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This is to certify that the
dissertation entitled

RELATING STRESS TO STRAIN AT THE
LEVEL OF GENE EXPRESSION

presented by

Stephen Jan Callister

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RELATING STRESS T0 STRAIN AT THE LEVEL OF GENE
EXPRESSION

By

Stephen Jan Callister

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

2004

ABSTRACT
RELATING STRESS To STRAIN AT THE LEVEL OF GENE EXPRESSION
By

Stephen Callister

The stress strain paradigm was investigated at the level of gene
expression for Saccharomyces cerevisiae using tools developed and adapted
from various fields including Ecology, Mathematics, and Engineering. Tools
presented in this dissertation were developed to calculate strain, i.e., an
aggregate measure of gene expression response, and to establish its
relationship to stress, i.e. the perturbation causing the response. Strain for the
Environmental Stress Response in S. cerevisiae was calculated using a Moment
of Area and compared across eight environmental perturbations. Additionally,
relative expression for a set of 169 genes making up the glycolysis, glycerolipid
metabolism, cell cycle, and MAPK signaling biochemical pathways was observed
for a series of applied osmotic stresses representing mild, hyper, and sever
osmotic Shock. To add biological significance to the stress strain paradigm,
stability and its associated aspects such as resistance, which is the ability of a
system to withstand the perturbation, resilience, which is rate at which a system
returns to steady state, and reactivity, which is the rate at which a system departs
from steady state were applied at the elvel of gene expression adding biological
significance to the observed strain. Results showed that with increased

perturbation magnitude a decrease in resilience, reactivity, and resistance

occurred. An overall decrease in stability resulted with increased strain as
measured by the Moment of Area. An exponential relationship between
perturbation magnitude and strain was observed on an individual gene basis,
biochemical pathway basis, and aggregate gene basis. This dissertation presents

the first application of relating stress to strain on a gene level.

Copyright by
Stephen Jan Callister
2004

DEDICATION

To my Father and Mother for instilling in me the desire to comprehend and
achieve beyond my perceived expectations. Also, to Charlene for her patience
and encouragement.

ACKNOWLEDGMENTS

The body of research contained in this dissertation was not possible
without the help and guidance of my advisor Dr. Syed A. Hashsham. It has been
an honor to work with him and I have thoroughly enjoyed observing his scientific
and engineering creativity. His commitment and expressed excitement to this
research has more than once carried me through periods of disappointment, and
his willingness to take the time and give valuable criticism helped keep this
research focused on the objectives.

I also need to express gratitude to my research committee, Dr. Bruce E.
Dale for his flexibility and willingness to not “stand in the way” during the last few
months of this research, Dr. Susan J. Masten for her perspective and realistic
advise, and Dr. James M. Tiedje for his patience in helping an engineer learn and
develop the molecular biology tools necessary for this research.

Mr. Sean M. Spellman gave hours of help with experimental set up and
sampling. RNA extractions were performed with the help of Mr. John J. Parnell.
Instrumentation set up and optimization was not possible without Dr. Annette P.
Thelen of the Genomics Teaching and Support Facility. To these individuals I
express my Sincere gratitude for rolling up your sleeves and jumping in to keep
things moving efficiently.

I need to express my appreciation to my parents, Jan and Jane Callister.
My father is credited for introducing me to and instilling in me the desire to try

and comprehend, at least to a small degree, my surroundings. Whether it was

vi

observing the stratigraphy of the Colorado Plateau, scanning the horizon on top
of Notch Peak, or fossil hunting in the Great Basin Desert he taught me as a boy
to never be afraid to ponder the answers associated with the difficult
interrogatives “How?” and “Why?”. My mother is credited for teaching me that
patience in oneself, hard work, trial and error, and faith are the required
ingredients for accomplishing a difficult task. During the pursuit of this Ph.D. she
continually reminded me of the long term benefits associated with what I was
undertaking, which can often be difficult to discern after the nth experimental
failure.

Finally, I owe the deepest gratitude to my wife, Charlene. She is the only
one, among all that have been mentioned, who has directly taken on the burden
of supporting me in this pursuit while delaying her own educational goals,

maintaining our home, and raising our two daughters. Thank you Charlene!

vii

TABLE OF CONTENTS

LIST OF FIGURES ...........................................................................
LIST OF TABLES .............................................................................

CHAPTER 1: INTRODUCTION
1.1 Background and Significance .....................................................
1.2 Stress, Strain, and Stability ........................................................
1.3 Choice of Monitoring Technology for Strain Quantification ...............
1.4 Choice of the Model Microorganism and Stress .............................
1.5 Objectives ..............................................................................
1.6 Hypotheses ............................................................................

CHAPTER 2: LITERATURE REVIEW
2.1 Pulse and Press Perturbations ...................................................
2.2 Stability and Generalized Expression Response Envelopes .............
2.3 Measures of Stability used in Ecology ..........................................
2.4 The Moment of Area as a Tool to Calculate Strain for the
Generalized Response Envelope ................................................
2.5 Equations used to Calculate the Aggregate Response Envelope .......
2.6 Physiological Response of S. cerevisiae to Osmotic Shock ..............
2.7 Transcriptional Response of S. cerevisiae to Osmotic Shock ............
2.8 Regulation of Specific Transcriptional Respnse to Osmotic Shock .....
2.9 Monitoring of mRNA using Reverse Transcriptase Real-Time PCR....
2.10 Current Analysis Tools for Gene Expression Data ........................

CHAPTER 3: MATERIALS AND METHODS
3.1 Sorting of Gene Expression Data for the ESR ...............................
3.2 Clustering of Relative Gene Expression Data ................................
3.3 Calculation of Strain from the Response Envelope .........................
3.4 Calculation of Strain for Large Data Sets ......................................
3.5 Selection of Genes and Primer Design .........................................
3.6 Experimental Approach for Quantitative Stress-Strain Response ......

CHAPTER 4: RESULTS
4.1 Application of the Moment of Area to Calculate Strain .....................
4.2 Development of Calibration Curves from cDNA Targets ..................
4.3 Growth of S. cerevisiae under the Applied Osmotic Stress ...............
4.4 Reactivity, Resilience, and Resistance in Response to Osmotic
Stress ....................................................................................
4.5 Calculated Strain for the Applied Stresses using the Moment of Area.

viii

X

xiii

1
4
7
9
12
13

17
19
22

24
29
30
32
36
37
41

47
48
48
49
51
53

65
73
76

77
82

CHAPTER 5: DISCUSSION

5.1 Strain as an Aggregate Response of the Transcriptome to Stress...... 89

5.2 Stability Parameters: Resilience, Reactivity, and Resistance ............ 90

5.3 Moment of Area as a Measure of Strain ....................................... 93

5.4 Relationship between Stress and Strain: The Modulus of Stability...... 96
CHAPTER 6: CONCLUSION AND FUTURE PERSPECTIVES

6.1 Conclusions ........................................................................... 99

6.2 Suggested Future Research ...................................................... 101

APPENDIX A: COMMON METRICS USED FOR MEASURING
SIMILARITY (NEARNESS), DISSIMILARITY, AND CONFIDENCE ............ 104

APPENDIX B: MATHCAD PROGRAM USED FOR CALCULATING THE
MOMENT OF AREA FOR LARGE DATA SETS ..................................... 106

APPENDIX C: DESCRIPTION OF GENES GROUPED ACCORDING TO
BIOCHEMICAL PATHWAY USED TO STUDY RELATIVE GENE
EXPRESSION TO OSMOTIC SHOCK .................................................. 110

APPENDIX D: GENES EXHIBITING A SIGNIFICANT INCREASE OR
DECREASE IN EXPRESSION STEPPING FROM 1.0 M TO 1.2 M NACL

BIBLIOGRAPHY .............................................................................. 123

LIST OF FIGURES

Some of the figures in this dissertation are in color.

Figure 2.1. (a) Pulse perturbations in which an instantaneous change either by
addition or removal of an environmental condition occurs followed by a return
to the pre-perturbed condition. Pulse perturbations are a function of
magnitude and duration. (b) Press perturbations in which change in an
environmental condition is maintained. Press perturbations are a function of
magnitude only. ........................................................................... 18

Figure 2.2. Generalized relative expression patterns in response to
environmental perturbation. An induction (a) or repression (b) in transcription
followed by a return to pre-perturbed expression levels. An induction (0) or
repression (d) in transcription followed by an establishment of new relative
expression levels. Patterns (e) and (f) could represent one of the other
expression patterns given a longer time-scale. Pattern (9) represents no
change in relative expression in response to perturbation. .................... 20

Figure 2.3. (a) Relative expression of Saccharomyces cerevisiae exhibiting
asymptotic and neighborhood stability to hyper-osmotic and temperature
perturbations (b) Application of the stability parameters to asymptotic and
neighborhood stability. .................................................................. 23

Figure 2.4. The Moment of Area encompasses the the stability parameters and
is measure of overall stability. Components of the Moment of Area applied to
asymptotic stability are shown. Components include the response envelope,
perturbation axis, moment arm, and center of mass. ........................... 27

Figure 2.5. Symbols applied to the response envelope showing how it
encompasses the stability parameters reactivity, resilience, and resistance.
.................................................................................................. 29

Figure 2.6. Physiological and specific transcriptional responses to osmotic
shock. Upon encountering an osmotic shock cell growth ceases until suitable
glycerol accumulation, triggered by the high osmotic glycerol (HOG) pathway,
allows for growth to resume. ........................................................... 36

Figure 2.7. Graphical representation of different comparison metrics used for
analysis of microarray data. (a) Pearson’s correlation in which the angle
between the mean of the gene expression vectors x and y is used to calculate
Similarity. (b) Pearson’s correlation around zero or often known as the
standard correlation, in which Similarity for the gene expression vectors x and
y is calculated as the angle from zero. (c) Euclidean distance is calculated as
the distance between the expression vectors x and y. .......................... 43

Figure 3.1. Schematic of the MathCadTM program used to calculate the
Moment of Area for large data sets. The program is divided into four sections.
Section one uses linear regression to fit the data to a statistical mode. Section
two calculates the statistics associated with the regression analysis. Section
three finds the components leading to the Moment of Area calculation.
Section four creates an output table containing all of the results. ............ 50

Figure 3.2. Design approach used for conducting osmotic Shock experiments.
RNA was extracted from roughly one hundred eighty samples checked for
genomic DNA contamination and reverse transcribed into cDNA. Standard
curves for real time PCR were developed in parallel to the RNA extractions. In
all, roughly 18,000 PCR reactions were carried out in 384 well optical plates.

Figure 4.1. Comparison of Moments of Area for the eight perturbations. (a)
Using the cumulative equation to describe aggregate response of the ESR
associated with the set of two-clusters and single cluster approach. (b) Using
the displacement equation to describe the aggregate response of the ESR
associated with the set of two-clusters and Single cluster approach. ....... 67

Figure 4.2. Standard curve development results. a) Results from the first
approach using small lengths of DNA ranging from 101 bp to 106 bp as
template for amplification. Good reproducibility was observed, but large
separation between lengths occurred at the 104 and 106 dilutions. b) Results
from the second approach using longer lengths of DNA encompassing the
Shorter amplicons. Amplicons were grouped closer together for all dilutions
compared to the first approach. ...................................................... 74

Figure 4.3. ODeoo measurements normalized by initial absorbance for
Saccharomyces cerevisiae. The vertical line represents the onset of the
perturbation. Retarded growth was seen followed by decreased growth rates
with increasing perturbation magnitude. ............................................. 76

Figure 4.4. Aggregate response envelopes of 153 out of 169 genes showing
expression to osmotic shock. The aggregate response was calculated using
the cumulative response equation described in the Materials and Methods
section. Resistance decreases until the 1.2 M NaCl perturbation. For this
perturbation and the 1.4 M NaCl perturbation resistance increased. ........ 78

Figure 4.5. Comparison of fold changes in relative gene expression stepping
from 1.0 M to 1.2 M NaCl. The largest fraction of genes at 1.0 M NaCI
showed at least a 2-fold increase in expression. Whereas, the largest fraction
of genes at 1.2 M NaCI Showed at least a 2-fold decrease in expression.
Percentages associated with the pathways indicate percent contribution in
terms of response for the given fraction of genes. 81

xi

Figure 4.6. Comparison of Moments of Area plotted against perturbation
magnitudes for (a) individual genes, (b) gene associated pathways, and (c)
the aggregate response of selected genes described in this research. 85

Figure 4.7. Modulus of stability values for individual genes normalized by the
aggregate value. Genes greater than 1.0 are less sensitive than genes below
1.0. More genes showed greater sensitivity to the stress imposed by osmotic
shock than less sensitivity compared to the aggregate. ........................ 88

Figure 5.1. Plot of moment of area versus perturbation magnitude in terms of

NaCl molar concentration. The domain of stability is depicted between the
lower bound of strain, Stmin, and upper bound of strain, Stmax. ................ 97

xii

LIST OF TABLES

Table 1.1. Description of eight perturbations administered by Gasch et al.,
(2000), in order to study relative gene expression in Saccharomyces
cere visiae. ................................................................................. 1 1

Table 3.1. Genes and their associated primers used in developing standards
for relative quantification of mRNAS. Two approaches were used in
developing the standard curves. In the first approach amplification was
attempted from small DNA templates associated with the genes ranging from
101bp to 106 bp. In the second approach, larger DNA templates were used
encompassing the smaller amplicons in hopes improving amplification. 64

Table 4.1. Residual comparison relative to their respective Moments of Area
for the eight perturbations. Relative residuals for the cumulative equation
were identical between the cluster approaches. This was not observed for the
displacement equation. .................................................................. 68

Table 4.2. Residual areas associated with the aggregate response equations
and cluster approaches. The residual areas are additive when applying the
cumulative equation. This property was not associated with the displacement
equation. .................................................................................... 70

Table 4.3. Comparison of estimated stability parameters and Moments of Area
for the eight perturbations. The differences in Moments of Area can be
evaluated in terms of the individual stability parameters. ..................... 72

Table 4.4. Calculated stability parameters corresponding to the aggregate
cumulative response envelopes Shown in Figure 4.4. .......................... 79

Table A.1. Additional metrics used for relating Similarity and dissimilarity of
relative gene expression data obtained from microarray studies. ........... 105

Table 0.1. Descriptions of genes, and their accompanying primer sets,
encoding proteins for the Glycolysis/GluconeogeneSiS pathway. ........... 111

Table C.2. Descriptions of genes, and their accompanying primer sets,
encoding proteins for the Glycerolipid Metabolism pathway. ................ 112

Table C.3. Descriptions of genes, and their accompanying primer sets,
encoding proteins for the Mitogen Activated Kinase (MAPK) Signaling
pathway. .................................................................................. 114

Table C.4. Descriptions of genes, and their accompanying primer sets,
encoding proteins for the Cell Cycle pathway. .................................. 116

xiii

Table 0.1. Genes exhibiting a significant increases or decreases in relative
expression at the time of maximum displacement. Comparison between the
1.0 M and 1.2 M NaCl perturbation magnitudes. ............................... 119

xiv

CHAPTER 1

INTRODUCTION

1.1 Background and significance

High throughput genomic technologies have dramatically increased our
ability to develop models to quantitatively predict the behavior of microorganisms
in natural and engineered systems (Schena et al.,1995; Lockhart, et al., 1996;
DeRisi et al., 1997). Many variations of the technology exist today, including the
glass slide based cDNA and oligonucleotides microarrays (DeRisi et al., 1997;
Agilent, Palo Alto, CA), in Situ synthesized oligonucleotide arrays (Affymetrix,
Santa Clara, CA; Xeotron, Houston, TX; NimbleGen, Madison, WI), and bead-
based systems (Spiro et al., 2000). Typically, whole genome expression studies
using the above technologies revolve around measuring relative changes in
messenger RNA of thousands of genes together (referred to as genome
expression pattern, response, or strain) to physical, chemical, or biological
perturbations (referred to as perturbation or stress). Knowledge of this response
is believed to be important in making new discoveries in many fields including
oncology- to develop drugs for the control of cancerous cells (Perou et al., 2000;
Swami et al., 2003), biotechnology- to produce proteins of commercial value, and
environmental engineering- to study the degradation of xenobiotic compounds
during bioremediation (Beliaev et al., 2002). In parallel to these, other low-
throughput but more quantitative technologies such as quantitative real time
polymerase chain reaction (RT-PCR) have also progressed towards higher

capacities (Hernandez et al., 2000; DeFrancesco, 2003). Quantifying the relative

abundance of mRNA from thousands of genes is more economically feasible
using the microarray platform. Quantifying the absolute abundance of a few
hundred mRNAs is better accomplished by RT-PCR.

Since the inception of microarray technology, approximately a decade
ago, more than one thousand studies have been reported covering dozens of
whole genomes of various microorganisms (Wodicka et al., 1997; Cho et al.,
1998; Hecker and Engelmann, 2000; Hinchliffe et al., 2003). Many of the data
analysis tools applied to these studies were initially developed using experiments
performed on the Sacchaormyces cerevisiea (yeast) genome because of
experimental data publicly available from the laboratories of Pat Brown and
Jospeh DeRisi (DeRisi et al., 1997; Gollub et al., 2003). The sharing of gene
expression data and results, although initially lagging, has taken on new meaning
in the fields of bioinformatics, genomics, and microbiology. A number of
mathematical tools now exist to cluster and analyze the deluge of genome
expression data under varying environmental conditions and extract qualitative
(and often quantitative) information (Eisen et al., 1998; Xia and Xie, 2001; Autio
et al., 2003; Laws et al., 2003).

