptionally co—express. In E. coli K-12, up to 70% of the transcriptional units are
“monocistronic,” having just one ORF (Blattner et al., 1997). S. aureus is calculated to have
62% of its transcriptional units as monocistronic with an average operon size of 3.47. About
90% of operons have 5 or less ORFs, and only a marginal amount have any more than 10
ORFs (Wang et al., 2004; Huerta et al., 1997). The largest predicted operon in S. aureus
Mu50 contains 29 ORFs and encodes ribosomal proteins. The two largest predicted operons
in E. coli K-12 contain 11 ORFs each, and encode phenylacetic acid degradation and sugar
transport functions (Huerta et al., 1997). Algorithms for operon (or transcriptional unit)
detection have been extended to analyze a variety of other Bacteria and Archaea (Stormo &
Tan, 2002; Liu et al., 2003), yet there does not yet appear to be a well-curated database with
predicted operon structures on all of the fully sequenced genomes- Other algorithmic efforts

are being developed to better quantify the accuracy of operon predictions compared to

24

evidence from sequence and expressional data (Bockhorst et al., 2003).

It is possible to arrive at some correspondence between an organism’s set of ORFs versus
metabolic capabilities necessary for the organism’s lifestyle. Tamas et al. (2002) identify B.
aphidicola APS as requiring a set of ORFs active in sulphur assimilation since it is
endosymbiotic to an aphid that, eating legumes, does not ingest as much cysteine as the
grass-eating aphid host of B. aphidicola Sg. Evidence suggests that sulphur assimilation
genes became inactive in response to cysteine-rich conditions of B. aphidicola Sg (Tamas
et al., 2002).

While there are existing systematic catalogues of taxa, phenotypes, and some
corresponding metabolic and physiologic characteristics (Garrity, 2001), there is not yet an
up—to—date synthesis that equates the ORF complement to the phenotype. Analysis of
clusters of orthologous groups (COGS) has been one effort in this direction where functional

7? 6‘

categories such as “RNA processing and modiﬁcation, extracellular structures,” and “cell
motility” are identiﬁed (Tatusov et al., 1997b). The link, however, between unique ORFs and
speciation (Konstantinidis & Tiedje, 2004), as well as the restriction of important
orthologous sets to taxonomic boundaries (Kurland, 2000), suggests that ORF similarity
alone cannot fully map the metabolism and physiology.

While functional assessments of ORFs partly rely on anecdotal approaches,
characterization of ORFs may be a meaningful step in the accelerating rise of available
sequence, ecological, and evolutionary information. Schilling et al. (1999) describe a
cascading succession of various knowledge domains that are rising up to characterize the
genome, transcriptome, proteome, metabolome, and beyond. This succession may be
currently evident from the increasing number of tools available to access and characterize the
content and metadata surrounding the growing numbers of strains, chromosomes, and

genomic structures such as ORFs (Murzin et al., 1995; Koonin & Galperin, 2003; Chung &
Yona, 2004; Kent et al., 2005; Wang et al., 2004).

25

1.5 Summary and Objectives

Aspects of genomic stability have been found to relate to the ecological lifestyle of a
prokaryotic organism (Ochman 85 Davalos, 2006), and various underlying factors of
chromosomal topolog and expression suggest that the organization of ORFs may have a
functional role in the physiology of the organism (Deng et al., 2005; Képés, 2004; Kunisawa
& Otsuka, 1988; Svetic et al., 2004; Lathe et al., 2000). Prokaryotic diversity relates to
overall genome content, and recombinative expansions and modiﬁcations can allow for a
faster tempo of change than possibilities attributable to single point mutations (Bentley &
Parkhill, 2004). Mechanisms, such as those involving mobile elements, are providing some
ability to account for structural changes in genome organization and the density of insertion
sequence (IS) elements on the genome that can be an indicator of lifestyle (Moran & Plague,
2004). Many of these studies have drawn their observations and results from the recent
increase of publicly available, fully sequenced genomes. There remain, however, a variety of
past hypothesis-driven approaches to genomic organization that have not yet been carried
forward to the present set of fully sequenced genomes. In particular, there is a set of studies
that have sought to account for whether gene density is non-random on the Escherichia coli
chromosome (Bachmann et al., 1976; Jurka & Savageau, 1985; Kunisawa & Otsuka, 1988;
Williamson et al., 1993). In the past, based on the predicted locations of protein-coding
sequence, gene density has been evaluated as the number of ORFs per equal-sized segments
of a replicon (Jurka & Savageau, 1985). Yet, some ORFs may be more important or “real”
than other ORFs (Snyder & Gerstein, 2003; Larsen & Krogh, 2003). Conserved orthology has
been an initial approach to characterizing functional roles of ORFs (Bentley & Parkhill, 2004;
Tatusov et al., 1997b), and the genomic context can be predictive of gene function (Wolf
et al., 2001).

While operon structures and genomic landmarks such as oriC may play a role in the
functional expression of an ORF (Jin et al., 2002; Wolf et al., 2001), they are not the only
factors underlying the conserved positioning of conserved ORFs. The relative locations of
multiple sets of orthologs show evidence of conservation across the entire stretch of a genome
despite extensive, localized rearrangement and ﬂuid-like alteration of operons (Horimoto

et al., 2001; Lathe et al., 2000; Wolf et al., 2001). The functional consequences of

26

recombinative change have been a topic of substantial interest and modelling (Terzaghi &
O’Hara, 1990; Wolf & Arkin, 2003; Snel et al., 2002), and a question arises as to what kind of
physiological limits may exist for a prokaryotic organism in terms of radical alterations to
ORF organization. For instance, mobile elements are thought to disrupt functional barriers
like replichore balancing (Preston et al., 2004) and cotranscriptional association with the
direction of replication (Andersson et al., 1998; Briiggemann et al., 2003).

My hypotheses of physical clustering initially approach the question of ORF density and
organization by segmenting the physical chromosome into spatial regions. There are three
basic hypotheses: 1) ORF density is random; 2) there is periodicity to the distribution of
ORF densities on the chromosome; and 3) ORF densities form localized shapes that are
non-random and interdependent with other regions on the chromosome. A controlling
parameter to the evaluation of these hypotheses is the actual segmentation size (region length
in base pairs) used to count up numbers of ORFS per segment. A parallel hypothesis relates
to some ORFS being more important than other ORFS, and my fourth hypothesis is that
only a limited subset of 75% of annotated ORFS are truly coding for function (Jackson et al.,
2002; Tatusov et al., 2003).

An additional set of hypotheses is based on the notion that varying arrangements of
open reading frames would, in part, reﬂect different sets of recombinative events occurring in
the midst of evolutionary dynamics. In this set of hypotheses, I seek to evaluate whether
there is any intragenomic aspect of ORF clustering that occurs robustly as a uniform
property of each prokaryotic organism. These hypotheses are: 1) there is cotranscriptional
association with the direction of replication for all prokaryotic organisms; and 2) the physical
clustering of ORFs within COGS is non-random. I also seek to revisit my three spatial
hypotheses based on evaluation of a 75% subset of ORFS constructed by ﬁltering out those
annotated ORFS that are putative false positives. As a testable outcome to the study, I
would postulate that a meaningful measure of the internal physical clustering of ORFS would
show some characteristic of vertical ancestry, and that outliers from a trend of vertically
conserved ORF organization are attributable to the activity of mobile elements.

The recent increase in the number of publicly available, fully sequenced genomes has led

to an opportunity for revisiting questions concerning the nature and organization of ORFS.

27

By investigating relationships between distributions of ORFS on fully sequenced prokaryotic
chromosomes, this study measures the internal physical clustering of open reading frames.
The performance of ORF organization as an indicator of vertical evolution can be assessed
from estimated times of divergence from a last common ancestor as they are available in
published studies (Battistuzzi et al., 2004) and there are initial summaries of mobile element

densities that may account for variation within the data set (Moran & Plague, 2004).

28

Chapter 2: Methods and Developed
Methodology

2. 1 Analytical Design

There is difﬁculty with establishing parameters for how genomic organization inﬂuences
the phenotype of a strain, and I did not ﬁnd previously developed parametric methods for
fully characterizing ORF organization on the genome as a product of evolution. In order to
arrive at legitimate statistical inferences, I structured the analysis to take into account the
limited sample Size and, where possible, avoid a priori assumptions.

Figure 1 is a synthesized view of how this study navigates between approaches to
random and non-random resamplings and inference based on a structured approach to data
analysis (Lunneborg, 2000). The data set provides ORF annotations that contain a
potentially separable mixture of both real ORFS and putative false positives. I sought to
establish a Signiﬁcant ﬁltering between real and false ORFS and further compare the results
of this distinction to random assignment of “realness.” To examine this distinction over the
chromosome, I conducted segmentation analyses to examine ORF clustering by delineating
sections of the chromosome and, as a negative control, shufﬂing the x1, 3:2, 3:3, ..., 277,, series of
ORF regions of segmentation size r (Figure 2). Systems of simulation and comparisons
against the likely phylogenetic tree are two approaches for evaluating the potential types of
causes that might be associated with given chromosomal organizations of ORFS. In the event
that random resampling may not allow for testing inferences of causality or population, I
sought to perform basic subsampling to see how the data may be robustly described and
effectively interpreted. A robust description that has signiﬁcant coverage across either the
phylogeny or functional grouping may lead to more conﬁdent assessments of constraints
associated with the underlying natural system.

It is in the form of a rough conﬁrmatory analysis (Behrens, 1997; Darlington, 1990) that
I moved beyond a merely correlative approach to evaluate what underlying physiological and

phenotypic relationships may relate the arrangement and mobility of genomic structure to

29

Yes

 

 

 

Are Cases 3
Random Sample?

 

 

 

No

Yes

 

 

ll

 

Are Cases
Randomly Assigned?

 

 

 

No

l
SUBSAMPLES

Inference of robust,
descriptive properties
of variance

 

4; BOOTSTRAP Population inference

ORF subsets can be randomly chosen instead
of chosen based on evolutionary importance.

ORF arrangements can be viewed as
counts of equal—sized segments, and these
segments shufﬂed.

 
   
 

Causality

RERANDOMIZATION inference

Through simulation, can measure effect of
randomly assigned strategies of expansions
and modifications of ORF arrangements.

Can also conduct independent and

directional comparisons between different

subsets of genome-sequenced strains and contrast
with expectations based solely on chance.

PHYLOGENETIC CLADES : LIFESTYLE GROUPS

Lactobacillales

Gammaproteobacteria : Host-Associated
Enterobacteriales : Freeliving
not Enterobacteriales I
l
Actinobacteria :
Archaea I
I
I

Figure 1: Resampling strategies and randomization design. Differing assumptions (shown in
boxes) underlying a data set control the different ways (shown in ovals) there are for describing
and resampling the data. My speciﬁc techniques for assaying the data are described in the

text outside of each oval.

30

 

'=Xi+1' Xi

Figure 2: Calculation of regional ORF counts. The DNA sequence of a chromosome is subdi-
vided into regions of equal physical length in base pairs. The locations of region boundaries are
symbolically represented by the series ..., xi, :5,- + 1, xi + 2,132- + 3, The translational start
point of each ORF, shown as a straight vertical edge, is used as the reference point for counting
within each region. Two region—based ORF counting series are presented. The upper series is a
count of all ORFS occurring within each region. The bottom series is a count corresponding to
a ﬁltered subset of ORFS (indicated by slashed shading). The process of counting is illustrated
by the curved lines descending from the ORFS in of each chromosomal region to the associated
ORF count.

the optimal function of the prokaryotic organism. With hypotheses concerning ORF density
(Jackson et al., 2002), organization (Kunisawa & Otsuka, 1988; Jurka & Savageau, 1985),
and the role of mobile elements (Bentley & Parkhill, 2004; Ochman & Davalos, 2006), I

sought to investigate general correspondences and detailed variation.

2.2 Data Assembly

2.2.1 Collection of Genome Data

The data set of fully sequenced prokaryotic genomes was accessed from the National
Center for Biotechnology Information (NCBI) public archives (Wheeler et al., 2000) in
March, 2004. Data set ﬁles in these archives are distributed per chromosome and plasmid
replicons. For the 155 fully sequenced genomes, there were 234 sets of ﬁles corresponding to
165 chromosomes and 69 plasmids available from the FTP address
ftp://ftp.ncbi .nlm.nih. gov/genomes/Bacteria/. There were four ﬁle formats for each of
the replicons (Table 1). Speciﬁc versions of genomes corresponding to the original time of
download can be accessed by visiting
http://www.ncbi.nlm.nih.gov/entrez/sutils/girevhist.cgi.

The species of Archaea and their associated chromosomal accession numbers are

31

Aeropyrum pernir (NC-000854), Archaeoglobus fulgidus DSM 4304 (NC.000917),
Halobacterium Sp. NRC-1 (NC.002607), Methanocaldococcus jannaschii (NC.000909),
Methanopyrus kandleri AV19 (NC.003551), Methanosarcina acetivorans C2A (NC.003552),
Methanosarcina mazei Goel (NC-003901), Methanothermobacter thermautotrophicus str.
Delta H (NC-000916), Nanoarchaeum equitans Kin4—M (NC.005213), Pyrobaculum
aemphilum str. IMZ (NC.003364), Pyrococcus abyssi (NC.000868), Pyrococcus furiosus DSM
3638 (NC.003413), Pyrococcus horikoshii (NC.000961), Sulfolobus solfataricus (NC.002754),
Sulfolobus tokodaii (NC-003106), Thermoplasma acidophilum (NC.002578), and
Thermoplasma volcanium (NC.002689).

The species of Bacteria and their associated chromosomal accession numbers are
Agrobacterium tumefaciens str. C58 (Cereon) (NC.003062, NC_003063), Agrobacterium
tumefaciens str. C58 (U. Washington) (NC-003304, NC_003305), Aquifer aeolicus VF5
(NC-000918), Bacillus anthracis str. A2012 (NC.003995), Bacillus anthracis str. Ames
(NC.003997), Bacillus cereus ATCC 10987 (NC.003909), Bacillus cereus ATCC 14579
(NC.004722), Bacillus halodurans (NC.002570), Bacillus subtilis subsp. subtilis str. 168
(NC-000964), Bactemides thetaiotaomicron VPI-5482 (NC.004663), Bdellovibrio
bacteriouorus (NC.005363), Biﬁdobacterium longum NCC2705 (NC.004307), Bordetella
bmnchiseptica (NC.002927), Bordetella parapertussis (NC.002928), Bordetella pertussis
(NC-002929), Borrelia burgdorferi B31 (NC.001318), Bradyrhizobium japonicum USDA 110
(NC-004463), Brucella melitensis 16M (NC.003317, NC_003318), Brucella suis 1330
(NC-004310, NC_004311), Buchnera aphidicola str. APS (Acyrthosiphon pisum)
(NC.002528), Buchnera aphidicola str. Bp (Baizongia pistaciae) (NC.004545), Buchnera

aphidicola str. Sg (Schizophis graminum) (NC.004061), Campylobacter jejuni subsp. jejuni

Table 1: Descriptions of four ﬁle formats for the NCBI prokaryotic genome FTP repository.

 

Format Description

 

. asn ASN stands for abstract syntax notion

.gbk a readable plain text version of the .asn ﬁles

.faa FASTA-formatted listing of amino acid sequences

.ffn PASTA-formatted listing of coding strand nucleotide sequences

 

32

NCTC 11168 (NC.002163), Candidatus Blochmannia ﬁoridanus (NC.005061), Caulobacter
crescentus CB15 (NC.002696), Chlamydia muridarum (NC.002620), Chlamydia trachomatis
(NC-000117), Chlamydophila caviae GPIC (NC.003361), Chlamydophila pneumoniae AR39
(NC-002179), Chlamydophila pneumoniae CWL029 (NC.000922), Chlamydophila pneumoniae
J 138 (NC-002491), Chlamydophila pneumoniae TW—l83 (NC.005043), Chlorobium tepidum
TLS (NC-002932), Chromobacterium violaceum ATCC 12472 (NC.005085), Clostridium
acetobutylicum (NC-003030), Clostridium perfringens str. 13 (NC.003366), Clostridium
tetani E88 (NC-004557), Corynebacterium diphtheriae (NC.002935), Corynebacterium
eﬁ'iciens YS—314 (NC.004369), Corynebacterium glutamicum ATCC 13032 (NC.003450),
Coxiella bumetii RSA 493 (NC.002971), Deinococcus radiodurans R1 (NC.001263,
NC_001264), Enterococcus faecalis V583 (NC.004668), Escherichia coli CFT073
(NC.004431), Escherichia coli K-12 (NC-000913), Escherichia coli 0157:H7 (NC.002695),
Escherichia coli Ol57:H7 EDL933 (NC.002655), Fusobacterium nucleatum subsp. nucleatum
ATCC 25586 (NC.003454), Geobacter sulfurreducens PCA (NC.002939), Gloeobacter
violaceus (NC.005125), Haemophilus ducreyi 35000HP (NC.002940), Haemophilus inﬂuenzae
Rd KW20 (NC.000907), Helicobacter hepaticus ATCC 51449 (NC.004917), Helicobacter
pylori 26695 (NC.000915), Helicobacter pylori J99 (NC.000921), Lactobacillus johnsonii
NCC 533 (NC-005362), Lactobacillus plantarum WCFSl (NC.004567), Lactococcus lactis
subsp. lactis (NC.002662), Leptospira interrogans serovar lai str. 56601 (NC.004342,
NC_004343), Listeria innocua (NC-003212), Listeria monocytogenes EGD-e (NC.003210),
Mesorhizobium loti (NC.002678), Mycobacterium avium subsp. paratuberculosis str. k10
(NC.002944), Mycobacterium bovis subsp. bouis AF 2122/ 97 (NC.002945), Mycobacterium
leprae (NC.002677), Mycobacterium tuberculosis CDC1551 (NC.002755), Mycobacterium
tuberculosis H37Rv (NC.000962), Mycoplasma gallisepticum R (NC.004829), Mycoplasma
genitalium (NC.000908), Mycoplasma mycoides subsp. mycoides SC (NC.005364),
Mycoplasma penetrans (NC.004432), Mycoplasma pneumoniae (NC.000912), Mycoplasma
pulmonis (NC.002771), Neisseria meningitidis MC58 (NC.003112), Neisseria meningitidis
Z2491 (NC.003116), Nitrosomonas europaea ATCC 19718 (NC.004757), Nostoc sp. PCC
7120 (NC.003272), Oceanobacillus iheyensis HTE831 (NC.004193), Onion yellows
phytoplasma (NC.005303), Pasteurella multocida (NC.002663), Photorhabdus luminescens

33

subsp. laumondii TTOI (NC-005126), Pirellula sp. 1 (NC.005027), Porphyromonas
gingivalis W83 (NC-002950), Prochlorococcus marinus str. MIT 9313 (NC.005071),
Prochlorococcus marinas subsp. marinas str. CCMP1375 (NC.005042), Prochlorococcus
marinas subsp. pastoris str. CCMP1986 (NC.005072), Pseudomonas aeruginosa PAOl
(NC-002516), Pseudomonas putida KT2440 (NC.002947), Pseudomonas syringae pv. tomato
str. DC3000 (NC.004578), Ralstonia solanacearum (NC.003295), Rhodopseudomonas
palustris CGA009 (NC.005296), Rickettsia conorii (NC.003103), Rickettsia prowazekii
(NC.000963), Salmonella enterica subsp. enterica serovar Typhi (NC.003198), Salmonella
enterica subsp. enterica serovar Typhi Ty2 (NC.004631), Salmonella typhimurium LT2
(NC.003197), She'wanella oneidensis MR—l (NC.004347), Shigella flermeri 2a str. 2457T
(NC-004741), Shigella flexneri 2a str. 301 (NC.004337), Sinorhizobium meliloti
(NC-003047), Staphylococcus aureus subsp. aureus MW2 (NC.003923), Staphylococcus aureus
subsp. aureus Mu50 (NC.002758), Staphylococcus aureus subsp. aureus N315 (NC.002745),
Staphylococcus epidermidis ATCC 12228 (NC.004461), Streptococcus agalactiae 2603V/ R
(NC.004116), Streptococcus agalactiae NEMBI6 (NC.004368), Streptococcus mutans UA159
(NC.004350), Streptococcus pneumoniae R6 (NC-003098), Streptococcus pneumoniae TIGR4
(NC-003028), Streptococcus pyogenes M1 GAS (NC.002737), Streptococcus pyogenes
MGAS315 (NC-004070), Streptococcus pyogenes MGAS8232 (NC.003485), Streptococcus
pyogenes SSI-l (NC.004606), Streptomyces avermitilis MA-4680 (NC.003155), Streptomyces
coelicolor A3(2) (NC-003888), Synechococcus sp. WH 8102 (NC.005070), Synechocystis sp.
PCC 6803 (NC-000911), Therrnoanaerobacter tengcongensis (NC.003869),
Thermosynechococcus elongatus BP-l (NC.004113), Thermotoga maritima (NC.000853),
Theponema denticola ATCC 35405 (NC.002967), Peponema pallidum (NC.000919),
Tropheryma whipplei TW'08/27 (NC.004551), Tropheryma whipplei str. Twist (NC.004572),
Ureaplasma urealyticum (NC.002162), Vibrio cholerae (NC.002505, NC_002506), Vibrio
parahaemolyticus RIMD 2210633 (NC-004603, NC_004605), Vibrio vulniﬁcus CMCP6
(NC-004459, NC_004460), Vibrio vulniﬁcus YJ016 (NC.005139, NC_005140), Wigglesworthia
glossinidia endosymbiont of Glossina brevipalpis (NC.004344), Wolbachia endosymbiont of
Drosophila melanogaster (NC.002978), Wolinella succinogenes (NC.005090), Xanthomonas

aronopodis pv. citri str. 306 (NC-003919), X anthomonas campestris pv. campestris str.

34

ATCC 33913 (NC-003902), Xylella fastidiosa 9a5c (NC.002488), Xylella fastidiosa Temeculal
(NC-004556), Yersinia pestis C092 (NC.003143), and Yersinia pestis KIM (NC.004088).

I inspected the data of these chromosomes for annotated circular or linear topologies and
also identiﬁed those genomes with multiple, distinct chromosomes based on information in
the NCBI data ﬁles and in the literature. Other key attributes to the chromosomes were
their physical lengths and NCBI taxonomy.

I evaluated other general qualities to the data set such as associated plasmids as well as
changes to ORF lengths and ORF annotations over time. I identiﬁed the sequenced plasmids
associated with each of the 155 genomes based on the NCBI data ﬁles and compared this to
what was characterized in the literature. I evaluated the number of fully sequenced genomes,
ORF counts, and distribution values for ORF lengths at three different dates: December
2002, March 2004, and June 2005. As a prelude to intensive analysis of ORF data, I
identiﬁed changes to the ORF accession versions as they occurred between the three different
dates of December 2002, March 2004, and June 2005. Based on changes in ORF accession
version numbers, I counted up and characterized the changes to ORFS and the number of

associated genomes.

2.2.2 Management of ORF Data

The scope of the data set involved 447,551 ORFS present on 165 chromosomes as well as
other associated chromosomal attributes that were originally sourced from the NCBI
(Wheeler et al., 2000). I did the initial parsing of NCBI data ﬁles with various small perl
scripts and manual investigations of resultant output. I managed BLASTP calculations and
statistical analyses among the ORFS with a controllable analytical software pipeline I
constructed across a set of ﬁve computers. To make a clear division between the initial
parsing and subsequent analyses of speciﬁc ORF subsets, I developed a web application
named MYCROW (Matrix-Yanking Coding Region Objects Workbench) as a front-end to
my software pipeline. The central feature of MYCROW is to allow users to retrieve speciﬁc
chromosomal sets of ORF records that provide ﬁelds containing various descriptive and
quantitative characteristics for each ORF. I developed a simple XML approach to manage

the packaging, installation, upgrading, and running of service scripts and application ﬁles

35

Table 2: Abbreviated labels for chromosomal accession numbers.

 

 

Accession Label N CBI Name

NC-000854 A.pnx. Aeropyrum pemir

NC-000917 Arch.ful. Archaeoglobus fulgidus DSM 4304
NC-002696 Caulcre. Caulobacter crescentus CB15

NC-003450 Cor.glut. Corynebacterium glutamicum ATCC 13032
NC-002662 Lac.lact. Lactococcus lactis subsp. lactis

NC.003552 Mt.acet. Methanosarcina acetivorans C2A
NC.003901 Mt.maz. Methanosarcina mazei Goel

NC-002755 tbl551 Mycobacterium tuberculosis CDC1551
NC-000962 th37Rv Mycobacterium tuberculosis H37Rv
NC.000908 M.gen. Mycoplasma genitalium

NC-000912 M.pnm. Mycoplasma pneumoniae

NC.002771 M.pulm. Mycoplasma pulmonis

NC-003272 Nostoc Nostoc sp. PCC 7120

NC-000868 Py.aby. Pyrococcus abyssi

NC.000961 Py.hor. Pyrococcus horikoshii

NC-003413 Py.fur. Pyrococcus furiosus DSM 3638

NC-003103 R.con. Rickettsia conorii

NC.000963 R.pro. Rickettsia prowazekii

NC-002737 S.pyog. Streptococcus pyogenes Ml GAS
NC-003028 Str.pnm. Streptococcus pneumoniae TIGR4
NC.002754 Sulf.solf. Sulfolobus solfataricus

NC-003106 Sulf.tok. Sulfolobus tokodaii

NC-000911 Synec. Synechocystis sp. PCC 6803

NC-004113 Thelon. T hermosynechococcus elongatus BP-l
NC-003919 Xn.axon. X anthomonas aronopodis pv. citri str. 306
NC.003902 Xn.cmp. Xanthomonas campestris pv. campestris str. ATCC 33913
NC-004556 X.fas. Xylella fastidiosa Temeculal

 

36

associated with the MYCROW system as it emerged from a prototype into a reliable
laboratory solution.

Two of the ﬁve computers were used for archiving and curating the data set. The
front-end archive computer was used to dynamically compile speciﬁc data sets for further
analysis, and was set up as a web server to provide an interface for specifying and retrieving
various matrices of ORF-speciﬁc data. The back-end archive computer handled and
processed a pipeline of information coming from external sources such as NCBI. Much of the
parsing of NCBI genome ﬁles and sequence-level BLAST calculations occurred on the
back-end archive computer. Both archive computers ran FreeBSD 4.9 or higher.

I used the other three of the ﬁve computers for data analysis of the curated, retrievable
data set. One of these computers was used as a relational database and archive of statistical
methods. The database was run with MySQL version 3.23 or higher. The interactive data
analysis was distributed on 2 other computers. All three of these computers ran Mandriva
Linux version 10.0 or higher. The “8” statistics language (Chambers & Hastie, 1992) was
used to perform most of the statistical calculations, and was run on the “R” statistical
environment (R Development Core Team, 2005). Perl and R were the primary software
languages used to write necessary algorithms on both the curatorial and data analysis
computers.