A primary goal of data analysis for experiments involving environmental
perturbation and genomic response is to establish (to the extent possible)
predictive rules for the behavior of a microorganism for the system of interest
(reactor, human body, soil, aquifer, surface water etc.). The predictive rules of
behavior can be established on many organizational levels including community,

population, proteome, and transcriptome. On a transcriptome level, none of the

analysis tools at present have the capability to find a quantitative aggregate
measure of relative gene expression for a group of genes; whether it be a cluster
of genes, a pre-defined gene set, or whole transcriptome. The aggregate
measure of gene response is referred too as strain throughout this dissertation. A
measure of strain is needed to compare the effect of different types and
magnitudes of perturbations on the transcriptome. This information in turn may
be useful in the direct control and management of gene expression and indirectly
in the control and management of the microorganism. Past studies related to the
existence of quantitative relationships, if any, between strain and applied
perturbation (referred to as stress subsequently) have not been undertaken,
because tools to calculate an aggregate measure of expression did not exist.
This posed some problems for the research presented in this dissertation,
because no published information on the aspect of relating stress to strain in a
quantitative manner on a transcriptome level was found. Hence, many
comparisons were made to studies that closely resembled the objectives and
hypotheses of this study. It is of course possible to draw parallel from dose-
response studies and toxicity evaluations at the organism level, but none of the
studies related to analysis of gene expression patterns have adopted the
approach presented here.

It is well known that many physical, chemical, social, and economic
systems behave according to a stress-strain paradigm. Young’s modulus of
elasticity (extension in the length of a wire per unit area per unit of applied load)

used to measure the strength of a material is an example of this type of

relationship important to comparing materials used in civil engineering.
Ecologists routinely study ecosystems as a perturbation-response problem and
characterize it as less or more stable. Economists forecast (to the extent
possible) the change in economic activity due to an event such as a decrease in
the interest rate. The hole in ozone layer is an example of the strain caused by
intentional and unintentional release of chlorofluoro-carbons (CFCS). The
foundation for this research is that “within limits”, such a stress-strain relationship
also exists for genomic systems and can be quantitatively studied by employing
aggregate measures of “stress and strain”. Such quantitative relationships will
have potential utility in control and management of microorganisms in all areas of

science.

1.2 Stress, Strain, and Stability

An aggregate measure of strain can be obtained from application of
stability principles from ecology. Ecologists analyze and measure the response of
a system by its response envelope (Nuebert and Caswell, 1997). A response
envelope is simply the curve describing the behavior of a state variable in
response to an applied stress. It is generally parabolic in shape but other
responses are possible. Gene expression patterns can also be considered as
response envelops. In ecology, the state variable is often the biomass or number
of species, or the abundance of a nutrient. In gene expression studies, the
response envelope will be attributable to the relative abundance of mRNAs
associated with individual genes. Indeed, in genomics, not all envelopes are of

the traditional parabolic shape. Five other common shapes of response are:

inverse of a parabola, a step-up response, a step-down response, and no
response at all to the stress, implying no detectable deviation from pre-perturbed
expression following the onset of a stress. It is obvious that genomic responses
are more complex and may require additional tools for analysis compared to the
response envelopes that are generally considered in ecology. However, as
presented later in this dissertation, the mechanistic mathematical equations
developed to analyze the response envelope can be applied to genome
expression patterns of many types.

“Stability" is a system-associated property extracted from the response
envelope. Its origins are rooted in the physics of perturbed motion (Merkin,
1997). In ecology, this property has been used in different manners (Grimm et
al., 1992), requiring a specific definition for this research. Stability is the ability of
a system to remain at equilibrium following a perturbation (Holling, 1973;
Harrison, 1979; Sennhauser, 1991). Although equilibrium is commonly equated
to stability in an ecological sense the use of steady state is more appropriate in

the case of relative gene expression. Steady state is defined in this research as:

M

Steady State 2 = O. (1 .1)

Where, Ax(t) represents the difference between the perturbed, xp(t), and pre-
perturbed expression, xe(t), of an individual gene, or system of genes. In this
case, a system is defined as a set of related genes found within a gene cluster or

predefined group, such as those making up the glycolyis pathway for

Saccharomyces cerevisiae. Certain aspects of stability, or stability parameters,
are commonly used to quantify this property. The two most common parameters
are resistance and resilience. Resistance is a measure of the magnitude of
response, i.e., the maximum change in the parameter of interest in response to
perturbation. Resilience is often described either as the time required for the
system to return to its pre-perturbation state or rate at which the system returns
to its pre-perturbed state. The exact definition used in past studies has often
depended on the author’s prerogative. Resilience applied to gene response
envelopes is described in more detail in Chapter 2. Since resistance and
resilience are both quantitative terms (differing in units, however), they can be
combined appropriately to yield a single measure for a single response envelope.
And, for many response envelopes, strain calculated from the aspects of stability
can be added together to describe the system as a whole (Grimm et al., 1992).
Therefore, a value of strain made up of thousands of gene response envelopes is
theoretically feasible. Such a summation of stability parameters calculated as
Moments of Area for Six response envelopes was used to describe the functional
stability of an anaerobic microbial community (Hashsham et al., 2000). The
research presented, proposes to use the same concept of calculating the
Moment of Area of response envelopes extended to genome expression
patterns.

It is well known that only a certain percentage of genes respond to an
applied stress. These are generally those genes that are related to a group of

proteins useful in averting the effect of the applied stress. It may belong to a

single pathway or spread over a few pathways. It is apparent that an aggregate
measure of expression response (in terms of strain) iS possible, but comes at the
cost of losing resolution, i.e., information about the type of genes or pathways
responding to that stress is lost. Such loss of resolution is common in all
calculations that result in an index. The benefit of calculating an index becomes
obvious when we consider that two very different types of perturbation (e.g.,
temperature and hydrogen peroxide) can be compared to each other via this
index. This would not have been possible by cluster analysis or any other
mathematical analysis that is currently in use in data analysis. It is possible,
however, to calculate the strain for one gene, one pathway, a group of genes
responding to the stress, or the whole genome. By keeping the gene identities
included in an analysis constant, the comparison of strains may be made more

biologically meaningful.

1.3 Choice of Monitoring Technology for Strain Quantification

After some initial analysis, it became clear that the cost of testing the
applied concepts was prohibitive on microarrays. Experiments on genome
expression patterns yield relative expression ratios. These ratios must be
obtained preferably in triplicate for good data analysis. Adequate description of
time series data often requires a minimum of five to seven temporal points,
judiciously selected at times that represent important changes in the expression
ratio. In addition, the experiments needed to be conducted at several magnitudes

of stress to be linked to the magnitude of strain. In terms of microarrays,

considering six different magnitudes of stress including the control, and applying
. a factor of safety of 40% extra because some microarrays may not yield good
results, at least one hundred microarrays will be needed. Combining the cost of
labeling and hybridization buffer, the total cost was estimated at more than
$50,000 in supplies. Therefore, an alternative approach was adopted. This
approach used quantitative real-time PCR and reverse transcription of the
mRNA. Quantitative real-time PCR is often used to validate expression ratios
obtained from microarray experiments because it provides better quantitative
information and can be conducted to yield absolute amounts of the mRNA.
However, RT-PCR becomes uneconomical and more time consuming for more
than a few hundred genes. The strategy of making quantitative RT-PCR
economical stems from limiting genes to a smaller set that has been shown to be
relevant to the type of stress. Yet, the cost saving strategy for a smaller number
of genes can also be achieved for the microarray platform, especially if the
microarray is printed in house. Therefore, the determining factor between a
microarray of a smaller set of genes and RT-PCR was the reliability in
determining the magnitude of strain. RT-PCR quantification of mRNA is more
reliable with the possibility of absolute quantification. Hence, RT-PCT of a set of
genes responding to the model stress was chosen as the best option for this

research.

1.4 Choice of the Model Microorganism and Stress

The type of microorganisms or stress that can be used for validation of the

stress-strain relationship is abundant. Therefore, organism selection for the

purpose of this study was carried out based on the following two characteristics:

i)

The microorganism’s whole genome expression pattern should be
well studied with respect to the type of stress and response so that
an informed selection can be made about the set of genes that are
relevant to the stress. This was essential because of the use of RT-
PCR based quantification instead of the microarray-based
quantification.

Initial data on whole genome expression patterns must be available
in the public domain so that mathematical tool development for
quantifying the strain can be accomplished before conducting a

more extensive stress-strain experiment.

S. cerevisiae satisfies the above two requirements. It is one of a few

organisms in which the effects of and response to osmotic shock have been

extensively studied (Hohmann and Mager, 1997). Briefly, upon encountering

osmotic shock, growth ceases and the cell’s volume decreases until the internal

production of glycerol reduces the water potential sufficiently for growth to

resume. Glycerol is the only compatible osmolyte produced by S. cerevisiae and

its production in response osmotic shock results from transcription of GPD1 and

a host of supporting genes (Hohmann and Mager, 1997; Martijn et al., 1999,

2000 & 2001; Mager and Siderius, 2002).

Increased levels of mRNA for GPD1 have been observed with greater
osmotic Shock, suggesting a relationship between the magnitude of the
perturbation and response. The potential dependence between perturbation
magnitude and response of this gene suggests that other genes related to
glycerol production, or to maintaining cellular viability, should also exhibit greater
response with greater osmotic Shock. Currently, no quantitative description of this
relationship exists for relative gene expression of S. cerevisiae in response to

osmotic shock.

S. cerevisiae has been extensively used as a model organism to study the
whole genome response to a number of stresses. Gasch and co—workers
collected data on the relative gene expression of S. cerevisiae to a variety of
environmental perturbations (Gasch et al., 2000). Eight of twelve perturbations,
which are summarized in Table 1.1, were selected for addressing hypothesis 1
described below. Relative mRNA abundance was monitored by Gasch et al.,
(2000), over time using a full-scale genome microarray developed by Pat Brown
and colleagues at Stanford University (Shalon et al., 1996; DeRisi et al., 1997).
This microarray contained the PCR amplification products of approximately 6400
distinct genes along with positive controls for normalization and negative controls
to monitor hybridization quality. The data from these experiments is publicly
available from the Stanford Microarray Database (Gollub et al., 2003).
Hierarchical clustering of differentially expressed genes (relative expression
greater than 2-fold change) revealed two clusters of a combined total of

approximately 900 genes. This set of genes was labeled by Gasch et al.,(2000),

Table 1.1. Description of the eight perturbations administered by Gasch et
al.,(2000) in order to study relative gene expression in Saccharomyces.
cerevisiae.

   

EnvirMmentubaon
(Cellular Stress)

Description

 

1. Temperature Shock from 25° to 37° C

Cells were grown at 25°C collected by centrifugation,
and suspended in media at 37°C. This temperature
was maintained throughout the experiment.

 

2. Temperature shock from 37° to 25°

Cells were grown at 37°C collected by centrifugation,
and suspended in media at 25°C. This temperature
was maintained throughout the experiment.

 

3. Hyper-osmotic shock

Cells were grown to an 00600 of 0.6 and
supplemented with media at containing 2 M sorbitol.
Final concentration of sorbitol was 1.0 M.

 

4. Hypo-osmotic Shock

Cells were grown in the presence of 1.0 M sorbitol,
collected by centrifugation and suspended in media
without sorbitol.

 

5. Hydrogen peroxide shock

Cells were grown to early log phase and H202 added
for a final concentration of 3.0x10“ M. Culture volume
and concentration were maintained throughout the
experiment.

 

6. Menadione shock

Menadione bisulfate previously suspended in water
at a concentration of 1.0 M was added to the cell
culture for a final concentration of 1 mM.

 

7. Diamide shock

Diamide was added to the cell culture to a final
concentration of 1.5x10’3 M.

 

8. DTT shock

Cells were grown at 25°C and dithiothreitol was

 

added for a final concentration of 2.5x10'3 M.

as the Environmental Stress Response (ESR). One cluster of approximately 600
genes showed repression in transcription followed by a return to relative
expression prior to the perturbation. The other cluster of approximately 300
genes exhibited an induction in transcription also followed by a return to relative
expression prior to onset of the perturbation. The ESR was induced as a
transitional response to maintain cellular conditions optimal for growth and
survival. Many of the genes responding to these perturbations were also
confirmed by Causton et al., (2001), and labeled as the Common Environmental

Response.

11

The above study by Gasch et al., (2000), and Causton et al., (2001),
would serve as an excellent starting point to explore if genome expression
patterns can be summarized in terms of strain. However, it would be important
that the numerical values of strain retain meaningful differences for comparison
of stress and developing the stress-strain relationships. It became clear that data
from various types of stresses obtained by Gasch et al., (2000), would be useful
for this purpose. However, it was also clear that the previously performed
experiments were not specifically designed for the purpose of testing the
existence of a stress-strain relationship. Therefore, a series of controlled
experiments would need to be performed to fully explore the validity of the
hypothesized relationships. The following sections describe the objectives and

hypotheses for this study.

1.5 Objectives

Two objectives of this study are put forth. Objective 1): To develop a
mathematical tool to calculate strain, i.e., an aggregate measure of gene
expression response, from the response envelopes of a set of genes responding
to the applied stress, and Objective 2): To study the relationship between stress
and strain at the level of gene expression for a set of selected genes in S.
cerevisiae under a series of applied osmotic stresses.

Completion of the first objective is necessary before the second objective
can be met. The first objective uses existing data from Joe DeRisi’S laboratory

(Gash, et al., 2000) for initial tool development. This tool is then applied to the

12

experimental data obtained as part of this research to accomplish the second

objective.

1.6 Hypotheses
The following three hypotheses will be tested as part of this study. They
are essentially sub-hypotheses emanating from the more fundamental question

of whether stress iS related to strain in biological systems.

Hypothesis 1 — The magnitude of strain for the set of genes labeled as ESR in
S. cerevisiae, can be calculated using the Moment of Area method and will be a
function of the type of stress. It will also be relatively insensitive to various

methods employed to calculate it.

Since all response envelopes have areas, calculation of strain is trivial.
Whether this calculated area retains the resolution with respect to various types
and magnitudes of stresses is key to determining the usefulness of this
approach. Proof of this first hypothesis determines the fate of the second
hypothesis that relates to the magnitude of stress. Also, the mathematical tools

developed to test the first hypothesis are essential for the other two.

Hypothesis 2 —The magnitude of strain is related to the magnitude of stress for
the set of genes responding to that stress. This relationship is most likely non-
linear and exists within a range given by minimum and maximum values of the

stress.

13

This range exists because strain may not be detectable below a certain
lower value of stress due to limitations posed by the detection limit of the
monitoring tools. Similarly, above a certain value of the stress an organism may

not be able to respond in any manner except inactivity or death.

Hypothesis 3 — Moment of Area is a better measure of the strain than resistance
or resilience alone because it combines and emphasizes delayed response of
the microorganisms under higher magnitudes of stress and it gives equal weight
to induction and repression.

This last hypothesis emanates from the need to reconcile the numerous
parameters that have been used to study stability of a system in ecology. For
example, resistance, resilience, reactivity, declivity, time of return, time of
maximum response, and many other parameters represent various aspects of
the response envelope (Grimm et al., 1992). The details of these parameters, the
subtle differences, and their utility in obtaining strain are presented in Chapter 2.
Testing this last hypothesis iS also essential because of the need to analyze
response envelopes that are generated by induction as well as repression. For
example, Gasch et al., (2000), observed two clusters of genes within the ESR,
although in opposite directions, one representing induction and the other
repression. Both returned to the expression levels prior to the perturbation. The
third hypothesis tests if both clusters can be combined to make a single cluster

using the moment of the area approach. Assuming that the stability of the ESR is

additive, then the Moment of Area calculated from the set of both clusters should

quantitatively agree with the Moment of Area from the Single cluster.

are:

Five tasks were completed in order to test the above hypotheses. They

Review the current technologies used to group related genes
according to patterns of relative gene expression in response to
environmental perturbation. This was essential to device methods
to calculate Moment of Area and stability parameters.

Evaluate various parameters of stability theory in ecology, and
adapt the most suitable option to obtain strain from response
envelopes of relative gene expression.

Develop mathematical tools to automatically calculate the stability
parameters from the response envelopes of relative gene
expression.

Conduct stress-strain laboratory experiments using S. cerevisiae
and at least five different magnitudes of osmotic stress (selected
because maximum information is available for this type of stress on
yeast). The experiment involved growing S. cerevisiae, applying
the stress, and collecting mRNA for quantification by reverse
transcription and real-time PCR.

Use the mathematical tool developed in Task 4 to calculate strain

and relate it to the corresponding stress.

IS

Completion of the above tasks was carried out in three phases. In the first
phase, a review of the current qualitative analysis techniques used to analyze
relative genome expression was conducted. This phase was important to
develop an understanding of how expressed genes are grouped in a systematic
manner. The second phase evaluated various methods to calculate stability
parameters and applied the best option to develop mathematical tools for
calculating strain from response envelopes of whole genome expression
patterns. Existing data from Gasch et al., (2000), on yeast was used for this
second phase. The third phase involved experimentation and application of the
mathematical tools developed in phase 2. S. cerevisiae was subjected to varying
magnitudes of stress (osmotic shock), messenger RNAS were harvested and
quantified using quantitative PCR. The response envelopes obtained by this
experiment were analyzed to calculate strain and study its relationship with the
applied stress.

The remaining chapters of this dissertation are arranged in the following
manner. Chapter 2 describes the pertinent literature available on stress, strain,
and stability. Chapter 3 presents the materials and methods employed in this
study including the mathematical tools. Chapters 4 and 5 present the results
obtained and the associated discussion. Finally, conclusions are presented in
Chapter 6. Appendices are provided to document the MathCad program used for
conducting calculations, list of genes used in the analysis with corresponding

pathways.

16

CHAPTER 2

LITERATURE REVIEW

2.1 Pulse and Press Perturbations

A perturbation is responsible for causing the transcriptional response
necessary to counteract the resulting cellular stress. Two distinct types of
experimental perturbations described by Bender et al., (1984), are: “pulse” and
“press”. Figure 2.1 graphically depicts both pulse and press perturbations. Pulse
perturbations are instantaneous changes in an environmental condition followed
by a return to steady state. Press perturbations are changes in an environmental
condition that are continually maintained over the period of the study or for a
specified time. Responses to pulse perturbations are commonly of short duration
compared to the duration of press perturbations, which invoke long-term
responses to the permanent change (lnchausti, 1995). Currently, perturbation
experiments focusing on gene expression have focused on the press type
(Siderius et al., 1997; Gasch et al., 2000; Causton et al., 2001; Alexandre et al.,
2001; Zhang et al., 2002).