The front-end web server computer ran with an Intel Pentium 4 ® CPU 1.60 GHz
computer chip, and 750 MB RAM memory. The back-end archive server ran with an Intel
Pentium 4 ® CPU 2.40 GHz, and 750 MB RAM memory. The statistics archive and MySQL
database server ran on a Pentium II ® 400 MHz computer chip, and 500 MB RAM memory.
One of the computers for interactive data analysis ran on a AMD Athlon ® 1.67 Hz
computer chip, and 500 MB RAM memory. The other computer used for interactive data
analysis ran on a Pentium III ® 931 MHz computer chip, and 500 MB RAM memory.

For the purposes of a ﬁnal, expedited run of the bootstrap residue calculations, a
128-processor computer was used, courtesy of the MSU High Performance Computing Center
(http://www.hpc.msu.edu/)

Screenshots of the MYCROW user interface are shown in Figures 3 and 4. The options

for the retrieval ﬁelds associated with ORF records are: similarity score (based on

37

expectation score < 10_6), GenBank accession number (the sequence-unique “geninfo”
number was used for this), annotation, function, product, amino acid length, nucleotide
length, chromosome location of the translational start point, chromosome location of the
translational end point (excluding stop codon), polarity (orientation on chromosome),
chromosome shape, chromosome size, a series of numbers quantifying the period-three signal
in the DNA, organism identiﬁer (NCBI taxon id), organism name (the N CBI epithet-like
name), translation table (the value is based on descriptions at EMBL), statistical proﬁle (%

GC, codon counts), DNA sequence, and amino acid sequence.

2.2.3 Taxonomic and Phylogenetic Categorizations

I applied a taxonomic hierarchy to the data set of fully sequenced genomes by using the
taxonomic rankings and nomenclature from the National Center for Biotechnology
Information (NCBI). The chromosomal accession numbers were used as a querying list for
the NCBI Taxonomy Common Tree application
(http://www.ncbi .nlm.nih. gov/Taxonomy/CommonTree/wwwcmt . cgi). The data was
parsed, and an outline of taxonomic groups built, by tallying up those taxonomic groupings
that contained less than 20 representative strains.

For subsampling, I generally used ﬁve taxonomy-based groupings of genomes. These
taxonomic groupings are: Archaea - 17 genomes; Actinobacteria - 13 genomes;
Enterobacteriales - 17 genomes; Gammaproteobacteria without Enterobacteriales - 20
genomes; and Lactobacillales - 13 genomes.

I built four phylogenetic trees with times of divergence based on estimates from
Battistuzzi et al. (2004) to characterize samplings of Archaea, Gammaproteobacteria, Bacilli,
and Actinobacteria. I evaluated the growth of phylogenetic range by looking at the number
of available chromosomes, species with more than one representative strain, and number of
representative phyla for each year since the beginning of 1995 based on associated date of
publication in the literature or submission to GenBank.

I also sought to evaluate the relationship of the set of 155 genomes with natural diversity
of the prokaryotic biota based on an historical reference on infectious disease (Hoeprich,

1972) and my own classiﬁcations of ecological and lifestyle categories based largely on

38

 

Construct a data set

ORFS are tagged with their Gen/"to (GI) numbers

0 Select one or more ORF attributes

I— Homology Score (based on expectation score<10'6)

I- GenBank Accession Number

I- Annotation

I- Function

I" Product

I- Amino acid length

I- Nucleotide length

I— Chromosome location; translational start point

I- Chromosome location; translational end point (excluding stop codon)
l— Polarity (orientation on chromosome)

I- Chromosome Shape

I" Chromosome Size

I- DNA Fourier Signal

I- Organism ID

I- Organism Name

I- Translation Table (the value is based on descriptions at EMBL)
I" statistical proﬁle (% GC, codon counts, fairly large)

I- DNA sequence (warning, this could produce a large file)

I'- Amino acid sequence (warning, this could produce a large ﬁle)

 

 

 

Figure 3: Selecting ORF attributes for retrieval from the online MYCROW information re-
trieval web page. The user constructs the columns of a data set by selecting checkboxes
corresponding to ORF features of interest.

39

 

° Select one or more of the following organism/chromosome sets

Organisms (1+ chromosomes)

 

All organisms

Aeropyrum pemix

Agrobacterium tumefaciens str. C58 (Cereon)
Agrobacterium tumefaciens str. C58 (U. Washington)
Aquifex aeolicus VF5

Archaeoglobus fulgidus DSM 4304

Bacillus anthracis str. A2012

 

Individual chromosomes

 

All chromosomes

Aeropyrum pemix (circular); 1.7M: NC_000854)
Agrobacterium tumefaciens str. C58 (Cereon) (circular); 2.8M; NC_003062)
Agrobacterium tumefaciens str. C58 (Cereon) (linear); 2.]M; NC_003063)
Agrobacterium tumefaciens str. C58 (U. Washington) (circular): 2.8M; NC_003304)
Agrobacterium tumefaciens str. C58 (U. Washington) (linear); 2.1M; NC_003305)
Aquifex aeolicus VF5 (circular): 1.6M; NC_000918)

 

Anna.-.

0 Filter choice #1

IORF ATTRIBUTE I '??‘?‘???? I I

0 Format the output

 

|'~7 Prepend the dataset with descriptive header information

I Tab I ﬁeld delimiter

Get it! I CLEAR J

 

 

 

 

Figure 4: Selecting a set of chromosomes or organisms from the online MYCROW information
retrieval web page. Options for conditionally ﬁltering the set of ORFS based on ORF attributes,
and options for formatting the output are provided in addition to the chromosome and organism
selection windows.

40

descriptions in the original genome journal publications.

2.2.4 External ORF-Based Data Sets

A study from Covert et al. (2004) focuses on Escherichia coli K-12, and uses functional
predictions and microarray assays of gene expression to better characterize bacterial
networks. Their “Supplementary Data 6” data ﬁle provides raw microarray data organized
into treatments of one wild-type strain and six knockout mutant strains growing under
aerobic versus anaerobic conditions. Of the 3699 ORF regions listed in the microarray data,
3309 of these regions (89%) had identiﬁers that mapped to ORFS within the MYCROW
database records for Escherichia coli K-12. There were 3 strain replicate trials for each type
of strain under both aerobic and anaerobic conditions. The resulting 42 characterizations of
gene expression (present, absent, marginal) were evaluated to assess the general
transcriptional expression of each ORF.

The analysis of Bacillus subtilis by Biaudet et al. (1997) characterizes 19 phenotypic
consequences of mutation associated with 554 genes. In that study, mutations are found to
range in effect from single phenotypic changes to six phenotypic changes. The phenotypic
categories are: osmotic stress, oxidative stress, temperature and pH stress, electron transfer,
general stress, stress by metals, starvation stress, N or C sources, glucose effect, amino acid
induction and repression, amino-acids and translation, macromolecules, protein/ secretion,
envelope/lysogeny, envelope/ AP / BG, cell cycle, competence, sporulation, and germination.
There were 533 of the 554 genes that had unambiguous matches to B. subtilis ORFS inside
the MYCROW database based on identiﬁer information.

I compared the degree of paralogous representation of my ORF similarity clusters (as
calculated by the criteria of section 2.5) to paralogy sets as calculated by (Pushker et al.,
2004) for 4 strains of Escherichia coli, 3 species of Pseudomonas, 4 strains of Streptococcus

pyogenes, and 3 strains of Staphylococcus aureus.

2.2.5 Mobile Elements

Data on IS element density for 50 genomes came from a study by Moran & Plague

(2004). From their graphical plot of IS density, I assayed density values by intervals of 1 IS

41

element per 350,018 bp to construct boundaried bins of i / 350018 to (i + 1) / 350018 where
i = {1,2, 3, ..., 34, 35}. The characteristic IS element density for each genome was set to the
value of i. The data for IS element served to comparatively characterize underlying molecular

factors of disruption to chromosomal organization.

2.3 Dot Matrix Evaluation of Conserved Chromosomal
Organization

To build dot matrices, I used data from the NCBI GenePlot application (Wheeler et al.,
2000) to gather the symmetrical best hits of ORFS as they occur between pairs of genomes. I
translated the identiﬁers of the bidirectional best hits, as catalogued by the NCBI GenePlot
application, to base pair coordinate information from ORF objects stored inside the
MYCROW data ﬁles. Each dot matrix represents a pairwise comparison upon which a
greater-ranging phylogenetic analysis can be conducted. I constructed a set of nine
phylogenetic comparisons where each comparison involved three strains with characterized
times of divergence from Battistuzzi et al. (2004). Among these sets of three strains, two of

the strains were more closely related to each other than to a third more “distant cousin.”

2.4 Measuring Mutual Information

Mutual information (W'eaver & Shannon, 1949; Feeny & Lin, 2004; Church & Hanks,
1990) was a measurement approach for two contexts. As applied to the dot matrix plots, I
divided the plots into square windows sag, y of a given size w (see Figure 5). The remaining,
sometimes rectangular, windows on the mth row and nth column were also included in the
analysis. These square (and remaining) windows were summed up by columns
(Cy = 2;”: 1(32', y)) and rows (rm = 2?: 1(s$,,;)). I calculated the total sum as
t = 233"“: 1 :3“ = 1(333, y). For each square window 31:, y containing plotted points
(513.1! ¢ 0), I calculated the pointwise mutual information by Equation 1. The average
pointwise mutual information was the arithmetic mean of all values of I C(x, y) where

317,31 ¢ 0. I evaluated the average pointwise mutual information for various window sizes,

42

w = 10 kb, 20 kb, 30 kb, , 150 kb. I wrote a function that ran in the “R” statistics

package, version 1.9.1, to perform this calculation.

81? , )
10013.31) =10g2 (T c (1)
in“

My second context of usage was to evaluate the lag average mutual information (AMI)

 

calculations for neighboring window-Sized calculations of intrachromosomal organization (see
section 2.8). I calculated lag mutual information (in this case based on natural logarithms)
with the “mutual” function of the “tseriesChaos” package, version 0.1-6 with the “R”
statistics package, version 2.3.0. For a given window—sized calculation of intrachromosomal
organization Gw(h) on a chromosome h and the ORF densities based on that window w,- (see
the P and Q measures of Section 2.8.3), the AMI was calculated for various lag comparisons
b based on the following procedure. At most, 16 bins u,- on the ORF densities series dz- were
determined. The mutual information I L (x, y) b between each pair of differing bins, U1; and
uy, was calculated as Shown in Equation 2. Let H (w, i, h) = Cw,(h). The b value is the
amount of lag between the two series, 3' = H(w, 1, h), H(w, 2, h), H(w, 3, h), ..., H(w, N, h)
and k = H(w,b + 1, h), H(w,b + 2, h), H(w,b + 3, h), ..., H(w,b + N, h). A circular boundary
condition was applied where H (w,i + N, h) = H (w, i, h). Two counting functions were used.
There was a counting function that determined the number of j or k values falling within a
given respective bin q(ux) or q(uy). There was also a counting function that determined the
number of j and k values jointly falling within two bins q(ug;, uy) at the speciﬁed lag b. I
veriﬁed performance of the “tseriesChaos” package’s “mutual” function by custom-writing a

separate function that produced the same results over various test cases.

q(u$iu)
sense

I compared the lag AMI series for the different measures of intrachromosomal

ILfiI’, ylb =108

organization described in Section 2.8.3.

43

 

 

 

 

 

 

 

 

 

 

 

W
W C

Figure 5: Calculating the pointwise mutual information on a dot matrix of conserved ORF
organization. A grid of m rows and n columns is applied to a dot matrix based on a given
window size 11). Rows (rm), columns (Cy) and squares on the grid (rm) are regions used for
counting up relative densities to the overall number of dots on the dot matrix.

44

2.5 Speciﬁcation of Operational ORF Subset

Similarity counts were evaluated for each of the 447,551 ORFS. The Similarity count was
the inclusive number of ORFS in the set of 447,551 ORFS that matched a similarity ﬁlter for
a given ORF based on characteristics of the amino acid sequences. The similarity ﬁlter
involved two requisite criteria: a BLASTP expectation score 3 10—6, and an amino acid
length difference of at most :I: 10%. To avoid computational times exceeding one month, I
did not calculate 447,551 consecutive one-to-many BLASTP comparisons, nor did I run a
BLASTCLUST computation on the entire set of 447,551 ORFS. Rather, I developed a
speedier approach that took 8 days on the archive computer. This approach is done by
calculating sets of ORF that range in length by 10%. The parameters for length variation are
incremented stepwise by 5%. BLASTCLUST is then calculated on each length-based set of
ORFS. Then, for each ORF, I re-tallied the computed similarity clusters to identify the
putatively matching ORFS that were within a length range of i 10% of the particular ORF.
I performed one iteration of resolving transitive relationships.

I then categorized each ORF by the number of similar ORFS in the data set of 447,551
ORFS. An ORF that was not “similar” (according to the criteria of 10% length and S 10—6
expectation score similarity) to any other ORF was in a cluster of size 1. A pair of ORFS
that were only similar to each other were in a similarity cluster of size 2. I characterized
O-ORFS as belonging to similarity clusters of size 2 6, and the putatively false set of ORFS

(S-ORFS) as belonging to similarity clusters of size S 5.

2.6 Running Tally

I developed an approach I call a “running tally” to measure the nonrandomness of
chromosomal clustering and ORFS. Running tallies contrast the spatial chromosomal
clustering attributable to original assignments of ORF properties with the clustering effect
due to randomized assignments of ORF properties. Figure 6 illustrates how the running tally
approach can visually present both the magnitude and shape of the natural invariance
compared to a randomized control. The running tally approach is similar to that of plotting

and measuring a random walk (Pearson, 1905).

45

I initially used running tallies on the ORFS of each chromosome to assess both the
inclusion and exclusion of ORFS within COGS as well as the associated coding strand
(polarity). Polarity data came from the MYCROW web application. COG data was accessed
from the COG database, ftp://ftp.ncbi .nih.gov/pub/COG/COG (Tatusov et al., 1997b,
2003), and represents data updated on March 2, 2003. The scope of NCBI’S COG database
limited the evaluation to just 67 (41%) of the 165 chromosomes. Of these 67 chromosomes,
there were 4 Actinobacteria, 13 Archaea, 12 Gammaproteobacteria, 3 Lactobacillales and 32
bacteria belonging to other taxonomic classes. I also used running tallies to evaluate the
clustering of O-ORF and S—ORF assignments.

I used a bootstrap to calculate the z-score difference between running tally measures
related to two negative controls versus those running tally measures involving original
assignments. I measured the difference between each pairwise comparison by calculating the
integral area between the two running tallies. I characterized the z-score value by the
standard deviation 0 of the distribution calculated by measured differences among pairs of
negative controls. Signiﬁcance was evaluated by bootstrap where, for multiple times, the area
between running tallies of 50 randomized assignments versus the non-randomized assignment
was calculated. The mean of these 50 measurements was calculated. This step was repeated
100 times so that there were 100 means from which a bootstrap estimate mt was calculated.
This estimate was contrasted with 50 x 100 measurements between the running tallies from
pairs of two randomized assignments from which an estimate m f was calculated and a

standard deviation 0 . The z-score difference between m and m was characterized as
f t f

(mt - mf)/of.

2.7 Simulation of Informational Expansion and

Modiﬁcation

I built a simulated model of recombination similar to an expansion-modiﬁcation system
(EMS) (Li, 1991), yet my simulation model is a probabilistic context-sensitive grammar as
opposed to a probabilistic context—free grammar. My test was to see whether various initially

set parameters of the simulation model can be inferred retrospectively from a measurement of

46

ORF Scoring Annot#1 .23} ,1
Annot#2 1:) -1

I-WWZWW --|

-1 -1-1-1 -1 -1 +1+1+1 +1 +1o+1 +1 +1 +1 +1

@1444 -5 ~6-5-4-3 -2 -1-2-1 01 2 3
+5-—

 

 

Running tally

 

 

 

 

Randomized --.=,._-7_.- -------- f, ----- _, -- _,_, -----------------
'- '7 d, " I \
Assignments Lifer/M ——~' '4 :11“ I if" N 2" 3114;51

Figure 6: My method for counting up a running tally for original and randomized ORF annota-
tions. Two annotation states are evaluated and scored with either a +1 or a -1. A deliberately
constructed non-random pattern of ORFS is shown in the uppermost solid rectangle. A pattern
of ORFS based on randomized assignments of ORF annotations is shown at the bottom of the
ﬁgure in a dashed boundaried rectangle. A running tally series for the upper pattern of ORFS
is plotted with closed circles and solid lines. The running tally series for the lower pattern of
ORFS is plotted with small squares and dotted lines.

47

the constructed pattern built with simulated expansions and movement of information.

The symbolic structure of my EMS-like model consists of a series of letters from the set
{A,B,C,D,E,F,G,H} as described in Equation 5. Various functions T1;(S) and Dg;(S) are
abstractions of cut-and-paste ( “translocation”) and tandem copy operations on the model
replicon. While my symbolic model is not applicable to the physicochemical detail of
recombinative change, it serves to 1) validate the idea that different sizes and stochastics
associated with mobile and duplicating segments of a sequence can produce an interpretable
signature and 2) test assumptions about how a given measure corresponds to underlying
model parameters. To investigate segmentation patterns within the ﬁnal output series of
alphabetic symbols produced by each simulation (3;; E S) I calculated densities of “H”
characters within windowed subseries of each generated sp.

Equations 3 and 4 show a sequence of 8 letters that is triplicated to form a sequence that
is 24 letters in length. Depending on the value for n in Equation 4, other replicate structures
of octets can be generated (e.g., n = 2, duplicated octets; n = 4, quadruplicated octets; or
n = 5, quintuplicated octets). The n parameter acts to both set the length of the starting
sequence and establish an initial, non-stochastic pattern.

The Dg;(S) rule system (Equation 9) is to tandemly duplicate a randomly selected
internal 6-letter sequence. For example, the sequence ABCDEFGHABCDEFGH can have a
randomly selected 6-letter subsequence - AB(CDEFGH)ABCDEFGH - that, when
duplicated, creates ABCDEFGHCDEFGHABCDEFGH. The N (Y) = 6 condition is an
adjustable, initial parameter for the simulation, and I evaluated this condition over a range of
conditions N(Y) = 2 to N(Y) = 12.

The T 3(S ) rule system (Equations 6 - 8) involves identifying two locations of a “HA”
subsequence. A target location for this translocational event is then identiﬁed and the
translocation event performed. A more detailed illustration of this system is shown in Figure
63 in Chapter 5.

My stochastic rule system is shown in Equation 11 where q is a uniformly distributed
random variable on the interval [0, 1].

In a rough sense, I meant for the original simulation design to have one letter

corresponding to 10,000 bases. Based on this relationship, 500 letters equals 5,000,000 bases,

48

a value that is loosely representative of a prokaryotic chromosome’s size. The simulation ends

once the sequence expands to more than 500 letters.

.11 a {A, 3,0, D, E, F, 0,11}

.1 -—+ ABCDEFGH

Ls{awx=1}

n=3

L—->[.rrr[:r=J}

: If 3(W, X, Y, Z)

: If 301". X, Y, Z)

 

SI SE A!“

(W e 11*)
/\ (X e M‘)

/\ (Y e HAM‘HA) ,S —+ WYXZ
/\ (Z e M")

/\ (s 2 WHAXYZ)
(w e M‘)

X e HAM‘HA)

,S —+ WYXZ

zems

 

M
/\(Y€M*)
M
M

s a WXYHAZ)

49

(W e M“)
X e M‘)
T3(S) : If —+3(W,X, Y, Z)

Z 6 M‘)

 

/\ (
A (Y e HAAPHA) .3 -+ S (8)
/\ (
A ((s s WHAXYZ) v (s a WYXHAZ))

(X e M‘)

01(5): If3(X, Y, Z) A (Y E M) ,s—» XYYZ (9)
A (Z G M“)

/\ (N(Y) = 6)

 

(X E III”)
/\ (Y E 111‘)
02(5): If m3(X, Y, Z) I ,S —> S (10)
/\ (Z 6 AI”)
/\ (1V(Y): 6)

S—> 733(5) {1‘9} (11)

Bails) {Q}

There is a total of three parameters that can be speciﬁed for each simulation trial: 1) the
stochastic incidence q of tandem copy events (Dx(S)) versus cut-and-paste events (T1(S)),
2) the size of tandem copy events speciﬁed by the N (Y) condition in Equations 9 and 10, and

3) the number of consecutive octets representing the starting sequence (Equation 4).

2.8 Measures of Internal Physical Clustering

2.8.1 ORF Density Calculation and Randomization

Let C be the set of chromosomes where C = {01,02, C3, "-1616416165l- Let A,- be the set
of ORFS on each chromosome c,- as they are annotated from the NCBI microbial genomes
database (Wheeler et al., 2000). Based on the O-ORF subset deﬁnition arrived at in Chapter

4, deﬁne R,- C A, as the set of O-ORFs for a given chromosome Cir and let r1: 6 R1; As

50

measured from a somewhat arbitrary zero—point on a chromosome c231 let P(rx) represent
the translational start point of each O-ORF r3. When dividing the chromosome length L
into 6-sized segments, let A(a, b) represent the number of ORFS for which

a S P(rx) < (a + b). A(6n,6) is the number of ORFS for which 6n 3 P(T‘1‘) < 6(n + 1).
Let F be the O-ORF density series {A(06,6),A(16,6), A(26,6), ...,A((n — 1)6, 6), A(n6, 6)}

I evaluated chromosomal segmentation sizes 6 ranging up to 150,000 bp. Shufﬁing
involved rearrangement of 6—sized segments. For each segmentation size 6, I constructed 10
shufﬂed chromosomes for each of the 165 chromosomes to generate a set of 1,650 shuffled
versions of chromosomes. Shufﬂing was done by randomizing the ordering of A(6n, 6)
observations to produce the x set. Let x 2 X1, X2, ..., X10 be independent, identically
distributed shufﬂed samples from the ordered sequence of translational start point counts F.
For example, if F = {A(06,6), A(16, 6), A(26, 6), A(36, 6), A(46, 6)}, then a random
reassignment of order could be X1 = {A(36, 6), A(26,6), A(46, 6),A(16, 6), A(06, 6)}.

To contrast F with x, I used the bootstrap procedure by resampling shufﬂed versions of
the 165 chromosomes. For both unshufﬂed and shuffled versions of chromosomes, I calculated
various measures of internal physical ORF clustering (Section 2.8.3). My objective was to use
the distribution of measures on the X set as a basis for assessing measures of F (the
unshuffled chromosome) versus any single X,- (a shufﬂed chromosome). A more detailed

description of how bootstrap calculations were organized is in Section 2.8.4.

2.8.2 Lag k Autocorrelation

For a series of ORF densities of length N, I calculated kth neighbor product-moment
autocorrelations by lagging the series by k and dividing a covariance by the product of
deviations as shown in Equation 12 (Box & Jenkins, 1976). B represents either N — k or N
for linear or circular chromosomes respectively. Let dz- = Fi' With respect to circular
chromosomes, a circular boundary condition applies where d,- + N = dza For each analyzed

chromosome, a series of Pearson product moment autocorrelation r values

1The zero location on a chromosome was based on NCBI’s data ﬁles and does not deﬁni-
tively correlate with any natural landmarks on the chromosome such as oriC. For example,
annotated locations of non-zero oriC on chromosomes include locations 915,732 (on a sequence
of 2,841,490 bp), 4,788,169 (on a sequence of 5,528,445 bp), and 3,840,051 (on a sequence of
4,599,354 bp).

51

(r1,r2, r3, ...,rB _1) is generated.

,k z 2.”: 1w.- —H><d.-+i ——?1‘>
(B —1>\/Z(d.-— 71)? 2w.- .. k — 3)?

 

 

(12)

2.8.3 Scalar Residue Measures of Internal Clustering

To quantify the interdependence among consecutive values in a lag is autocorrelation
series (rk, rk + 1177: + 2, ...), I calculated a sum of squared differences as shown in Equation
13. I compared the E (F) value to similarly calculated values based on shufﬂed versions of the
ORF count series E (Xi), and the deviation from the bootstrapped distribution of

shufﬂed-based values calculated.

k<(N—1)

E(F) = 2 (r1. — wk- 1)? (13)
1:23

The calculated deviation was relative in that I compared the bootstrapped distribution of

abs(E (F) — E(Xi) to the bootstrapped distribution of abs(E(X,) — E(Xj)) as described in
Section 2.8.4.

I also developed an alternate measure of ORF arrangement that is similar to that
described for the Angular quuency Transform of Sandvik et al. (2004). This alternate
measure treats the ORF count series as a pseudophase space. The trajectory angles 62- and
rotations w are measured on the pseudophase space, and frequency of occurrence evaluated.

The transform of F2- to 92- was done through the plotting of a: and y coordinates as described

in Equations 14 - 16.

(frat/1P (FivFi+1) (14)
(Iiv$i+11$i+2) = (63541117242) (15)
(yiayi-I-lty’i-I-Z)=(Fi+11Fi+29Fi+3) (16)

The angle 62- and its rotational direction to is calculated with the three points (xi, y,),

52

(r,- + 1, 31,- + 1), (r,- + 2,11,; + 2). Clockwise rotations are represented by w = 1.
Counter-clockwise rotations are represented by w = —1. The rotational angle 62' is the
product of w and 62:; 62- = 6,- * w.

I assessed the heteroscedasticity of the angular change distribution of 6, values on the
pseudophase space based on shuffled versions of the ORF count series (see Section 2.8.4). I
evaluated D(F, Xi) as the average Kolmogorov-Smirnov (KS) statistic (Young, 1977)
between the distribution of 8,- values from F versus the 62- distribution from a randomly
selected (with replacement) Xi- I compared D(F , X z) to measures of the KS statistic
between two shuffle-based distributions, D(X iv X j)' The bootstrapped difference between the
mean characteristic value of D(F, X 21) and the mean characteristic value of 00%, X j) was an
angular frequency residue P (Ci, 6) of a given chromosome cz- and segmentation size 6.

Both P(c2-, 6) and Q(c,-, 6) were evaluated for multiple O-ORF density series based on

segmentation sizes ranging from 500 bp to 150,000 bp.

2.8.4 Bootstrapping

For each segment size and chromosome, the differences were resampled 10 times based
on measures of the unshuﬂied version versus a randomly selected (with replacement) shuffled
version from a set X of 10 shufﬂed versions. The mean of these 10 values was computed,

v = '55. The process for computing 1) scores was repeated 20 times to produce the values

V = {121, ..., v20}. The mean of these 20 values was computed, b = V. The process of
computing b scores was repeated 10 times to produce the values B = {b1, ..., blo}. The
process for computing B was repeated 10 times for the pseudophase angular assay (related to
the D function) and 20 times for the lag k-based assay (related to the E function of Equation
13). The means for each of the B assays were selected as the characteristic scores for the
evaluated segment size and chromosome. As a random control, the characteristic scores were
recalculated with a pool of ten random shufﬂed versions substituting (at random) for the
unshufﬂed version for each of the mean(B) calculations. The scheme of calculating processes
repeating other sub-processes led to an initial sampling iteration count of 10 and resampling
iteration counts of 4,000 for Q(c2-, 6) scores (based on the E comparisons, Equation 13) and

2,000 P(cz-, 6) scores (based on D(F, Xi) — D(X 2', X j) comparisons) for each segment length 6

53

and chromosome 6i The bootstrapping iterations on the averaged 1) values were respectively
200 and 100. Overall, I ran 2,970,000,000 calculations of these scalar measures for internal
physical clustering. Multiple trials of this entire process led to characteristic scores that were
generally at most :l:5% different from repetitious calculations of characteristic scores for the
same segment size and chromosome. The Q scores were termed as symmetry scores, and the

P scores were termed as symmetrical shape scores.