Quantification of the magnitude and duration of a perturbation is difficult
for those occurring naturally, and often only the effects (direct and indirect) are
quantified rather than the perturbation (Bender et al., 1984; Yodzis, 1988).
Experimental perturbations resulting from artificial manipulation of the
environment or community are quantifiable. Quantification of the pulse

perturbation is a function of both the magnitude and duration. Because the

duration of press perturbation may continue to infinity (or the period of study),
quantification is a function of magnitude only.

The administration and quantification of press perturbations is simpler, but
inherent problems can result in selecting the time scale for observing the
response (Yodzis, 1988). Conclusions based on press perturbations must be
based within the boundaries of the observed response. On the other hand, pulse
perturbations can be more difficult to administer and quantify, but the time scale
for observations is easier to determine. Observations in the case of pulse
perturbations are made until the environmental condition or community has

returned to its pre-perturbed state.

1?)

le.d) me)

 

 

 

 

 

 

Magnitude
Magnitude

----——---
\
\

‘=

 

 

 

 

Duration Duration

Figure 2.1. (a) Pulse perturbations in which an instantaneous change either by
addition or removal of an environmental condition occurs followed by a return
to the pre-perturbed condition. Pulse perturbations are a function of magnitude
and duration. (b) Press perturbations in which change in an environmental
condition is maintained. Press perturbations are a function of magnitude only.

18

2.2 Stability and Generalized Gene Expression Response Envelopes

Stability has generally been defined as the ability of a system to remain at
equilibrium following a perturbation (Holling, 1973; Harrison, 1979; Sennhauser,
1991, Grimm et al., 1992). It is worth noting that in ecological literature, the
concept of stability is often elusive, confusing, and subjective. Hence many other
definitions can also be found. For the purpose of this research, the above
definition will be used with the exception that “equilibrium” will be substituted with
“steady state”. A system that exhibits no displacement from steady state in terms
of an observed parameter following a perturbation is deemed perfectly stable.
However, once a system is displaced from steady state, it can either return to its
pre—perturbed condition, or establish a new steady state. The former is known as
asymptotic stability, and was first described by the Russian mathematician,
Liapunov in the early 20th century (referenced in Harrison, 1979; Merkin, 1997).
The establishment of a new steady state is known as neighborhood stability and
results from the perturbation permanently altering the environment (Lewontin,
1969; Sutherland, 1981; Murray, 1993; Hernandez, 2003). These two types of
stability have been extensively discussed and debated by theoretical and
empirical ecologists over several decades with demonstration to a few well-
characterized ecosystems (Pim, 1982).

The above definitions associated with stability are applicable in general to
any response envelope. Hence, they may be applied to the response envelope of

gene expression pattern(s) for a single gene or a group of related genes that

19

 

 

 

 

1-

 

 

 

 

 

 

Relative Gene Expression

{)1 9)

 

 

 

 

Time

Figure 2.2. Generalized relative expression patterns in response to
environmental perturbation. An induction (a) or repression (b) in transcription
followed by a return to pre-perturbed expression levels. An induction (c) or
repression (d) in transcription followed by an establishment of new relative
expression levels. Patterns (e) and (f) could represent one of the other
expression patterns given a longer time-scale. Pattern (9) represents no
change in relative expression in response to perturbation.

20

result from an environmental perturbation. Figure 2.2 summarizes the
generalized patterns of relative gene expression. Response a represents a
transcriptional activation until suitable physiological conditions of the cell are
restored followed by transcriptional repression at which point remaining mRNAs
are translated or degraded to pre-perturbed expression levels. Contrasting
response a, is response b in which transcriptional repression is followed by
activation to achieve pre-perturbed expression levels. Responses a and b might
occur when the perturbation momentarily changes environmental conditions after
which the environmental conditions returns to its pre-perturbation state.
Responses c and d denote induction and repression, respectively, until a new
equilibrium expression level is achieved to maintain suitable physiological
conditions. These responses might occur when the perturbation results in the
establishment of new environmental conditions. It is unclear whether responses e
and f will ultimately look like responses a and c or b and d, respectively, due to a
shortened time scale of observation. Because all systems tend to a recognizable
equilibrium following small perturbations (Pimm, 1982), the continuing trend of
responses e and f is unlikely. Finally, response 9 represents no change in

expression from the resulting perturbation.

Evidence of these generalized expression patterns was demonstrated by
Wen et al. (1998) while studying the temporal gene expression of the central
nervous system. Euclidean clustering identified five basic “waves” of gene
expression, comparable to responses a, c, e, f and 9 that characterized central

nervous system development. Evidence for responses 3 and b were presented

2]

by Gasch et al. (2000) following the study of gene expression in S. cerevisiae to

a number of perturbations including temperature and osmotic shock.

2.3 Measures of Stability used in Ecology

Figure 2.3a shows asymptotic stability for a cluster of genes responding to
osmotic shock and neighborhood stability for a cluster of genes responding to a
shift in temperature from 37° to 25° C (Gasch et al., 2000). These two sets of
response envelopes are similar to the generalized response envelopes
presented in Figure 2.1 a and c. The stability parameters resilience, and
resistance (Figure 2.3b) can be used to describe specific aspects of asymptotic
and neighborhood stability. An additional stability parameter, reactivity, is also
shown in Figure 2.3b. Until now, these aspects of stability have predominately
been applied to analyze response envelopes of parameters at the organism level
(Viragh, 1989; Mittelbach et al., 1995; Grandpre and Bergeron, 1997). Application
at the genome expression level will be attempted in this research for the first
time.

Resilience and reactivity have units of inverse time and describe the
relative change in abundance of mRNAs governed by the rates of transcription,
translation, and translocation in Eukaryotes. The more resilient a cluster of
genes, the more rapidly it returns to pre-perturbation state following the
perturbation. Further, those genes that did not respond at all, as represented by
the generalized response envelope i in Figure 2.2, are considered perfectly

resilient. Mathematically, resilience is defined as (Neubert and Caswell, 1997):

22

 

a)

 
 

\

MI“ I”: I

l.
.
r1
////

 

 

I
(I
I
i
/

 

    

 

 

b)

Reactivity |.

Relative Gene Expression

 
 

Resilience

Reactivity

Resistance
Resistance

 

 

 

 

 

 

Time

Figure 2.3. (a) Relative expression of Saccharomyces cerevisiae exhibiting
asymptotic and neighborhood stability to hyper-osmotic and temperature
perturbations (b) Application of the stability parameters to asymptotic and
neighborhood stability.

23

Resilience (1/time) a

[ 1 dAX(t)]. (2.1)
“me x(t) dt
Where, Ax(t) represents the difference between the perturbed, xp(t), and pre-
perturbed expression, xe(t), state of the system. According to Equation 2.1, as t
approaches co, the greater the negative value of dAx(t)/dt, the more rapidly xp(t)
approaches x9(t) and the greater the stability of the system in terms of resilience
(Harrison, 1979, DeAngelis, 1980; Nuebert and Caswell, 1997).

Reactivity is a less commonly described stability parameter, but is

complementary to resilience. Mathematically, reactivity is defined as (Nuebert

and Caswell, 1997):

 

Reactivity(1/time) E _1_ dAX(’)]. (2.2)

limto —>tmax[x(t XV)

Where, to—>tmax is the limit taken from the time at which the perturbation begins,
to, to the maximum displacement from steady state, tmax. The larger the positive
value of dAx(t)/dt the more rapidly xe(t)—>xp(t) aS to——>tmax. AS with resilience, a
larger reactivity value indicates greater stability in that the system reacts more
quickly to remove the affects of the perturbation. The more reactive a cluster of
genes the more rapidly the cluster reacts to the perturbation to restore steady
state expression. A comparably larger resilience and reactivity denote greater

stability (Harrison, 1979; Sutherland, 1981; Nakajima, 1992; Ives, 1995).

24

Resistance is defined as the maximum displacement from the pre-
perturbed state (Harrison, 1979; Pimm, 1984) and is defined mathematically aS

(Nuebert and Caswell, 1997):

Resistance (unitless) a [My ]. (2.3)
max X 0

Resistance is the ability of the gene cluster to withstand the perturbation. It
has been compared to the concept of buffering capacity in ecology (Grimm et al.,
1992). On a molecular scale, the less resistant a gene cluster the larger the

magnitude the displacement.

2.4 The Moment of Area as a Tool to Calculate Strain for Generalized
Response Envelope

A dilemma originates when dealing with multiple response envelopes and
multiple stability measures (i.e., number of parameters). Consider a case where
resistance is high but reactivity and resilience are small because the Slopes of
each limb of the response envelope are small. A system could be more stable
with respect to one parameter and less stable with respect to another making an
overall determination of stability difficult. The problem is compounded when
trying to compare multiple response envelopes Therefore, a single measure of
stability that integrates multiple envelopes and multiple stability parameters is

required. Hashsham et al., (2000), presented the Moment of Area as a measure

25

of overall stability incorporating resilience, resistance, and reactivity. They proved
the utility of this measure in comparing the functional stability of anaerobic
reactor communities perturbed by glucose. Mathematically, the Moment of Area

is defined as:
i
Moment of Area (timez) -=- ZAI-ti . (2.4)
0

Where, A,- is the area under the response envelope for the ith compound and t; is
the moment arm of the envelope (Figure 2.4). Modifying the original definition, A,-
can represent the area of the response envelope and t,- its corresponding
moment arm, for a single gene, an aggregate of clustered genes, or set genes
involved in a biochemical pathway.

The moment arm is calculated as the distance from the center of mass of
the response envelope to the perturbation axis, a vertical line extending from the
starting point of the perturbation (Hashsham et al., 2000). The center of mass
represents a point of symmetry on which the stability parameters act, similar to
describing the center of mass of an object on which distributed forces act. AS a
component of the Moment of Area, the moment arm accounts for possible lag
time from the onset of the perturbation to the gene cluster response, effect of the
shape of different amplification envelopes, and emphasizes the response that
occurs over a longer duration. Units associated with different types of
perturbations, such as temperature or concentration does not appear in the

Moment of Area. Therefore, differences between Moments of Areas are a

26

 

| Perturbation

8 1(— Response Axrs
'6 . Envelo e I

g p I Moment
5. I Am

x
LLI I

a, I

c I

In
(D ' Center of
m I Mass
.2 l

“a I
'0': I
m |
\
H... ‘ s
_ 1—_ :23”. — - - : 3;-

 

 

 

 

 

Duration

Figure 2.4. The Moment of Area encompasses the the stability parameters
and is measure of overall stability. Components of the Moment of Area applied
to asymptotic stability are shown. Components include response envelope,
perturbation axis, moment arm, and center of mass.

reflection of differences in stability, which allow for comparisons between i)
commonly expressed genes across different environmental perturbations, ii) the
response of a set of genes to different magnitudes of the same perturbation, or
iii) the variations just described but with different genomes. AS with the other
stability parameters a larger Moment of Area indicates a lower degree of stability.

The response envelope encompasses all the stability parameters
described previously. To demonstrate this, consider the asymptotic stable
response of a single gene, i. Dividing the response of i at tmax, the area of the

response envelope for each half can be found by integrating (Figure 2.5):

27

A.=

I

dt+ j

. dt. (2.5)
(to) tmax X,- (to)

 

 

tmax xpi(t)_xei(t) “’0 XPIII)‘Xei(t)

to X

Where, xp,-(t) is the perturbed expression, er(t) is the expression prior to the
perturbation and x,-’(t) describes the initial expression prior to the perturbation of
gene i. If expression is at steady state prior to the perturbation, then x,-'(t)= XeI(t).
Making the substitution, Ax;(t,)= xp,-(t)- xei(t), taking the anti-derivative of Equation

2.5, and assigning the appropriate limits results in Equation 2.6.

[ 1 )dAxl-(t): [ 1 mm} [ 1 dAXI-(t)]
x;(t) dt limt0—>tmax xii“) dt limtmax-—>t,Jo XII“) dt .

Equation 2.6 describes the amplification envelope of gene i as the overall

 

 

 

rate of change of relative expression governed by reactivity for to < t _< tmax and
resilience for tmax _< t < to... If the relative response of gene i exhibited
neighborhood stability, then there is no return to pre-perturbed steady state.
Hence the resilience portion of Equation 2.6 is non-existent and the overall rate

of change of relative expression is governed by reactivity only.

28

 

 

 

 

 

 

 

 

 

 

 

 

 

 

tmax tmax

Figure 2.5. Symbols applied to the response envelope showing how it
encompasses the stability parameters reactivity, resilience, and resistance.

2.5 Equations used to Calculate the Aggregate Response Envelopes

The above exercise for a Single gene can be expanded to consider an
aggregate response of a group of genes, with the Moment of Area being the sum
of aggregate response envelopes for multiple gene sets or clusters multiplied by
their respective moment arms. Two approaches for calculating the aggregate
response are shown mathematically by Equations 2.7 and 2.8 The cumulative
response equation (Equation 2.7) sums the variance of each gene over all genes

in the set or cluster at each measured time point according to:

 

i [x i(t)—x;(t):r
cap-Z " . .
1 [’90)]2

29

 

(2.7)

Where, X,,,-(t) is the perturbed gene expression and X'i(t) is the expression prior to
the perturbation. The relative displacement equation is Similar to equation 2.7
with the exception that the square root is taken after summing the variances

according to:

 

on: :[xpm—xxt)? (2.8)

: [MOT

Equation 2.8, designated in this dissertation as the relative displacement
equation, was initially proposed to compare the resilience of energy flow among
different ecosystems (O’Neill, 1976), and has found applications in determining
the stability of nutrient cycling (DeAngelis, 1980; DeAngelis et al., 1989;
DeAngelis 1992; Cottingham and Carpenter, 1994). Its application to the stability
of gene expression as an aggregate measure is novel and represents a new

quantitative tool for analyzing microarray data.

2.6 Physiological Response of S. cerevisiae to Osmotic Shock

S. cerevisiae, like all other unicellular organisms, has developed
mechanisms to counteract changes in transmembrane water potential due to
natural fluctuations in external osmolytes. Because of its commercial importance,
the response of S. cerevisiae to osmotic Shock has consistently been a focus of
attention. Exposure to salt solutions, used in de-watering processes during mass

production, subject S. cerevisiae to high osmotic pressures (Attfield, 1997).

30

During dough fermentation the osmotic pressure experienced by S. cerevisiae
has been Shown to nearly double (Benitez et al., 1996). Thus, development and
identification of new yeast strains with increased osmotolerance is an ongoing
research interest.

Three physiological events occur in S. cerevisiae upon encountering
sudden increases in osmotic conditions. In the first event, a decrease in turgor
from loss of intercellular water results in the reduction of the cell volume
(Blomberg, 2000). Depending on the severity of the osmotic Shock the cell
volume has been Shown to decrease by as much as 30% to 60% its original
volume (Benitez et al., 1996; Hohmann, 1997; Klis et al., 2002). The ability of the
cell wall to withstand such a dramatic change is mainly attributed to the presence
of the elastic properties associated with the membrane protein 81,3-Glucan,
which has a Shape comparable to a wire spring (Klis et al., 2002).

In the next event, growth ceases until adaptation to the new environment.
For S. cerevisiae adaptation primarily occurs by accumulation of glycerol in the
cytosol through internal production and by restricting transport to the outside
through the glycerol-specific channel protein, fps1p (Andreishcheva and
Zvyagilskaya, 1999; Ilomberg, 2000). Trehalose, another osmolyte, has also
been observed to accumulate in the cytosol. However, the level of accumulated
trehalose compared to glycerol indicates that it does not have a substantial
impact on osmotic resistance (Blomberg, 2000). The accumulation of inorganic
osmolytes such as KCI and NaCl to counteract osmotic stress has not been

observed in S. cerevisiae, and is rarely observed in any other unicellular

31

organism, because of severe impacts on metabolic function due to ionic
properties associated with these inorganic compounds (Yancey et al., 1982).

In the final physiological event, the cell volume expands and growth
resumes. Yet, the imposed stress does have its costs. The cell volume does not
return to its pre-stressed state, growth rate is retarded, and population viability is
impacted. The extent of these costs varies with S. cerevisiae strains. Hohmann
and Meger, (1997), indicate that for the commonly studied W303-1A and YPH
strains growth has been observed at 1.7 M NaCl; whereas, some strains Show no
growth in as little as 0.35 M NaCl. In terms of viability, most strains exhibit a 10%
survival rate after addition of NaCl to a final concentration ranging from 1.0 M to
1.38 M (Blomberg, 1997). However, viability has also been shown to depend on
the stage of growth. Yeast populations are less viable after an osmotic Shock
during early log phase growth compared to an osmotic Shock during late log
phase growth. The reason for increased sensitivity during early log phase has not
been clearly explained, but could be a result of thermodynamic or genetic

considerations.

2.7 Transcriptional Response of S. cerevisiae to Osmotic Shock

The transcriptional response of S. cerevisiae to osmotic Shock can be
grouped into two categories: the general stress response, which is associated
with the expression of a number of stress genes across many different
perturbations, and the specific stress response associated with expression of
genes to a Specific perturbation. In the case of osmotic Shock, if NaCI is used as

the osmolyte generating the perturbation, a Slightly expanded specific response

32

is observed compared to the specific response generated following the addition
of sorbitol. This occurs because metal toxicity associated with Na’, generates an
additional response compared to an equivalent stress caused by addition of
sorbitol. In spite of this, NaCI is generally preferred over sorbitol because of
lesser amounts required to generate the genomic response. A 1.2 M NaCl is
equivalent to 1.8 M sorbital for generating a water activity of 0.960 (Hohmann
and Mager, 1997).

The general stress response in S. cerevisiae is connected to a cis-
regulatory element common to genes showing expression to heat shock,
oxidative stress, nutrient starvation, and other encountered stresses. This cis-
regulatory element was first identified by comparison of promoter regions for
C‘IT1, (a catalase), DDR2 (involved in DNA damage repair), and HSP12 (heat
Shock chaperon) as a five base pair consensus sequence, CCCCT, and was
subsequently named the stress response element (STRE) (Ruis and Schiiller,
1995). Targeting this consensus sequence are the transcriptional factors
Msn2/Msn4p that are negatively regulated by the cAMP-PKA Signaling pathway.
A search of the yeast genome for this element resulted in 186 potentially
regulated STRE genes with roughly 50 of these known to be functionally related
to stress response (Kobayashi et al., 1993; Marchler et al., 1993; Martinez-Pastor
et al., 1996; Eustruch, 2000.).