2.8.5 Harmonic Symmetry of ORF Density and the Windowed

Asymmetric Deviation

My goal was to 1) identify those segmentation sizes 6 (500 bp, 1,000 bp, 1,500 bp, ...,
149,500 bp, 150,000 bp) most closely associated with non-shufﬂed series of O-ORF densities
(F) and 2) characterize and compare the degrees of non-randomness attributable to measures
of internal physical clustering. To accommodate the inﬂuence of neighboring segmentation
sizes, a further objective was to inspect windows of Q(ci, 6) values covering multiple
segmentation sizes 6.

I ﬁrst evaluated the simulated outputs sp 6 8 (Section 2.7) to investigate whether
Q(sx, 61) was related to Q(sa;, 62) when the difference in segmentation sizes (61 — 62) for
computing density of “H” letters was predictive of the initial model parameter T. To
evaluate how differences in Q values relate to underlying segmentation related factors of
61 — 62 and T, I applied a fast Fourier transform (F FT) to each T-based series
{Q(sx, 1), Q(sx, 2),Q(sx, 3), ...,Q(s$, 29), Q(s$, 30)}. My theory for this is that insertions of
predictable sizes T should produce similar values of Q(s;1;, 61) and Q(s;1;, 62), and the
frequencies associated with the higher FFT-computed amplitudes should inversely relate to
the periodicity-generating effect of a particular T value.

With the assumption that mobile elements guide the insertion of new DNA into a
replicon of a restricted or non-restricted range of insertion size (comparable to a potentially
heritable T-like parameter characteristic of a lineage), I sought to determine the range of
segmentation sizes that captured a signiﬁcant overall rise and fall of Q values. I ran windows
of 51 values (25,000 kb) on series of 300 Q(cz-, 6) values where 6 ranged from 500, 1,000,

1,500,..., 149,500, 150,000. For a given window start point I, the 51 values corresponded to a

54

6-based series of r, z + 500,1 + 1, 000, 1' + 1, 500, ..., I + 25, 000. To ﬁlter out small-scale
effects and characterize the relative amplitude of the overall rise and fall for this range, I
calculated the ﬁrst spectral modulus from an FFT on the series of 6-based Q values for a
given Ci and 1‘ (Figure 7). The ﬁrst spectral modulus is the square root of the sum of squared
sine and cosine coefficients associated with a frequency value of 1, and I termed this value to

be the windowed asymmetric deviation.

 

a) b)

A1

 

 

 

 

500 x x+25kb 150,000 500 x x+25kb 150,000
Segmentation Size Segmentation Size
in base pairs in base pairs

Q Measure of Internal Physical Clustering
Q Measure of Internal Physical Clustering

 

 

 

 

Figure 7: Illustration of the windowed asymmetric deviation measure. An amplitude A1 is
measured for a period-1 wave on a windowed series of Q values. Subﬁgures a and b show how the
characteristic A1 value can change based on a different window start point 1:. A1 is calculated
as the ﬁrst spectral modulus of the FFT on a window of the 300 Q values corresponding to
segmentation sizes 6 ranging from 500 bp to 150,000 bp.

55

Chapter 3: Diversity and Stability of
Chromosomal Organization and

Content

3.1 Taxonomy of Chromosomal Data

3.1.1 Patchiness of Taxonomic Representation

Based on the NCBI taxonomy (Wheeler et al., 2000), the scope of analysis for the 155
strains with fully sequenced genomes involves 16 phyla, 82 genera, and 126 species. These
taxonomic groupings are consistent with an externally developed phylogeny (Battistuzzi
et al., 2004). A visual outline of this taxonomy (Fig. 8) is a key to the relative representation
of various taxonomic groups. Some groups are well-represented while others are not. The two
most prominent phyla in Fig. 8 are the Proteobacteria and Firmicutes, each containing over
several dozen strains with fully sequenced genomes. At the class level, the
Gammaproteobacteria are disproportionately well-represented, representing 24% of the 155
genomes in this study. Seven phyla have only one representative genome. These seven,
sparsely represented phyla are Nanoarchaeota, Thermotogae, Aquiﬁcae,
Deinococcus-Thermus, Plantomycetes, Chlorobi, and Fusobacteria.

A bias for certain types of organisms exists in the data set of 155 strains with fully
sequenced genomes. In particular, by using names of species as listed in a widely-cited,
historical reference on infectious diseases (Hoeprich, 1972), I calculated a signiﬁcant bias for
pathogenic bacteria in the set of 155 strains. 50 (32%) of the 155 strains were implicated, by
their epithet, as belonging to one of the 99 pathogenic bacterial species indexed by Hoeprich
(1972). Of the 52 genera I found indexed by Hoeprich (1972), 25 (48%) genera were present
in the set of 155 strains. Of the 99 infectious disease species I found listed in Hoeprich

(1972), 35 (35%) of these correspond to species in the set of 155 strains. Also, from the

56

— 4 Crenarchaeota (phylum)

 

 

 

 

 

 

 

 

 

 

Archaea — 12 Euryarchaeota (phylum)
—- 1 Nanoarchaeota (phylum)
+—--- 8 Cyanobacteria (phylum)
—- l Alteromonadales (order)
— 17 Enterobacteriales (order)
— 1 Legionellales (order)
3 Pasteurellales (order)
Gammaprot. ‘— 3 Pseudomonadales (order)
-— 4 Vibrionales (order)
—— 4 Xanthomonadales (order)
Proteobacteria 12 Alphaproteobacteria (class)
8 Betaproteobacteria (class)
2 Deltaproteobacteria (class)
5 Epsilonproteobacteria (class)
J— 13 Bacillales (order)

 

 

 

Bacteria Bacilli l—- 13 Lactobacillales (order)
— 8 Mollicutes (class)

‘— 4 Clostridia (class)

-— 4 Spirochaetes (phylum)

 

Firmicutes

 

— 1 T hermotogae (phylum)

— 1 Aquiﬁcae (phylum)

— 7 Chlamydiae (phylum)

— 1 Deinococcus- Thermus (phylum)
-— 1 Planctomycetes (phylum)

— 2 Bacteriodetes (phylum)

+—- 1 Chlorobi (phylum)

--- l3 Actinobacteria (phylum)

 

—- l Fusobacteria (phylum)

Figure 8: Taxonomic scope of 155 fully sequenced genomes. The patchiness of taxonomic
branch representation for 155 genomes is shown by an outline of groupings where each branch
contains less than 20 distinct genomes. The hierarchical structure and naming of taxonomic
units is based on the NCBI taxonomy. Higher level taxa are labelled underneath their corre
sponding branch line. Gammaprot. = Gammaproteobacteria.

57

vantage point of making closely related strain—to—strain comparisons, the 35 infectious disease
species in the set of 155 strains corresponded to 50 strains (32%). By contrast, there are 91
species in the set of 155 strains that are not present in Hoeprich (1972). These 91 species
correspond to 105 of the 155 strains.

The bias of pathogenic bacteria representing approximately one third of the 155 strains
is further characterized by sets of closely related strains. For the 21 sets of strains having the
same species name (Fig. 13b), 19 of these sets associated with pathogenic bacteria compared

to only 2 sets associated with non-pathogenic bacteria.

3.1.2 Evolutionary Times of Divergence

Fig. 9 - 12 show how the 155 genomes of this study relate to a reconstructed timescale of
prokaryotic evolution based on a universal last common ancestor of 4,250 million years ago
(Ma) (Battistuzzi et al., 2004). Timescale reconstruction for the Archaea involved a 1,200
Ma fossil calibration (Battistuzzi et al., 2004) (Fig. 9). Timescale reconstruction for the
Bacteria involved a 2,300 Ma minimum geological calibration (Fig. 10 - 12). Based on these
timescale reconstructions, I found that membership within the same genus corresponds to a

time range of 6 Ma - 1,300 Ma.

3.1.3 Comparative Power of Data Set

The breadth and depth of the 155 genomes (165 chromosome sequences) has accumulated
over time with increasing comparative power and phylogenetic coverage as shown in Fig. 13.
21 species are present for which there was more than one representative strain and
corresponding genomic sequence. 48 fully sequenced genomes had at least one other closely
related genome sharing the same species name. Overall, the data set of 155 genomes contains
well over a dozen different sampling points for studying broad, phylum-independent patterns

as well as for evaluating distinctions among strain-to—strain comparisons.

58

f1.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2392
460 bi.
2625
481
462
2623
462
b
“ 3124
c
_ 3124
d
_. 715
e .—
2663 f
g
f
3781
1332
1628
540 1332
612 2960
3500

 

 

Methanosarcina acetiuorans

Methanosarcina mazei

Archaeoglo‘bus fulgidus
Thermoplasma acidophilum
Thermoplasma volcanium
Methanococcus jannaschii
Mtb. thermoautotrophicus
Pyrococcus furiosus
Pyrococcus abyssi
Pyrococcus horikoshii
Methanopyrus kandleri
Sulfolobus solfataricus
Sulfolobus tokodaii
Aeropyrum perniz

Pyrobaculum aerophilum

Figure 9: Times of divergence for 15 Archaea. Branch length units are in millions of years
(Ma). a=233 Ma. b=215 Ma. c=254 Ma. d=188 Ma. e=323 Ma. f=338 Ma. g=377 Ma.

59

a
Salmonella enterica

a
Salmonella typhimurium

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

288 Escherichia coli
411
d —— Yersinia pestis
212 , _
e 487 Haemophilus influenzae
"‘ 212
.. Pasteurella multocida
Vibrio cholerae
364 861
Buchnera aphidicola
1387 _
Pseudomonas aerugmosa
543 , _
X ylella fastidiosa
1208

 

 

 

f
437 r— Xanthomonas campestris

 

f
'— Xanthomonas aronopodis

Figure 10: Times of divergence for 12 Gammaproteobacteria. Branch length units are in
millions of years (Ma). a=6 Ma. b=102 Ma. c=96 Ma. d=105 Ma. e=57 Ma. f=106 Ma.

328

 

Streptococcus pneumoniae

385

 

 

1103 328

 

Streptococcus pyogenes

 

713

 

Lactococcus lactis

 

1561

 

Staphylococcus aureus

927
255 355 Bacillus halodurans

927 . . .
279 Bacillus subtilis

 

 

 

 

 

 

 

 

 

a
1246 l— Listeria innocua

 

E Listeria monocytogenes

Figure 11: Times of divergence for 8 Bacilli. Branch length units are in millions of years (Ma).
a=36 Ma.

60

279

 

 

 

 

 

— Mycobacterium leprae
649
452 — Mycobacterium tuberculosis
928 , ,
Corynebacterrum glutarmcum
1380

 

 

Streptomyccs coelicolor

Figure 12: Times of divergence for 4 Actinobacteria. Branch length units are in millions of
years (Ma).

3.1.4 Replicon Topology, Size, and Composition

The number and variety of distinct chromosomes constituting each overall genome varied
between one and two. A majority (145, 94%) of the 155 genomes contained only a single
distinct chromosome. Two distinct chromosomes appeared in the following 10 of the 155
genomes: (Agrobacterium tumefaciens C58 U. Washington and C58 Cereon; Brucella
melitensis 16M; Brucella suis 1330; Vibrio vulniﬁcans CMCP6 and YJ016; Vibrio cholerae;
Vibrio parahaemolyticus; Deinococcus radiodurans; and Leptospira interrogans).

While the replicon topology for most of the chromosomes was circular, ﬁve of the
chromosomes were linear. The genomes with linear chromosomes are Borrelia burgdorferi
B31, Agrobacterium tumefaciens (2 strains, C58 U-Washington and C58 Cereon),
Streptomyces coelicolor A3(2), and Streptomyces auermitilis MA-4680. The A. tumefaciens
genomes have two topologically distinct chromosomes where one chromosome is circular and
the other is linear.

The sizes of the 165 chromosomes range from 360 kb (one of the two distinct
chromosomes present inside Leptospira interrogans serovar lai str. 56601) to 9,100 kb
(Bradyrhizobium japonicum USDA 110). Tables 3 and 4 show genus—level and species-level
variation in genome sizes based solely on DNA associated with distinct chromosomes. Even
with this restricted consideration of genomic content, variation within a genus can be almost
three—fold such as with fully sequenced strains of Mycoplasma and Treponema. As
characterized by Tables 3 and 4, the range in median genome size differences among members
of the same genus is 256 kb compared to a 52 kb difference among members of the same

species. Differences among members of the same species are generally quite small in

61

 

175
150 ~ (a) sequenced chromosomes
125
100
75
50
25

0 ﬂ 4 1 1 1 1 1

1995 1996 1997 1998 1999 2000 2001 2002 >2002
Year of Publication

 

I

 

 

U

 

 

 

 

 

Cumulative Number of
Chromosome Sequences

25
20 l
15

5 . .———I_—l
O 1 1 1 1 1 1

1995 1996 1997 1998 1999 2000 2001 2002 >2002
Year of Publication

 

(b) species with multiple genome-seq. strains

 

 

I

 

 

 

 

 

 

Cumulative Number of
Closely Related Sets

 

 

 

 

 

E ‘1‘ (C)

3 E‘ 15 . represented phyla

E n.

2 B 10 -

5 i

s s 51

E 11’

D

O 0 1 1 1 1 1 1 L 1

1995 1996 1997 1998 1999 2000 2001 2002 >2002
Year of Publication

Figure 13: Comparative scope of available chromosomes and genome-sequenced over time.
Annual trends showing the cumulative total of (a) number of sequenced chromosomes, (b) sets
of two or more genome-sequenced strains belonging to the same species, and (c) number of phyla
with one or more sequenced genome-sequenced strains. Start and stop dates are 1995/ 7/ 28
(Haemophilus inﬂuenzae) to 2004 / 3/ 20. Years are based on date of cited publication for the
genome (or corresponding species set or phyla). When there is not a regular publication, the
date of online publication (i.e., “epub”) or time of initial full sequence submission to GenBank,
was used.

62

Table 3: Conservation of total genome size for various genera.

 

 

Genusa No. of Size Range Genome Sizes
species (kb) (Mb)
Brucella 2 20 3.3, 3.3
Therrnoplasma 2 20 1.6, 1.6
Chlamydia 2 30 1.0, 1.0
Listeria 2 67 2.9, 3.0
Xanthomonas 2 99 5.1, 5.2
Haemophilus 2 131 1.7, 1.8
Rickettsia 2 157 1.1, 1.3
Pyrococcus 3 170 1.7, 1.8, 1.9
Pseudomonas 3 215 6.2, 6.3, 6.4
Sulfolobus 2 297 2.7, 3.0
Streptomyces 2 358 8.7, 9.0
Mycoplasma 6 779 0.58, 0.82, 1.0, 1.0, 1.2, 1.4
Corynebacterium 3 820 2.5, 3.1, 3.3
Clostridium 3 1,141 2.8, 3.0, 3.9
Bordetella 3 1,253 4.1, 4.8, 5.3
Lactobacillus 2 1,316 2.0, 3.3
Methanosarcina 2 1,655 4.1, 5.8
Treponema 2 1,705 2.8, 1.1

 

3The listed comparisons involve strains that are of different species, but belong to the same
genus.
comparison to most genus-level comparisons, except for the differences between
Prochlorococcus marinas strains and Escherichia coli that each approach a one million base
pair (Mb) difference in genome size.

Based on the available data for fully sequenced genomes, I found genomes to be variable
in their number of corresponding plasmids. There were 69 sequenced plasmids of variable
topology, and these belonged to just 30 of the 155 genomes. 51 of the plasmids are annotated
as having a circular topology, and the data ﬁles for 18 other plasmids do not have an
annotated topology. I found that many of the plasmids without an annotated topology were
reportedly linear (Ikeda et al., 2003; Casjens et al., 2000; Ivanova et al., 2003). As
characterized by available data ﬁles, 11 of the fully sequenced genomes have just 1 plasmid,
and 12 of the fully sequenced genomes have 2 plasmids. The Yersinia pestis C092 genome
has 3 plasmids. Nostoc sp. PCC 7120 has 6 plasmids. Borrelia burydorferi B31 has 21
plasmids. I found the range of plasmid size to be 1,286 base pairs to 2,095,000 base pairs.

The ﬁrst to third quartile range of plasmid size is 25,110 to 161,600 base pairs. The median

63

Table 4: Conservation of total genome size for various species.

 

 

Species No. of Size Range Genome Sizes
strains (kb) (Mb) ~
A. tumefaciens 2 0.7 4.9, 4.9
Tropheryma whipplei 2 1 0.9, 0.9
Chl. pneumoniae 4 4 1.2, 1.2, 1.2, 1.2
Myco. tuberculosis 2 8 4.4, 4.4
Shigella ﬁerneri 2 8 4.6, 4.6
S. enterica 2 17 4.8, 4.8
Helicobacter pylori 2 24 1.6, 1.7
Buchnera aphidicola 3 25 0.641, 0.641, 0.641
Streptococcus pyogenes 4 48 1.9, 1.9, 1.9, 1.9
Streptococcus agalactiae 2 51 2.2, 2.2
Yersinia pestis 2 53 4.6, 4.7
Staphylococcus aureus 3 63 2.8, 2.8, 2.9
Vibrio vulniﬁcus 2 85 5.1, 5.2
Neisseria meningitidis 2 88 2.2, 2.3
Streptococcus pneumoniae 2 122 2.0, 2.2
Bacillus anthracis 2 134 5.1, 5.2
Xylella fastidiosa 2 160 2.5, 2.7
Bacillus cereus 2 188 5.2, 5.4
Prochlorococcus marinus 3 753 1.7, 1.8, 2.4
Escherichia coli 4 889 4.6, 5.2, 5.5, 5.5

 

plasmid size is 40,340 base pairs. I found instances where plasmids were not included as part
of the fully sequenced genome data, such as for the three plasmids of Yersinia pestis KIM

(Deng et al., 2002).

64

 

 

 

 

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Chromosome Size (Mb)

Figure 14: Number of annotated ORFS versus genome size for 155 genomes. The slope is 893
ORFS per Mb of chromosomal DNA (intercept = 94). r2 = 0.97.

3.2 Structural Constraints of Chromosomal

Organization and Content

3.2.1 Open Reading Frames

NCBI data ﬁles for fully sequenced genomes present a total of 447,551 annotated open
reading frames (ORFS) for 155 genomes. Based on these ORF annotations, I found that a
total amount of 415,890,648 base pairs (bp) of 483,773,411 bp (86.0%) encodes for amino
acids from chromosomal DNA. Per organism, this ratio of total ORF content to chromosome
size varied from 49.5% (Mycobacterium leprae) to 96.8% (Pirellula sp. 1) and encompassed a
ﬁrst-to—third quartile range of 84.1% to 89.5%. I calculated there to be, on average, a density
of one ORF for every 1,086 bp for the set of 165 chromosomes. The ﬁrst quartile value is one
ORF for every 1,140 bp, and the third quartile value is one ORF for every 1,020 bp. The
lowest density is one ORF for every 2,036 bp (M. leprae), and the highest density is one ORF
for every 853 bp (Pyrobaculum aerophilum str. 1M2). Fig. 14 shows a strong linear
correlation of annotated ORFS versus total chromosomal content and corresponds to a
density of one ORF for every 1,112 bp. I found that the annotated locations and lengths of
ORFS remains relatively constant across various versions of data in the NCBI database.

I characterized ORF lengths by the number of encoded amino acids (aa) typically

65

 

30000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

25000 — ﬁll-5T (a)
20000 — . '
15000 4 T
10000 —
I; 5000 —
9 0 I I I
g 0 500 1000 1500 2000
g 5000 (b) 50 (c)
z 4000 —- 40 -
3000 — 30 -
2000 —l 20 -
1000 — L 10 -—I~I_|_'_~
0 I I I 0 I I T
1000 3000 5000 5000 10000 15000 20000

ORF Length (number of encoded amino acids)

Figure 15: Distribution of 447,551 ORF lengths for 155 genomes. ORF lengths are shown as
the number of encoded amino acids (aa) in each ORF. ORF length histograms are shown for
three different scalings: (a) 0 to 2,000 aa, bin size = 25 aa; (b) 1,000 to 5,000 aa, bin size =
250 aa; and (c) 5,000 to 20,000 aa, bin size = 1,000 aa.

associated with the translated protein product. Fig. 15a shows an L—shaped distribution of
ORF lengths. Most ORFS (> 95%) range in size from 0 to 705 aa. Only 1.4% of ORFS are
greater than 1,000 bp (Fig. 15b and 15c). The average ORF length is 310 a with a standard
deviation of 237 aa. The median ORF length is 265 aa.

Fig. 16 shows the L-shaped distribution to be a robust property that occurs across
various taxa. The plotted 127 aa line is an indicator of a common protein domain size of 14
kDa (Savageau, 1986). The plotted ﬁrst quartile mark ‘11 ranged from 235 aa to 267 aa. The
ﬁrst quartile mark was about twice that associated with the common protein domain size of
127 aa. These markings on the frequency peak structures of Fig. 16 visually conﬁrm a
scenario of modular protein structure where proteins are composed of one or multiple
domains. Fig. 17 portrays all 5 distributions together, with a cubic-spline smoothing of each

frequency distribution from Fig. 16. The smoothing function fails to produce lengthy,

66

monotonic regions of increases or decreases in ORF length frequency for ORF lengths > 127
aa. There does appear to be a plateau between 127 aa and 254 aa that has an internal range
of variation to be at least 10% in relative frequency.

A lognormal transform of the ORF length distribution is shown in Fig. 18. The ﬁt of
Fig. 18 to a normal distribution is p < 0.01 based on a Shapiro-Wilk test (Royston, 1982).
The skewness value (Joanes & Gill, 1998) on the lognormal transform was -0.32.

Distributions with a longer than normal left side have negative skewness values.

67

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68

3.2.2 ORF Arrangement

For a pairwise comparison of conserved ORF organization, I examined bidirectional best
hits of ORFS by constructing dot matrix plots with the physical coordinates of each ORF’S
translational start point. Fig. 19 shows the conservation of ORF arrangement among two
sets of strains sharing the same species name. A high level of conservation was indicated by a
generally non-interrupted line proceeding from the bottom left to the upper right of each dot
matrix, and membership within the same species correlated well with this pattern. Fig. 20
shows two dot matrix comparisons between genomes that belong to the same family or genus,
but do not share the same species name. There was substantially less disruption of conserved
ORF organization in Fig. 19 compared to Fig. 20. The degree of conservation was quantiﬁed
for various segmentation sizes 6 through the use of average pointwise mutual information
(APMI), a property I evaluated for 6 = 10 kb, 20 kb, 30 kb, ..., 150 kb. Fig. 21a shows the
average APMI for species-level comparisons and genus-level comparisons. A smaller
segmentation size 6 corresponded to a higher amount of measured information common to
the relative ORF locations from each pairwise comparison. Higher values of APMI indicate a
greater degree of information between the paired genomes compared to lower values of
APMI. Mutual information is generally interpreted in units of bits, and APMI values can be
meaningfully compared across different chromosomes of different lengths and also for
different segmentation sizes 6. Visually, it appears that Fig. 19a and 20a each respectively
outperform Fig. 19b and 20b, and the APMI measures are consistent with this. For Fig. 20,
the APMI based on 6 = 40 kb has a 28% reduction in value compared to an 8% reduction in
value for APMI based on 6 = 10 kb. I generally found the 40 kb-based APMI values to have
a proportionately greater decline in value compared to the 10 kb-based APMI values across
various phylogenetic comparisons.

To investigate pairwise comparisons of genomic organization with an estimated time of
divergence from a last common ancestor, I evaluated conservation for the comparisons listed
in Table 5, and used the times of divergence characterized in Fig. 25 - 33. Fig. 21b shows the
average APMI E for comparisons from column 1 of Table 5 and the averaged APMI
G = {Lg-3 for comparisons from columns 2 and 3 of Table 5.

Table 6 lists the the correlations and slopes of how various 6-based APMI values relate to

69

 

 

 

 

 

 

 

 

O
o —
N
- - - Actinobacteria
8 _ {i ------ Archaea
.— n
(D .
E ,- ,U‘l “\JIK’I‘.“ I, ---- Enterobactenales
0 ..'II:’ \l'"? Gammaproteobacteria
q- I . .. ‘2 . - - - u
3 8 _. ' 9"." ’ 'u" 2“ l: I (excluding Enterobact)
m "' lg, ,‘ ---- Lactobacillales
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0 - 7:, J “I“ °"""’ “xv-375%
I I I I T T
O 200 400 600 800 1000

ORF Length (number of encoded amino acids)

Figure 17: ORF length frequency distributions among 5 taxonomic subgroupings. The series
of frequency values for a bin size of 1 aa is smoothed with a cubic spline. Only those ORFS 3
1,000 encoded amino acids in length are shown. Enterobact = Enterobacteriales.

70

 

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1 10 100 1000 10000

ORF Length (number of encoded amino acids)

Figure 18: Log-transformed distribution of ORF lengths for 155 genomes. A natural logarithm
was calculated for each of the ORF lengths, and the log-transformed values of ORF length were
aggregated into a histogram with bin sizes of 0.25. The x-axis is labelled with a transformed
power of 10 scaling. A ﬁtted bell curve with a mean at 245 aa is shown with a dotted line.

 

 

 

 

 

 

 

 

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Figure 19: Comparison of ORF organization between two Mycobacterium tuberculosis strains
and two Escherichia coli strains. (a) M. tuberculosis CDC1551 versus H37R. (b) E. coli K-12
versus 0157zH7. The APMI values for segmentation sizes 6 of 40 kb and 10 kb are indicated
at the top of each dot matrix.

71

Table 5: Diverging set of phylogenetic comparisons.a

 

 

Pairwise Closest Pair Closest & Closest &
Comparisons Distant Ancestor Distant Ancestor
A Py.aby+Py.hor. Py.aby.+Py.fur. Py.hor.+Py.fur.

B lVIt.acet.+lVIt.maz. lVIt.acet.+Arch.ful. Mt.maz.+Arch.ful.
C Sulf.solf.+Sulf.tok. Sulf.solf.+A.pnx. Sulf.tok.+A.pnx.
D tb1551+th37Rv tb1551+Cor.glut. th37Rv+Cor.glut.
E Nostoc+Synec. Nostoc+Th.elon. Synec.+Th.elon.

F S.pyog.+Str.pnm. S.pyog.+Lac.lact. Str.pnm.+Lac.lact.
G l\/I.gen.+l\ll.pnm. M.gen.+M.pulm. M.pnm.+M.pulm.
H R.pro.+R.con. R.pro.+Caul.cre. R.con.+Caul.cre.

I Xn.cmp.+Xn.axon. Xn.cmp.+X.fas. Xn.axon. + X.fas.

 

3’The closest pair column is a comparison between the two most closely related strains rel-
ative to comparisons involving a more distant last common ancestor (two rightmost columns).

The abbreviations used are deﬁned in Table 2.

(a)

 

 

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Figure 20: Comparisons of ORF organization for two Mycobacterium species and two species
from the Enterobacteriales. (a) M. tuberculosis H37R and M. leprae. (b) Escherichia coli
K-12 and Yersinia pestis C092. The APMI values for segmentation size 6 of 40 kb and 10 kb
are indicated at the top of each dot matrix.

 

 

 

 

 

 

 

 

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Segmentation Size (6)

Figure 21: APMI values on dot matrix plots for various taxonomy-based comparisons of chro-
mosomes. (a) The values of averaged APMI species—level comparisons are shown by solid lines
and closed circles. The values of averaged APMI genus-level comparisons are shown by dashed
lines and open circles. (b) Averaged APMI values E (solid lines and closed circles) and 5
(dashed lines and open circles) are shown. la is the average APMI between the two more
closely related strains listed in the ﬁrst column of Table 5. a is the average of the averaged
APMI values, I—b and 75, corresponding to those comparisons listed in the second and third
column of Table 5. The horizontal dotted lines indicate the zero-point, at or beneath which
information is independent or disassociated. The APMI values are calculated for segmentation
sizes 6 of 10 kb, 20 kb, 30 kb, ..., 150 kb.

73

Table 6: Correlation of APMI with time of divergence.“

 

 

6 m r
10 kb -0.421 0.434
20 kb -0.479 0.472
30 kb -0.517 0.508
40 kb -0.509 0.512
50 kb -0.477 0.490
60 kb -0.456 0.494
70 kb -0.398 0.459
80 kb -0.350 0.438
90 kb -0.297 0.401

100 kb -0.216 0.318
110 kb -0.222 0.342
120 kb -0.102 0.192
130 kb -0.141 0.241
140 kb -0.077 0.145
150 kb -0.009 0.000

 

”Average pointwise mutual information values are calculated for various segmenta-

tion sizes 6 from the pairwise comparisons described in Table 5 and associated times

of divergence. The slope m and correlation coefﬁcient r are shown for a linear rela-

tionship.
an estimated time of divergence. In particular, for the highest correlating segmentation size,
6 = 40 kb, Fig. 22 shows how APMI pairwise comparisons from Table 5 relate to estimated
times of divergence. For all 6, the r values are very weak or statistically insigniﬁcant. The
best performing range of 6 values in terms of r > 0.4 appears to be for 10 kb to 90 kb. For 6
= 40 kb, the comparisons among the Archaea (A, B, and C) have the slopes m A = 0.77,
m3 = 0.35 and mo 2 0.21, and the comparisons among the Bacteria (D, E, F, G, H, and I)
have the slopes mD =1.8,mE =1.2,mp = 0.11, mg =1.4, my = 0.58, and m, =1.5.

The Ia — I (1 difference between averaged APMI values for each of the nine sets of
comparisons is shown in Fig. 23a and 23b. The highest differences are seen for the D, G, and
H series that reach their highest respective values at 6 = 30 kb, 6 = 40 kb, and 6 = 60 kb.
The average expectation for these lineage—based comparisons is shown in Fig. 23c. The
differences between Fig. 23c and generalized species-versus-genus comparisons (Fig. 23d) are

shown in Fig. 24, and have the highest. values for segmentation sizes 6 of 10 kb and 30 kb.

74

 

 

 

Pointwise Mutual lnforrnation

 

l l l l
2 3

O
_L
b

Time of Divergence (billions of years)

Figure 22: APMI values on dot matrix plots for various times of divergence. The letters
represent pairwise comparisons described in Table 5. For each of the 9 letter pairs (18 plotted
points), the leftmost letter is the APMI value for the corresponding pairwise comparison from
column 1 in Table 5. The rightmost letter is the APMI value for the average of pairwise
comparisons from columns 2 and 3. APMI values are calculated for a segmentation size of 6 =
40 kb. For a ﬁtted line with a slope of 0.51 Ga’l, the r correlation coefficient is 0.51.

75

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76

 

 

 

 

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Segmentation Size (6)

Figure 24: Difference between averaged W—values of lineage and species-genus comparisons.
The ordinate value represents, for a given 6, the difference between m and n values from the
Fig. 23c and 23d respectively.

To more closely inspect the relationship of estimated times of divergence from a common
ancestor to the loss of conserved genomic organization, I visually assayed 9 dot matrix
comparisons among a total of 3 Archaea (Fig. 25-27). I further assayed 18 dot matrix
comparisons among a total of 18 Bacteria (Fig. 28-33). Overall, each ﬁgure (Fig. 25 - 33)
contrasts the similarity of genomic organization of two most closely related genomes to the
similarity seen with a third, more distant “cousin.” Shown in Fig. 25 is a set of three paired
comparisons among Pyrococcus furiosus, Pyrococcus abyssi, and Pyrococcus honkoshz’i. This
comparative set of Pyrococcus species presents a case of how the loss of ORF organization
may be directly related to longer times of estimated divergence. The two most closely related
strains, P. abyssi and P. hom'koshz'z', appear to have longer regions of successively matching
ORFS than comparisons with P. furiosus.

I found that the Archaea appear visually to relate the time of divergence to the loss of
conserved genomic organization (Table 7). The ordering based on times of divergence was
fully consistent with my visual orderings of the observed loss of conserved genomic

organization, prior to consideration of APMI values. The APMI values for 6 = 40 kb (140)

77

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 25: Comparisons of conserved ORF organization among three Pyrococcus strains. (a)
times of divergence from a last common ancestor. (b—d) relative locations of bidirectional
best hits between ORFS are plotted based on pairwise comparisons among three chromosomes.
The averaged pointwise mutual information for each dot plot is calculated and shown for
segmentation sizes 40 kb and 10 kb.

and 6 = 10 kb (110) did not however perfectly equate to the times of divergence.
Inconsistencies of APMI values in a divergence time-based ranking generally involved Fig.
25c-d and 26c-d. The sets of comparisons involving genomes of strains that diverged > 2.5
Ca (Fig. 26c-d, and 27c-d) are essentially negligible in terms of any observable conservation.
For times of divergence < 1 Ga (Fig. 25, 26, and 27) conserved regions are present across the
chromosomes, and there are regions that are at least 100 kb in length for each pairwise
comparison.

In addition to the three subtrees of Archaea, I evaluated six subtrees of the Bacteria for

conserved patterns of ORF organization and these are shown in Fig. 28 — 33. The phyla that

78

(a)

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N
r 3'66‘3 A. fulgidus La),
: 2 s
: r - ~ua M. acetivorans g
L - - 1' §
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E

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(c)

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OMb 2Mb 4Mb

M. acetivorans C2A

Figure 26: Comparisons of conserved ORF organization among two Methanosarcz'na strains
with A. fulgz'dus. (a) times of divergence from a last common ancestor. (b-d) relative locations
of bidirectional best hits between ORFS are plotted based on pairwise comparisons among three
chromosomes. The averaged pointwise mutual information for each dot plot is calculated and

shown for segmentation sizes 40 kb and 10 kb.

79

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2.1.5:.291, :afI‘: .. 12:, -
(O'SMb - ....- .i';°"'-:.-‘. 5:31: '- 33:. "'
f 5332"" , "5". at!
=7- 3-1 '- 12.1.:- -2- r5231-
.. Lu- - g ' L A :L a gain _' . . .c _ r‘ 1.1.. .- z A
OMb W I OMb I I

OMb 1Mb 2Mb OMb 1Mb 2Mb

S. solfataricus P2 8. tokodaii str. 7

Figure 27: Comparison of three Crenarchaeota strains. (a) times of divergence from a last
common ancestor. (b-d) relative locations of bidirectional best hits between ORFS are plotted
based on pairwise comparisons among three chromosomes. The averaged pointwise mutual
information for each dot plot is calculated and shown for segmentation sizes 40 kb and 10 kb.

80

(a)

   
  
  
 
 

 

(b) I[40kb],l[10kb]: 4.7, 7.7

4Mb - fr-
1- 928" a C. Iutamic m ' '--‘
1 " g " 3Mb -- —
: ’E- ‘3" t M tub. CDC1551 2Mb 1 ,_
1... ' .

d

'-..--1Mtub H37Rv 1Mb-l -

 

 

_ = 4Ga = 4000Ma

 

OMb

M. tuberculosis CDC1551

OMb 2Mb 4Mb

M. tuberculosis H37Rv

 

 

 

 

 

 

 

 

N N
g (c) hl[40kb],l[10kb] 3.0.6.5 g «9 114mm], "111cm: 3. o, 6. 6
*- 3Mb —::'.:x-'fi. are .5”: 1; “‘11— 1. 3Mb — 1111.111. 311.: 21:-“.5 1: 15511.
o -. 15"». o -. .. -..-c
2 _- .. ~.- :45?- ..:; . . .9 P‘s-"‘5 1% ' '.~.1-:'I-.‘
< 2Mb _.--:. f}.- -:._ < 2Mb _..-.. -‘ 5.:- "K -:._.
§ 1" I: 3""? ’:-.5 :131'. 1 § 1151.? 3""? ‘3.’ 3 13.211.
.9 -.': 1 L1?- ;:}:‘::.1,‘ 1“ I" .2 :1'. .g' . 3:.3153‘ .5 :5.
E 1Mb —_LV..~:,F.': 1::x'1;;.‘:;‘11‘:2=.°°— E 1Mb “f”- 1'}? “I354" ‘xtgi—
1‘9. *,,-.':1..-,’°':~'. -° '...'.- -:-'.-: '.1 1‘9. 3131,11; ;.:_ -'.' .:- 1.
3 3:: Ir; 15:-taut; we. ' ..: ':. .' 3 3:: w. ‘3':- ':.36 :«n ..: y"..-
B: .~.."'-:'-.-.:- .-'.1".~'-’ '-'--~".-"-'>‘° T» :44. '-'_.2\--:‘>~~
(SOMD II‘II 0.0Mb IIL‘II
OMb 2Mb 4Mb OMb 2Mb 4Mb
M. tuberculosis CDC1551 M. tuberculosis H37Rv

Figure 28: Comparisons of conserved ORF organization among two Mycobacterium tubercu-
losis strains and Corynebactem’um glutamz‘cum. (a) times of divergence from a last common
ancestor. (b-d) relative locations of bidirectional best hits between ORFS are plotted based on
pairwise comparisons among three chromosomes. The averaged pointwise mutual information
for each dot plot is calculated and shown for segmentation sizes 40 kb and 10 kb.

are represented by these bacterial subtrees are the Actinobacteria, the Cyanobacteria, the
Firmicutes, and the Proteobacteria.

Bacteria show various visual trends of synteny that do not necessarily correspond with
estimated times of divergence as seen with the analyses involving Xylella fastidiosa and
Streptococci. Overall however, there appears to be a general trend of inverse correspondence
where a greater time of divergence corresponds to a lower amount of conserved ORF
arrangement. For times of divergence (TOD) much greater than 1 Ga. synteny appears to be
essentially lost.

My visual groupings of the dot. matrix comparisons for a ranking of conserved ORF

81

(a) (b) I[40kb1, l[10kb1: 2. 5, 6.2

 

 

 

,8 6Mb —~
r- 19"‘3- T.elongatus 5 5Mb
' 0
4Mb
. n.
: 71-5-6MaNostocsp. d. 3Mb
L- -.: (I)
0
'- - - Synechocystis sp. .9. 2Mb
g 1Mb
— = 4Ga = 4000Ma OMb
Synechocystis PCC 6803
(c) I[40kb1,|[10kb1. 2.2, 5.9 (‘1) 1.1401161, I[10kb]: 1.7, 55
g 2Mb —_"f'-3;~" %
3. ‘13
m . I" m
a: :1»), -. o:
g 1Mb 4 g
m -' c»
K H
OMb —

 

 

 

 

 

 

OMb 2Mb 4Mb 6Mb

Nostoc sp. PCC 7120 Synechocystis PCC 6803

Figure 29: Comparisons of conserved ORF organization among Nostoc sp. PCC 7120, Syne—
chocystis sp. PCC 6803, and Themosynechococcus elongatus BP—l. (3) times of divergence
from a last common ancestor. (b-d) relative locations of bidirectional best hits between ORFS
are plotted based on pairwise comparisons among three chromosomes. The averaged pointwise
mutual information for each dot plot is calculated and shown for segmentation sizes 40 kb and
10 kb.

82

32_

r-

_a- L. lactis subsp. lac

Ma 3.8 pyogenes

- -. S. pneumoniae

— = 4Ga = 4000Ma

(c)

I[40kb],lc[10kb]:1.,9 5. 5

 

2Mb -

1Mb 4; I--

 

I'- If. V ':.‘f'. 13.2.:
": ~I .. z ' l
O.- .. g I ‘. II '1
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t . . " .I «e . . II
. I a ' -x ' I.- .
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.. C. .I '. ‘- .. 4'
.r .o 0" Q . . . 4. A
. I ‘I
. I I... l I .I ' H, .9
I ‘. . ‘.. ' ... .I ..
l g a .
_. , ........O 2“ .' ...“:
‘5'? ' 0’6 ." *I ‘..I I.“
- t s I .. '
‘ . . ‘II. - IL. ...
. I. ‘ j - .9

 

L. lactis subsp. lactis l|1403

 

OMb

OMb

S. pyogenes M1 GAS

(b)

 

1.5Mb 4.5-2“."

 

OMb

l[40kb],l[1 Okb]: 2.0, 5.5

 

 

' . I. I. It.

. I... - 'I. . ‘ .. 0’
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If & ...“ I. .‘. I- If
I ~ .0 f
i" °'~ '. '-." 12.9
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S. pneumoniae TIGR4
l[40kb], I[10kb]: 1 .9, 5. 5

 

N

Z

O'
l

E
0'
l

 

 

L. lactis subsp. lactis "1403

 

OMb

OMb

. ..:“: 9:10": ':-.:-: ..:-“:2: l; ...-5"}:
. . c 1 * l: : .~;'.’......;.“—
"' ‘ : ' .0. .° . 'I ' o .
' . ‘ . o :g- $ .I. o. o
."-.%I- :'.I;.C::.".I : :‘. .~
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I . . .I ' _
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. .9" . .p .33.). u' i:- \
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'3' D'- t: a} L" 5". :. . ' .3 11
I I O . .l' . ... . l.. . ‘ ~ .‘ I.
g; a; . :: .‘ 9:. 3" .3 01‘ .1 ..
. CO. I ~ I I . .... 9 a
I”. ‘3‘... ’05 '. :9 d‘-' O: :- ‘
. .9 I u .I . I I. ' r ...I:. 'ﬂ‘ l
I I .. I I 9 i I
I T

S. pneumoniae TIG R4

Figure 30: Comparisons of conserved ORF organization among S. pyogenes, S. pneumoniae,
and L. lactis. (a) times of divergence from a last common ancestor. (b—d) relative locations of
bidirectional best hits between ORFS are plotted based on pairwise comparisons among three
chromosomes. The averaged pointwise mutual information for each dot plot is calculated and
shown for segmentation sizes 40 kb and 10 kb.

83

(a) (b) I[40kb],l[10kb]: 2.6, 5.0

 

 

 

[\
CO
.- _1._5_G-a I . cl)
' — M. pu moms E 0.4Mb .. . . / _
1 3 . .
i 1.71 _'a M. genitalium E - - . ./, . .
1.--, . $0.2Mb - "'7 ' “ ” _
'- - - I M. pneumoniae a: . / .
E .
_ = 463 = 4000Ma OMb I

 

OMb 0.5Mb

M. pneumoniae M129

 

 

 

 

 

 

 

 

& (c) 11101551,I[10kb]:o.7,4.o E (d) I[fl(1kb],|[10kb]:1.0,ﬁ4.3
O _ .' ". ' '. ..' ..' ‘ ._ O — _.-_. '. .',.v‘ .. .... \..
20.8Mb _. ._ 20.8Mb .. WP
30.6Mb - j.=— 30.6Mb -,-: ' ..-'{.:-—
80.41/16 ' — §O.4Mb - L « .- . '—

- . a? 2 o ‘ - . ' .... ~ -'I'
30 2Mb ‘13-" . .. .. — 30.2Mb -, '. z. . . .-
3 OMb ' ‘ . 3 OMb ' * ‘ ‘°."

OMb 0.5Mb OMb 0.5Mb
M. genitalium G-37 M. pneumoniae M129

Figure 31: Comparisons of conserved ORF organization among three Mycoplasma strains.
The averaged pointwise mutual information for each dot plot is calculated and shown for
segmentation sizes 40 kb and 10 kb. (a) times of divergence from a last common ancestor.
(b-d) relative locations of bidirectional best hits between ORFS are plotted based on pairwise
comparisons among three chromosomes. The averaged pointwise mutual information for each
dot plot is calculated and shown for segmentation sizes 40 kb and 10 kb.

84

(a)

2,3Ga
' —
: 2:59Ma
L

C. crescentus

FI. conorii

'- - -. R. prowazekii

— = 4Ga = 4000Ma

 

 

 

 

(c) '[40kb], I[10kb]: 2.3, 5.5
In —' 3“; (3.153.... .- . 2 "'--:\ '1
E E}. f . - . 1‘“ "i
3 M 5 .':I° .:-.. —
S f :53 :' :2 '
t y. ._|'- .:._.. ( ..‘;.:.'.‘
2Mb A”... .3 -_... I. ', ..: ...‘_ ~—
?: 1Mb -:.:" ‘j; -: -..-‘_
d *2: . .- .' v... '6':
OMb ... 1. ‘ Lglj-
OMb 1Mb

Fl. conorii str. Malish 7

Figure 32: Comparisons of conserved ORF organization among two Rickettsia strains and
Caulobacter cmscentus. (a) times of divergence from a last common ancestor. (b-d) relative
locations of bidirectional best hits between ORFS are plotted based on pairwise comparisons
among three chromosomes. The averaged pointwise mutual information for each dot plot is

 

 

 

 

 

 

 

 

N (b) I[40kb],l[10kb]: 3.4, 5.8

.C .

.9

B 1Mb — —

2

a w;

$0.5m — ~

8

a: OMb 1 ,
OMb 0.5Mb 1Mb
R. prowazekii str. Madrid E

(d) l_[40kb],l[10kb]: 2.2, 5.4

3 {mi-- "’.',-‘,.' ':::4.:

0 3Mb —'.= f .. -. —

3 ..'.-~ ‘.;' . Ed:

2 . ...,. ..,_.._,, r 5 --.-~-.-:...

q: 2Mb -...., .5 :..".,‘.'..; 5... ,—

3 1Mb “'2' . "- ' :4—

6 5‘ ”..,0'; ' .5:

OMb '~ :l'. .‘. 4'; ' '-'l

OMb 0.5Mb 1Mb

H. prowazekii str. Madrid E

calculated and shown for segmentation sizes 40 kb and 10 kb.

85

. fastidiosa Temecula1

Figure 33: Comparisons of conserved ORF organization among two X anthomonas strains and
(a) times of divergence from a last common ancestor.
d) relative locations of bidirectional best hits between ORFS are plotted based on pairwise
comparisons among three chromosomes. The averaged pointwise mutual information for each

Xylella fastidiosa Temeculal.

(a)
543-8

1

r----1.

.-..-

X. fastidiosa

.- - MPX. campestris

- -. X. axonopodis

— = 4Ga = 4000Ma

I[40kb],l[10kb]: 3.,1 6.6

 

 

”‘3‘“.‘3 ..:-...”.‘m:
. 00", :QI ..:. f";‘..o.
.'--"-':"r':-."'-t.-"'-'. ' -.~'-".‘
.' " ‘1."‘5’ ' ’ '--°" 9' ’ 1' 4—
II I...’ 0"... . .‘. ..g: '0": §~
.. .I ‘ 'I." r .. . I '0. ‘
n - ‘I’ g'. u .. S o .0.
.... IO». s“ ..d C... :3. .‘ J
I: . ...: 3'. O . .g'u . . g I :-
.If.‘ 9" w' . o. "..'-o.-
‘3‘. ..:. ‘3‘: d: u.- 3")". o' 3' -
I. f‘ 0’ :' ... k . “:l"; 0..
5'....‘ .I£l..f:l‘.‘ 9' "I"
r: "f. 0.. ...-I . . t’..."
...-3’... . ..I I" .0 .' .“
. a. . '8’». n ‘o:: .‘o '..
:3: I.“ . *z'f. I '0'.
" . A L A -!

 

 

X. campestris str. ATCC 3391

X. fastidiosa Temecula1

X. campestris str. ATCC 33913

(b)

4Mb
3Mb
2Mb
1 Mb
OMb

 

I[40kb],l[10kb]: 3.7, 7.3

 

 

X. axonopodis pv. citri str. 30

(d)

 

2Mb -'

1Mb -

 

OMb -

I..- ‘0

11401161, 11101161: 3. 0, 6.

{

 

X. axonopodis pv. citri str. 30

dot plot is calculated and shown for segmentation sizes 40 kb and 10 kb.

86

Table 7: Relationship of time of divergence to quantitative indicators of conserved ORF orga-
nization for pairwise comparisons of archaeal chromosomes.“

 

Comparison Fig. ToD I40 110
Mt.acet. vs Mt.maz. 26b 223 Ma 3.3 6.9

 

Py.aby. vs Py.hor. 25b 338 Ma 2.2 5.7
Py.aby. vs Py.fur. 25c 715 Ma 1.9 5.5
Py.hor. vs Py.fur. 25d 715 Ma 2.1 5.6
Sulf.solf. vs Sulf.tok. 27b 1.3 Ca 2.1 5.7
Mt.acet. vs Arch.ful. 26c 2.6 Ga 2.5 5.9
Mt.maz. vs Arch.ful. 26d 2.6 Ca 2.3 5.8
Sulf.solf. vs A.pnx. 27c 3.0 Ga 1.8 5.2

Sulf.tok. vs A.pnx 27d 3.0 Ga 1.8 5.2

“APMI values I 40 and 110 are calculated for 6 = 40 kb and 6 = 10 kb for the pairwise
comparisons in Fig. 28-33. ToD is the time of divergence from a last common ancestor.
When multiple ﬁgures are listed in the same row, the averaged 140 and [10 values
are presented. The abbreviations used for organism names are. deﬁned in Table 2.

 

87

Table 8: Relationship of time of divergence to visual and quantitative indicators of conserved
ORF organization for pairwise comparisons of bacterial chromosomes.“

 

 

Comparison(s) Fig. ToD V.R. I40 110
tb1551 vs th37Rv 28b recent 1 4.7 7.7
M.gen. vs M.pnm. 31b 171 Ma 1 2.6 5.0
R.pro. vs R.con. 32b 250 Ma 1 3.4 5.8
Xn.cmp. vs Xn.axon. 33b 106 Ma 2 3.7 7.3
S.pyog. vs Str.pnm. 30b 328 Ma 4 2.0 5.5

(Xn.cmp.& Xnaxon.) vs X.fas. 33c-d 543 Ma 4 3.1 6.6
(S.pyog.&Str.pnm.) vs Lac.lact. 30c-d 713 Ma 4 1.9 5.5
Nostoc vs Synec. 29b 756 Ma 4 2.5 6.2
(tb1551&th37Rv) vs Cor.glut. 28c—d 928 Ma 3 3.0 6.6
(Nostoc&Synec) vs Th.elon. 29c-d 1 Ga 4 2.0 5.7
(M.gen.&l\f1.pnm.) vs M.pulm. 3lc-d 1.5 Ca 4 0.9 4.2

(R.pro.&R.con.) vs Caul.cre. 32c-d 2.3 Ca 4 2.3 5.4

“APMI values 140 and 110 are calculated for 6 = 40 kb and 6 = 10 kb for the
pairwise comparisons in Fig. 28-33. V.R. is the visual ranking (1: “strong diagonal”;
2: “diagonal plus scattering”; 3: “vestigial diagonal”; and 4: “noise”). ToD is the
time of divergence from a last common ancestor. When multiple ﬁgures are listed in
the same row, the averaged I 40 and [10 values are presented. The abbreviations used
for organism names are deﬁned in Table 2.

 

organization among bacteria as listed with times of divergence from a last common ancestor
(TOD) are: #1, “strong diagonal”, ToD are recent to 250 Ma - Fig. 28b, 31b, 32b; #2,
“diagonal plus scattering”, ToD is 106 Ma — Fig. 33; #3, “vestigial diagonal”, 928 Ma — Fig.
280-d; and #4, “noise”, ToD are 328 Ma to 2,300 Ma — Fig. 29b-d, 30b-d, 31c-d, 32c-d, and
33c-d. Table 8 shows the times of divergence, visual rank, and APMI values for 6 = 40 kb
and 10 kb.

As a preliminary assessment of intragenomic structure, Fig. 34 and 35 help characterize
the invariant arrangement of ORFS based on both polarity and COG membership. For my

population of 165 chromosomes, I inspected the z-score values of signiﬁcance (number of

88

Table 9: Normalized ranges of polarity tallies.“

 

 

 

 

 

 

Characteristic All ORFS 1...100 201...300 401...500
Lifestyle Mdn Mean Mdn Mean Mdn Mean Mdn Mean
Oblig. ancient 0.14 0.15 0.29 0.29 0.26 0.26 0.28 0.32
Oblig. recent 0.08 0.09 0.26 0.29 0.26 0.32 0.29 0.28
Freeliving repl. 0.09 0.10 0.24 0.26 0.24 0.28 0.29 0.28

 

“Bacterial chromosomes are grouped into three characteristic lifestyle categories: obli-
gate ancient host associated, obligate recent host associated, and free-living replicative
stage. The normalized range of polarity tally is the difference between the highest and
lowest points of the tally divided by the number of ORFS. The second column eval-
uates the entire stretch of the chromosome for each bacteria. The third, fourth, and
ﬁfth columns look at selected sets of ORFS where ORFS are numbered consecutively
from the start point of the chromosomal annotation.

sigma 0 units separating original and randomized assignments of polarity and COG
membership) from my running tally methodology. The average polarity running tally z-score
difference was 79.70 (p < 0.0001). Only 10 of the 165 chromosomes (6%) had a z-score

< 1.640. Of these 10 chromosomes, the two most predominant phyla were Cyanobacteria

(n = 3) and Euryarchaeota (n = 2). The average COG running tally z-score difference was
14.380 (p < 0.0001), yet 14 of the 67 chromosomes (21%) had 2 < 1.640. Of these 14
chromosomes, the three most predominant phyla were Proteobacteria (n = 4), Euryarchaeota
(n = 2), and Firmicutes (n = 2). 49 of 67 chromosomes were signiﬁcant (:-score 2 1.64) for
both polarity and COG membership.

Based on the approximate lifestyle boundaries of chromosome size shown in Figure 36,
there was an almost two-fold steeper descent and ascent of the polarity-based running tally
for obligate, ancient host-associated genome-sequenced strains compared to the genomes of
recently host—associated and freeliving strains (Table 9). This overall range of the polarity
tally did not uniformly correspond to changes for localized regions of the chromosome. The
start point of chromosomal annotations (most likely near to the origin of replication) did not
manifest a steeper descent or ascent of the polarity-based running tally for the genomes of

obligate, ancient host-associated strains.