Despite the presence of the STRE, genes containing this element often
show different patterns of expression (Estruch, 2000). This has been explained

by the presence of additional stress induced regulatory sequences in the

33

promoter regions. For example, Gasch et al., (2000), observed that expression of
the TRX2 cluster was induced for a variety of stresses, but super-induced upon
change of the cellular redox potential. Genes in this cluster contained an
additional promoter sequence targeting the transcription factor Yap1p,
responsible for inducing transcriptional response under oxidative stress
(Fernandes et al., 1997). Therefore, the STRE in combination with additional
condition specific promoter sequences result in enhanced expression of genes
related to the specific stress. This redundancy adds to the assurance that the
appropriate genes necessary to mediate the effects of the stress are transcribed.
The use of_high throughput technologies for studying gene expression has
of lately expanded the notion of the general stress response to beyond those
genes solely containing the STRE. Gasch et al., (2000), observed differential
expression in roughly 1200 genes (constituting ~19% of the genome) to different
stresses. Out of this, the expression of 180 genes was significantly impacted by
either Msn2/Msn4p double mutants or over-expression of Msn2/Msn4p. Similarly,
Causton et al., (2001), observed differential expression in roughly 10% of the
genome, with 47 of 216 induced genes having the STRE Site. Additionally, of the
283 genes exhibiting repression, 133 contained a previously unknown consensus
sequence, GATGAG, which occurred within 600 bp of the transcription start Site.
All of this points to a much more complicated general stress response composed
of multiple and redundant transcriptional regulatory Sites, the products of which
may be directly and indirectly involved In mediating the effects imposed by the

stress.

34

The main mechanism for the accumulation of glycerol results from
induction of GPD1, GPP2, and a host of other supporting genes with numbers
estimated from 200 to 1000 (Mager et al., 2002). Translation of GPD1 and GPP2
results in a NAD+ dependent glycerol-3-phosphate dehydrogenase and a
glycerol-3-phosphatase, respectively. As shown in Figure 2.6, dihydroxyacetone
phosphate (DHAP) produced from the isomerization of glyceraldehyde-S-
phosphate during glycolySis is catalytically reduced by Gpd1p to glycerol-3-
phosphate (Gly-3-P). Gly-3-P is then dephosphorylated by Gpp2p producing
glycerol.

Two homologous genes for GPD1 and GPP2 have also been identified
and named GPD2 and GPP1, respectively. Although GPD1 and GPD2 produce
glycerol-3-phosphate dehydrogenases their physiological assignments have
been shown to differ. Evidence for this was demonstrated by protein deletions in
which Gpd1pA mutants exhibited normal growth under anaerobic conditions, but
poor glycerol production at high osmolarity (Larsson et al., 1993). Whereas,
Gpd2pA mutants exhibited poor growth under anaerobic conditions when glycerol
was needed for redox regulation, but normal growth under osmotic shock
(Hohmann and Mager, 1997). Differential expression of GPP1 and GPP2 have
been demonstrated in the presence of increased external osmolytes indicating

functional Similarity (Norbeck et al., 1996; Martijn et al., 2000).

35

Osmotic HOG Pathway

Sh ck /

h 1
Growth Arrest i s o

 

 

 

   
 
  
 

    

fl

 

  
 
   
   

 

Water Outflow, Glycerol
Cell volume
decreases ssk2 gpp1, gpp2
I Gly-3-P
NAD+
Glycerol Accumulation gpd1
(mrnutesvto hours) NADH
” Cell volume
increases
cholysns

\\.

Growth Resumes

 

 

 

 

 

K sko1

Figure 2.6. Physiological and specific transcriptional responses to osmotic
shock. Upon encountering an osmotic shock cell growth ceases until suitable
glycerol accumulation, triggered by the high osmotic glycerol (HOG) pathway,
allows for growth to resume.

 

2.8 Regulation of Specific Transcriptional Response to Osmotic Shock

GPD1 contains three transcriptional activation sites demonstrating its
redundancy for osmotic shock. One site contains the stress response element
connected to the general stress response, another site corresponds to the Msnp1
transcriptional factor of which little is known as to its regulation. The final
transcriptional activation Site corresponds to the Hot1p activator. This activator is
regulated by the high osmotic glycerol pathway (HOG), which is one of four
known pathways associated with the mitogen activated phosphorylation kinase

(MAPK) signaling pathway. Another important pathway that is related to osmotic

36

shock, and also a part of MAPK, is the PKC pathway, which is responsible for
cell wall integrity (Hohmann and Mager, 1997). All pathways associated with
MAPK have a characteristic cascade of kinase activity.

As demonstrated in Figure 2.6, following an osmotic perturbation a two
component osmo-sensor (Sln1p & Ypd1p) in the cell wall activates the control
kinase (Ssk1 p) by dephosphorylation, which in turn directly interacts with the
MAPKKK (Ssk2p/Ssk22p). A cascade of kinase activity proceeds with activation
of MAPKK (Pszp) and activation by dual phosphorylation of the MAPK(Hog1p).
Active Hog1p is translocated across the nuclear membrane where it directly
interacts with Hot1p. Although Hot1p has not been directly observed to bind with
the ORF encoding GPD1, glycerol production has been shown to dramatically
decrease with a HOT1 mutant (Rep et al., 1999). Hog1p has also been shown to
regulate other transcriptional factors including Sko1p, which activates
transcription of ENA1 encoding an ATPase involved in Na+ extrusion
(Andreishcheva and Zvyagilskaya, 1999). Alternative activation of Hog1p was
demonstrated bypassing the control kinase and MAPKKK by way of the synthetic

high-osmolarity sensitive sensor, Sho1p (Maeda et al., 1995).

2.9 Monitoring of mRNA using Reverse Transcriptase Real-Time PCR
Real-time PCR allows for either the absolute or relative quantification of

mRNA by monitoring the PCR amplification process in real-time using a

fluorescent reporter. The mRNA is first converted to cDNA by reverse

transcription. This cDNA is used as template in the amplification process. As the

37

PCR reaction progresses amplified DNA increases exponentially over the
number of selected reaction cycles until one or more components of the reaction
mixture become limiting. At this point the rate of amplification decreases and the
amplification curve levels off. Quantification occurs by extending an arbitrary
horizontal line through the linear portion of the amplification curve, which is an S-
shaped curve depicting amplification of the target with increasing cycle number;
and finding the corresponding reaction cycle value (x-value) defined as the cycle
threshold, Ct. The cycle threshold is compared to a standard curve equating the
initial amount of target to Ct. Samples containing a larger initial amount of target,
or larger copy number, have smaller Ct values. Whereas, samples with a
relatively smaller amount of initial target, or copy number have larger Ct values.

Absolute quantification has been demonstrated in studies measuring the
abundance of isolates from mixed communities and mRNAs in gene expression
studies (Rantakokko—Jalava and Javala, 2001; Ayala-del-Rio, 2002; VVIckert et
al., 2002). For abundance of isolate(s), standards composed of quantified target
sequences are used to prepare the standard curve. For mRNA quantification,
however, the standard curve must account for the efficiency of reverse
transcription of mRNA to cDNA (Bustin, 2000). This is accomplished by
generating target DNA sequences then in-vitro transcribing them back to RNA.
The RNA is then reverse transcribed to cDNA along with the RNA of the
unknowns.

Measuring the relative abundance of gene expression is less complicated

and two approaches are commonly used. In the first approach, a standard curve

38

is created, but the absolute abundance of target sequence does not need to be
determined. Only the dilution number associated with each standard in the curve
is required. The dilution number of the unknown is determined from the standard
curve and divided by the calibrator i.e., the dilution number of the gene in which
the unknown will be relative too. The other approach of measuring relative gene
expression from real-time PCR data uses a mathematical computation known as
the delta delta Ct (2440’) computation (Livak and Schmittgen, 2001). The MC!
refers to the difference between ACT” - ACm. Where, ACT” is the difference
between the cycle threshold of a reference, known as an endogenous control,
and unknown sample, q, and AC“), is the difference between the cycle threshold
of the endogenous control and cycle threshold of the gene selected as the
calibrator. This computational method relies on the assumption that the
amplification efficiencies of the reference, calibrator, and unknown are
approximately equal. An endogenous control must be included for both absolute
and relative quantification to account for minor differences in the amount of
starting template of unknown samples to be compared. A gene that does not
exhibit a change in expression for the condition studied may serve as an
endogenous control. Common endogenous controls include ribosomal DNA,
GAPDH, and B-actin (Toshihide et al., 2000).

Monitoring real time amplification commonly occurs by way of one of two
generalized approaches. The first approach uses DNA binding dyes that directly
react with double stranded DNA. SYBR green | is the most commonly used DNA

binding dye for monitoring PCR amplification (Karsai et al., 2001). This dye emits

39

a fluorescent signal upon intercalating with double stranded DNA. As the amount
of amplified DNA increases the fluorescence emitted by SYBR green I is
proportional. However SYBR green I is unable to discriminate between target
and non-target amplified DNA resulting from non-specific binding of primers.
Therefore, results are sensitive to false positives. Similarly, the presence
genomic DNA contamination in reverse transcribed samples can result in high
background fluorescence. Identification of false positives can be accomplished
by generating a melting temperature (Tm) curve (Ririe et al., 1997). The Tm is the
temperature at which the double stranded DNA of the amplicon separates and is
dependent of the nucleotide composition. A peak is generated that should
correspond to the specific Tm of the amplicon as the temperature of the reaction
mixture is raised. Additional peaks, or broad peaks indicate the presence and
significance of non-target amplified DNA.

The second approach depends on hybridization of specific probes
containing fluorescent reporter systems to the amplicon of interest. Three
techniques make up the second approach for monitoring amplification. The
Taqman assay (Perkin Elmer and Applied Biosystems) utilizes a third probe
specific to a region on the amplicon bound by the specific template primers. This
probe contains a fluorescent reporter on the 5’ end and a fluorescent quencher
on the 3’ end. During the annealing and extension step the probe hybridizes to
the amplicon and 5’-exonuclease activity of the DNA polymerase cleaves the
probe separating the reporter from the quencher allowing for the fluorescent

emission of the reporter to be monitored. The Molecular beacons (Stratagene)

4O

assay also relies on a reporter and quencher system except the probe containing
the two dyes forms a hairpin loop due to self-complimentarity on both ends. In
the hairpin loop, the dyes are close enough so that the emission from the
reporter is quenched. At the correct annealing temperature, conformational
transition separates the ends of the probe, which then binds to its complimentary
sequence. The separation of the reporter and quencher is large enough so that
emission is no longer quenched. The final technique relies on two separate
hybridization probes one of which contains a fluorescein dye on the 3’ end and
the other contains an acceptor fluorophore on the 5’ end. The excitation
spectrum of the acceptor fluorophore overlaps the emission spectrum of the
fiuorescein donor resulting in fluorescence resonance energy transfer when the
3’ end is brought into close contact of the 5’ end. The resulting emission is a red
fluorescence. When the two probes are separated, only the background
fluorescein donor emission is present. This last technique results in the greatest
target specificity because of the combined specificities of the template primers

and hybridization probes (Bustin, 2000).

2.10 Current Analysis Tools for Gene Expression Data

Current tools for analysis of relative gene expression data rely heavily on
systematic methods originally designed for inferring evolutionary history from
hierarchy relationships (Planet et al., 2001). The use of systematic methods,
applied to expressed genes, assumes that meaningful insights into molecular
function can be inferred from similar patterns of expression (Planet et al., 2001).

This assumption is also valid when describing the stability of clusters of genes to

41

environmental perturbation. Because all systematic methods contain biases, it is
important to have a basic understanding of the systematic method selected when
grouping genes for stability analysis.

All data obtained from gene expression studies is grouped by placing each
gene in a row and each condition studied, or each observed time point for a
single condition in a column. This forms the gene expression matrix in which
expression is studied by comparing profiles of genes by comparing rows, or
profiles of samples by comparing columns (Brazma and Vilo, 2000; Altman and
Raychaudhuri, 2001). Each entry in the expression matrix is a gene expression
vector thought of as a point in m-dimensional space (Brown et al., 2000). Once
the expression matrix has been established, analysis proceeds by calculating
similarity, dissimilarity, or confidence between expression vectors using a
statistical metric, then establishing relationships among the expression vectors
using clustering.

Among the numerous metrics available for calculating similarity,
dissimilarity, or confidence, Pearson’s correlation, including its modifications, and
Euclidean distance have found broad application to studying relative gene
expression. Pearson’s correlation is a measure of directional similarity between
two gene expression vectors in which each vector is treated as unit length
(Sherlock, 2000). The directional similarity can often be taken around the mean

of the two vectors (Figure 2.7a), or around another arbitrarily defined reference

42

b) c)

Response

 

9x

 

 

 

 

9y

 

 

 

Time or Condition

Figure 2.7. Graphical representation of different comparison metrics used for
analysis of microarray data. (a) Pearson’s correlation in which the angle
between the mean of the gene expression vectors x and y is used to calculate
similarity. (b) Pearson’s correlation around zero or often known as the
standard correlation, in which similarity for the gene expression vectors x and
y is calculated as the angle from zero. (c) Euclidean distance is calculated as
the distance between the expression vectors x and y.

line (Figure 2.7b). Although Pearson’s correlation excels at capturing similarity in
terms of shape without regard to magnitude it is not robust to outliers (Eisen et
al., 1998; Sherlock, 2000). Heyer et al., (1999), found that this lack of robustness

resulted in false positives; genes receiving a high score of similarity in terms of
function or co-regulation, but in reality are dissimilar.

Euclidean distance is a measure of dissimilarity and takes into account
both direction and magnitude (Legendre and Legendre, 1998). As shown in
Figure 2.7c, it is calculated as the distance between two points making up the
hypotenuse of an arbitrary right triangle using the Pythagorean formula. It is often
overly robust by giving high dissimilarity scores to expressed genes with the
same shape, but different magnitudes (Heyer et al., 1999). Alternative metrics to

Pearson’s correlation and Euclidean distance are described in Appendix A. There

43

is no “absolute” for choosing the best metric, rather consideration should be
given to whether the shape of the expression pattern or the magnitude is of more
importance (Brazma and Vilo, 2000).

The result of calculating a similarity, dissimilarity, or confidence value for
each pair of genes for all genes in the gene expression matrix, is a n2 matrix,
known as a similarity matrix. Values in the similarity matrix are clustered so that
important inferences about gene function, and regulation can be made. Most
clustering analysis is categorized as supervised or unsupervised. Supervised
clustering uses learning algorithms such as support vector machines (SVM)
(Brown et. al., 2000), Bayesian networks (Long et al., 2001), and others to define
classifiers that represent certain groups of functional genes. Functionality of
unknown expressed genes is determined by comparing the classifiers to
expression data.

Unsupervised clustering is performed without a priori knowledge to
classification and consists of hierarchical and non-hierarchical methods.
Hierarchical algorithms form a similarity tree by grouping related genes into
clusters and connecting related clusters at nodes. Nodes of related clusters are
connected using branches, with the length of a branch indicating the distance
between adjoining clusters. Algorithms building a similarity trees in the fashion
are described as agglomerative, meaning the tree is formed from top to bottom.
Spellman et al., (1998), in a seminal example of applying agglomerative
clustering to microarray analysis, associated clusters of genes with their

corresponding transcription factors for S. cerevisiae during its cell cycle.

44

The relevancy of genes to their associated clusters when progressing
higher up the similarity tree is one disadvantage of agglomerative clustering
(Sherlock, 2000). When genes are clustered together, an average expression
profile of the profiles making up the cluster is used to represent that cluster
(Eisen et al., 1998). As a cluster grows from top to bottom, the average
expression profile of the cluster may not accurately reflect the profiles contained
in the smaller clusters (Sherlock, 2000). To compensate for this, Alon et al.,
(1999), demonstrated the use of a divisive clustering algorithm, or a “bottom to
top” approach of building a similarity tree. In this approach, genes are randomly
assigned to two clusters and then re-assigned to maximize the probability of
each cluster. Each cluster is then divided and the processes of re-assignment
continues until each cluster is made up of a single expression profile.

Non-hierarchical clustering is useful for grouping gene expression data,
collected over time, into families of patterns associated with important events.
Common algorithms include K-means (Hartigan, 1975; Heyer et al., 1999), Self-
organizing maps (Tamayo et al., 1999; Sherlock, 2000), CAST clustering (Ben-
dor et al., 1999), and QT clustering (Heyer et al., 1999). An important example of
non-hierarchical clustering was demonstrated by Cho et al., (1998), in
characterizing genes associated with the periodic events of DNA replication,
chromosome segregation, and mitosis for S. cerevisiae. Unlike hierarchical
clustering, the user must specify values influencing the number of resulting
clusters in the output. This gives the user more control over the clustering

process and alleviates the problem of relevancy associated with agglomerative

45

hierarchical clustering. However, the user should have some external criteria or
notions as to the number of clusters desired (Planet et al., 2001). If the number of
resulting clusters is too few, important groups of genes are not separated. If the
resulting number of clusters is too many, genes that should be grouped together
are separated. User control associated with non-hierarchical clustering makes
this approach ideally suited for grouping similar responses according the
characteristic patterns of gene expression in response to environmental

perturbation.

46

CHAPTER 3

MATERIALS AND METHODS

3.1 Sorting of Gene Expression Data for ESR

Raw gene expression data for the eight environmental perturbations listed
in Table1.1 was obtained publicly from the Stanford Microarray Database
(www.dnachip.org). ESR genes and their corresponding expression values were
located and removed from the raw data by comparison to a downloadable list of
these genes, also publicly available on the Stanford Microarray Database.
Relative expression was calculated and zero transformed according to (Eisen,

1998;

Relative expression = CHZDN — CH1D . (3.1)

CH 10

 

The symbols used in equation 3.1 correspond to the data format
associated with the software, GeneScanm. Where, CH2DN is the background
subtracted and normalized emission from fluorescently labeled nucleotides;
labeled with the carbocyanine dye derivative, Cy-3, incorporated into cDNA
during reverse transcription. Fluorescent emission from this fluorophore
represented the transcriptional response of ESR to the perturbations. CH1D is
the background subtracted emission from cDNA containing incorporated
nucleotides labeled with another derivative of the fluorescent carbocycanine

dyes, Cy-5, and corresponds to transcription of genes prior to the perturbation.