89

(a) Bacillus subtilis (b) Escherichia coli

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

o — o "
o ' s x x
o O — \ I
.9 ‘ ‘T X .’
I -' \\ I,
— 8 \\ ’I
§ 8 -
“1' I I I I I I
2. 0 1000 3000 0 1000 3000
E
D)
.g (c) Vibn'o cholerae (d) Yersinia pestis
o _ \\ ’1 O \‘ [I
8 "' \ I 8 _. \ I
I — \\ ’1 1? \\ II
C _ \\ I, - \\\ I,
a J \\ ’I 8 \\ [I
‘I- v O _ v
I I I I I C}: I I I I
0 1 000 2000 0 1 000 3000
ORF Count

Figure 34: Running tally graphs of polarity along four chromosomes. The thick line represents
increments and decrements based on whether an ORF has an assigned polarity value of 1 or
not. The dotted diagonal represents random expectation where polarity values are randomly
assigned to a chromosomal set of ORFs. The dashed lines forming a V-shape represents the
pattern if polarity values were not intermingled. (a) Bacillus subtilis subsp. subtilis str. 168.
(b) Escherichia coli K-12. (c) Vibrio cholerae (large chromosome). ((1) Yersz'nz'a pestis C092.

90

 

 

 

 

 

 

 

 

 

 

 

(a) Bacillus subtilis o (b) Escherichia coli
8
N
o o
E s
o o
O O
8 8
‘T 'T
2. 0 1000 3000 0 1000 3000
E
g o (c) Vibrio cholerae 8 (d) Yersmia pestis
: 8 m
3 v- N
(I
8
I!)
o 1—
8
o s
o o
8. 51’

 

 

 

 

 

 

 

0 1000 2000

ORF Count

Figure 35: Running tally graphs of COG membership along four chromosomes. The thick line
represents increments and decrements based on whether an ORF is a member of a COG or
not. The dotted diagonal represents random expectation where COG membership is randomly
assigned to a chromosomal set of ORFS. The dashed lines forming a V-shape represents the
pattern if all COG non-members were together followed by COG members. (a) Bacillus subtilis
subsp. subtilis str. 168. (b) Escherichia coli K-12. (c) Vibrio cholerae (large chromosome).
((1) Yersinia pestis C092.

91

3.2.3 Chromosome Size

I found that the smallest fully sequenced prokaryotic genome was represented by the
Nanoarchaeum equitans chromosome (491kb) and the largest prokaryotic genome was
represented by the Bradyrhizobium japonicum chromosome (9.1Mb). Across the set of 155
genome-sequenced strains, I found that genome size (as represented by chromosomes) was
suggestive of ecological boundaries (based on Wilcoxon rank sum calculations) in terms of my
own, ad hoc, ecological grouping. I also inspected taxonomic rankings to assess the general
degree to which genome size could be a distinguishing characteristic of shared ancestry.
Expectation of the difference between median genome sizes is represented by the symbol A.
The Archaea (genome size, 491kb - 5.8Mb) and Bacteria (genome size, 580kb - 9.1kb) are
statistically different based on median genome size (p < 0.03; 95% conﬁdence interval (bp):
—1, 730, 369 < A < —91, 633). The Alphaproteobacteria (1.1Mb - 9.1Mb) versus
Gammaproteobacteria (616kb - 6.4Mb) do not however represent a signiﬁcant difference in
the medians of genome sizes (p < 0.89; 95% conﬁdence interval (bp):

—1, 408, 279 < A < 1, 595, 946). The Lactobacillales (1.9Mb - 3.3Mb) versus
Enterobacteriaceae (616kb - 5.7Mb) represent only a weak signiﬁcance in median genome size
difference, and the interpretation is inconclusive based on the conﬁdence interval (p < 0.059;
95% conﬁdence interval (bp): —2,778, 116 < A < 1, 154, 717).

Fig. 36 presents the distributions made by the 165 prokaryotic chromosome sizes
(5: = 3.1 Mb, if = 2.7 Mb, and s = 1.83 Mb). The distribution of chromosome sizas appears
multimodal. The declining trends at the lower and upper limits of the distribution may
reﬂect a limit to the overall size of a prokaryotic genome. There is evidence for relationships
between multimodal ranges of genome size and “regimes” of recombinative change; most
intracellular endosymbiotic bacteria have low levels of recombination and smaller genomes
(genome size range 640kb to 1.3Mb), compared to free-living bacteria with bigger genomes
such as those in the soil (genome size range 4.2Mb to 9.0Mb) (Moran & Plague, 2004). The
plotted lifestyles and boundaries of Fig. 36 are based on Ochman & Davalos (2006) and
Moran & Plague (2004).

While I did not ﬁnd that chromosome size directly corresponded to general taxonomic

distinctions for taxonomic rankings such as phylum, class, order, and family, I did ﬁnd

92

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.o an .o .o
2 22 2 2
‘0. “3°. 0 o
0 P0] In ‘—
: v"! 7 ’39” ' : *w1 :
:52/ : s6 '
25 - :83 é; :16 ; 1:2; 5
'§§~%Z :38 ' QC)? 1
:0‘2/ 39$ I 0.3 :
> 20 - :%° / 63 : i327. :
8 :f-=§’ 4 ‘g‘é’ ' '58 .
0) IO 0 l as :
3 1 _ Q) 1 g |
g 15 — : Q0: : a :
h I— | I 1
“- “ :
10 ~ —
Z W :
5 - H a
O _ E , H m i

I I I I

 

I I I I I I I

OMb 2Mb 4Mb 6Mb 8Mb 10Mb
Chromosome Size in Megabases (Mb)

Figure 36: Histogram of 165 chromosome sizes. Bin size is 500,000 base pairs. Chromosome
sizes are shown for 165 different chromosomes coming from 155 genome-sequenced strains.
Frequencies of archaeal chromosome sizes are indicated by shaded boxes stacked above the fre-
quency counts of bacterial chromosomes shown by unshaded boxes. The approximate bound-
aries for three lifestyle-based ranges of genome sizes are listed at the top of the ﬁgure and are
indicated by vertically descending, dashed lines.

93

evidence for conservation of chromosome size from a last common ancestor. While the overall
linear relationship between a change in chromosome size compared to time of divergence from
a last common ancestor does not fully account for variation (1‘2 = 0.24), the slopes in Fig.
37a are uniformly positive and support a general property of conserved genomic size. I found
that a change in chromosome size is independent of the shared pointwise mutual information
for various segmentation sizes. Fig. 37b characterizes the independence of chromosomal size
with respect to APMI for 6 =40 kb (140). While a change in chromosome size (ACS)
increases with a greater time of divergence, the trend for I 40 is to decrease. To evaluate the
effect of a joint consideration of both I 40 and changed chromosomal size (AC5), I evaluated
both AC's/I40 (Fig. 37c) and ACS — 140 (Fig. 37d). The joint considerations had stronger

linear correlations (r 2 0.6).

94

 

 

 

 

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Figure 37: Relationship of divergence time from a last common ancestor to changes in chro-
mosome size and pointwise mutual information. The letters represent pairwise comparisons
described in Table 5. (a) Absolute difference in chromosome size for various times of diver-
gence, m = 0.73, r = 0.49. (b) The absolute difference in chromosome size versus the APMI
for 40 kb ((ACs) - I 40), m = 0.1 and r = 0. (c-d) Chromosomal difference for various times
of divergence based on joint considerations of APMI and chromosome size. (c) The product of
absolute difference in chromosome size with the reciprocal of the APMI for 40 kb (lACs | / I 40),
m = 0.37 and r = 0.60. (d) The absolute difference in chromosome size with the reciprocal of
the APMI for 40 kb (lacsl - I40); m = 1.24 and 'r = 0.66.

95

3.3 Discussion

The data set of 155 genomes does not reﬂect an accurate accounting for the overall
ecological and phylogenetic diversity of bacteria (Cohan, 2004). The estimated number of
prokaryotes on earth is 4 — 6 x 1030 with 92 to 94 percent of these prokaryotes being in soil
subsurface regions: “marine sediments below about four inches and terrestrial habitats below
about 30 feet” (Schloss & Handelsman, 2004). I found ecologies other than soil subsurface
regions to be oversampled in the data set of fully sequenced genomes. Despite the patchiness
of taxonomic representation, the set of fully sequenced genomes has been a key component in
contemporary interpretations and estimations of prokaryotic diversity concerning genomic
organization and phylogeny (Moran & Plague, 2004; Ochman & Davalos, 2006; Battistuzzi
et al., 2004; Horimoto et al., 2001). Taxonomic estimates based on available ribosomal data
are for 35,498 species and 50 phyla, and a total estimation of a planetary species count is 105
to 107 (Schloss & Handelsman, 2004). While only a paltry 126 species are represented by the
set of 155 genomes, the 16 represented phyla provide a broad phylogenetic coverage (32% of
50). In this sense, the set of 155 genomes may reasonably characterize wide-ranging aspects
of the prokaryotes. A variety of replicon structures characterizes each of the 155 genomes in
terms of linear and circular chromosome topologies and compositions of single or multiple
distinct chromosomes. I did not ﬁnd plasmid sequence data to be consistent between the
public NCBI data archive of genomic sequences and the literature. The functional deﬁnition
of a plasmid as being of a non-essential, and possibly non-stable, association with a viable
organism may allow for it to be considered separately from a chromosomal representation of
a genome.

Comparing the organization of ORFS can be an effective technique for identifying
divergent recombinations (Horimoto et al., 2001; Kalman et al., 1999; Rocap et al., 2003;
Zivanovic et al., 2002). Yet, there are large gaps of time in the estimated phylogeny for which
the data set may not be large enough to resolve every recombinative event with sufﬁcient
statistical power (Fig. 8 - 12), and multiple sets of mobile elements can be expected to
produce complex trajectories of altered chromosomal arrangement (Gray, 2000). Based on
their representative sample sizes inside my analyzed data set, the Proteobacteria (n = 68)

and the Firmicutes (n = 38) have the greatest comparative power to reconstruct distant

96

recombinational events. Yet, the Proteobacteria and F irmicutes are well-populated with
pathogenic and symbiotic bacteria, and modern analyses of genome size and structure are
predisposed to produce categorizations aligned with host-associated lifestyles (Bentley &
Parkhill, 2004; Moran & Plague, 2004; Ochman & Davalos, 2006). While divergence from last
common ancestors between various prokaryotic strains extends back several billion years or
more, a focused perspective on host association only relates to a time span stretching back to
the Cambrian age 600 Ma and, more recently, the emergence of mammals 107 Ma (Rokas

et al., 2005). The inclusion of Archaea in the analysis helps obviate a limited view of past
history since the Archaea appear to strictly exclude pathogenicity as a form of host
association. While some Archaea are host-associated commensals, this phenotype may be
primarily due to metabolic pathways atypical of the bacteria that do not beneﬁt from
mortality of the host organism (e.g., methanogenesis) (Gill ct al., 2006). Based on phenotypic
descriptions inside genomic sequence publications, I found only one of the 17 Archaea in the
data set of 155 genomes to be host associated was Methanosarcina acetivorans (Galagan

et al., 2002).

An accurate evaluation of character evolution as a consequence of recombination would
require treatment of a patchy taxonomy by speciﬁcation of a uniform taxon (Grafen &
Ridley, 1997). As Fig. 17 demonstrates, I used broad, mutually exclusive groupings based on
the taxonomy to conduct my subsampling. For a ﬁner-grained treatment, I attempted to
contrast the effects of genus membership with effects of species membership, although species
and genus deﬁnitions are not yet fully deﬁned (Cohan, 2002). Generally, in my analysis, the
sets of closely related strains and species (Tables 3 and 4) are distributed among various
lineages, and this supports the usage of the available data set to characterize dynamics of
chromosomal organization that are common to the prokaryotes. A ﬁner resolution to identify
speciﬁc selection pressures associated with various lineages in various environments may be
achieved by greater numbers of representative strains. I did not arrive at a uniform taxon
that was useful for approaching hypotheses of speciﬁc recombinative character states. Ideally,
the rate of heritable changes produced by chromosomal reorganization could have been
analyzed for correspondence with generational or chronological measures (Pagel, 1994).

The scope of the represented taxonomy appeared to support a goal to identify common

97

limits and general characteristics of prokaryotic change as relates to ORF organization. To
accomplish uniformity with the analysis, I sought to inspect prevalent “units” of information
on prokaryotic chromosomes, and the most uniformly annotated feature appeared to be that
of open reading frames (ORFS). The identiﬁcation and annotation of these ORFS
signiﬁcantly relies upon automated assessments of ORF regions and similarities to other
“known” ORFS (Frishman et al., 1998). A common software tool for identifying ORFS on a
DNA sequence is Glimmer (Salzberg et al., 1998), although there are ongoing efforts to
better characterize the degree of conﬁdence associated with a computer-generated annotation
(Larsen & Krogh, 2003). The need for updating these initial annotations is dire (Roberts

et al., 2004). While ORFS may be more uniformly annotated in the NCBI data ﬁles than
other genomic features, a struggle has been to arrive at a better estimation of real ORFS
versus “not real” ORFS and, perhaps, take into account the natural dynamics of gene loss
and formation (Skovgaard et al., 2001; Snel et al., 2002). While the number of annotated
ORFS on a chromosome appears to correspond strongly to one ORF for every 1,112 base
pairs of chromosomal DNA (see Fig. 14), the number of chromosomal base pairs that encode
each ORF varies. Consistent with my ﬁndings for the data set of 155 genomes (Fig. 15 - 18),
a large set of ORF lengths generally follows an L-shaped, lognormal frequency distribution
(Skovgaard et al., 2001) that is locally disrupted in a fashion suggestive of underlying,
discretely-sized, multidomain protein structures (Wheelan et al., 2000; Savageau, 1986). The
lognormal distribution of ORF sizes may be partly explained by a physical model of
fragmentation (Azad et al., 2002) where, starting from the right-side of the distribution,
there is an exponential growth in the number of ORFS as the ORF length decreases.
Potentially then, those ORFS experiencing a higher degree of arbitrary, nonsense mutations
will constitute a closer ﬁt to a lognormal distribution than ORFS encoding a protein
structure that is strongly conserved in an inviolate form. As seen from Fig. 16 and 17, those
ORFS that range in length from 0 to 127 aa are comparatively non-disrupted in their
frequency distribution compared to ORFS long enough (2 127 aa) to contain a protein
domain. The entire distribution of ORFS demonstrates some non-lognormality based on a
rightwards shift of the distribution (Fig. 18). For ORFS that are most important to the

ﬁtness of an organism, I postulate that their log-scaled distribution of lengths would range

98

higher in value and have a greater characteristic of non-normality relative to a set of falsely
annotated, or putatively noisy ORFS.

ORFS that are members of clusters of orthologous groups (COGS) are a possible lower
bound to the total number of annotated ORFS that correspond to real proteins (Skovgaard
et al., 2001). In practice, COGS are established by bidirectional best hits, and this strong
conservation of sequence is used as a basis to infer vertical divergence from a common
ancestral ORF. This characteristic of bidirectional best hits is also useful for assaying
conserved ORF organization among related genomes (Zivanovic et al., 2002) as demonstrated
by Fig. 19 and 20. Comparisons among genomes belonging to the same species tend to
produce a diagonal line from the bottom left to the upper right. The slight deviation observed
for the comparison of Escherichia coli strains in Fig. 19b is likely attributable to prophage
insertions (Hayashi et al., 2001; Canchaya et al., 2003). For more distant times of divergence
from a last common ancestor, Fig. 25 - 33 show patterns of dispersal for orthologous ORFS.

Across multiple lineages, I did not ﬁnd a constant relationship of the time of divergence
to the degree of disruption for visual and quantitative assays of conserved ORF organization,
although a general trend was evident. There are competing possibilities concerning the
interpretation of dot matrix plots of conserved ORF organization. While comparisons with a
distant relation Pyrococcus furiosus (715 Ma) exhibit less conservation (Fig. 25c-d) than for
more closely related Pyrococcus species (338 Ma, Fig. 25b), this may relate to more than just
a rate of recombinative change over time. There is a set of 23 homologous insertion sequence
elements exclusively present in P. furiosus (Zivanovic et al., 2002; Lecompte et al., 2001)
that is closely associated with putative locations of rearrangement on the P. furiosus
chromosome, and this greater amount of mobile elements may also account for the greater
pattern of disruption. The conservation of ORF organization of Yersinia pestis compared to
Escherichia coli (Fig. 20b) is less than among Pyrococcus species (Fig. 25) despite similar
times of divergence (Battistuzzi et al., 2004). This may in part correspond to the
disproportionately high degree of IS elements in the Yersinia pestis genome (3.7%) (Parkhill
et al., 2001b) where there are > 100 IS elements (Deng et al., 2002). Other heavily disrupted
dot matrix plots with relatively recent (5 1 Ga) times of divergence are for the set of

Cyanobacteria (Fig. 29) and a set of Lactobacillales (Fig. 30). The dense pattern seen for

99

the Cyanobacteria may be attributable to the prevalence of transposase genes in freshwater
cyanobacteria and the complex adjustments needed to support free-living oxyphototrophy in
an unstable aqueous environment (Dufresne et al., 2003). The extensive scattering and
rearrangement for Streptococcus pyogenes may be due to phage activity (Nakagawa et al.,
2003). By comparison, the Mycoplasma lineage relies on homologous recombination due to
direct repeats more so than IS elements (Rocha & Blanchard, 2002), and there is less
scattering involving solitary ORFS seen on the dot matrix plot in Fig. 31b). While the dot
matrices are interpretable from closer analyses oriented for speciﬁc genomes, I did not ﬁnd a
simple relationship involving mobile elements, or strong correlation with time, that would
uniformly account for the diversity of dot matrix pattern across various lineages. Overall,
there is a variety of factors that may underly the patterns of the dot matrix plots, and a
comparative study would beneﬁt from a greater sample size to conﬁrm many of the putative
relationships with recombinative mechanisms and strategies for genomic plasticity.

Phylogenetically broad patterns of genomic content and reorganization implicate aspects
of microbial ecology (Terzaghi & O’Hara, 1990; Moran, 1996). I found evidence for
relationships between multimodal ranges of genome size and “regimes” of recombinative
change where most intracellular endosymbiotic bacteria have low levels of recombination and
smaller genomes (genome size range 640kb to 1.3Mb) compared to free-living bacteria with
bigger genomes such as those in the soil (genome size range 4.2Mb to 9.0Mb). Ochman &
Davalos (2006) propose a high degree of instability for genomes that are 2 Mb to 5 Mb in
size. If this instability means a greater rate of departure from this size range than rate of
entry per organism, then the trough in frequency for chromosome sizes between 3.5 Mb - 4
Mb and the chromosome size frequency peaks at approximately 2 Mb and 5 Mb are
consistent with such a differential ﬂux in genomic content (Fig. 36).

The internals of genomic structure offer some evidence to account for the diversity of
ORF organization. A potential consequence for varying degrees of activity of mobile elements
may implicate a difference in colinearity of transcription and replication. A reduced
correspondence of polarity of ORFS with the replichores is reported for P. furiosus where the
primary pattern is for only the highly transcribed ORFS to correspond in transcriptional

polarity with direction of replication (Zivanovic et al., 2002). My running tally method

100

implicated astronomically high levels of signiﬁcance for both ORF polarity and COG
membership organization. I found that my measure is inconsistent with the claim by
Briiggemann et al. (2003) that the Vibrio cholerae and Yer‘sinia pestis chromosomes do not
manifest a cotranscriptional effect. Overall, based on my running tally measure, only 84% of
chromosomes were signiﬁcant for organizational patterns of both ORF polarity and COG
membership, and the pattern of ORF polarity was more pronounced than for COG
membership. Almost half of the Cyanobacteria genomes were not signiﬁcant for my
polarity-based measure of organization, and there was a steeper descent and ascent of the
polarity-based running tally for obligate, ancient host-associated genome-sequenced strains
(Table 9). I did not ﬁnd any further, simple indicators to account for the variation of z-scores
in terms of mobile elements or taxonomic groupings. There was some evidence of the the
polarity tally being inﬂuenced by more than just a cotranscriptional effect; the indistinct
change in tally near the origin of replication for obligate, ancient host-associated
genomesequenced strains would be consistent with the origin of replication as a hot spot of
localized rearrangements, perhaps due to the greater availability of a single-stranded
intermediate at the origin. The pattern of COG member clustering did not correspond to any
simple indicators of lifestyle or taxonomy. Broadly considered, the non-random pattern of
COG member clustering may be attributable to regulatory (Lathe et al., 2000) and
functional (Li et al., 2005; Wolf et al., 2001) constraints on sustainable schemes of genomic
reorganization as well as paralog-forming pathways of gene addition (Snel et al., 2002; Liang
et al., 2002).

Compared to other types of functional assessments such as operons and promoters, ORF
data on the 155 genomes is better annotated and may have greater analytical power both in
representative size, and the potential for consistent informational treatment. Also, ORFS
appear, as a population, to address meaningful comparisons for metabolic, ecological, and
evolutionary questions (Bentley & Parkhill, 2004; Konstantinidis & Tiedje, 2004).
Additionally, there are simple quantities that detail an ORF object: start, stop and length
are all generally determined by integers corresponding to a zero point on a replicon sequence.
There is a reasonable level of accuracy (> 99%) for identiﬁcation of ORF start and stop

points (Delcher et al., 1999). A quantitative approach based on these simple, exactly

101

described values may be more readily achievable than, for example, estimated kinetics of
macromolecular bindings to various consensus-based estimates of promoter sequences. A
meaningful evaluation of ORFS as a population across the phylogeny may require some
uniform capacity to determine those ORFS that encode for proteins that are important to the
physiology of the cell.

Approachas to characterizing ORF sequence conservation have largely involved simplistic
ORF comparisons of similarity. A principal criterion of COG assignments is based upon
bidirectional best hits (Tatusov et al., 1997b). Bidirectional best hits relate to a pairwise
comparison between organisms where an ORF in one organism’s genome matches most
closely to a particular ORF on the other organism’s genome, and vice versa. A COG must
contain at least three members from three reasonably separate lineages. Overall, 75% of
annotated, prokaryotic ORFS belong to COGS (Tatusov et al., 2003).

The calculation of COGS, as described, has deﬁciences. The parameters of COG
Similarity are lax enough to avoid false negatives but, subsequent to the BLASTP search,
putative COG groupings have to be manually inspected and sometimes split apart (Tatusov
et al., 1997b). The bidirectional best-hit criterion is a pairwise comparison of ORF
similarities that ignores meaningful information that can come from comparisons involving
several or more ORFS (Park et al., 1998). Pairwise comparison is not just limiting for the
assessment of orthology. Over half of the paralogous gene relationships in Mycoplasma
genitalium are not accounted for when just pairwise sequence comparisons are utilized
(Teichmann et al., 1998).

By relaxing or tightening a ﬁlter for sequence conservation, various temporal
relationships can be investigated. The identiﬁcation of recent paralogs has involved length
similarity of 95% or more and sequence Similarity of 95% or more (this implicates about 5%
of ORFS) (Kawarabayasi et al., 2001). For larger familial groupings (52% of ORFS),
Kawarabayasi et al. (2001) considers amino acid identity higher than 30% for over 70% of the
entire ORF region. There have been a variety of efforts to better deﬁne the meaningful
cut-off values for BLAST-like similarity computations and how they relate to structure and
function (Chung & Yona, 2004; Bern & Goldberg, 2005; Sadreyev, 2003; Pagni & Jongeneel,

2001; Krasnogor, 2004). A current trend has been for inspecting protein domains (Birkland

102

et al., 2005; Yang et al., 2005; Service, 2005). While Similarity values may sometimes be too
restrictive and miss out on larger protein family or functional relationships, being too relaxed
can impede discernment of underlying trends associated with conserved domains.
Comparisons of biological function is appropriate when there is sequence—level identity of 25%
(Krasnogor, 2004). Yet, for sequence-based identities of 20—30%, only one half of the domain
repertoire relationships are Shown in Mycoplasma genitalium (Teichmann et al., 1998).

If the task is to approach a uniform separation of ORF sets that is meaningful across
different lineages, a heuristic may utilize patterns of ancestral conservation while
accommodating some range of natural divergence. I propose a separation be sought only
along generalized objectives to characterize efﬁciently an approach that removes about
10—30% of the ORF S, separates multiple regimes of variance, and correlates with expected
factors of sequence features and functional genomics information. Only after arriving at a
plausible distinction of ORFS, can a speciﬁc, hypothesized ratio of operational versus Silent
annotated ORF S be evaluated. Reducing the complex nature of genomic content and
organization into comparable events of change across the phylogeny requires some capacity to
establish limits and parameters for recombinative units. Prior to evaluating speciﬁc
hypotheses concerning the nature of ORF clustering, the natural ﬂuctuations of the
ORF-ome and the prevalence of putatively false or Silent ORFS in the annotated data ﬁles
presents a challenge for broadly distinguishing those ORFS of functional and evolutionary

importance to the composition and organization of a chromosome.

103

Chapter 4: Subsets of Open Reading

Frames

4.1 Comparative Parameters of Sequence Conservation

Ideally, the identiﬁcation of a generally legitimate, “real” subset of ORFS would reduce
observational noise, and further provide some account for the ﬂuctuations and evolutionary
pressures that inﬂuence the set of ORFS in a given prokaryotic genome. As described in
Section 1.4, conservation of sequence is a reasonable basis for inferring the importance of
ORFS, and effective approaches have involved measures of sequence similarity (Snyder &
Gerstein, 2003), ORF length (Skovgaard et al., 2001), and grouped similarities involving
more than just two sequences (Park et al., 1998). I sought to construct a general ﬁlter with
the parameters L (identity of ORF length), B (identity of ORF sequence), and S, size of a
Similarity cluster. S is evaluated as an inclusive count of a similarity set. If a sequence is only
similar to itself, then S = 1. If an ORF sequence is Similar to 4 other ORFS (in addition to
itself), then S = 1 + 4 = 5. As S > 2 for a given ORF, information exceeding that of a
pairwise comparison is incorporated. S is interdependent with the constraints of similarity
speciﬁed by L and B.

I evaluated the strength of similarity between any two ORFS as a function of B and L.
The basis for a length constraint is that it enforces some conformity for the internal
structural integrity of two ORFS with Shared ancestry (Wheelan et al., 2000), and further
focuses the assessment of similarity to the distribution of “immutable” ORFS, as opposed to
those ORF S altered by gene fusions and ﬁssions. Localized alterations to ORF content and
structure may have structural and functional consequences in terms of important motifs such
as conserved domains. Constraining L so as to achieve this distinction is not a well-modelled
proposition, so L was characterized as being, at most, :t:10%. For example, with
L —+ [—10%, +10%], an ORF length of 200 aa would match ORFS of lengths 180 aa to 220 aa

but not lengths < 180 aa or > 220 aa. By Spot checking a few test cases, I found that a L

104

constraint of i10% was effective in reducing erroneous homologies that might otherwise be
inferred from low-complexity protein domains.

A value of B s 10’6 is the default for the BLASTCLUST application, where B is the
expectation score of a BLASTP comparison among ORFS clustered by similarity. The default
parameters of BLASTCLUST reportedly work to “anecdotally” identify closely related
protein families from closely related prokaryotes, and “virtually eliminate false positives”
(Wolf, 2004). The parameters of “coverage” (-L 0.0) and “score density” (-S 0.0) were set
so as to not be evaluated by the BLASTCLUST algorithm.