47

3.2 Clustering of Relative Gene Expression Data

To separate genes according to the two clusters observed by Gasch et al.,
(2000), relative expression data was imported into GeneSpringTM software
(Silicon Genetics, Redwood City, CA) and a similarity matrix created using a
modified Pearson’s correlation (Legendre and Legendre, 1998). The non-
hierarchical K-means clustering algorithm was used to sort genes into patterns of
induction and repression (Brazma and Vilo, 2000). Clustering results were
exported to ExcelTM and manually sorted to remove genes with missing data
points. These results were verified against results obtained by both Gasch et al.,

(2000), and Causton et al., (2001).

3.3 Calculation of Strain from the Response Envelope

Least squares regression was used in conjunction with the general linear
model, y(t)=,Bo+ fl1t1+fl2tz+nfiktk+a to estimate the partial slopes of the response
envelopes. The area of each amplification envelope was determined by
integrating the general linear model, from the start of the perturbation to the last
observation. The center of mass for each amplification envelope was also

determined from the general model according to (Fishbane et al., 1993):

b b
It - Y(t)dt J(y(t))2 dt
x coordinate = §3_—’ y coordinate = 0.5 a b (3.2)
MW MW!
8 a

48

Where, y(t) is the specific model for each response envelope, b is the time of the
last observation, and a is the starting time of the perturbation. The aggregate
response equations (Equations 2.7 and 2.8) were used to calculate the relative
displacement as described previously. Results of the two methods were

compared for the ESR genes.

3.4 Calculation of the Strain for Large Data Sets

To expedite the process of calculating the Moment of Area for a large
number of response envelopes a program was developed using MathCad”. A
flow diagram for the calculation approach is displayed in Figure 3.1. The program
was made up of four parts. Data representing amplification envelopes of cluster
aggregates, or individual genes were imported as a text file to part one. Here,
linear regression takes place using the least squares method to calculate the
coefficients (partial slopes) of the regression model (Longnecker and Ott, 2001).
These coefficients were then exported as a text file, and used in parts two and
three.

In part two, a statistical analysis of the regression model was done by
calculating the sum of squares of the residuals, sum squares of regression, and
total sum of squares. The above sum of squares was used to calculate the
residual standard deviation, and coefficient of determination. These statistical
measures are used to evaluate the error associated with the regression model,
goodness of fit, and predictive capability, respectively. Statistical equations to

calculate these parameters can be found in Longnecker and Ott, (2001).

49

 

 

 

 

 

 

 

 

 

Regression Analysis
(Least Squares Method) ‘

 

 

 

Export
5 Coefficients (—
E...a.a.t>stt ......

 

 

3

 

Calculate Area
of
Amplification
Envelope

 

 

SS(Total)

 

 

 

l N

SS(Regression)

 

 

SS(Residual)

 

 

Y

Coef. Determination

(

 

 

 

I Residual Std. Dev.
Statistic Calculated:

 

 

 

 

 

 

 

 

 

 

 

 

Find Center of Mass 3

x-coordinate and
y-coordinate

 

O
I
O
O
C
C
O
I
v
C
O
O
O
O
C
I
O
O
O
l
O
O
O
O
O
C
I
C
O
O
C
I
I
1
v
C

 

 

 

 

 

 

 

 

 

 

 

Calculate Moment
Arm

 

 

 

 

 

 

 

 

 

Calculate Moment
of Area

 

 

 

 

 

 

 

 

 

Create Output
Table

 

 

 

 

 

__) Export Output
Table as .txt*

 

 

 

 

 

Figure 3.1. Schematic of MathCadTM program used to calculate the Moment
of Area for large data sets. The program is divided into four sections. Section
one uses linear regression to fit the data to a statistical mode. Section two
calculates the statistics associated with the regression analysis. Section three
finds the components leading to the Moment of Area calculation. Section four
creates an output table containing all of the results.

50

In part three, the coefficients of regression were used to find the area, x-
coordinate, and y-coordinate of the center of mass according to Equation 3.2,
and moment arm of the response envelopes. Using the areas and moment arms,
the Moments of Area were calculated using Equation 2.4. Results from parts one,
two, and three were exported to part four of the program where an output table
was generated and exported as a text file. A detailed description of each part of

the MathCadTM program is found in Appendix B.

3.5 Selection of Genes and Primer Design

One hundred sixty nine genes were selected for observation to osmotic
shock. The selection criteria were based on: 1) whether the genes had previously
exhibited significant expression to osmotic shock from published microarray data
(Gasch et al., 2000; Martijn: et al., 2000; Causton et al., 2001), 2) whether the
genes had been previously described in connection to osmotic shock, but did not
exhibit significant expression indicated by microarray results (Hohmann and
Mager, 1997), and 3) whether the genes were connected with one of the four
biochemical pathways noted as important to osmotic shock. These pathways
included one regulatory pathway-the MAPK signaling pathway, and three
metabolic pathways- glycolysis/gIuconeogenesis, glycerolipid metabolism, and
cell cycle. Identification of genes associated with the four biochemical pathways
were obtained from the Kyoto Encyclopedia of Genes and Genomes (KEGG)
database (Kanehisa and Goto, 2000).

In addition to the 169 genes, RDN18-1 that encodes 18S rRNA was

included as an endogenous control for normalization. Components of the

51

ribosome in eukaryotes are often used for normalization (Toshihide et al., 2000).
However, post-transcriptional modifications can make designed primers
ineffective for amplification of cDNA (Venema and Tollervey, 1999). Therefore,
YBR011C (IPP1) that encodes a pyrophosphatase was also included as an
endogenous control (Kurilova et al., 1993). Changes in expression of YBR011C
to shifts osmotic shock have not been observed, and its use for normalization
has been demonstrated (Norbeck and Blomberg, 1997; Martijn et al., 1999).

Primers for each gene were designed using Primer ExpressTM 2.0 (Perkin
Elmer Applied Biosystems, Foster City, CA). Design parameters included a
melting temperature ranging from 58° C to 62° C, GC content ranging from 45%
to 55%, length ranging from 20 bp to 22 bp, and amplicon length (size of the
amplified PCR product) ranging from 100 bp to 110 bp. Short amplicons are
ideally suited for quantitative PCR because of better amplification efficiency due
to an increased likelihood for complete denaturing. This allows effective binding
of primers to their target sequences. PCR efficiency also increases due to shorter
extensions times required by polymerization (Bustin, 2000). If possible, at least
one primer was designed to cross an intron; hence, increasing primer specificity
for the target (Wrckert et al., 2002). Additional design parameters not listed here,
but included in the software were set according to the manufacturer’s
suggestions. Appendix C describes the 169 genes, including primers, according
to the four biochemical pathways mentioned above.

Specificity of primers was evaluated by: 1) using stand alone BLAST and

the yeast nucleotide database contained in GenBank (www.ncbi.nlm.nih.gov), 2)

52

ethidium bromide staining of the amplified products using gel electrophoresis,
and 3) analyzing a dissociation curve for each primer pair following RT-PCR
using an ABI Prism 7900HT (Perkin Elmer Applied Biosystems, Foster City, CA).
Primers showing fewer than 3 mis-matches to non-target sequences as indicated
by BLAST, were discarded. Primers resulting in the formation of multiple
amplicons as indicated by double bands on gels following electrophoresis were
also discarded. Finally, dissociation curves with multiple peaks were matched to

their primer sets and disregarded in the final data analysis.

3.6 Experimental Approach for Quantitative Stress-Strain Response

An overview of the experimental approach used to study osmotic shock in
S. cerevisiae is outlined in Figure 3.2. Osmotic shock was induced using a 5.0 M
NaCl solution added to batch cultures resulting in press perturbations of
increasing magnitude (0.5, 0.7, 1.0, 1.2, and 1.4 M). Previous experiments
showed a final concentration of 0.4 M NaCl was required to induce osmotic
shock; whereas a 1.4 M NaCl concentration resulted in no resumption of growth
(Wuytswinkel et al., 2000). Biological replication of each perturbation was
conducted in triplicate. In addition, negative controls were included for each
perturbation to monitor gene expression under non-perturbed growth conditions.

An average of eight time point samples, including time zero, were
collected for each replicate and negative control for the six perturbations resulting
in roughly 180 samples to be processed in preparation for relative gene
expression quantification. Total RNA was extracted and quantified followed by

detection of genomic DNA contamination using no RT control procedures. If the

53

 

Growth Perturbation
Experiment

 

 

 

 

I 5 Perturbations X 3 Replicates = 18 Experiments

 

 

 

Stored Samples

 

 

 

 

 

RNA Extraction

I.

No RT Control Yes Add. DNase

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Gemmic DNA? Treatment PCR Amplification 3 Calibration
of Standards Curves
Reverse
Transcription . _ .
Dilution Series 5 Paints/Calibration

 

 

 

 

 

 

 

 

 

Real Time PCR
Plate Preparation

l

Real Time PCR ‘

 

 

 

 

 

 

 

 

 

 

L Repeat real time PCR for remaining replicates.

 

 

Preliminary Analysis

 

 

 

 

Figure 3.2. Design approach used for conducting osmotic shock experiments.
RNA was extracted from roughly one hundred eighty samples checked for
genomic DNA contamination and reverse transcribed into cDNA. Standard
curves for real time PCR were developed in parallel to the RNA extractions. In
all, roughly 18,000 PCR reactions were carried out in 384 well optical plates.

54

presence of genomic DNA was significant, additional enzymatic treatment
occurred until the presence of genomic DNA could not be detected using no RT
controls. Total RNA was then reverse transcribed to cDNA, purified, and
quantified in preparation for real time PCR.

Real-time PCR was conducted on six of the eight time point samples
using SYBR l green as the fluorescent reporter to quantify gene expression
relative to accompanying calibration curves. Each time point sample for each
perturbation acted as template for the 169 genes shown previously to be
differentially expressed to osmotic shock. Preliminary analysis showed success
in the experimental design for the five perturbations. In all, more than 18,000
PCR reactions were carried out in roughly 50 384 well plates, which included

calibration standards, negative controls, and no template controls.

Growth of S. cerevisiae and application of osmotic stress. S.
cerevisiae strain W303 was obtained from the American Tissue and Culture
Collection (ATCC 200060). Cells were grown in batch culture at 30° C in YDP
medium containing 2% bacto-peptone (DIFCO, Detroit, MI), 1% yeast extract
(DIFCO, Detroit, MI), and 2% glucose. A 10x solution containing the peptone and
yeast extract was prepared separate from a 10x solution of glucose and then
combined following sterilization to prevent a darkening of the medium.

Application of osmotic shock to S. cerevisiae proceeded by harvesting an
overnight culture by centrifugation at 3500 rpm for approximately five minutes.

Cells were suspended in YDP without glucose and diluted to an ODsoo of 0.2.

55

The cell suspension was divided into four equal parts of 360 ml and 40 ml of a
1.11 M glucose solution was added. Final ODsoo of the cell suspension with
glucose was approximately 0.16. The four cell suspensions were placed on an
environmental orbital shaker set at 100 rpm and 30° C. Growth was monitored
using a Shimazdu UV-160 spectrophotometer until early log phase growth
(approximate ODeoo 0.4). An appropriate volume of a 5 M NaCl solution was
added to three of the cell suspensions to create a final NaCl concentration of
either 0.5 M, 0.7 M, 1.0 M, 1.2 M, or 1.4 M. The fourth cell suspension not
receiving any NaCl served as a negative control for gene expression not related

to osmotic shock.

Harvesting of cells during osmotic shock. Just prior to the onset of
osmotic shock a 15 ml sample was collected from each cell suspension and used
to represent gene expression at time 0. During the perturbation cells were
harvested a regular intervals from all cell suspensions until growth resumed,
indicated by three consecutive increases in ODsoo. To avoid gene expression not
related to osmotic shock, harvesting proceeded according to established
protocols (Causton et al., 2001.). Briefly, 15 ml volumes were withdrawn from
each cell suspension and pelleted by centrifugation at 3500 rpm for 3 minutes at
room temperature. The medium was decanted and pellets were immediately
plunged into liquid nitrogen then stored at —80° C until RNA extraction, which

occurred within one month of harvesting to avoid degradation.

56

RNA extraction. Total RNA extraction of the stored samples proceeded
according to modifications of the hot acid phenol extraction method developed by
Schmitt et al., (1990). While being kept on ice, cell pellets were suspended in 400
pl AE buffer (50 mM sodium acetate, 10 mM EDTA [pH 5.3]) and transferred to
1.5 ml centrifuge tubes. Immediately, 40 ul of a 10% SDS solution was added
followed by addition of an equal volume of double distilled phenol at pH 5.3
(Ambion, Austin, TX) equilibrated in AE buffer and prepared within one week of
use. Samples were mixed, incubated at 65° C for 6 minutes, then rapidly chilled
in a dry ice ethanol bath until the appearance of phenol crystals. Following the
chilling step, samples were allowed to thaw slightly then centrifuged at room
temperature for 2 minutes at 14,000 rpm. The aqueous phase was transferred to
a new tube and extracted again with acid phenol.

To the transferred aqueous phase, an equal volume of
phenol/chloroform/lsoamyl alcohol (Sigma, St. Louis, MO) was added, mixed by
vortexing and centrifuged at room temperature for 5 minutes at 14,000 rpm. The
aqueous phase was transferred to a new tube. DNase I (Ambion, Austin, TX)
was added to the above aqueous sample to achieve a 10 units per ml solution
and the sample was incubated at 37° C for 30 minutes. To inactivate the enzyme,
an additional acid phenol extraction was performed and the aqueous phase was
transferred to a new tube.

Total RNA was precipitated by addition of 0.1 volume 3 M sodium acetate,
[pH 5.3], and 2.5 volumes ice-cold 95% ethanol. Samples were placed at -20° C

overnight. RNA was harvested by centrifuging at 4° C for 30 minutes at 14,000

57

rpm. The supernatant was decanted and RNA washed once in ice cold 80%
ethanol, and centrifuged at 4° C for 20 minutes at 14,000 rpm. The supernatant
was decanted and the RNA pellet was allowed to dry, then suspended in 50 ul
Tris-EDTA [pH 8.0] (Ambion, Austin, TX). A 5 pl sub-sample was removed and
reserved for RNA quantification, and to check for the presence of genomic DNA
contamination.

All solutions and supplies used for RNA extractions were either purchased
RNase free or treated with DEPC (diethyl pyrocarbonate) according to standard
protocols (Fedorcsak and Ehrenberg, 1966). All glassware was Placed in a 180°
C furnace for at least 8 hr to destroy residual RNase (Sambrook et al., 1989).
Additionally, prior to each extraction, a hood dedicated to RNA extraction was
cleaned to reduce or destroy residual RNase activity using either a 10% bleach

solution or RNase wipes (Ambion, Austin TX).

Check for Genomic DNA Contamination. To check for genomic DNA
contamination in the extracted RNA samples, a no RT control was performed.
Briefly, 20 ng of RNA template obtained from each of the RNA sub-samples and
added to a reaction cocktail (Karsai et al., 2002) containing 10 mM Tris-HCI (pH
8.5), 50 mM KCI, 2 mM MgCl2, 0.15% Triton x-100 (Sigma, St. Louis, MO) and 40
uM dNTPs (Promega, Madison, WI). One unit of taq polymerase (Promega,
Madison, WI) was added to this mixture along with 12 pmoles of both forward
and reverse primers targeting a 104 bp region of the RDN18-1 (18$ rDNA) open

reading frame. Design of the forward primer (5’-

58

TGAACCCAATCATCCAAGACAC-S’) and reverse primer (5’-
TI'GTGGGAAAGCACCATAGTTG-3’) followed guidelines described in the gene
selection and primer design section (Section 3.6).

Final reaction volume of the above components was 25 pl, which
underwent PCR following a protocol described previously (Ayala-del-Rio, 2002).
Briefly, it consisted of a pre-dwell for 2 minutes at 94° C followed by a denaturing
step for 30 seconds at 94° C, an extension step for 30 seconds at 55° C, and an
elongation step for 1 minute at 72° C. The denaturing, extension, and elongation
steps were repeated 40 times. A final post-dwell of 1 minute at 72° C occurred
following completion of the repeated steps. A positive control containing genomic
DNA template instead of RNA template, and negative control lacking any
template were also included for quality control.

Amplified products from PCR were detected using electrophoresis on a
3% (wt/vol) agarose gel (Gibco BRL) in 1x TAE (Tris-acetate-EDTA). The
presence of a band of the same size compared to the positive control indicated
genomic DNA contamination. It was suspected that poor digestion of genomic
DNA resulted from the presence of NaCl, which can significantly reduce activity
of the DNase I enzyme. Total RNA in contaminated samples was precipitated as
described above and suspended in 500 pl DEPC treated water to which 55 pl
DNase buffer (Ambion, Austin, TX) and 6 units of Turbo DNase I (Ambion,
Austin, TX) were added. This modified enzyme is more robust to NaCl than
traditional DNase I. The mixture was incubated at 37° C for 30 minutes and

enzyme inactivated with a phenol/chloroform/isoamyl alcohol extraction.

59

Precipitation, harvesting, and quantification of the treated samples proceeded as
described previously. RNA samples free of genomic DNA were reverse
transcribed using a High Capacity cDNA Conversion Kit (Applied Biosystems,
Foster City, CA) and purified using Qiagen PCR purification columns (Qiagen,
Valencia, CA). Purified cDNA was quantified by measuring absorbency at 260

nm and stored at -80° C.

Real-time PCR. The reaction cocktail used for SYBR“ Green I real time
PCR was adapted from Karsai et al., (2002). It consisted of 1x SYBRTM Green I
buffer described above. To the reaction cocktail was added 1.0 unit of Taq
Polymerase, 0.375 pl of SYBRTM Green I (Molecular Probes, Eugene, OR)
diluted from 10,000x to 1000x prior to addition, 2.3 pM 6-ROX (6-carboxy-x-
rhodamine, Molecular Probes, Eugene, OR), 10 ng cDNA, and 12.5 pmoles of
forward and reverse primers.

Thirteen pl of the reaction cocktail minus primers was distributed to 384
well optical plates (Applied Biosystems, Foster City, CA) using a Biomek 2000
workstation (Beckman Coulter, Fullerton, CA). Two pl of each primer were also
added to each well using the workstation. PCR was performed on an ABI
7900HT (Applied Biosystems, Foster City, CA) using the reaction conditions

described in the previous section.

60

Production of Taq. Because the consumption of Taq was expected to be
cost—prohibitive, it was produced in the laboratory using Thermus aquaticus DNA
polymerase expressed in Escherichia coli INValphaF’ (lnvitrogen, San Diego,
CA) following protocols established by Engelke et al., (1990), and Pluthero,
(1993). E. coli containing the taq polymerase gene on pTaq plasmid under the
control of the lac promoter was grown in LB broth containing 80 mg l’1 ampicillin.
Induction of Taq polymerase occurred by addition of IPTG (iso-propyl-1-thio—B-D-
galactopyranoside, Sigma, St. Louis, MO) to a concentration of 125 mg I". Cells
were harvested, lysed, and soluble proteins separated by centrifuging. Soluble
proteins containing the polymerase were salted out using ammonium sulfate and
dissolved in 50 mM Tris-HCI [pH 7.9], 50 mM glucose, and 1 mM EDTA. Crude
purification of the protein extract occurred by dialysis using a Spectra/Por 50,000
MWCO membrane (Spectrum Labs, Rancho Dominquez, CA) against a 50%
(vol/vol) glycerol solution with two changes in dialysis solution every 12 hours.
The purified extract was diluted in half with a storage buffer solution containing
50 mM Tris-HCI [pH 7.9] 50 mM KCI, 0.1 mM EDTA, 1 mM dithiothreitol, 0.5 mM
PMSF (phenylmethylsulfonylfluoride, Sigma, St. Louis, CA), and 50% (vol/vol)
glycerol. The diluted extract was stored at —20° C. The Taq polymerase
contained in the purified extract was evaluated against purchased Taq

polymerase (Promega, Madison, WI) to estimate the activity units per micro-liter.

6|

Calibration curves for real-time PCR. Common practice using real-time
PCR includes a standard curve on each plate for each unknown amplicon. This
was not economically feasible for the 170 genes selected for this research.
Rather, it was assumed that SYBRTM green I could not discriminate between
amplicons of different genes, but could discriminate between amplicon length,
i.e., the longer the amplicon the more dye intercalates between the two DNA
strands resulting in greater fluorescence per amplicon. Two approaches were
used for development of standard curves. In the first approach, primers were
used to generate PCR products of length 101 bp, 104 bp, and 106 bp
representing the smallest, average, and largest amplicon lengths for the 170
genes. The PCR products were purified using 10,000 MWCO spin columns
(Millipore, Bedford, MA), and quantified by measuring absorbance at 260 nm.
Purified products were then adjusted to the same absorbance. A 1:10 dilution
series was created from each purified and adjusted PCR product to be used as
the starting template for the standard curves. Four dilutions, 10°, 102, 10“, and
10°, from each series were evaluated for linearity and agreement in cycle
threshold (Ct).

It seemed plausible that poor amplification from the short pieces of DNA,
generated in the first approach might occur. Therefore, in the second approach
additional primers were designed (Table 3.1) that encompassed the primers used
in the first approach. Amplified PCR products using these new primers were
roughly 1000 bp. These PCR products were purified using Qiagen PCR

purification columns (Qiagen, Valencia, CA), quantified, then adjusted as

62

previously described. A 1:10 dilution series from each product was created and
six dilutions, 10°, 10", 102, 10°, 10°, and 10°, from each series was used as
starting template for the standard curves. Amplification of these templates

occurred satisfactorily using the original primers designed in the first approach.

63

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CHAPTER 4

RESULTS

4.1 Application of the Moment of Area to Calculate Strain

Moment of Area results for the environmental stress response are
described using two comparisons. Both comparisons are used to demonstrate
that the Moment of Area is relatively insensitive to the method used to calculate
it. In the first comparison, Moments of Area resulting from the relative cumulative
response equation (Equation 2.7), and the relative displacement equation
(Equation 2.8) are compared. These equations were used to describe the
aggregate response of the ESR. Their comparison is made to determine which
equation is better suited for this purpose and to fulfill the first objective of
development of tools for describing strain.

The second comparison looks at the cluster approach used to calculate
the Moment of Area. Recall that Gasch, et al., (2000), observed that the ESR
was comprised of two clusters, one representing induction and the other
repression. To demonstrate the relative insensitivity of the Moment of Area, the
Moment of Area resulting from combining both clusters into one (single cluster),
then calculating the aggregate response envelope using either equations 2.7 or
2.8 is compared to the summed aggregate response envelopes of each cluster

multiplied by their respective moment arms (set of two clusters).

65

Comparison of equations used to calculate the aggregate response
envelope. Moments of Area for the ESR perturbed by the eight stresses
(described in Table 1.1) are shown in Figure 4.1. Figure 4.1a compares the
Moments of Area associated with the aggregate response envelopes calculated
using the cumulative response equation (i.e., Equation 2.7) and Figure 4.1b
compares the Moments of Area resulting from the displacement equation (i.e.,
Equations 2.8). Error bars in Figures 4.1a and 4.1b represent residual error
propagated through the Moment of Area calculation. Both aggregate methods
resulted in qualitative agreement of the ESR to the different perturbations, but
differed by an order of magnitude in their calculated values. Smaller values
associated with the displacement equation were expected due to the square root
being taken after summation of relative expression values rather than before
summation of relative expression values as with the case of the cumulative
equafion.

Table 4.1 lists the coefficients of variation calculated from the residual
standard deviation for each perturbation divided by their respective Moments of
Area. This was done to evaluate which aggregate response equation was more
suited to the regression model used for linear regression. For all perturbations,
except osmotic shock and temperature shock from 25° C to 37° C, the
contribution of the residual error to the Moment of Area was greater for the
aggregate response envelope described by the displacement equation than the
aggregate response envelope described by the cumulative equation. In the case

of the two exceptions, the contribution of the residual error to the calculated

66

 

 

 

 

 

 

3)
5e+7
- ESR composed of two clusters
ESR composed of one cluster
“A
.g 4e+7
E, 1e+7// //
x .
"8‘
*5 Key:
«2, 1-Hyper-osmotic shock
E E 2-Hypo-osmotic shock
; .r 3-Temperature shock
T E if: from 250-370 0
0 _ . ,. .
4-Temperature shock
1 2 3 4 5 6 7 8 from 37°—25°C
b 5-Hydrogen Peroxide
) Exposure
3.5e+6 6-Menadione Exposure
- ESR composed of two clusters 7-Diamide Exposure
3_0e+6 — ESR composed of one cluster
‘3‘ 8-DTT Exposure
5: 2.5e+6 -
E
3; 2.0e+6 ~/ /
775 // //
g / /
X
0)
.g 5.0e+5 -
._<_1.

 

 

 

Figure 4.1. Comparison of Moments of Area for the eight perturbations. (a)
Using the cumulative equation to describe aggregate response of the ESR
associated with the set of two-clusters and single cluster approach. (b) Using
the displacement equation to describe the aggregate response of the ESR
associated with the set of two-clusters and single cluster approach.

67

Table 4.1. Comparison of residuals relative to their respective Moments of Area
for the eight perturbations. Relative residuals for the cumulative equation were
identical between the cluster approaches. This was not observed for the

dis lacement eo uation.

 
      

     

      

 

 

 

 

 

 

 

 

 

 

 

 

 

0 0
0)
§ 1‘2 K? s
‘5 Q To ?\ 'R
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4.. e 0 6 Q. Q. 5’ to g .9
:3 a E s. .5, E. a s .«o .s
o <( O I l~ i~ :1: 2 Q Q
Stat 0“ Cumulative equation 0.35 0.02 0.23 0.15 0.04 0.10 0.08 0.05
0..
clusters Displacement equation 0.34 0.14 0.21 0.43 0.17 0.18 0.12 0.18
Single Cumulative equation 0.35 0.02 0.23 0.15 0.04 0.10 0.08 0.05
cluster Dis lacement uation 0.26 0.01 0.22 0.47 0.10 0.15 0.13 0.19

Moment of Area was approximately the same between the two aggregate
response equations. Therefore, the regression model was more suitable for the

cumulative equation than the displacement equation.

Effect of clusters. Within Figures 4.1a and 4.1b a comparison between
the two-cluster approach to represent the ESR versus the single cluster
approach (i.e., both clusters combined into one) to represent the ESR is made. In
Figure 4.1a the Moments of Area and the residuals associated with the two
approaches exhibited 99% agreement. This demonstrated that when the
cumulative equation was used to calculate the aggregate response envelopes of
the ESR, residual error from linear regression had little impact on the Moments of
Area.

However, a different result was observed for Moments of Area for the two

cluster approaches in Figure 4.1b. Here, the use of the displacement equation to

68

calculate the aggregate response envelopes resulted in worse agreement,
ranging from 71% to 84%, between the Moments of Area. The lack of agreement
can be explained by observing the residual error associated with linear
regression propagated to the area of the aggregate response envelopes (i.e., the
A,- term in the Moment of Area equation). Table 4.2 compares this propagated
residual error (residual area) for the single cluster and set of two clusters. Once
again, the summed residual areas of the set of two clusters and the residual area
of the single cluster are equal, confirming that the Moment of Area is less subject
to error associated with linear regression when using the relative cumulative
response equation. However, the summed residual areas of the set of two
clusters do not agree with the residual area of the single cluster using the
displacement equation. In fact, the summed residual areas of the set of two
clusters were consistently larger than the area of the single cluster. This helps
explain why the Moments of Area associated with the set of two clusters in
Figure 4.1b were consistently larger than the Moments of Area associated with
the single cluster.

Hence, linear regression of the aggregate response envelopes calculated
from the displacement equation resulted in a worse fit than linear regression of
the aggregate response envelopes calculated using the cumulative response
equation. This difference in fit may result from taking the square root after

summation of the relative expression values required by the displacement

69

Table 4.2. Residual areas associated with the aggregate response equations
and cluster approaches. The residual areas are additive when applying the
cumulative equation. This property was not associated with the displacement

e uafion.
Cumulative Equation Displacement Equation I

 

 

 

 

 

 

 

 

 

Residual Area . Residual Area .
. Resrdual Area for . Resrdual Area for
Appmac“ f°' 333°“ Diamide (min) ”RE???” Diamide (min.)
Cluster l gRepressed) 301 0 1 064 480 37
Cluster 2 (Induced) 5479 5300 367 380
Cluster 1 & 2 Summed 8489 4384 847 417
Single Cluster Approach 8489 4384 482 361

equation, which tends to “flatten” the parabolic shape of the aggregate response
envelopes. This “flattening” could result in larger differences between the
predicted responses using the regression model and measured responses. Thus,
a different regression model may be more suitable for the fitting the aggregate
response envelopes calculated using the displacement equation. This was not
investigated because Moments of Area in Figures 4.1a and 4.1b exhibited
qualitative agreement, regardless of the aggregate response equation. However,
because the regression model in combination with the cumulative response
equation was better suited for Moments of Area, these results were carried on to

the next analysis.

Comparison of strain for various perturbations. For the magnitudes of
the perturbations tested, the stress imposed on the ESR by exposure to DTT
resulted in the largest Moment of Area and hence least stability compared to the
Moments of Area for the other perturbations. This comparison cannot easily be
made in a quantitative manner without the approach being developed here.

Hypo-osmotic shock resulted in the smallest Moment of Area, and hence the

70

greatest stability of the ESR. Normalization by the Moment of Area of hypo-
osmotic shock showed that the stability of the ESR was roughly the same for
hypo-osmotic shock and temperature shock of 25° to 37° C, over twice as stable
compared to osmotic shock. Additionally, the normalization showed that the ESR
for hypo-osmotic shock was five times as stable compared to temperature shock
37°-25° C, six times as stable compared to diamide exposure, approximately
seven times as stable compared to hydrogen peroxide exposure, and twelve
times as stable compared to menadione exposure. The stability of the ESR to
hypo-osmotic shock was ninety times more stable than to DTT exposure.

Such large differences in stability can be evaluated in terms of the stability
parameters. Calculated values for the stability parameters are displayed in Table
4.3. These values were found by taking the natural logarithm and fitting the data
to the equation y(t)=,80 + ,61x, where ,61 is either the value for resilience or
reactivity. In terms of resistance, the ESR was most resistant to the hypo-osmotic
shock and least resistant to diamide exposure, which is also consistent with their
Moments of Area. In terms of reactivity and resilience, the ESR was most
reactive and resilient to osmotic shock, but least reactive to DTT exposure and
least resilient to menadione exposure. It is interesting to note that although the
ESR proved most stable to hypo-osmotic shock it was neither the most reactive
nor most resilient. However, it was the most resistant suggesting that this
attribute of stability contributed most to the overall stability. Likewise, the ESR

showed the smallest stability to DTT exposure even though it was neither the

71

Table 4.3. Comparison of calculated stability parameters and Moments of Area
for the eight perturbations. The differences in Moments of Area can be evaluated

 

 

 

 

 

 

 

 

 

 

 

 

 

 

in terms of the individual stabili carameters.
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Reactivity(1/min) 0.163 0.085 0.137 0.074 0.066 0.035 0.086 0.005
Resilience(1/min) -0.034 -0.015 -0.015 -0.012 -0.015 -0.003 -0.024 0005
Resistance (unitless) 69.4 13.9 27.7 63.7 78.1 52.6 118.7 32.9
Moment ofArea (min2) 1.5x106 5.1x105 8.3x105 3.0x106 3.7x106 7.0x10“3 3.2x10° 4.7x107

 

 

least resilient nor resistant. In this case however, the ESR exhibited the smallest
reactivity, by an order of magnitude compared to the other perturbations

suggesting it contributed most to the overall stability.

Contribution of clusters to the Moment of Area. The magnitudes of the
temperature perturbations and the magnitudes of the osmotic perturbations were
the same, but in opposite directions. The stability of the ESR resulting from a
decrease in 12° C was less than the stability of increasing the temperature by 12°
C. With the osmotic perturbations, the ESR was less stable with increased
osmolarity due to the addition of 1 M sorbitol and more stable upon removal of 1
M sorbitol. The difference in stability can be explained by different contributions
of the clusters originally observed by Gasch et al., (2000), to the overall stability.
The calculated percent contribution of the two clusters to the overall Moment of

Ar ea for hyper-osmotic shock showed that the induced cluster contributed
r0'49th 67% compared to the 33% contributed by the repressed cluster. The

oF’lilosite was observed for the hypo-osmotic shock. The induced cluster

72

contributed roughly 32% and the repressed cluster contributed 68%. This pattern
was not observed for the repressed and induced clusters associated with the
temperature perturbations. Here, the repressed clusters contributed most to the
overall Moments of Area for both shifts in temperatures, i.e., roughly 58% for the
temperature shift from 25° C to 37° C, and roughly 80% for the temperature shift

from 37° C to 35° C.

4.2 Development of Calibration Curves from cDNA Targets

Calibration curves were developed using standards composed of three
target lengths, 101 bp, 104 bp, and 106 bp. Two approaches were employed in
generating amplicons from the targets using RT-PCR. The first approach
involved amplification directly from the short targets described above. The other
involved amplification of the short targets from larger DNA fragments roughly,
1000 bp, which encompassed the sequence of short targets. Figure 4.2a shows
calibration curves resulting from first approach and Figure 4.2b shows the
calibration curves resulting from the second approach. Approximate copy number
is shown above each dilution. Both approaches showed good reproducibility per
size of template, except for the 10“ dilution of RND18-1, which encodes the 185
rRNA. Differences in the Ct values for this dilution ranged from roughly 15 to 25.

No apparent explanation for this poor reproducibility was discovered. For the first

73

 

 

 

 

 

 

 

 

 

 

 

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25 n O 105
w 20 _
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15 d
10 ‘ o 106bp
O 101bp 10'
5 - v 104bp(RDN18-1) 9

 

 

 

 

10'7 10'6 10‘5 10“ 10‘3 10‘2 10’1 10° 101

 

b) 35 DllUthl‘l
30° 102
I 3'3
25~ 10‘
a o
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15~ . 10’
o
106
O 106bp
o 101bp
54 v 101bp(YBR01IC)

 

 

 

10-7 10*" 10-5 10-4 10-3 10-2 10-1 10° 101
Dilution

Figure 4.2. Standard curve development results. (a) Results from the first
approach using small lengths of DNA ranging from 101 bp to 106 bp as
template for amplification. Good reproducibility was observed, but large
separation between lengths occurred at the 10“ and 10*5 dilutions. (b) Results
from the second approach using longer lengths of DNA encompassing the
shorter amplicons. Amplicons were grouped closer together for all dilutions
compared to the first approach.

74

approach (Figure 4.2a), the 10'3 dilution containing 10° copies represented the
upper bound of amplification for the given PCR components and conditions. No
amplification occurred for the 10'1 dilution containing 1010 copies. The upper
bound of amplification for the second approach (Figure 4.2b) was not reached
within the range of dilutions tested. However, it appears from visual extrapolation
that amplification could have occurred with template copies greater than 107.
Disagreement between the amplicon sizes increased with dilution for both
approaches used to generate template. However, comparison of the two
approaches showed that a better agreement between amplicon sizes existed for
the second approach. For the 104 and 10° template copy numbers of the first
approach, roughly 10 cycle thresholds separated the 106 bp and 104 bp
amplicons. In comparison, the number of cycle thresholds of the second
approach separating the same amplicon sizes for the 104 copy number was
insignificant and less than 4 for the 10° copy number. Significant difference in
cycle thresholds of the second approach was not observed until 103 and 102 copy
numbers. A statistical F-test comparing the slopes and y-intercepts (calculated
for the 100 through 10'5 dilutions), between the different amplicon sizes, failed to
rejected the null hypothesis (p-value S 0.05) indicating that there was insufficient
evidence that one of the slopes and intercepts was statistically different from the
others. Thus, it was concluded that the slight difference in amplicon lengths
would not statistically influence the resulting cycle threshold values of the

unkowns.