If L —-+ i10% and B 5 10’s, the remaining objective for deﬁning an initial sequence
conservation threshold for ORFS relates to the value of the similarity cluster size, S. As S
increases, the pervasiveness of the ORF as an immutable unit of evolution across phylogeny
is justiﬁed. Two aspects to the performance of a given S-based constraint involve 1) random
similarity matches versus truly homologous matches, and 2) the phylogenetic range of
observed matches. In the set of 155 genomes, there were a variety of closely related strains in
the data set with up to 5 members of the same Species, so an S value of 5 may sometimes
only implicate a recently emerged last common ancestor. AS ORFS with larger S values are
identiﬁed, this may encompass a larger phylogenetic range by implicating more distantly
related lineages. An S value of 155 would implicate an ORF common to all 155 genomes.

If an ORF matches just one other ORF different than itself (S = 2), then there may be a
signiﬁcant chance for the match to be a false positive. A BLASTP expectation score
threshold of B 3 10"”, corresponds to an expectation for ﬁnding a single (10’2 x 100 = 1)
false positive match against a set of 100 other sequences (Koonin & Galperin, 2003). In a
Bayesian sense, if B s 10‘6 , then the percent chance for a false positive match (S = 2) to
another ORF from the 165 chromosomes is 45% (447, 550 x 10‘6 = 0.45). For an ORF to
have two other false positive matches (S = 3), the probability is 0.45 x 0.45 = 0.20. When
S = 5 and S = 6, the Bayesian-calculated probabilities approach statistically acceptable
levels of signiﬁcance, respectively 0.454 = 0.041 and 0.455 = 0.018. While S 2 5 signiﬁcantly
implicates a true match with at least one other ORF (p > 0.95 for a legitimate set of
“twins”), S 2 6 implicates the existence of at least two other matches (a legitimate set of

“triplets”) and a potentially wider range of phylogenetic coverage. If a ﬁltered ORF subset.

105

were to be based on evolutionary information from more than just two ORFS, S 2 6 would
be the preferable constraint. Generally considered, ORF S with high S values would more
likely belong to an evolutionarily conserved subset compared to ORFS of relatively low S
counts such as S = 1. ORFS belonging to very large similarity clusters may be pervasively
Similar due to strong sequence features of evolutionary importance or because of ubiquitous
low-complexity subsequences such as those that encode for coiled-coiled regions. For the
analysis, ORFS corresponding to S > 40 were given an inclusive S value of “40+” so as to
not resolve complex transitive relationships of ORF similarity cluster assignments. I termed
the subset of ORFS with S > 40 as the “ubiquitous” subset of ORF S (U-ORFS). Based on
the statistical considerations of length |L| S 10%, sequence similarity B S 10‘6 and
Similarity cluster size S 2 6, I arrived at an initial distinction for operational ORFS
(O-ORFS) versus a “Silent”, putatively false subset of ORFS (S-ORFS) with the expected
relationship of U-ORFS C O-ORF S. The subset of O-ORFS that does not include U-ORFS
(6 S S S 40) is a subset that I termed as the N-ORF subset. A summary of ORF subset

terminology is shown in Table 10.

4.2 Paralogous ORFS

I evaluated my similarity clusters for possible instances of paralogy where two or more
ORF S in the same similarity cluster belonged to the same chromosome. Objectives for this
assay were to 1) evaluate the presence of intragenomic pattern attributable to duplication of
content, and 2) analyze and infer taxon-based constraints for paralog formation. The number
of recorded paralogs inside the deﬁned similarity clusters for the 165 chromosomes
(2 S S S 40) ranged from 1% (Chlamydia trachomatis MoPn) to 18% (Methanosancina
mazei) of the total number of annotated ORFS for each evaluated chromosome. I compared
my putative paralogs to a more expansive effort at characterizing paralogy (Pushker et al.,
2004). Pushker et al. (2004) characterize a a range of 10% to 50% of ORFS on a given
chromosome as belonging to a paralogous cluster of ORF S. My calculation of paralogs for the
165 chromosomes discarded the U-ORF group (S > 40), and this may be signiﬁcant Since the

average paralogous family Size often exceeds 40 (Pushker et al., 2004). A possible

106

Table 10: Names and descriptions of open reading frame subsets.

 

Subset Name

Description

 

ORFS

O-ORFS

S-ORFS

U-ORFS

N-ORFS

C-ORFS

X-ORFS

The full set of ORF S as they are currently annotated in N CB1-
based data ﬁles of fully sequenced prokaryotic genomes.

Putatively operational ORFS. This subset consists of those
ORF S belonging to Similarity clusters of size 3 6.

Putatively silent ORFS (putative false positives in the full,
annotated set). This subset consists of those ORFS belonging
to similarity clusters of Size 3 5.

Putatively ubiquitous ORFS. This subset consists of those
ORF S belonging to Similarity clusters of size > 40.

Putatively operational, but not ubiquitous, ORFS. This sub-
set consists of those ORFS belonging to similarity clusters of
Size 2 6 and S 40.

The subset of ORFS that are members of a COG (cluster of
orthologous groups). This subset covers 25 functional classi-
ﬁcations of COGS, including the R and S functional classes
that are respectively for “general function predictions” and
“unknown functions.” C-ORF S are only established for the
67 chromosomes for which COG assignments have been con-
ducted.

The subset of ORFS that are members of one of the 67 chro-
mosomes for which COG assignments have been conducted,
yet are not members of a COG.

 

107

consequence to inspecting the N-ORF group (1 S S S 40) and not the U-ORF group may be
to limit the general evaluation of paralogy to those ORFS that are more recently diverged
and are limited to a particular branch on the phylogenetic tree.

Fig. 38 - 41 Show distances between paralogous pairs for various sets of closely related
genomes based on data from my similarity cluster calculations as well as from Pushker et al.
(2004). The pattern of paralogy on each chromosome implicates hot spots of duplicated
content and distances between Similar ORFS in a way that may be visually diagnostic of the
species-level taxonomy. Some of the wild-type Escherichia coli strains (Ol57:H7 and
CFT073) have high peaks in frequency for long distances between related paralogs that are
Similar in value to the ﬁrst bin (< 5, 000 bp) (Fig. 38). Most of the Streptococcus pyogenes
strains have distinctly elevated frequency peaks for related paralogs that are more than
100,000 bp apart (Fig. 40). Most of the paralogs for chromosomes of the Pseudomonas
Species appear to be separated by distances less than 5,000 base pairs (Fig. 39). In addition
to having high frequency peaks for related paralogs that are 0 to 10,000 bp apart,
Staphylococcus aureus species have a Slight upswing in frequency for distances greater than
10,000 bp approaching 200,000 base pairs (Fig. 41). For many of the low frequency distances
between paralogs, Pushker et al. (2004) characterize paralogy for well over 10x the number
of paralogous ORFS that I place into similarity clusters. By contrast, the distinctly high
frequency peaks of paralogs from my Similarity clusters (Fig. 38—41[a,c,e,g]) versus the
paralogy clusters of Pushker et al. (2004) (Fig. 38-41[b,d,f,h]) are generally less than an order
of magnitude (10x) different in value for examinations of identical locations on the respective

histograms.

108

50

40-

30
20
1 0

50

40-

3O
20
10

50
4O
30
20
1 0

Frequency

50
40
30
20
1 0

Figure 38: Frequency of distances between related paralogs for four strains of Escherichia coli.
Only those distances < 200,000 base pairs are Shown. Bin sizes are 5,000 bp. (a,c,e,g) Show
the distances between all pairs of paralogs based on similarity clusters involving ORFS on the
same chromosome where 6 _<_ S S 40. (b,d,f,h) are based on data from Pushker et al. (2004).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) (b)
Escherichia coli K—1 2 Escherichia coli K—1 2
4
.. ...n _ Hillirllllnnﬂhmllllﬂhmlliﬂ
F T I I l I
(0) (d) E. coli
E. coli 0157:H7 ' 0157:H7
- - l
J
l 1 Illlll
m. 11.1. ...ml .11.. _ -
I l l I I l
(e) In
. E. coli ‘ . E. coli
0157:H7 EDL933 - 0157:H7 EDL933
“-1”er ll IL n mill-Ill 4 HI
I I I l I j
(9) (h)
. E. coli 01:1073 ‘ E. coli CFI'073
'lﬂﬂm n .— 11 nnn _1 WW
I l I F l j
o 105 2x105 0 105

Distance Between Related Paralogs (bp)

Frequency values higher than 50 are truncated on the plot and range from 54—150.

109

2x105

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 — 1 .
(a) (b)
40 ‘ Pseudomonas aeruginosa Pseudomonas aeruginosa
30 - ‘
20 - ‘
1o — -
0 _ LlTln. ..l'lnn m n r“ n _
I I I r I I
50 - -
(C) Nd)
> 40 ‘ P. putida KT2440 ‘ P. putida KT2440
o .r
c: 30 '1 ‘
8
E 20 - —
u. 10 _ _
0 _ n'lnl'l rn nnn-.... nil-Ln _ , ,,,,,,
f I l I T I
50 - '
i (e) I (i)
40 - P. syringae str. DC3000 ‘ P. syringes; str. DC3000
30 -— - ‘
20 - "
1o — —
0 _ 11m... II n 1.1 _
I I I r I I
o 105 2x105 0 105 2x105

Distance Between Related Paralogs (bp)

Figure 39: Frequency of distances between related paralogs for three strains of Pseudomonas
species. Only those distances < 200,000 base pairs are shown. Bin sizes are 5,000 bp. (a,c,e)
Show the distances between all pairs of paralogs based on similarity clusters involving ORFS
on the same strain’S chromosome where 6 S S S 40. (b,d,f) are based on data from Pushker
et al. (2004). Frequency values higher than 50 are truncated on the plot and range from 52-232.

110

50- -

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a) (b)
40 d S. pyogenes M1 GAS — 8. P1099095 Ml GAS
30 '- ‘—
20.. -
10 - ‘-
0 __ [Tl-n n an ._
f I I I I I
50 - —
(C) (d)
40 ‘ S. pyogenes MGA88232 ‘ S. pyogenes MGA88232
30 - -
20 r _
10 - n A
3 0 d 1 T .... I d I I '
C
3 50
E (e) (f)
40 ‘ S. pyogenes MGAS315 — S. pyogenes MGA8315
30'— r '
20 ‘ —
‘° ‘ III ill] ‘ ”'ILnHImrulfh IL
0 J JiL n ,n, M _ [II-nnn .4 1""
I I 1 I I I
50 - T
(9) (h)
40 ‘ S. pyogenes SSI—1 S. pyogenes SSl—1
30 - —
20 r T H
I f I I I I
o 105 . 2x105 0 105

Distance Between Related Paralogs (bp)

Figure 40: Frequency of distances between related paralogs for four strains of Streptococcus
pyogenes. Only those distances < 200,000 base pairs are Shown. Bin sizes are 5,000 bp.
(a,c,e,g) Show the distances between all pairs of paralogs based on similarity clusters involving
ORFS on the same strain’s chromosome where 6 S S S 40. (b,d,f,h) are based on data from

Pushker et al. (2004).

111

2x105

(a) (b)
40 _ Staphylococcus aureus _ Staphylococcus aureus
30 - subsp. aureus Mu50 - subsp. aureus Mu50

204 —

10q '-
0 lnnn nnndm -mhmhthlmﬁm
I l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 — -
(e) (d)
> 40 _ Staphylococcus aureus F Staphylococcus aureus
g 30 - subsp. aureus N315 - subsp. aureus N315
3 —l
g 20 j -
“- 1o — L - H II [1” II
0 d an n nm _mlln _ In
I I l I I I
50 - -
(a) (f)
40 ‘ Staphylococcus aureus B Staphylococcus aureus
30 - subsp. aureus MW2 ‘ subsp. aureus MW2
20 — -
‘° ‘ ‘ 111111111111an
0 _ r“ n ..:-1111 _
I I I I I ﬂ
0 1o5 2x1050 105 2x105

Distance Between Related Paralogs (bp)

Figure 41: Frequency of distances between related paralogs for three strains of Staphylococcus
aureus. Only those distances < 200,000 base pairs are shown. Bin sizes are 5,000 bp. (a,c,e)
Show the distances between all pairs of paralogs based on similarity clusters involving ORFS
on the same strain’s chromosome where 6 S S S 40. (b,d,f) are based on data from Pushker
et al. (2004). Frequency values higher than 50 are truncated on the plot and range from 56-336.

112

4.3 Findings for an Operational ORF Subset

4.3.1 Differences in Length and Similarity Cluster Size

Lognormal, multimodal ORF length distributions have been previously reported
(Skovgaard et al., 2001). As would be expected for a theoretical ﬁt to a normal distribution
of log-transformed ORF lengths, I investigated how similar the sample mean is to the sample
median (Table 11). The S-ORF and O-ORF subsets (n=140,805 and n=306,746) had a
stronger theoretical ﬁt to a lognormal model than the entire set of ORFS (n=447,551). The
difference in median and mean values for the S-ORF subset was consistent with a
distribution slightly skewed to the left, and the difference in median and mean values for the
O-ORF subset was consistent with a distribution skewed to the right. The observed ranges of
ORF length medians across the taxonomic groupings were 246-286 aa (all ORFs), 126-187 aa
(S-ORFs), and 291-329 aa (O-ORFs) Although the median values for O-ORF lengths were
almost twice that of S-ORF lengths, the variance of lengths produced a signiﬁcant overlap
between the two ORF length distributions as shown in Fig. 42.

The relative numbers of ORFS, S-ORFs, O-ORFs and U-ORFS for each taxonomic
grouping are shown in Table 12. Proportionally, the ﬁve subsamplings of O-ORFS ranged
between 54.5% (Archaea) to 82.0% (Enterobacteriales). The ﬁve subsamplings of S-ORFs
ranged between 18.0% (Enterobacteriales) to 45.5% (Archaea). These ranges broadly
encompass a predicted 3:1 ratio of O—ORFs to S-ORFs. The Archaea had the lowest relative
percentage of U-ORFs. Proportional trends for O-ORFs, S-ORFS, and U-ORFS are further
characterized by Fig. 43. The Enterobacteriales set had the second greatest number of
representative ORFS in the set of 447,551 ORFS and had the highest proportional amount of
O-ORFS (82.0%), possibly due to the large number of Enterobacteriales genomes present in
the data set acting by relation to elevate the similarity cluster sizes specifying the O-ORF
subset. Yet, the Enterobacteriales O-ORF set shows a similar trend of length perhaps
indicating that the B and L thresholds compensate for over-representation of the
Enterobacteriales taxon. The taxonomic grouping with the highest proportional number of

S-ORFs is the Archaea.

113

Table 11: O-ORF and S-ORF comparison of ORF length norms for 6 taxonomic groupings.“

 

 

 

 

 

All ORFS S-ORFS O-ORFS
Taxonomic Group Mdn an.Mean Mdn an.Mean Mdn an.Mean
All 155 265 245 (-7%) 157 160 (+2%) 310 299 (4%)
Actinobacteria 286 269 (-6%) 187 189 (+1%) 329 324 (-2%)
Archaea 246 232 (—6%) 169 175 (+4%) 310 294 (-5%)

Enterobacteriales 262 244 (-7%) 134 140 (+4%) 291 275 (-5%)
Cam. no Ent. 271 250 (-8%) 153 152 ( 0%) 315 307 (-3%)

Lactobacillales 254 234 (-8%) 126 133 (+6%) 289 281 (-3%)

0A1] 155 = all of the 155 genomes. 5 taxonomic subsamplings were taken from this set
of 155 genomes. Gam. no Ent. = Gammaproteobacteria without Enterobacteriales.
The two statistical norms for ORF lengths are a median (Mdn), and a lognormal mean
(an.Mean; the exponential function of the mean of the logarithm-transformed ORF
lengths). The percentage increase or decrease from the median to the lognormal mean
is indicated. ORF length units are in the number of corresponding amino acids to
their translated product.

 

114

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o

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0.2

 

 

0.0
o s s s s s s s s g s
1- N CO V In (D I\ no P

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Figure 42: Relative frequency distributions of S-ORF, O-ORF, and U-ORF lengths for 155
genomes. Only the subset of ORFS that are S 1000 aa in length is presented (441,040 out of
447,551 ORFS). The x-axis is labelled with the boundaries of each bin (bin size = 100 aa).

116

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ORFS occur within various ranges of similarity cluster sizes more tightly bounded than
S 2 6 (Fig. 44). I found that as the ORFS were evaluated for the discrete set of similarity
Cluster size intervals, S = {1, 2, 3, ..., 39, 40}, the S—ORF versus O-ORF distinction appeared

to separate two regimes of variation (Fig. 45, 46 and 47).

118

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The relationship between median ORF lengths and associated similarity cluster size is
shown in Fig. 45-46. For the S—ORFs, there was a steady rise of median ORF lengths from a
lower bound of 100 aa to values ranging from 160-250 aa. The changes in median ORF
lengths were variable between different subsampled sets from the 155 genomes. For S values
between 1 and 5, the Actinobacteria rise from 160 aa to 250 aa. The Enterobacteriales rise
from about 100 aa to 160 aa. Except for the Actinobacteria, the median ORF lengths
appeared to reach 250 a for S 2 20. For O-ORFs, there is a less steep ascent of median
ORF length that proceeds from values greater than 200 aa to values greater than 280 aa.
The O-ORF ascent in median ORF length is somewhat continuous, and had various rises and
falls of 50 aa to 100 aa in magnitude occurring for differential changes in the similarity
cluster size of z 5.

A log-log relationship accounted for how the number of ORFS equates to increasing
range intervals of S as shown in Fig. 47 where the range intervals of S are [1,1], [1,2], [1,3],
..., [1,40]. The second value for each interval is the similarity cluster size limit, 0. The most
inclusive S range of [1,40] (c = 40) includes all those ORFS with 1 g S S 40, but not S > 40.
The logarithm of the number of ORFS characterized by [1, c] was directly proportional to the
logarithm of c. The slopes and correlations of three linear ﬁts were calculated for various
ranges of the similarity cluster size limit (c H [1,40], c —> [1,5], and c —+ [6, 40]), and in all
comparisons, the slope for c —-> [1, 5] is 23% to 100% steeper than the slope for c -+ [6,40].
The largest distinctions between c —> [1, 5] and c —+ [6,40] were for the Actinobacteria and
the Archaea. For all taxonomic groupings examined, the linear ﬁts associated with c —> [1,5]
and c —+ [6,40] had the strongest correlations with a linear ﬁt, although all of the ﬁtted lines

signiﬁcantly accounted for variation (7‘2 > 0.97).

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123

I inspected the linear relationship between observed distributions and expected
distributions (as calculated from sample means and standard deviations) for the
log-transformed lengths of various subsets of ORFS (Fig. 48-50). Fig. 49 presents positive
skewness values (w > 0), implicating a non-normal leftwards shift to the distribution of
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(w < 0), implicating a non-normal rightwards shift to the distribution of ORF lengths. These
directional shifts were consistent with my ﬁndings for the arithmetic mean’s relationship to

the median (Table 11).

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127

4.3.2 Composition of Phyla within ORF Similarity Clusters

I investigated the number of ORFS in each similarity cluster belonging to the same
lineage based on membership within one or all of 7 different phyla (Fig. 51 and 52). For each
analysis, a random selection of 1000 ORFS came from the phylum (or 7 phyla) under
evalation. The Proteobacteria and Firmicutes had the highest degree of similarity clusters of
sizes 6 to 15 containing members within the phyla. Yet, at least 25% of Proteobacteria and

F irmicutes similarity clusters tended to have non-phylum members for S 2 6.

4.3.3 Expressional, Phenotypic, and Functional Aspects of the
ORF Subsets

I evaluated expressional, functional, and phenotypic aspects of the O-ORF and S-ORF
subsets to more fully assess their empirical correspondence with a distinction of real ORFS
versus unreal ORFS.

I assessed published transcriptional data for 3,309 ORFS of Escherichia coli K-12
(Covert et al., 2004) and compared patterns of presence or absence of transcriptional
expression to the similarity cluster size stored in the MYCROW database. In this set of 3,309
ORFS, there were 2,112 U-ORFs (64%), 290 S-ORFS (9%), 3,019 O-ORFS (91%), and 2,787
C-ORFs (84%). By comparison, for the total set of annotated ORFS for E. coli K-12
(n=4,311), there were 2,388 U-ORFs (55%), 513 S-ORFs (12%), 3,798 O-ORFs (88%), and
3,153 C-ORFs (73%).

For the 42 separate assays of transcriptional expression on the set of 3,309 ORFS, 1,992
ORFS were designated “present” for all 42 transcriptional assays of expression, 331 ORFS
were designated “absent” for all 42 transcriptional assays of expression, and 780 ORFS had
marginal or conﬂicting expression designations of presence and absence among the 42
transcriptional assays. Of the 2,323 ORFS that are either uniformly present or absent across
the 42 assays of transcription, 86% are transcriptionally present compared to 14% that are
absent. Of the 1,992 transcriptionally present ORFS, there is a ratio of 22:3 for ORFS
belonging to a COG and a 24:1 ratio for ORFS belonging to the O-ORF subset. Of the 331

transcriptionally absent ORFS, there is a 1:3 ratio for ORFS belonging to the O-ORF subset

128

 

 

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Figure 51: Membership within phyla for similarity clusters. All 7 phyla (Actinobacte-
ria, Crenarchaeota, Cyanobacteria, Euryarchaeota, Firmicutes, Proteobacteria, Spirochaetes;
148 genomes) and, separately, the three phyla, Crenarchaeota (4 genomes), Spirochaetes (5
genomes), and Cyanobacteria (genomes) are examined. Each plot is based on 1000 randomly
selected ORFS and their corresponding similarity clusters. Black: median percentage member-
ship of similarity cluster belonging to the same phylum. Blue: the ﬁrst quartile of percentage
memberships for same phylum. Red: the relative percentage of ORFS belonging to each range
of similarity cluster sizes.

129

 

 

 

 

 

 

 

 

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Similarity Cluster Size

Figure 52: Membership within four other phyla for similarity clusters. Four separately con-
sidered phyla: Euryarchaeota (12 genomes), Actinobacteria (13 genomes), Firmicutes (38
genomes), and Proteobacteria (68 genomes). Each plot is based on 1000 randomly selected
ORFS and their corresponding similarity clusters. Black: median percentage membership of
similarity cluster belonging to the same phylum. Blue: the ﬁrst quartile of percentage mem-
berships for same phylum. Red: the relative percentage of ORFS belonging to each range of
similarity cluster sizes.

130

and a 3:7 ratio of ORFS belonging to a COG. Both in terms of proportional categorization
(86% versus 91%) and ratios of association (24:1 and 1:3), the O—ORF versus S—ORF subsets
were more closely aligned with expectations for transcriptional expression for E. coli K—12
than a COG-based distinction.

Covert et al. (2004) also propose various ORFS as having functional and regulatory
importance based on growth and no growth predictions for 143 types of media conditions
such as “growth on citric acid”, “growth on methionine”, and “growth on adenosine.” Of the
ORFS (99 of 110) that were unambiguously mapped to ORFS within the MYCROW
database, 98 (99%) of these ORFS were O—ORFs and 80 (80%) were U—ORFs. Only one ORF
was an S-ORF and it belonged to a similarity cluster size of 5.

Table 13 shows the association between number of phenotype effects and similarity
cluster size S based on data for Bacillus subtilis (Biaudet et al., 1997). Of the 352 genes that
only have a single phenotypic effect when mutated (66%), 28% of them were S—ORFs. Of the
181 genes that have two or more phenotypic effects (34%), only 19% of them were S-ORFs.
261 of the 533 ORFS were U-ORFs (49%) and 140 ORFS were N-ORFs (26%). 73% of
S-ORFS had a single phenotype effect, whereas only 63% of N-ORFS and 64% of U-ORFs
had a single phenotype effect. Quadruple and sextuple phenotype effects occurred exclusively
for O-ORFs. Overall, multiple phenotypic effects were found to be more closely associated
with O-ORFs than S-ORFs, although inactivation of S-ORFs is generally associated with a
phenotypic consequence.

Also, as seen in Table 14, examination of data for Bacillus subtilis (Biaudet et al., 1997)
showed an increase in “single phenotype” ORFS for S—ORFs compared to ORFS that are not
in COGS, and a proportionately greater amount of “multiple phenotype” ORFS for O-ORFs
compared to C-ORFs. The evidence, while not exhaustive, is consistent with the O-ORF
versus S-ORF distinction relating to whether or not an ORF is expressed and whether or not
there is signiﬁcant operational consequence to the organism’s physiology.

For functional grouping of ORFS, the functional classiﬁcation of COGS was evaluated
based on NCBI’s COG database that contained data for 67 (41%) of the 165 chromosomes.
For this sampling of 67 chromosomes and their total numbers of ORFS, the mean and median

levels of O-ORFs were both equal to 68% whereas the mean and median levels of C-ORFs

131

 

 

Table 13: Phenotypic inactivation associated with Bacillus subtilis O-ORFs and S-ORFs.“

All ORFS S-ORFs O-ORFs

Number of Affected #ORFS Rel.% #ORFs Rel.% #ORFS Rel.%
Phenotypes

 

 

 

 

 

1 01‘ more 533 100.0% 132 24.8% 401 75.2%
2 or more 181 100.0% 35 19.3% 146 80.7%
3 or more 47 100.0% 10 21.3% 37 78.7%
4 or more 13 100.0% 0 0.0% 13 100.0%

 

“533 ORFS, when mutated, ranged from single phenotype effects to six phenotypic
effects. The number of ORFS (# ORFS) is shown as well as the relative percentage
(Rel.%) that number of ORFS to the total sample of ORFS for the given range of
phenotypic effects.

Table 14: ORF counts from Bacillus subtilis for single and multiple phenotypes based on COG
and O-ORF categorizations.

 

S-ORF X—ORF O-ORF C-ORF
Single Phenotype ’ 97 84 255 268

 

Multiple Phenotypes 35 32 146 148

 

were both equal to 74% (based on 25 functional classes). An expectedly stronger association
was observed between O-ORFs and C-ORFs (median, 64%) compared to O-ORFs and
X-ORFs (median 4%). An expectedly stronger association was also observed between
S-ORFs and X-ORFs (median, 20%) compared to S-ORFs and C-ORFs (median, 11%). The
“General function prediction only” and “Function unknown” subsets of COGs amounted to
about 11% and 7% respectively of 161,990 ORFS for 67 chromosomes.

Linear modelling, as shown in Fig. 53 and 54, further investigated how categories of
COG and O-ORF membership scale with comparison to the total count of ORFS for a given
replicon. In these models, the proportional measure of O-ORFs to total ORFS was 73% and,
for COGS, 72%. The strongest linear associations were for the subset of ORFS that are jointly
both O-ORFs and C-ORFs, and the separately considered O-ORF and C-ORF subsets. The
next strongest linear association was for the X-ORFs. Although still accounting for most of
the original variability (7‘2 > .5), both the S-ORF subset and the joint intersection subset of

the S-ORF and C-ORF subsets showed markedly reduced linear correlation coefficients,

132

 

suggesting that the number of S—ORFs is less likely to relate directly to the total ORF count.
The scattering of dots away from the ﬁtted line in Fig. 53c and 53c-d occurs between 2,000
annotated ORFS and 2,500 annotated ORFS. Based on a relationship of one ORF for every
1,100 base pairs of chromosomal DNA, the increased pattern of scattering attributable to
S-ORFS likely occurs for chromosome sizes > 2 Mb, corresponding to a a proposed distinction
of microbial ecology and genomic stability (Fig. 36) (Ochman & Davalos, 2006). Further
measurement showed the canonical correlation, 7‘2, to be different for ranges of total ORF
counts < 2, 000 compared to > 2, 000. The 1‘2 value for the S-ORF subset count where total
ORF count < 2, 000 is 0.58 compared to 0.43 for the X-ORF subset. For total ORF counts
> 2, 000, r2 for the S-ORF subset count is 0.39 compared to 0.65 for the X—ORF subset.

As ORF sets are examined by 25 different functional COG categories, Fig. 55 shows
there to be close correspondence between the number of O-ORFs and overall number of
ORFS for a given COG category. The greatest variation appears to be for the COG
categories of “general function prediction only” and “function unknown” where the number
of corresponding O-ORFS drops, with an inverse rise in the number of S-ORFS.

Table 15 shows how the percentage amounts of S—ORFs can vary for different functional
COG categories across different subsets of the genomes. Most ORFS that are not in a COG
are S—ORFS (77%). For most all categories, the Archaea have the highest percentage of
S—ORFs. The Actinobacteria generally have the second highest percentage association of
S—ORFs with functional COG categories except for the categories of cell motility (N) and
secondary metabolites biosynthesis, transport and metabolism (Q). If S-ORFs truly mean
“not operational”, the lower values of Actinobacteria S-ORFs for categories N and Q is

consistent with the soil lifestyle (Garrity, 2001).

133

 

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Total ORF Count

I r

2000 4000 6000 8000

Figure 53: ORF membership subset comparisons with total ORF counts. Each of the four
plots shows the relative proportions of the O-ORF, C-ORF, S—ORF, and X—ORF subset ORF
counts, where each point corresponds to one of 67 genomes. A ﬁtted line is shown along with

slope (m) and r2.

134

 

 

   

 

 

 

 

 

 

 

 

 

 

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Total ORF Count
Figure 54: ORF membership intersecting subset comparisons with total ORF counts. Each of
the four plots shows the relative proportions of various intersections of ORF subsets, where
each point corresponds to one of 67 genomes. A ﬁtted line is shown along with the slope (m)
and 1‘2.

135

 

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Figure 55: Number of ORFS, O—ORFs, and S-ORFS for various COG—based categories of

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136

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If the COG set includes falsely annotated ORFS, I theorize that the O-ORFs inside
functional classiﬁcations of COGS should enhance the positive and negative genome size
correlations characterized for various functional groupings (Bentley & Parkhill, 2004;
Konstantinidis & Tiedje, 2004). Table 16 shows how the O-ORF counts for the J, L, D and F
set of COG functional categories enhanced the predicted negative genome size correlation,
and even more strongly enhanced the predicted positive genome size correlation associated
with the K, T, N, Q, and C set of COG functional categories. The deﬁnitions of the R, S,
and X groups suggest a gradient of decreasing functional evidence for their respective sets of
ORFS, and the decreasing proportion of O-ORFs inside each group corresponds to this

gradient.

138

 

 

 

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139

4.4 Non-Stochastic Clustering of O-ORFs

For my population of 165 chromosomes, I inspected the z-score values of signiﬁcance
(number of sigma 0 units separating original and randomized assignments of O—ORF
membership) from my running tally methodology. The O-ORF running tally z-score
difference was 14.90. There were 28 of the 165 chromosomes (17%) that had a z-score
< 1.640. Of the 14 of the 67 chromosomes evaluated for COG membership with COG-based
z-scores < 1.640, 7 (50%) had O-ORF-based z-scores < 1.640.

4.5 Discussion

I established the parameters for distinguishing real ORFS from putative, false ORFS by
general statistical expectations. As shown by Fig. 55, I found the O-ORF subset to follow
trends similar to a COG membership subset of ORFS (C—ORFs). C-ORFs have been
previously reported by Skovgaard et al. (2001) as a lower bound to the total number of
annotated ORFS that correspond to real proteins. As shown by Table 17, my O-ORF
speciﬁcation follows a higher threshold parameter of similarity cluster size (S), and has
requisite criteria for ORF length similarity (L) and sequence similarity (B). Despite
signiﬁcantly different approaches to threshold parameters, similar percentages of ORFS
belong to the subset of O-ORFs (73%) compared to the subset of C-ORFS (72%). While the
O-ORF speciﬁcation involves a variety of more stringent threshold parameters, it neither
imposes the orthologous bidirectional best hit criterion of COGS, nor does it require sequence
conservation to exist across three distant lineages. The inclusion of paralogs and recently
evolved ORFS in the similarity cluster scoring of O-ORF membership may meaningfully
account for differing results for the prevalence of O-ORFs compared to C-ORFs.

Based on Fig. 54a and 54d, there are about 64% of ORFS per chromosome inside both
the C-ORF and O—ORF subsets compared to 19% that are not inside either of the subsets. I
expect the O-ORF speciﬁcation to be better aligned with a real ORF speciﬁcation versus the
C-ORF speciﬁcation based on greater pairwise comparison thresholds for homology, and the
inclusive scoring of paralogs and recently evolved ORFS that are a likely source of functional

and real ORFS (Snel et al., 2002; Kurland et al., 2003; Liang et al., 2002; Konstantinidis &

140

 

(a) Bacillus subtilis (b) Escherichia coli

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

O
8
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o 8
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ORF Count

Figure 56: Running tally graphs of O-ORF membership along four chromosomes. The thick
line represents increments and decrements based on whether an ORF is an O-ORF or not.
The dotted diagonal represents random expectation where O-ORF membership is randomly
assigned to a chromosomal set of ORFS. The dashed lines forming a V-shape represents the
pattern if all S—ORFS were together followed by O-ORF members. (a) Bacillus subtilis subsp.
subtilis str. 168. (b) Escherichia coli K-12. (c) Vibrio cholerae (large chromosome). (d)
Yerszim'a pestis C092.

141

Table 17: Threshold parameters of sequence conservation for the operational ORF subset
(O-ORFS) and the COG membership subset (C—ORFs).

 

Threshold O-ORF C-ORFa
Length Similarity :l:IO% i33‘7o

 

Sequence Similarityb S 10‘6 < 10‘3

Similarity Cluster Size 2 6 2 3

 

aSpeciﬁcation criteria for COGS include bidirectional best hits involving three disparate
lineages and manual inspection and splitting of tentative clusters. COG analyses are not based
on explicit thresholds for sequence similarity. The length similarity and sequence similarity
values for COGS characterize the retrospective 90% conﬁdence interval for how any two pairs
of ORFS belonging to the same COG correspond in similarity.

bBLASTP expectation score for a pairwise comparison.

Tiedje, 2004). By comparison, the C-ORF speciﬁcation requires distant orthologies. In my
study, several analyses provided evidence that the O—ORF set is a more optimal speciﬁcation
for real ORFS compared to the C-ORF set. A greater proportion of O-ORFS are transcribed
compared to C-ORFS. The O-ORF and S-ORF speciﬁcation may also be effective for further
characterizing functional groups relevant to ﬂuctuations in genome size and associated
prokaryotic lifestyles (Table 16). The S-ORF, O-ORF transition between S = 5 and S = 6
appears to be an accurate point of separation for different regimes of variation seen for 1)
ORF length and similarity cluster size (Fig. 45) and 2) frequency of ORFS associated with
various similarity cluster sizes (Fig. 47). Overall, the hypothesis of a coding space limit
(Jackson et al., 2002), where 75% of the total set of annotated ORFS would be expected to
be real, is supported by two independently developed sets of parameters for O-ORFs and
C-ORFS as Shown by the linear relationships in Fig. 53.

Transcriptional expression data (Covert et al., 2004) and data from studies of phenotypic
inactivation (Biaudet et al., 1997), when applied to the O-ORF and S—ORF subsets, do
indicate that some of the S—ORF assignments confer a phenotype or are transcribed.
Intriguingly, those ORFS with the highest number of phenotypic effects are all O-ORFS, and
this may relate to a high degree of interaction with other proteins (Table 13). Protein
evolution is rapid, and only the most highly interactive proteins have a slow rate of evolution
(Jordan ct al., 2003). The ongoing ﬂuctuation of gene loss, modiﬁcation, and addition would

indicate that there are some ORFS that are in the process of becoming S-ORFS or are in the

142

process of becoming O-ORFS. Beyond this study, a closer inspection as to the properties of
gene loss versus gene addition may further characterize the natural dynamics that account
for putative distinctions between real and falsely annotated ORF S. A more reﬁned heuristic
might be arrived at by formally characterizing differences between exemplar sets of ORFS
with none, some, or all known features of evolutionary and functional importance.

The O-ORF speciﬁcation allows for paralogy, and Fig. 38—41 help characterize the degree
to which paralogy contributes to the O-ORF speciﬁcation. Precise characterizations of
paralogs versus non-paralogs may be difﬁcult to arrive at as evident by conﬂicting
estimations of paralogy for various strains (Nelson et al., 2002; Pushker et al., 2004;
Andersson et al., 1998; Simpson et al., 2000), and it may be difﬁcult to comprehensively
characterize and compare dynamics of paralogy formation across a broad phylogenetic range.
Yet, my more constrained, independently developed ﬁlter of sequence conservation effectively
characterizes the higher frequencies of distances between related paralogs when compared to
data from Pushker et al. (2004). These high frequency peaks may represent recent formations
of paralogs involving the duplication and translocation of a single region containing a cohort
of ORFS, or these peaks may represent two differently located hot spots of tandemly
duplicating sets of similar ORFS. The paralogy analysis establishes visual distinctions
between four different sets of closely related strains, and this implies different lineage-speciﬁc
constraints of chromosomal mobility and ORF duplication.

The O-ORF similarity cluster size speciﬁcations are inclusive of the effect of paralogs
whereas the speciﬁcation of COGS is designed to exclude paralogs. The presence of paralogy
signiﬁcantly increases as a function of genome size (and, correspondingly, total ORF count)
(Pushker et al., 2004). For genome sizes < 2 Mb, the percentage of paralogs ranges from 0 to
20 (Pushker et al., 2004). For genome sizes > 2 Mb, the percentage of paralogs ranges from
10 to 50 (Pushker et al., 2004). The X-ORF subset may more signiﬁcantly include the
paralogs (which are by deﬁnition excluded from the C-ORF set) than the S-ORF subset. The
presence of paralogs may account for the higher correlation of X-ORFS (r = 0.81) versus the
correlation of S—ORFS (r = 0.62) for total annotation counts exceeding 2,000 ORFS (Fig.
53c).

If S-ORFS are interpreted as trending away from duplicate elements (quasi-independent

143

of paralogous, lateral, or orthologous originations), then they may represent either newly
made ORFS, unique ORFS, or signiﬁcantly “destroyed” and mutated sequences. Subsets
based around COG membership (C-ORFS and X—ORFS) scale in closer association with the
annotated ORF count compared to O-ORF and S—ORF membership. While assessments of
COG membership may be ideal for characterizing the vertically inherited functionality of a
genome, ﬂuctuations such as the recombinative generation of paralogs and attenuation of
expression, may be better approached with the O-ORF versus S—ORF criteria. The
production of noise has been proposed as a key feature of recombination in pathogenic
organisms (Wolf & Arkin, 2003).

The characteristics of organisms as conferred by their O-ORF chromosomal organization
may be problematic to compare across lineages. Typically, uniform taxons should be
characterized to each contribute single data points to a comparative analysis (Grafen &
Ridley, 1997), yet my O-ORF speciﬁcation is likely to be biased by the over-representation of
Proteobacteria and Firmicutes in the set of 155 genomes. Fig. 51-52 shows how the impact of
phylum over-representation inﬂates the similarity cluster Size S. While there is an elevating
effect on the S score for each ORF, Fig. 43 does establish that sizable populations of S-ORFS
(S S 5) are still characterized for taxonomic classes and orders of the Proteobacteria and
Firmicutes. Moreover, the limited inclusion of paralogs is evidence that the B and L
thresholds for similarity work to reduce O-ORF membership for ORFS that signiﬁcantly
ﬂuctuate their composition, and phantom similarities among atrophying sequences within an
over-represented higher taxonomic rank may in this sense have been somewhat avoided.
Lateral gene transfer (LGT) may complicate the inferred ancestries of orthology for various
ORFS (Koonin et al., 2001), and phylogenetic trees based on ORFS such as metabolic and
environmental genes do not concur with rRNA phylogenies (Pace, 1997). LGT only accounts
for z 6% of the ORFS (Kurland et al., 2003) however, and if an ORF is laterally transferred
and conserved, that would be a case for inclusion in the O-ORF subset.

Further investigation of meaningful boundaries to ORF subsets could integrate the
results of more expansive analyses (Allen et al., 2003; Glasner et al., 2003) with more precise
characterizations of similarity based on protein structure (Chung & Yona, 2004) and

expectation concerning ORF length (Larsen & Krogh, 2003). From the standpoint of

144

comparatively characterizing recombinative events as functionally important data points in
the context of an evolutionary model, the emergence and role of genes in functional groupings
and metabolic pathways may help to more closely establish the consequences associated with
associated chromosomal rearrangements along phylogenetic branches. There are a variety of
efforts that seek to comprehensively evaluate the functional and metabolic dynamics of ORF
populations within each genome (Karp et al., 2005; Caspi et al., 2006) and their relationship
to phenotype (Schilling et al., 2006). Yet, from a contemporary standopint, based on the
recent, “unprecedented” discoveries of decayed ORFS (Ochman & Davalos, 2006), it is
currently a meaningful step to focus upon a broad distinction between an operational subset
of ORFS compared to contrasting or randomly selected subsets. While there may be complex
dynamics of ORF populations, a more inferrential, prescribed approach may suffer from a
priom’ assumptions, estimation error, and also hinder repeatability of an analysis to the
expanding data set of fully sequenced genomes.

I evaluated the clustering of O-ORFs by the same running tally methodology used to
characterize the statistical signiﬁcance of C-ORF and polarity-based clustering. The degree of
statistical signiﬁcance for O-ORF clustering is similar to the degree of statistical signiﬁcance
established for C-ORF clustering. The terms “shufﬂing” and “ﬂuidity” have been used to
characterize the relocations of ORFS over time (Zivanovic et al., 2002; Lathe et al., 2000),
and the negative control used for establishing the sigma a unit for the bootstrapped z-score
difference in distributions is based on a context of completely random, stochastic resamplings
of ORF designations as either S-ORFS or O-ORFs. This style of stochastic assignments may
be drastically and predictably different than natural processes of ORF addition and loss
(Snel et al., 2002), and may also relate to possible ﬁtness constraints on the recombinative
relocation of ORFS (Wolf et al., 2001; Lathe et al., 2000). The degree of non-stochastic
positioning of O-ORFS and C-ORFs may 1) better support a proposed model of localized
rearrangements of chromosomal organization that does not fully obliterate a global
conservation of ORF organization (Horimoto et al., 2001), and 2) act to retain localized
positioning of ORFS so as to better optimize regulatory expression or protein-protein
interaction (Lathe et al., 2000; Svetic et al., 2004) . A more reﬁned approach to measuring

chromosomal organization so as to inductively characterize probable pathways and

145

 

limitations of recombinative change would involve a more accurate treatment of underlying

factors and dynamics more reﬁned than a negative control of completely shuffled ORFS.

146

 

Chapter 5: Measures of Internal

Physical O-ORF Clustering

5.1 Lagged Autocorrelations of O-ORF Densities

To investigate periodic invariance of O-ORF density, I evaluated lag k autocorrelations
on the series of O-ORF densities (Equation 12). I found a general, 6-dependent, property to
unshufﬂed ORF densities where there appeared to be similarity between neighboring values
on lag k autocorrelation series (Fig. 57a, 57c, 57e). This property of similarity between
neighboring rk values contrasted with what I observed for lag k autocorrelation series
computed from shufﬂed series of ORF densities. Fig. 57b, 57d, 57f present extreme cases of
neighboring dissimilarities along lag k autocorrelation series calculated from shufﬂings of
ORF densities. Similarity between neighboring Tk and Tk + 1 values generally occurred
within the range of -—0.2 < Tk < 0.2 and did not rely on the ﬁrst neighbor r1 autocorrelation
value to be greater than 0.3. This weak smoothness property appeared limited to 6 values
ranging from 20 kb to 80 kb. While the weak smoothness property involving rk m We + 1 and
—0.2 < rk < 0.2 may be evidence against both a purely random distribution of O-ORF
densities and strong periodic effects related to O-ORF organization, it may also evidence for
a third hypothesis where O-ORF densities form localized variances or shapes that are
non-random and interdependent with other regions on the chromosome. To better assess the
potential for such a hypothesis, I sought to further model and characterize by approximation
the observed non—random smoothness on the lag k autocorrelation series. Elucidating a
possible, underlying rule-based system associated with ORF densities is a prerequisite for
hypothesis-driven testing.

I postulate that the smoother series of rk values in Fig. 57a, 57c, and 57e is an effect of
similarly-sized expansions e that act to make a Tk autocorrelation value similar to a rk + 1
autocorrelation value based on a segmentation size 6 where e z 6. When e is generally similar
to 6, I describe this as a scenario of constrained sizes of expansion that do not perturb

segmentation-based symmetries of chromosomal organization. A more asymmetric variability

147

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 57: Lag k autocorrelation values calculated on ORF density series built with segmenta-
tion Size 6 = 40 kb. k starts at 1. The right column (b, d, f) represents 7‘ values corresponding
to shufﬂed density series. The left column (a, c, e) is for the non-shuffled density series. (a,b)
Bacillus subtilis. (c,d) Vibrio cholerae (large chromosome). (e,f) Pyrococcus furiosus.

148

to O-ORF densities would correspond to 6 values where e —- 6 7e 0, potentially resulting in

larger differences between rk and rk + 1 autocorrelation values.

5.2 Scalar Residue Measures

5.2.1 Sum of Squared Differences on Lagged Autocorrelation

Series

To non-parametrically measure the degree of symmetry for various segmentation sizes 6,
the Q(Ci, 6) symmetry score is based on a bootstrap comparison of sum of squared differences
on the rk series for shufﬂed and unshufﬂed versions of an O—ORF density series F (Equation
13). The ﬁrst-neighbor autocorrelation value TI is not included in the Q scoring. High values
in the Q series correspond to reduced squared differences between 7k and Tk + 1, generally
implying a higher degree of symmetry where Tk z rk + 1 for the given segmentation size 6.
Fig. 58 shows the Q-based series of values for two groups of related genomes where the main
chromosome Ci for each genome is evaluated to produce the series
Q(ci,6 = 10 kb),Q(cz-,6 = 20 kb),Q(cz-,6 = 30 kb), ...,Q(c2-,6 = 150 kb). Genus-based
relatedness is apparent for both Sulfolobus and Mycobacterium when compared to the distant

relations shown in Fig. 58c and 58f respectively.

149

 

 

 

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150

My postulate is that the Q scoring of symmetry indicates symmetry-conserving
expansions where 6 z e and rk z Tk + 1. Yet, there may be the effect of Tk z rk + 1 z 0, in
which case there is minimal signal with which to assert that 6 = 6. Yet, if
Tk 2 We + 1 z rk + 2, I hypothesize that regions on a Q(cz-, 61-) series would more powerfully
imply an e constrait of symmetry-conserving expansions if a harmonic were observed where
Q(cz-,6) z Q(cz-,j x 6) where j is an integer.

Based on my postulate that a measure of the internal physical clustering of ORFS would
show some characteristic of vertical ancestry (Section 1.5), I expect signiﬁcant instances of
heritability to be associated with a measure of segmentation-based symmetries among O-ORF
densities. To investigate pairwise comparisons of chromosomal organization as characterizaed
by the Q(cz-, 6) scorings of symmetry for 6—based values, I evaluated the cross-correlation
between pairs of Q-based scoring series among sets of related chromosomes (Table 18). For
each set of three chromosomes evaluated in each row of Table 18, the ﬁrst column of Table 18
shows the cross-correlation between the two most closely related chromosomes. For the 3
archaeal sets, the cross-correlation identiﬁes the most closely related chromosomes. Yet, of
the two most closely related chromosomes from the bacterial sets of comparisons, only the
strains of Mycobacterium tuberculosis correlate together, and the r = 0.33 value is weak.

To broadly assay intrachromosomal symmetries of O-ORF density across multiple phyla,
I constructed three series of values by chaining together the Q series of three sets of
chromosomes (01,02, C3) where the Q series were based on 6 = 10, 20, 30, ..., 150 kb. Based
on abbreviations listed in Table 2, the three sets of chromosomes were: C1 = (Py.aby.,
Mt.acet., Sulf.solf., tb1551, Nostoc, S.pyog., M.gen., R.pro., and Xn.cmp.}; C2 = (Py.hor.,
Mt.maz., Sulf.tok., th37Rv, Synec., Str.pnm., M.pnm., R.con., and Xn.axon.}; and C3 =
{Py.fur., Arch.ful., A.pnx., Cor.glut., Th.elon., Lac.lact., M.pulm., Caul.cre., and X.fas.}. In
this particular analysis, my measurement of dependence between Q(cz-, 6) and Q(ci, 6 + a) is
limited to a = 10 kb. I measured the ﬁrst neighbor autocorrelation 1'1 and also average
mutual information values for lags of 1, 2, 3, 4, 5, 6, and 7 on each of the 3 constructed series
(Table 19).

Based on Table 19, a putative result to the analysis is that lag 1 or lag 2 measures of

average mutual information are generally higher than the lag 3-7 measures of average mutual

151

 

Table 18: Cross-correlations 1‘ among sets of three chromosomes (c1,c2,c3) between se—
ries of Q(cz-,6) values for segmentation-based symmetries of O-ORF densities where 6 =
10, 20, 30, ..., 150 kb.a

 

 

Closest Pair Closest & Closest &
r Distant Ancestor r Distant Ancestor r
Py.aby+Py.hor. 0.37 Py.aby. +Py. fur. 0.017 Py. hor. +Py. fur. 0.17

Mt.acet.+l\lt.maz. 0.33 Mt.acet.+Arch.fu1. 0.11 Mt.maz.+Arch.ful. -0.35
Sulf.solf.+Su1f.tok. 0.78 Sulf.solf.+A.pnx. 0.36 Sulf.tok.+A.pnx. 0.32
tb1551+th37Rv 0.33 tb1551+Cor.glut. -0.11 th37Rv+Cor.glut. 0.075
Nostoc+Synec. -0.28 Nostoc+Th.elon. -0. 16 Synec. +Th.elon. -0.39

S.pyog.+Str.pnm. 0.069 S.pyog.+Lac.lact. -0.23 Str.pnm.+Lac.lact. 0.37

l\r‘I.gen.+M.pnm. 0.15 l\"I.gen.+l\'I.pulm. -0.028 M.pnm.+M.pulm. ~0.32
R.pro.+R.con. -0.20 R.pro.+Caul.cre. 0.14 R.con.+Caul.cre. -0.26
Xn.cmp.+Xn.axon. -0.50 Xn.cmp.+X.fas. -0.10 Xn.axon.+X.fas. 0.31

 

3The two most closely related chromosomes are c, and c2.

Table 19: Average mutual information of lagged series for Q(C2',(§) values of the symmetry
score where segmentation size 6 = 10, 20, 30, ..., 150 kb.

 

Average Mutual Information

 

 

Series r1 lag 1 lag 2 lag 3 lag 4 lag 5 lag 6 lag 7
Cl 0.49 0.66 0.54 0.46 0.44 0.48 0.55 0.49
C2 0.24 0.50 0.52 0.49 0.49 0.44 0.50 0.47
C3 0.20 0.59 0.55 0.50 0.53 0.52 0.54 0.52

 

152

 

information.

5.2.2 Frequency of Changes in Angular Variation on the O-ORF

Density Series

To further verify the aspect of segmentation-based symmetries implicating an underlying
expansionary characteristic of e = 6, I hypothesize that a similar analysis based on angular
change on the pseudophase-spaced series P(Ci, 6) should demonstrate predictable information
between P(cz-, 6) and P(cz-, 6 + a) where a. = 10 kb. The P(ci,6) scoring is based on a
comparison between angular frequency histograms D(F) for shufﬂed and unshufﬁed versions
of a pseudophased O—ORF density series F (Equations 14-16). High values of P(cZ-, 6)
indicate non-random angular relationships based on a Kolmogorov-Smirnov comparison with
a shuffled F series. Fig. 59 shows the P-based series of values for two groups of related
genomes where the main chromosome cz- for each genome is evaluated to produce the series
P(c2-,6 = 10 kb), P(ci. 6 = 20 kb), P(cz-,6 = 30 kb), ...,P(c2-,6 = 150 kb). Putative,
genus-based relatedness is apparent for both Sulfolobus and Mycobacterium compared to
distant relations shown in Fig. 59c and 59f respectively. The non-randomness of
pseudophased angular change appears to rise with increasing values of 6, and this may be an
artiﬁcial measurement effect due to the less densely populated histograms of angular

frequencies based on fewer densities being generated by larger segmentation sizes.

153

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154

Table 20: Average mutual information of lagged series for P(ci, 6) values of symmetric shape
for segmentation sizes 6 = 10, 20, 30, ..., 150 kb.

 

Average Mutual Information

 

 

Series r1 lag 1 lag 2 lag 3 lag 4 lag 5 lag 6 lag 7
1 0.70 0.87 0.71 0.70 0.65 0.55 0.53 0.52
2 0.66 1.1 0.96 0.95 0.87 0.79 0.80 0.82
3 0.53 0.74 0.85 0.77 0.78 0.70 0.73 0.64

 

Based on Table 20, and consistent with Table 19, a putative aspect to the analysis is
that lag 1 or lag 2 measures of average mutual information are generally higher than the lag
3-7 measures of average mutual information. The upwards rise in values characterized by Fig.

59 likely accounts for the high n values in Table 20.