75

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Time (min)
Figure 4.3. OD600 measurements normalized by absorbance at perturbation
onset for S. cerevisiae. The vertical line represents the onset of the

perturbation. Retarded growth was seen followed by decreased growth rates
with increasing perturbation magnitude.

4.3 Growth of S. cerevisiae under the Applied Osmotic Stresses

Growth of S. cerevisiae following the five osmotic stresses is shown in
Figure 4.3. Absorbance values presented for each perturbation were normalized
by their readings at the time of perturbation. Each perturbation occurred at
roughly 180 minutes indicated by the vertical line. The effects of the perturbations
were demonstrated by an arrest of growth following the perturbation, and a

resumption of growth but at a retarded rate. The time of arrested growth

76

increased with perturbation magnitude and the resumed growth rate decreased.
At 0.5 M NaCl growth arrest either did not occur or was not detected by the
measurement time scale. The rate of resumed growth was 1.47 x 10'2 i 4.5 x 10'
3 min", slightly less than the unperturbed growth rate (1.63 x 10'2 min"). At 1.4 M
NaCl, resumption of growth was not observed for 3 1/2 hrs. following onset of the
perturbation. The new growth rate, 2.58 x 10’3 :t 5.6 x 104 min", was an order of

magnitude less than the growth rate of the control.

4.4 Reactivity, Resilience, and Resistance in Response to Osmotic Stress
Using the developed tools described in Sections 4.1, gene expression
data was analyzed to determine the amount of strain for the five levels of applied
stresses (0.5, 0.7, 1.0, 1.2, and 1.4 M NaCl). Only 153 genes out of the original
169 were used in describing the aggregate response envelope. Cycle threshold
values could not be determined by real-time PCR for the remaining sixteen
genes and therefore they were not included in the analysis. The aggregate
response envelopes shown in Figure 4.4 were calculated for each perturbation
using the cumulative response equation. Asymptotic stability, i.e., a return to pre-
perturbed expression following perturbation, was displayed in response to each
perturbation. It was interesting to note that the time associated with the
occurrence of maximum displacement increased with an increase in the
magnitude of stress. Maximum displacement for the 1.4 M NaCI stress occurred
at a time that was approximately 6-fold longer than the maximum displacement

for the lowest stress tested (0.5 M NaCl). To see if the stability parameters also

77

 

2500

+ 0.5 M NaCl
—0— 0.7 M NaCl
+ 1.0 M NaCI

V 1.2 M NaCI
—I— 1.4 M NaCI

 
   
  

2000 -

1500 d

1000 3

500 -

Cumulative Response [Arfus x (rfus)'1]

 

 

 

l I I I I I

0 50 100 150 200 250 300 350

Time (min.)

Figure 4.4. Aggregate response envelopes of 153 out of 169 genes showing
expression to osmotic shock. The aggregate response was calculated using
the cumulative response equation described in Chapter 3. Resistance
decreases until the 1.2 M NaCI perturbation. For this perturbation and the 1.4
M NaCI perturbation resistance increases.

78

Table 4.4. Calculated stability parameters corresponding to the aggregate
cumulative res onse envelo es shown in Fi ure 4.4.

 

 

 

 

 

[NaCI] Reactivity (min' ) Std. Dev. Resilience (min' ) Std. Dev. Resistance Std. Dev.
0.5 1.2x10'1 2.2x10'2 6.4x10'2 1.9x10'2 1198 513
0.7 7.2x10’2 1 .7x10'2 -5.0x10‘2 2.5x10’2 1800 679
1.0 5.2x10‘T 2.6x10’3 -3.8x10'2 6.7x10’3 2194 210
1.2 3.0x10’" 6.0x10’3 -1.2x10‘2 1.5x10“ 972 272
1.4 7.9x10'3 3.4x10‘2r -7.Ox10'3 3.8x10‘3 1224 109

 

 

 

 

 

 

reflected this trend, reactivity, resilience, and resistance values were also
calculated. These values are listed in Table 4.4. Reactivity associated with the
0.5 M NaCI perturbation was two orders of magnitude greater than the reactivity
associated with the 1.4 M NaCI. Resilience also decreased with increased
perturbation magnitude. Resilience for the 0.5 M NaCl was roughly one order of
magnitude larger than resilience for the 1.4 M NaCI stress. Recall that a
comparatively larger negative value for resilience and a comparatively larger
positive value for reactivity denote greater stability associated with these aspects.
Thus, the aggregate response envelope was more stable in terms of reactivity
and resilience for the 0.5 M NaCI stress than the other stresses. Recall that for
resistance a comparatively larger value denotes lesser stability. Thus, stability in
terms of resistance, decreased for the 0.5, 0.7, and 1.0 M NaCI stresses but not
for the 1.2 and 1.4 M NaCI stresses. For these last two stresses, the resistance
suddenly increased and was similar in magnitude to the resistance displayed by
the 0.5 M NaCI stress.

The increased resistance stepping from 1.0 M to 1.2 M NaCI
corresponded to a 55% net reduction in the aggregate response at the time of

maximum displacement indicating a decrease in contribution of genes and

79

possibly of a shift in the make-up of significantly expressed genes. Forty nine
genes exhibited at least a 2-fold decrease in expression at the time of maximum
displacement from 1.0 M to 1.2 M NaCI. These genes accounted for roughly 83%
of the reduction in aggregate response. Within this percentage, genes making up
the MAPK signaling pathway showed the largest reduction, ~45%, followed by
the glycolysis pathway, ~44%, cell cycle pathway, ~8%, glycerolipid metabolism
pathway, ~3% (Figure 4.5).

Of interest is the number of genes in each pathway and the pathway's
contribution in the observed reduction in aggregate response. The MAPK
signaling pathway included 11 of the 49 genes. However, the cell cycle pathway,
which included 25 of the 49 genes, contributed least among the pathways. Even
more dramatic are the 6 genes of the glycolysis pathway, which accounted for
the second highest contribution in aggregate response reduction indicating the
significant role of these genes. One of which was identified as ALD3 (YMR169C)
encoding an aldehyde dehydrogenase known to respond to osmotic shock and
the general stress response mechanism of S. cerevisiae (Norbeck and Blomberg,
2000). Another gene within this pathway was identified as PDCB (YGR087C), an
isozyme of pyruvate decarboxylase (Eberhart et al., 1999). From the MAPK
signaling pathway was identified CTT1 (YGR088W), which exhibited the second
largest reduction in resposne and is known to encode a catalase that also plays a
role in the general stress response (Vlfiesser et al., 1991).

The gross reduction in aggregate response at the point of maximum

displacement was offset by an increase in relative expression. Twenty five genes

80

Number of Genes (x)

 

Figure 4.5. Comparison of fold changes in relative gene expression stepping
from 1.0 M to 1.2 M NaCl. The largest fraction of genes at 1.0 M NaCI showed
at least a 2-fold increase in expression. Whereas, the largest fraction of genes
at 1.2 M NaCl showed at least a 2-fold decrease in expression. Percentages
associated with the pathways indicate percent contribution in terms of

1.0M

 

1.2M

 

MAPK 19%

Glycolysis 15%

 

l—)

Glycerolipid 10%

 

x > 2-fold

Cell Cycle 56%

 

increase

(_J

2-f0ld > X

 

> 1-fold

 

T

1-fold > X

 

> 0.5-fold

 

Glycolysis 44%

 

r—-)

Glycerolipid
3%

 

MAPK 45%

 

x < 0.5-

 

 

fold
(_____J

 

 

Cell Cycle 8%

 

 

response for the given fraction of genes.

8!

 

exhibited a 2-fold increase in expression going from 1.0 M to 1.2 M NaCI
(Appendix D). Here, 7 of the 25 genes from cell cycle pathway contributed
roughly 56% to this increased response, followed by MAPK signaling, 3 genes
contributing ~23%, glycolysis, 5 genes contributing 15%, and glycerolipid
metabolism, 6 genes contributing 10%. Within the cell cycle pathway, the largest
contributing genes where connected with regulating cell growth including FUSB
(YBL016W), which is required for cell arrest during cell conjugation (Cherkasova
et al., 1999), and NET1 (YJL076W), which encodes a nucleolar protein involved

in mitosis regulation (Shou et al., 1999).

4.5 Calculated Strain for the Applied Stresses using the Moment of Area
The inconsistent behavior between the aspects of stability does not allow
for an overall comparison of stability for the aggregate gene responses
associated with the perturbation magnitudes. Therefore, the Moments of Area
were calculated for the aggregate response envelopes composed of the 153
genes yielding cycle threshold values according to the procedures described in
Chapter 3. Comparatively larger Moment of Area values denote lesser overall
stability. Thus, for the aggregate response envelopes displayed in Figure 4.5,
overall stability decreased with an increase in the magnitude of stress. This was
not surprising for perturbation magnitudes less than 1.2 M NaCI. However, the
decreased overall stability despite the increased resistances for the 1.2 and 1.4
M NaCI perturbations was surprising. Evaluation of the components making up

the Moment of Area revealed the influence of the moment arm on the overall

82

stability, which gives additional weight to response envelopes occurring over a
larger time frame.

The 153 genes were divided according to biochemical pathways, i.e.,
glycolysis, glycerolipid metabolism, MAPK signaling, and cell cycle pathways,
and the contribution of each pathway on the strain was evaluated. For the 0.5 M
NaCI perturbation, glycolysis and the MAPK signaling pathways were roughly
equal in their contribution to the Moment of Area and represented the largest
contribution followed by the glycerolipid and cell cycle pathways. The largest
contribution to the Moments of Area for the 1.2 M NaCl and 1.4 M NaCI stresses
came from the glycerolipid pathway. A transition from glycolysis as the largest
contributor to the glycerolipid metabolism pathway becoming the largest
contributor was observed for the 0.7 M NaCl and 1.0 M NaCI. Glycolysis
contributed least to the Moment of Area associated with the 1.4 M NaCI

perturbation.

4.6 Relationship Between Stress and Strain for Gene Expression Patterns
The Moment of Area calculated above for each magnitude of stress is
plotted in Figure 4.6. It showed an exponential increase with increase in the
magnitude of stress. This relationship was also observed on an individual gene
basis (Figure 4.6a), and for each group of genes making up the four pathways
(Figure 4.6b). Data in Figure 4.6c was linearized by taking the natural logarithm
of the Moments of Area. The slope of the linearized data was found by linear

regression. This slope is defined as the modulus of stability, which predicts the

83

strain associated with changes in stress. A modulus of stability of 4.14 :l: 0.12
[(minz) x M"] was calculated for the aggregate response composed of the 153
genes. This predicts that for every unit change in osmotic stress a change in 4.14
units of strain occurs. Hence, a comparatively larger modulus of stability value
denotes a greater change in strain per unit change in stress. Comparison of
modulus of stability values to a defined standard conveys a degree of sensitivity
to stress relative to the standard. The modulus of stability is of course specific to
many things including the microorganisms, the type of stress, the set of genes
included in the analysis, and the manner in which it was calculated.

The modulus of stability for genes grouped according to biochemical
pathway ranged from 5.31 :l: 0.33 [(minz) x M"] for the glycerolipid pathway to
3.92 :i: 0.21 [(minz) x M“] for glycolysis. This suggests that the stability associated

with the transcriptional response of genes making up the glycerolipid metabolism

84

 

1.2e+6
1.0e+6 4 0
8.0e+5 ‘
6.0e+5 «
4.0e+5 ‘

2.0e+5 4

 

0.0 1

 

1.8e+7 . , . T
1.6e+7 - b)

1.4e+7 ~—
1.2e+7 4
1.0e+7 — + Glycolysis
-O— MAPK Signaling
8.0e+6 ‘ -v— Cell Cycle
6.0e+6 - ‘V— GIYcerolipid
4.0e+6 —
2.0e+6 4

0.0 a
5.0e+7 i i i r i

4.0e+7 - f

3.0e+7 —

 
   

 

Moment of Area [(Arfus x (rfus)") x minzl

2.0e+7 —

1.0917 ‘ I

0.0~* ’

 

 

 

I I I I I

0.4 0.6 0.8 1.0 1.2 1.4 1.6
Perturbation Magnitude (M)
Figure 4.6. Comparison of Moments of area plotted against perturbation

magnitude for (a) individual genes, (b) gene associated pathways, and (c) the
aggregate response of selected genes described in this research.

85

pathway was more sensitive to changes in osmotic stress compared to the
aggregate modulus of stability. Whereas, the stability associated with the
transcriptional response of genes making up the glycolysis pathway was roughly
equal in sensitivity to the modulus of stability of the aggregate. Of interest is the
cell cycle pathway which had a modulus of stability (4.81 i 0.51 [(minz) x M"])
greater than the aggregate set of genes and almost equal to the glycerolipid
pathway, yet contributed the least to the aggregate Moment of Area for each
perturbation. This suggests that while the cell cycle demonstrated greater overall
stability per perturbation, it was more sensitive to osmotic shock compared to the
other glycolysis and MAPK signaling pathways.

Modulus of stability values for individual genes are shown in Figure 4.7
normalized by the aggregate modulus of stability. Only those genes that
exhibited a r2 value greater than 0.90 were included in this figure (roughly 110
out of 153 genes). Genes that were less sensitive to stress relative to the
aggregate modulus of stability are plotted below 1.0. Whereas, genes that were
more sensitive to stress relative to the aggregate modulus of stability are plotted
above 1.0. A larger number of genes exhibited greater sensitivity to osmotic
shock than lesser sensitivity. Of those genes that showed lesser sensitivity most
were part of the glycolysis pathway. The gene, PGM2, showed the least
sensitivity to osmotic stress among the genes plotted. However, no single gene
stood out among those exhibiting greater relative sensitivity to osmotic stress. A
few genes per pathway falling below 1.0 are labeled in Figure 4.7. Among these,

ALD3, which encodes an aldehyde dehydrogenase, proved more sensitive to

86

 

osmotic stress compared to the aggregate for both the glycolysis and glycerolipid
pathways. CDC24, which encodes a GTP/GDP exchange factor showed slightly
more sensitivity than STE7, which encodes a MAP kinase kinase. CDC20, a cell
division control protein showed slightly more sensitivity than its neighbor, MAD2.
A description of all the expressed genes indicated in Figure 4.7 can be found in

Appendix C.

87

Modulus of Stability [(minz) x M"]

Figure 4.7. Modulus of stability values for individual genes normalized by the
aggregate modulus of stability value. Genes greater than 1.0 are relatively
more sensitive to stress than the aggregate modulus of stability. Genes below
1.0 are less sensitive to stress than the aggregate modulus of stability. More
genes showed greater sensitivity to the stress imposed by osmotic shock than

2.5

 

-8 N
01 O
l I

.5
o

p
08 ALD3 MNT3
I

 

.0
0|
1

 

0.0

 

 

C0924 STE? cogzojADz
A503 1/ I I
O O
V I I O
’ 'v v I \i 0 ° 0
5 v "Wyn-u . I. 3...},
V
o C. V‘ I Q o O
Q '1',“ l‘." A O ’°+.9
PYK1 Q .
. TEC1 K m
.TCtB. V YJL218 PDZYEL032W BUBZ
PGK1 ALD4 DAK1 . Glycolysis
C v MAPK signaling
PGM2 I Gycerolipid
0 Cell cycle

 

less sensitivity compared to the aggregate.

88

 

CHAPTER 5

DISCUSSION

5.1 Strain as an Aggregate Response of the Transcriptome to Stress

This research is the first to demonstrate the use of the cumulative
response and relative displacement equations as a means of describing the
aggregate response of a set of genes to stress. This response could be from a
group of genes defined either as a cluster, or a specific functional set such as the
genes making up a biochemical pathway. Describing the aggregate response of
a group of genes has previously been reported in terms of a mean expression
ratio. Gasch et al., (2000), demonstrated the use of the mean expression ratio to
show the reciprocal responses of the ESR cluster to the osmotic and temperature
perturbations. Additionally, hierarchical clustering algorithms often rely on this
mean to build similarity trees from top to bottom (Eisen et al., 1998). However,
using the mean response to represent the group of genes relies on the
assumption that each expression profile within the group is a representative of
the group rather than an individual component.

In comparison, the cumulative response and relative displacement
equations used here to describe the aggregate response of the genes making up
the ESR and four biochemical pathways, assume that each expression profile is
an equally weighted contributor to the group of genes. Rather than measuring the
central tendency, these equations describe the total response of the cluster or

set of genes. Treating each expression profile as a contributor rather than a

89

representative has the disadvantage of being more sensitive to large erroneous
expression profiles. The mean ratio of the group, in such a case, is pulled toward
the erroneous profile, whereas the erroneous profile is propagated to the total
response with the cumulative or displacement equations.

Because of this sensitivity, the demonstration of experimental and
instrument reproducibility takes precedence. Good instrument reproducibility
associated with real time PCR has been demonstrated in the past (Bustin, 2000),
and is often used to validate gene expression measured using dense microarrays
(Talaat et al., 2002; Yuen et al., 2002). The research approach used in this
dissertation was similar to those studies in the sense that previously published
microarray data was used to select a specified number of genes, then real-time
PCR was used to measure their relative mRNA abundance. Because the Taq
polymerase used in this research was produced in house, and PCR conditions
were altered from those suggested by the equipment manufacturer, instrument
reproducibility was tested and found to be excellent, as shown in Chapter 4.
Rather than validating expression profiles using microarrays, experimental
replication was deemed a more suitable use of resources in order to give
statistical significance expression profiles used to generate the aggregate

responses.
5.2 Stability Parameters: Resilience, Reactivity, and Resistance

The biological significance associated with the aggregate responses to the

environmental stresses was demonstrated by comparison of their stability

90

parameters for eight different types of environmental perturbations (Figure 4.1).
Because the magnitudes associated with these perturbations varied, it is entirely
possible that under different perturbation magnitudes, stability in terms of the
stability parameters and Moments of Area could be different than those
estimated in Table 1.1. Normalization by the perturbation magnitudes introduces
non-equivalent units, i.e., molar concentration and temperature, reducing the
number of possible comparisons among the perturbations. However, if the
perturbations could be represented in terms of equivalents of stress, then a more
accurate picture of stability among the different perturbations for the ESR could
be formulated using the analysis and developed tools demonstrated in the
Results Chapter. This opens the possibility of addressing questions related to
controlling gene expression by interchanging different perturbations, i.e., can the
same aggregate response be generated or observed by very different types of
perturbations.