5.2.3 Taxonomic Correspondence

While there were some trends evident from the P and Q measures of O-ORF clustering
for 6 = 10, 20, 30, ..., 150 kb, the chaining together of unrelated chromosomes for Tables 19
and 20 does not allow for an inspection of phylogenetic differences between related organisms.
Also, while there was some correlation between the Q measure of segmentation-based
symmetries that may relate to phylogeny (Table 18), there was only a minor degree of
correlative pattern observed for bacterial chromosomes. To conduct a more detailed analysis,
I calculated the Q scoring of O-ORF density symmetries for 6 = 500, 1, 000, 1, 500, ..., 150, 000
bp. Fig. 60—62 contrasts the O-ORF density symmetry scores for a pair of two more closely
related chromosomes (leftmost columns) with a third more distantly related chromosome
(rightmost column). Compared to the low cross-correlation coefﬁcients for bacterial
comparisons in Table 18, there is a putative similarity that can be more strikingly observed
based on the more detailed examination of segmentation sizes,
(5 = 500, 1, 000, 1, 500, ..., 150, 000 bp, as shown in Fig. 61-62. FOr instance, in Fig. 61, the two
strains of Mycobacterium tuberculosis appear dramatically different than their distant relation
in the Actinobacteria, Corynebacterium glutamicum (928 Ma). A notable exception however
is for the Xanthomonadaceae set of strains in Fig. 62 where X anthomonas campestris shows

more similarity to Xylella fastidiosa than to X anthomonas axonopodis. Yet, the various peaks

155

and troughs associated with speciﬁc 52' segmentation sizes in Fig. 6062 do not perfectly align
from one chromosome to another and, despite the visual strong trend of consistency with
taxonomy, the 6-based values did not generally produce signiﬁcant correlative measures
between related chromosomes. Moreover, I did not ﬁnd a simple smoothing algorithm that

would work to generalize the outlying patterns of peaks and troughs.

5.3 Simulation of Informational Change

5.3.1 Development and Characterization of Simulation Model

My hypothesis is that regions on a Q(c2-, 6]) series can imply an e constrait of
symmetry-conserving expansions. The diagnostic invariance of this symmetry-conserving
expansion would be such that 6 z e and Q(cz', 6) z Q(cz-, 6 + e). I sought to develop a model
of simulated chromosomal expansions and modiﬁcations in order to evaluate if Q(cz-, 6)
symmetry scores of the simulation model output meaningful relate, as proposed, to
constant-sized expansions. The hypothesized relationship of a harmonic association with 6
implies that a measure to characterize the amplitudes of the harmonic (e.g., moduli of the
fast Fourier transform) should be able to characterize e.

Chromosome simulations were conducted as described in Section 2.7 across various
parameters, 5', N, and T. The relative stochastic level of occurrence between tandem
duplicating expansions and translocating modiﬁcations ranged, as a parameter, from 0.3 to
0.7 (S/ 10). The parameter, N , is deﬁned as the number of consecutively stringed octets a:
where x = ABCDEFGH, y = N, and my is the starting symbolic sequence. For the running
of each simulation trial, N ranged from 2 to 5 and the size of tandem duplications, T, ranged
from 3 to 12. A set of examples that helps illustrate the behavior of these parameters is
shown in Fig. 63. Segment size and counting was a function of consecutive subsequences of a
given length (i.e., segment size or “window” size on the output, simulation-based symbolic
sequence), and the number of “H” letters observed in the consecutively windowed

subsequences (i.e., a count).

156

Symmetry Score

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Figure 60: Q-based symmetry scores of O—ORF densities on 9 archaeal chromosomes. Each
row corresponds to a set of phylogenetically related strains. The ﬁrst two columns represent
the chromosomes with the most recent common ancestor in comparison to the third column.
Abbreviated strain names are deﬁned in Table 2. The Q(cz-, 6) measure is described in Sections

2.8.3 and 2.8.4.

157

Symmetry Score

Figure 61: Q-based symmetry scores of O-ORF densities on the chromosomes of 3 Actinobacte-
ria, 3 Cyanobacteria, and 3 Lactobacillales. Each row corresponds to a set of phylogenetically
related strains. The ﬁrst two columns represent the chromosomes with the most recent com-
mon ancestor in comparison to the third column. Abbreviated strain names are deﬁned in

-1

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Table 2. The Q(cz-, 6) measure is described in Sections 2.8.3 and 2.8.4.

158

 

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Segmentation Size

Figure 62: Q-based symmetry scores of O-ORF densities on the chromosomes of 3 Mollicutes
and 6 Proteobacteria. Each row corresponds to a set of phylogenetically related strains. The
ﬁrst two columns represent the chromosomes with the most recent common ancestor in com-
parison to the third column. Abbreviated strain names are deﬁned in Table 2. The Q(c,-,6)
measure is described in Sections 2.8.3 and 2.8.4.

159

 

 

Original Starting Sequence (the "N" parameter)

N = 1, ABCDEFGH
N = 2, ABCDEFGHABCDEFGH
N = 3, ABCDEFGHABCDEFGHABCDEFGH

Size of Tandem Duplications (the "T" parameter)

 

T = 5
ABCDEFGHABCDEFGH starting sequence
ABCDE / FGHAB I CDEFGH a window of 5 characters is randomly selected

ABCDE / FGHAB + FGHAB / CDEFGH this window is tandemly duplicated

T = 3
ABCDEFGHABCDEFGH starting sequence
A / BCD / EFGHABCDEFGH a window of 3 characters is randomly selected
A / BCD + BCD / EFGHABCDEFGH this window is tandemly duplicated

A "Translocation"

ABCDEFGHABCHABCDEFGHAB requires three "HA " subsequences
ABCDEFG / HA / BC / HA / BCDEFGHAB select a pair of 2 "HA " subsequences
ABCDEFGHABCDEFGHA / BC IB and move window to a 3rd "HA " subsequence

(at the end, an "HA " subsequence is lost)

The chance of a tandem duplication event occurring
versus a translocation event being attempted is a
constant stochastic deﬁned by the parameter S/ 10.

 

 

 

Figure 63: Examples of the abstract simulation for structural duplications and translocations
on a symbolic sequence.

160

 

5.3.2 Scalar and Spectral Measures of Model Output

Visual examples of symmetry scoring of simulation-produced symbolic output are shown
in Fig. 64 - 65. There was some correspondence between symmetry measures for similar, yet
non-identical, parameters of S, N, and T as shown in Fig. 66 - 68. The ordinate scale on the
simulation-based plots may not directly equate in meaning to the ordinate scale of the
Q—based symmetry measures shown in Fig. 58 and Fig. 6062, yet the ranges are comparable
when T is low (T = 3) and N is of an intermediate value (N = 3 or N = 5). An effect of a
small T parameter and high N parameter was to reduce the presence of low (< —10)
symmetry scores from measurements of small segment sizes. Visually, the T parameter
appeared to correspond to a periodicity of the symmetry scoring. S did not have a dramatic
impact on the symmetry scores.

Fig. 66 and 67 show how a spectral assessment with the fast Fourier transform (F FT) on
the Q series of symmetry scores may help reveal the underlying parameters to the simulation.
As T changes (Fig. 66), the moduli of the F FT series form peaks at locations corresponding
approximately to 30 / (T-l). To illustrate this relationship, a tandem duplication parameter of
6 would potentially result in repetitious measures of density for every 6 characters on the
simulated output sequence of characters. The Q series may preferentially measure this effect
for segment sizes of 6, 12, 18, 24, and 30 as might be inferred from the behavior of plots in
Fig. 64 - 65. This succession of preferential segment sizes (6, 12, 18, 24, and 30) corresponds
to a periodicity of 4 on a series from 1 to 30. Fig. 67 shows the visual effect on the FFT
modulus series for altering S and N parameters of the underlying simulation model and a
mathematical relationship between the structure of the FFT modulus series (Mod(fft(Q))
compared to the S and N parameters is not readily apparent.

As S, N, or T is offset by 1, Fig. 68 shows the degree to which the Q and
Mod(fft(Q))-based distributions are altered. Adjusting any simulation parameter by 1 does
not radically alter the Q series distributions (Fig. 68a — 68c) and, for alterations of S and N,
the Mod(fft(Q)-based distributions (Fig. 68d - 68e). Similarity between distributions is
signiﬁcantly lost for the Mod(fft(Q))-based distributions when T is altered, even by a single
increment (Fig. 68f). The Mod(fft(Q))-based assay, in this sense, demonstrates increased

sensitivity to relatively small changes in the size of tandemly duplicating expansions.

161

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 64: Scorings of segmentation-based symmetries for simulations of informational ex-
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162

     

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 65: Scorings of segmentation-based symmetries for simulations of informational ex-
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5.4 Investigating Phylogeny

Calibration was for a symmetric scoring based on 51 segmentation size values (25,000
bp), and the window for which 4 Streptococcus pyogenes chromosomes had the greatest
pairwise difference in their characteristic ranges of Q symmetry scores (see Fig. 69). The
rationale for this calibrating approach was to approximate the detection of divergence against
a lineage with known organizationally divergent properties at the subspecies level. A window
size of 25 kb approximates the general ﬂuctation of high and low symmetry scores observable
in Fig. 58 and 59, and putatively evident from the lagged average mutual information
analyses in Tables 19 and 20.

The ﬁrst spectral modulus from the 51-value window was used to characterize the range
of Q symmetry scores, and was termed the windowed asymmetric deviation. The highest
differences of windowed asymmetric deviations among S. pyogenes strains were the 75th
segmentation size, 37,500 bp, to the 125th segmentation size, 62,500 bp.

There were 24 sets of closely related species. The distribution of closely related species’
pairwise differences of windowed asymmetric deviation for 37.5 kb to 62.5 kb is shown in Fig.
70.

Fig. 71 shows the relationship of time of divergence from a last common ancestor to
differences in chromosomal structure and organization. I did not ﬁnd direct cross-correlations
between the individual measures of chromosomal structure and organization: chromosome
size, windowed asymmetric variation, and average pointwise mutual information, so the
covariance of these multiplied measures with times of divergence has added signiﬁcance. The
alphabetic letters in Fig. 71 correspond to pairwise comparisons among sets of three
chromosomes (the identity of which are described in Table 5). While linear correlations were
signiﬁcant (0.66 S r S 0.87), the “I” and “E” sets of chromosomes (Xanthomonadaceae and
Cyanobacteria) were conﬂicting in their relationship of difference in chromosomal structure
and organization to the estimated time of divergence from a last common ancestor.
Incidentally, similar to the analysis in Fig. 69, the highest correlations for the relationship of
difference in chromosomal structure and organization to the estimated time of divergence
from a last common ancestor occurred for windowed asymmetric deviations for the range of

segmentation sizes 6 = 37.5 kb to 62.5 kb.

167

 

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20
l

25 kb Sampling Window Start Point

Figure 69: Differences of windowed asymmetric deviations between S. pyogenes strains based
on a 25 kb window of segmentation sizes. For the 4 strains evaluated, there were 6 pairwise
comparisons. The start point for each 25 kb window is the abscissa value.

 

Frequency

 

10 15 20 25 30
l

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l

 

 

 

 

 

 

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Figure 70: Frequency of differences between windowed asymmetric deviations among closely
related strains of the same species. Bin size is 1. As expected, the higher, outlying windowed
asymmetric deviation values correspond to comparisons among S. pyogenes strains.

168

Fig. 72 shows the relationship of the windowed asymmetric variation to IS element
density. The highest correlation value relates to a ﬁrst modulus sampling window on the Q
series of 6 = 39,000 bp, 39,500 bp, 40,000 bp, ..., 64,000 bp. I did not ﬁnd signiﬁcant
correlation values (1‘ > 0.3) with IS element density for comparative measures of average

pointwise mutual information or for chromosome size.

169

(a) (b)

 

 

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Figure 71: Relationship of divergence time from a last common ancestor to differences in
chromosomal structure and organization. The windowed asymmetric deviation is based on a
characteristic range of residual summed squared differences on lag k correlation series calculated
from ORF densities 37,500 bp, 38,000 bp, ..., 62,500 bp. The letters correspond to comparisons
from Table 5. The letter with the smaller x coordinate value is the ﬁrst column comparison
of Table 5. The letter with the higher x coordinate value is the average of the second and
third column comparisons. (a) Absolute difference in windowed asymmetric deviation for
various times of divergence, m = 3.86,r = 0.66. (b) Product of the absolute differences in
chromosome size and windowed asymmetric deviation for various times of divergence, m =
11.6,r = 0.77. (c) Absolute difference in windowed asymmetric deviation divided by the
average pointwise mutual information for 40 kb (I [40]), m = 2.47,r = 0.72. (d) Product of
the absolute differences in chromosome size and windowed asymmetric deviation divided by
[[40], m = 5.54, r = 0.87.

170

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171

5.5 Discussion

There are a wide variety of approaches for quantifying how a measured complexity of
pattern may relate to underlying dynamics (Falconer, 1997; Casdagli et al., 1991; Stearns &
Magwene, 2003). My ﬁnal measure of a windowed asymmetric deviation may represent an
advancement beyond a cross-species or cross-strain interchromosomal correlation of gene
locations (Horimoto et al., 2001) in that the windowed asymmetric deviation is an
intrachromosomal residual value for comparison that may more directly implicate underlying
functional optima and mechanistic possibilities for change relating to the clustering of ORFs.
The symmetry scoring measure Q(cz-, 6) upon which the windowed asymmetric deviation is
based is the result of a fairly sophisticated algorithm that adds together the squared
differences along a lag k autocorrelation series and, by bootstrap, contrasts the outcome for
natural, unshufﬁed chromosomes versus artiﬁcially shuffled chromosomes. My Q(ci. 6)
measure did not emerge through a clear axiomatic procession of analysis upon a
well-parameterized model with pre-established properties, but more closely follows an
inductive measurement process (Goldfarb & Deshpande, 1997). The Q measure is based on a
bootstrapped contrast between sums of squared differences, and, in this sense, departs from
more conventional approaches involving means of squared differences. By directly measuring
the absolute difference of E (F) values with shuffling-based E (X ,-) values (Equation 13) prior
to any averaging, more of the residual structure may be evaluated separate from any
assumption of an interval-strength measurement property (Sarle, 1995) attributed to the
E (F) function. This is especially important based on the reported incidence of symmetries in
the spatial clustering of gene density being potentially attributable to the skewed frequency
distribution of gene densities, and not necessarily a consequence of non-shuffled chromosomal
organization (Jurka & Savageau, 1985).

The initial point of empirically based induction involved observations of the lag 1: series.
I developed two measures, Q(c,-, 6) and P(cz-, 6), to further quantify the observed invariance
where the intent for each of these measures was to independently quantify non-random effects
associated with localized variance on the series of ORF densities as opposed to directly
correlative assays of density magnitudes involving a deﬁned zero point. Both the Q(cz-, (5) and

P(cz-, 6) measures are based on approaches frequently used in time series analyses that may

172

be further developed to characterize an underlying temporal nature to the formation of ORF
clustering. The pseudophase space analysis of the P(cz-, 6) measure was based on an
embedding dimension of two. A more reﬁned approach to assaying invariance on a phase
space would select an embedding dimension sufﬁcient to accurately characterize nearest
neighbors on the dimensional projection (Kennel et al., 1992).

The model usage of my symmetry scoring measure Q(c,-, 6) was to help quantify the
constraint of chromosomal expansions for a segmentation size 6. I hypothesized a harmonic
relationship where consecutive chromosomal expansions of 6 would implicate chromosomal
expansions of 6 x j where j is an integer. If the symmetry scoring measure Q(c,~, 6) relates to
the likelihood of chromosomal expansion occurring for a given 6, then a reasonable
expectation would be for a harmonic effect where Q(ci, 6) z Q(ci, 6 x j). The simulation that
I constructed was a meaningful indicator as to the effectiveness of evaluating a harmonic
pattern on the Q series in order to infer underyling sizes of organizational expansion. The
windowed asymmetric deviation captures a one wave harmonic to characterize rising and
falling from high symmetry scores to low symmetry scores.

The ﬁnal set of r > 0.6 values in Fig. 71 demonstrates a relationship between structural
and organizational features of compared chromosomes versus time of divergence from a last
common ancestor. The windowed asymmetric deviation did not correlate with other
measures of chromosomal structure and organization such as chromosome size and average
pointwise mutual information. The windowed asymmetric deviation did correlate with time
of divergence from a last common ancestor, both by itself and as a jointly considered
indicator along with measured differences of chromosome size and average pointwise mutual
information. The advancement in methodology represented by the windowed asymmetric
deviation presents a novel capability to predict a time of divergence from a last common
ancestor independent from analyses of speciﬁc conserved sequences. The only sequence
analysis necessary to arrive at the windowed asymmetric deviation is to specify the locations
of O-ORF translational start points as they occur on a given chromosomal sequence. My
novel development of the windowed asymmetric deviation measure may be important to the
objectives of a polyphasic taxonomy (Stackebrandt, 2002). Recombinations may

conventionally be associated with transitions of evolutionary mode as evident from studies of

173

genomic plasticity (Romero & Palacios, 1997; Aras et al., 2003; Fuller, 2003; Terzaghi &
O’Hara, 1990), as well as the increasingly clear relationship between genome size, genomic
instability and lifestyle adaptation (Ochman & Davalos, 2006; Moran & Plague, 2004). The
strong trends of chromosome structure and organization for times of divergence in Fig. 71
may contrastingly implicate a fair degree of vertical ancestry possibly aligned with theoretical
notions of an evolutionary tempo (Woese, 1987). A direct evaluation of functional
conservation would be based on empirical data concerning viable and non-viable
reorganizations of the chromosome. An assessment of functional conservation across multiple
prokaryotic phyla would likely focus on common molecular factors of chromosome structure.
A characterization of chromosomal organization in terms of physical base pair locations, as
performed in this study, may aid in the objective evaluation of structure separate from
lineage-speciﬁc distributions of other chromosomal features.

While an inductive measurement process per se is not hypothesis driven, the correlative
ﬁndings suggest that the stability of chromosomal structure and organization can be
characterized over long periods of time. Throughout my analyses, I tried to apply my various
measures of chromosomal organization to various evolutionary trait software packages (Pagel,
1994; Huelsenbeck et al., 2001; Ronquist & Huelsenbeck, 2003). Even by relaxing various
assumptions, I had difﬁculty with producing a hierarchy manifesting consensus with current
taxonomy. My sample size may be too small or the various measures of chromosomal
organization may not yet fully characterize the heritable aspects of the complex
recombinational system. Based on the sample of fully sequenced genomes, the most powerful
and focused analyses would be for well-represented taxons such as the Proteobacteria and the
Firmicutes. An effort for identifying possible metabolic and ecological factors associated with
recombinative change, and organisms that transition between differing degrees of genomic
stability, may be necessary to more meaningfully characterize branch points of divergence
from common ancestors. The optimal relocationing of ORFS may require empirically-driven
analyses for effects associated with physical supercoiling and expression (Deng et al., 2005),
and optimal expression levels for growth and ﬁtness within the environment (Dekel & Alon,
2006).

The signiﬁcance to my measures of chromosomal organization may exceed that of simple

174

correlation with mobile elements and times of divergence spanning billions of years of
evolution. It is unexpected by chance for mobile elements and assessments of vertical
ancestry to both implicate windows almost exactly the same (about 37,500 bp - 62,500 bp).
The repeated implication of high average pointwise mutual information (APMI) for
segmentation sizes surrounding 6 = 40 kb in Chapter 3 is also generally consistent with the
37,500 bp - 62,500 bp window. The product of differences between the inverse APMI for 40
kb, chromsome size, and windowed asymmetric deviation act to increase correlation with a
time of divergence from a last common ancestor, and this may constitute evidence for
phylogenetic covariance of these structural and organizational properties.

For the various stages of the approximated model of organizational change to the
chromosome, there remain a variety of further empirically-driven treatments and efforts at
mathematical modelling that may more rigorously investigate speciﬁc molecular pathways of
change. The present informational analysis can also be extended by further development of
the abstract, simpliﬁed system of symbolic translocations and duplications. Presently, for
smaller values of the simulation model parameter T (i.e., 3 and 4), the Q symmetry score of
the simulated organization is more closely comparable to a natural chromosome based on an
ordinate range appearing to be predominantly between —1.0 and +1.0. Additional analysis
would be required to further ascertain meaningful correspondences between abstract,
simulated representations of chromosomal content and symmetry, and aspects of information
and noise inside natural chromosomes. A principal question may be to separately account for
how any large-scale periodicity to chromosomal organization relates to duplication of large

segments of the chromosome versus a relationship with nucleoid superstructure (Koonin

et al., 1996).

175

Chapter 6: Summary and Conclusion

Hypotheses concerning ORF composition and organization of prokaryotic chromosomes
were evaluated. Based on prior characterizations of coding content (Jackson et al., 2002;
Tatusov et al., 2003; Skovgaard ct al., 2001), this study evaluated the hypothesis that 75% of
annotated ORFS legitimately encode operational ORFS. This study also proposed and
addressed several hypotheses concerning the symmetrical or asymmetrical nature of ORF
clustering along prokaryotic chromosomes. The postulated outcome for a symmetrical
pattern of ORF clustering was correspondence with vertical ancestry and the effects of
mobile elements on detection of organization attributable to vertical ancestry. The ﬁndings of
this study correlate well with the postulated 75% subset of ORFS that likely have phenotypic
activity. In terms of a pattern of non-random clustering across 165 prokaryotic chromosomes,
the organization of the operational ORFS was generally non-random in relationship to the
contrasting 25% subset of non-operational ORFS. A segmentation analysis of ORF density
was conducted where ORFS were counted, based on the locations of their translational start
points, within consecutive segments for a given, physical segmentation length in base pairs.
For most chromosomes and segmentation sizes, a signiﬁcant periodic symmetry was not
observed on the series of ORF density values. Yet, a pattern of similarity between
neighboring lag k autocorrelation values (r k and rk + 1) was evident where the correlation
coefﬁcients occurred within the range of —0.2 < rk < 0.2. The weak pattern between rk and
Tk + 1 was hypothetically attributable to segmentary expansions that resulted in more
equalized rk and rk + 1 values. Development of a model to simulate organizational
expansions and modiﬁcations supported the efficacy of a proposed, hypothetical, harmonic
signal measure to detect constraints on segmentary expansion. When ﬁrst calibrated to a set
of Streptococcus pyogenes strains, the harmonic signal successfully correlated with postulated
outcomes for lengthy time periods of vertical divergence and the presence of mobile elements.

In the context of a dynamic analysis (Fig. 1), an avenue was explored in Chapter 4
where subpopulations of putatively “noisy” ORFS, likely not to contribute to phenotype,
were identiﬁed by a basic, heuristic approach that was not lineage-speciﬁc. Although the

ranges of protein lengths for an operational ORF subset (O-ORFs) and a putatively silent

176

ORF subset (S-ORFs) were overlapping, trends of non-normality associated with a
fragmentation model of protein structure robustly supported a subset distinction of the
annotated ORF set across different phyletic groupings. Across the set of 67 chromosomes for
which ORFS were assigned to COGS (C-ORFs), the percentage composition of each
annotated set of ORFS was analyzed. The annotated set of ORFS for each chromosome
generally (7‘2 > 0.9) consisted of a 72% subset of O-ORFs and a 73% subset of C-ORFs. The
O-ORF and C-ORF subsets were not identical and, overall, 9% O-ORFs were did not belong
to a COG. Functional, phenotypic, and transcriptional assays resulted in greater empirical
support for the O-ORF subset to be operational compared to the C-ORF subset. Examining
the underlying nature of annotated ORFS (the principal objects of evaluation) (Chapter 4)
was an essential step to take prior to the reconstruction of recombinative and evolutionary
dynamics attributable to ORF clustering in Chapter 5. I did not ﬁnd many of the invariant
characteristics of organization observed for O-ORFs to be present for either the total set of
ORFS or for randomly selected subsets of ORFS.

The correlative ﬁndings of this study for O-ORF organization establish an initial
measure for relating differences of chromosomal size and intrachromosomal organization to
times of divergence from last common ancestors. Future advancements might jointly estimate
times of divergence by a measure constructed with both 168 rRN A sequence analysis along
with differences in chromosome size and intrachromosomal organization. Conservation of
ORF organization appears to be global across a chromosome and conserved across diverse
lineages despite substantially localized disruptions (Horimoto et al., 2001).

Proposed functional barriers of conservation against recombinative change have been
supercoiling, replichore balancing, and cotranscriptional effects (Mahan et al., 1990). The
relationship of physicochemical chromosomal topology to genomic arrangement is becoming a
closely examined phenomenon where the supercoiling structure of the chromosome associates
with processes of transcription and gene expression (Deng et al., 2005). Estimates of physical
lengths associated with supercoiling domains range from 10 kb to 100 kb (Postow et al.,
2004; Miller & Simons, 1993). By contrast, analyses in this study implicate narrower ranges
of 40 kb or 37.5-62.5 kb as the physical ranges of segmentation sizes associated with

conserved ORF organization. While the dot matrix plots of Fig. 25-33 implicate mobility of

177

chromosomal segments greater than 10 kb, there also appear to be individual, potentially
orthologous ORFS that are distributed away from the main diagonal of conserved ORF
organization. There is also a lack of signiﬁcant periodic signal for long distances along the
chromosome (Fig. 57). Overall, the evidence suggests that supercoiling domains do not
deﬁne rigorous boundaries of ORF clustering, and this may be consistent with recent claims
that the supercoiling structure is dynamic and does not represent a ﬁxed scaffold (Deng

et al., 2005). A further informational study beyond conventional dot matrices and my own
scalar measures of ORF symmetry may evaluate additional features such as the origin of
replication for the chromosome, and the directions of transcription for each ORF. The
transcriptional orientation of an ORF speciﬁc to one of the two intertwined chromosomal
strands is a strongly conserved aspect of chromosomal organization, and results from my
running tally method stand in direct contrast to a recent report that a signiﬁcant association
of transcriptional directions with replication does not occur for Vibrio cholerae and Yersz'nz'a
pestis (Briiggemann et al., 2003). Other types of information spanning the length of
chromosomes may also be potentially evaluated; Hallin & Ussery (2004) present an online
“genome atlas” where aspects such as intrinsic curvature, stacking energy, position
preference, direct repeats, inverted repeats, GC skew, and percent AT are charted in
concentric fashion around demarcations of ORFS. A major future objective will be to test the
emergent hypotheses from informational analyses of chromosomal structure for
correspondence with how lethality (Mahan et al., 1990) and diversiﬁcation (Vulic et al., 1999)
result from alterations to ORF organization.

Beyond the scope of visual atlases, comparative studies of closely related strains, and
anecdotal reviews of genomic diversity, a challenge that this study sought to address was the
development of a quantitative data analysis that could be efﬁciently applied to the growing
set of fully sequenced prokaryotic genomes (Fig. 13). The rapid, ongoing increase of genomic
data is a strong basis for advocating that informational analyses aid in the gathering and
processing of observations. The ﬁnal ﬁnding in my study was for an approximated
characteristic of chromosomal organization that correlated well with vertical conservation
and mobile elements, and more precise characterizations will be likely possible in the future

with the greater amount of analytical power provided by a. larger data set.

178

A genome presents not just an extant view of an organism, but may also encode an
archaeology corresponding to previous states of adaptation or ancestry. In this study,
simulation was used to verify some of the properties associated with calculated, residual
values of ORF organization, and a sophisticated treatment based around measuring residual
signal led to characterizing prokaryotic diversity to a degree that would not be expected to
occur by chance. The properties of both natural and simulated variation provide evidence
that the developed measures of ORF organization are not due to artifacts of observational
noise or estimation error, and may represent interpretable signatures of past recombinative
change. The degree and utility for chromosomal organization to relate to ancestry and
divergence was signiﬁcantly established, and important questions concerning conservation of
information, evolutionary mode, tempo, and a legitimate polyphasic taxonomy (Zuckerkandl

& Pauling, 1965; Woese, 1987; Stackebrandt, 2002) may now be more addressable.

179

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