Because the method of calculating strain presented here has never been
used in genomics, no direct comparison to similar studies can be made. Indirect
comparisons are possible, however, between the results obtained from this study
and published research describing the expression of individual genes such as
GPD1 to stress. Rep et al. (1999), observed that the time of occurrence of
maximum relative expression of GPD1 increased, with an increase in NaCl
concentration. It was also accompanied by a decrease in the rate of induction
and rate of feedback, terms describing reactivity and resilience in this

dissertation. In contrast, Rep at al., (1999), did not report any estimation of the

91

kinetics associated with these rates. A lag time following the onset of the
perturbation and the start of induction with an increase in the magnitude of
osmotic shock is also known to occur (Rep et al., 1999, Wuytswinkel et al.,
2000). The reported lag time prior to induction or repression was not directly
observed in this research, perhaps due to the schedule of temporal sampling.

The decrease in reactivity and resilience with an increase in the
magnitude of perturbation observed for a single gene as well as for a larger set of
genes suggests that it is a general property of relative gene expression to
osmotic shock. In the case of GPD1, explanations for decreased stability in terms
of reactivity and resilience could stem from direct inhibition of the transcriptional
factors; Hot1p and Msn2/Msn4p, or indirect inhibition by an impeded high-
osmolarity glycerol signaling pathway (HOG pathway). Evidence of the latter was
presented by Wuytswinkel et al., (2000). Hog1p with a green fluorescent fusion
protein (GFP) was observed to accumulate in the cytoplasm with increased
osmolarity indicating hampered translocation across the nuclear membrane. It
was further demonstrated that the phosphatases responsible for inactivating
Hog1p were inhibited, retarding the reintroduction of Hog1p back to the
cytoplasm. The nuclear accumulation of activated Hog1p in mutants unable to
dephosphorylate this protein proved lethal under osmotic shock (Wuytswinkel et
al., 2000).

Hindered translocation and enzymatic activity resulting in impeded
transcription of GPD1 can possibly be extrapolated to the transcription of many

genes suggested by the decreased reactivity and resilience of the aggregate

92

response. Indeed, Wuytswinkel et al. (2000), hypothesized that this translocation
and hindered phosphatase problem might extend beyond the transcriptional
response of GPD1 to the general stress response. Supporting this hypothesis,
Yancey et al. (1982), in an earlier review on the molecular effects of osmotic
shock discussed the proportional increase in the Michaelis constant (Km) with
increased NaCl concentration on enzyme activity.

The three main stability parameters (resistance, resilience, and reactivity)
can be helpful in identifying the effect of such stresses on the general stress
response. These parameters may also be useful in identifying candidate genes

that are most relevant to nullify the effect of a given stress.

5.3 Moment of Area as a Measure of Strain

Relative gene expression is often compared by measuring the fold-change
in their expression (Causton et al., 2001; Rep et al., 2000; Yuen et al., 2002).
This is an appropriate comparison for relative gene expression at a single time
point. In this case, such an approach is less appropriate for time course
experiments because the relative expression of genes is dynamic. Hence, a fold
change comparison describes only one aspect of the response, in this case
resistance, and does not adequately describe the total response. This was
demonstrated by comparing the observed resistances of the aggregate
responses in Figure 4.5 and Table 1.1 and their respective Moments of Area with
increased osmolarity. An increase in resistance (i.e., decrease in fold-change)

occurred between the 1.0 M NaCl and 1.4 M NaCI perturbations, yet the

93

Moments of Area increased because they encompassed the total response. The
advantage of measuring the overall response using the Moment of Area also has
a disadvantage. The disadvantage in using the Moment of Area can be the
cumbersome calculation (at least at present) and the effect of residual error
associated with regression techniques can make precise calculations and
comparisons of overall stability difficult.

The amount of residual error was critical for deciding whether the relative
cumulative or displacement equations were better suited for calculating the
aggregate response envelopes and is directly related to the regression model
selected to describe the envelope. Because residual error results from the
difference in the predicted value and the measured value, it can be minimized by
the choice of an appropriate regression model. In the case of the linear
regression model used to describe the aggregate response envelopes calculated
from the displacement equation, hypothesis testing for lack of fit, i.e., whether the
linear model was appropriate, was not possible with the single experimental
observations made for response of the ESR. It is possible that different
regression models, even non-linear ones, would have more adequately
described the aggregate response envelopes. This would have been especially
true if the aggregate response envelopes exhibited neighborhood stability, which
was not observed for the ESR or genes associated with the different biochemical
pathways.

lntuitively, it seems that increased activity of the glycolysis, glycerolipid,

MAPK signaling, and cell cycle pathways would be required with osmotic stress,

94

and any stress for that matter, in order to meet additional cell maintenance and
energy needs. In terms of gene expression, this would be implied by an increase
in transcriptional response of associated genes. Hirayma et al. (1995), observed
an increased transcriptional response of genes making up glycolysis to increased
osmotic shock, supporting this observation. In terms of stability, the decreased
overall stability corresponding to progressively larger Moments of Area seems
logical considering the taxation on resources and energy requirements to repair
cell wall damage and produce glycerol. However, the observed change in
contribution of individual genes as well as genes associated pathways to the
overall stability is not easy to explain without a better understanding of their
transcriptional regulation.

It is interesting to note that on a pathway level, the observed shift from
glycolysis as the largest contributor to the Moment of Area to the glycerolipid
pathway indirectly correlates to the three categories of osmotic shock
experienced by S. cerevisiae W303. Mild osmotic shock in terms of NaCl
concentration, occurs from 0.4 M to 0.7 M, while hyper-osmotic shock occurs
from 0.7 M to 1.2 M. Finally, severe osmotic shock occurs at NaCI concentrations
greater than 1.2 M with an upper limit of possibly 1.7 M. Growth of S. cerevisiae
W303 has been observed even at 1.7 M NaCl concentration (Hohmann and

Mager, 1997; Wuytswinkel et al., 2000).

95

5.4 Relationship between Stress and Strain: The Modulus of Stability

The exponential relationship between the Moment of Area and
perturbation magnitude observed for the aggregate response of genes supports
the division of mild, hyper, and severe osmotic shocks. Up to 0.7 M NaCI the
amount of stress per unit strain (slope) remains close to zero. Between 0.7 M
NaCI and 1.2 M NaCI the slope transitions from close to zero to rapidly
increasing. At concentrations greater than 1.2 M NaCI the slope approaches
infinity. The range of NaCl concentrations for which the observed change in slope
transitions from zero to approaching infinity represents a domain of strain that
can be defined by upper and lower boundaries.

An upper boundary must exist for which an additional increase in
perturbation results in complete cellular failure either from complete dehydration
or cell wall failure. Blomberg, (2000), estimated this concentration at roughly 2.0
M NaCl for most S. cerevisiae strains using plating techniques. Although no gene
expression studies for concentrations greater than 1.4 M NaCI have occurred, it
is logical that the aggregate gene response would occur over a longer time
period and its maximum displacement would become increasingly smaller with
magnitudes of stress greater than 1.4 M NaCl. Theoretically, the aggregate
response becomes non-existent right before 2.0 M NaCI, which roughly coincides
with the concentration at which cellular failure happens. These theories are
based on the observed trend in aggregate response envelopes described in

Figure 4.5. Figure 5.1 theoretically depicts this upper boundary as a vertical line

96

 

5.0e+7

4.0e+7 ‘

3.0e+7 ‘

2.0e+7 “

1.0e+7 ‘

 

 

 

Moment of Area [(Aifus x (rfus)'1) x minz]

 

0.4 0.6 0.8 1.0 1.2 1.4 1.6
Perturbation Magnitude [NaCI]

 

‘

Domain of Stability
Stmin 81'

‘max

 

 

Figure 5.1. Plot of moment of area versus perturbation magnitude in terms of
NaCl molar concentration. The domain of stability is depicted between the
lower bound of strain, Stmin, and upper bound of strain, Stmax.

for the strain of the aggregate set of 153 genes, which is labeled as Stmax
(maximum strain)

Two scenarios are possible for defining this upper boundary. In the first
scenario, a collapse in the Moment of Area, from “transcriptional arrest”, at a
concentration greater than 1.4 M NaCI would result in an undefined modulus of
stability. The concentration at which this occurs would represent the upper
boundary of stability for the gene response of S. cerevisiae to osmotic shock. It

seems logical that “transcriptional arrest” would proceed the threshold of cell

97

death. However, whether this “transcriptional arrest” is an instantaneous
occurrence or gradual is uncertain on a single cell level. It seems more likely that
on a population level, transcriptional arrest would not be instantaneous reflecting
the different fitnesses of cells within the population as evidenced by the dramatic
reduction in, yet remaining cell viability following severe osmotic shock.

In the second scenario, the upper boundary would be represented as an
asymptote in which the amount of strain occurring at this magnitude of osmotic
shock is undefined. The amount of strain would infinitely increase as this
asymptote is approached. A weakness of this scenario is the apparent
disconnect between the strain becoming undefined and the need for increasing
transcriptional response as the asymptote is approached. This weakness seen
from a kinetic viewpoint suggests that the rates of transcription and translocation
responsible for the required transcriptional response would soon be unable to
meet the demands for maintaining cell viability.

A lower boundary of strain must also exist for which physiological
conditions are altered just enough so that a transcriptional response is required
altering, at least temporarily, transcriptional equilibrium. This lower boundary
represents the transition from perfect stability to either asymptotic or
neighborhood stability. The lower boundary is theoretically depicted in Figure 5.1,
and labeled as Stmin (minimum strain). The experimental determination of the
concentration of NaCI causing this initial transcriptional response is currently
dependent on the capability of equipment to resolve small changes in mRNA

abundance.

98

CHAPTER 6

CONCLUSIONS AND FUTURE RESEARCH

6.1 Conclusions

The objectives of this study were to develop mathematical tools to quantify
strain at a transcriptome level and to demonstrate these tools in a model
microorganism. Developing new tools to increase our understanding of gene
expression in response to environmental perturbation plays an important role in
genomics. It also indirectly plays an important role in areas that are utilizing the
information learned through genomics. For example, the ability not only to
quantitatively monitor, but also quantitatively describe the response of
environmentally important genes to stress has applications in the area of
biotechnology, biological process engineering, drug development, pathogen
disinfection, and remediation. Because many of the approaches used to fulfill
these objectives are new, or have been adapted from other fields, it was
necessary to demonstrate them in a well characterized model microorganism
such as S. cerevisiae. Vlfith this organism in mind, combined with the defined
objectives, the major findings are summarized below:

1. Gene expression response to environmental stresses can be

described by established definitions of stability.
2. Overall stability calculated from the Moments of Area of individual

response envelopes of genes are additive and statistically equate with

99

the overall stability of the aggregate response made up of the
individual genes.

. The defined environmental stress response of S. cerevisiae exhibited
the most stability to hypo-osmotic shock, and the least stability to DTl'
exposure for the magnitudes of the applied perturbations.

. Stability in terms of the parameters reactivity, resilience, and
resistance decreased with increasing osmotic shock. Overall stability
also decreased with increasing osmotic shock.

. Genes respnsible for glycolysis in S.icerevisiae contributed most to the
Moment of Area at a perturbation magnitude of 0.5 M NaCI. However,
a transition was observed as perturbation magnitude increased. At 1.4
M NaCI, genes belonging to the glycerolipid pathway contributed most
to the Moment of Area.

. An exponential relationship between overall stability and osmotic shock
was observed on an individual gene response, pathway response, and
aggregate response for S. cerevisiae.

. The modulus of stability was defined as the slope of the relationship
between stability and perturbation magnitude, which describes the
sensitivity of gene response to stress.

. Genes belonging to the glycerolipid pathway for S. cerevisiae were
most sensitive to stress from osmotic shock. Whereas, genes
belonging to the glycolysis pathway were least sensitive to stress from

osmotic shock.

100

The research presented in this dissertation combines concepts from
different fields including ecology, engineering, and mathematics and apply it to
genomics. An aim has been to preserve these concepts in their original form.
However, because of the compexity of the genome some concepts have been
slightly adapted to better fit our current understanding. For example, the
displacement equation was origanally intended to describe the resilience of
nutrient cycles not an aggregate response of a set of expressed genes. Also, the
stability parameters, particularly resilience, vary throughout the literature in
definition and calculation method. Indeed, one can become easily and rapidly
confused from reading theoretical papers on ecological stability. For the stability
parameters, the most adaptable definition was applied to observed gene
expression. Application of concepts from other disciplines to genomics is not
new, however. Clustering algorithms so often used to sort related genes
originated from systematic biology. It is expected that the presented concepts,
will serve as a basis for expanding our understanding of the biological

significance of gene expression to environmental perturbation.

6.2 Suggested Future Research

Future research directions utilizing the concepts presented in this
dissertation are potentially many. A few are briefly described below.

Two types of perturbations were defined as press and pulse and the
stability of gene response associated with press perturbations investigated.

However, the stability of gene response associated with pulse perturbations was

101

not investigated. This lack of investigation stemmed from a deficiency of
published gene expression data to this type of perturbation. However, such
perturbations are common. For example, the stability of genes important to waste
water treatment could be investigated in response to a simulated shock loading
of the reactor. Further, modeling the relationship between the pulse perturbation
and aggregate gene response could be adapted and tested from previously
proposed ecological models. An exactly similar experiment conducted with a
pathogen (e.g., Escherichia coli O157:H7) and one of the many possible
disinfectants will be of great value in providing information and modeling the
response of the same organism in the water distribution system to varying
concentrations of the disinfectant. Similar arguments can be advanced for
remediation.

lntuitively, gene response associated with the establishment of a new
equilibrium expression should occur, especially with constitutively expressed
genes. Quantification of this neighborhood stability was proposed but not
demonstrated in this research. This is because the aggregate responses that
were observed demonstrated or tended to return to pre-perturbed expression
despite the environmental change imposed by the press perturbation. However, it
has been observed with GPD1 and other related genes responding to osmotic
shock that following a return to pre—perturbed expression, expression slightly
increases possibly due to adaptation. The overall stability of genes previously
exposed to osmotic shock compared to the stability of genes never having been

exposed to osmotic shock could be investigated.

102

Finally, the application of high throughput genomic technologies to mass
microorganism identification is currently being evaluated. The Moment of Area
and modulus of stability concepts could easily be applied at the organism scale
to describe the stability of microbial communities. If the challenges of validating
organism specificity can be overcome then the stability of individual organisms
within the community as well as the stability of the aggregate community could
be evaluated to different environmental perturbations. Until specificity issues are
resolved the stability of a community “fingerprint” could be observed to different

perturbations.

103

APPENDIX A

COMMON METRICS USED FOR MEASURING SIMILARITY (NEARNESS),
DISSIMILARITY, AND CONFIDENCE

Metrics and associated equations for defining similarity, dissimilarity, or
confidence between expressed genes are displayed in the following table. Where
G represent the primary data of a gene for condition or time point iover a series
of m1 conditions and time points, with X and Y representing gene expression
vectors for comparison. For time series, in which expression profiles are
compared by rows in the expression matrix, the selected metric is normalized by
the number of time points in the series.

104

Table A.1. Additional metrics used for relating similarity and dissimilarity of

relative ene ex ression data obtained from microarra studies.
Metric Equation Category Source

 

 

 

 

 

 

 

 

 

 

 

Legrendre and
Euclidean _ "' 2 Distance Legendre, 1998;
D(X’Y)_ ;(Xi—Yi) Wenetal.,1998
m Pielou, 1984;
Manhattan _ _ Distance Xia and Xie,
D(X,Y)-§IXI YII 2001
m Pielou, 1984;
Chord Distance Xia and Xie,
D(X,Y)=Z(VX,-\/Z)2 2001
i=1
m X. — Y Y. — 7
Pearson or 5(X,Y)=Z[ ' II ' I
M°°'f'°° ‘=' (DX (DY Nearness Eisen et al., 1998
Pearson (See )2
footnote a) m G. _ E
(D = '
. I; I—m
Similar to Pearson’s with the exception that . .
Spearman objects are first ranked according to their Nearness Xla 23881X'e'
measured values.
Jackknife
(I) (2) (m) I Heyer et al.,
See footnote . Nearness
( b) J,_, = mmISX, ...S,,, ,...S,,, ,..5,,,, ) 1999
Zmin(X,. , 7,.)
R PerCem C(X, Y) = 100 — 100 ‘=‘ Confidence Pielou, 1984
emoteness m

 

Zmax(X..Y.-)

i=l

 

 

aEisen et al., (1998) uses Gofise. instead of the mean of G over m observations. Gags... represents a
reference or standard value in which to compare with G,.
t"l’he Jackknife correlation is really just the minimum value from a correlation set obtained by

deleting the ith observation and calculating a new value, SW”.

1 ()5

APPENDIX B

MATHCAD PROGRAM USED FOR CALCULATING THE MOMENT OF AREA
FOR LARGE DATA SETS

The following program was used to calculate the Moment of Area for large
data sets. The program can be divided into four areas: 1) linear regression
analysis, 2) statistical analysis, 3) Moment of Area calculation, and 4) generation
of and output table containing results. A detailed explanation of commands used
for the program can be found in the software manuals.

l06

MOA :=

 

Alc— READPRN "C:/test/test.txt" )

"Regression Analysis: finding coefficients"

for al 6 (1.. (cols(A1)— 1))

cIan" Iblalbi
dlai" Iblaibi‘
elalé— iblal,
flalt— ibl

glale— bel

 

81,0

Clc—augment(c1,dl)
D1+—augment(el,fl)

Eli—augment(Cl,Dl)
Flt—augment(E1,g1)

Gl+—(FI)T

bla'c—linfitIA1<0>,Al

0,:
31.0.3.0

”4,0

<l> ‘
3 ,AI

WRITEPRN"C:/test/coefficients.txt" ) :=Gl

"Regression Analysis: multiple regression statistics"

Hli—submatn'x(Gl,0,(rows(Gl)— l),1,(cols(G])— 1))
for hl e 0.. (cols(Hl)— l)
for ile 0.. (rows(Al)- l)

jInf—mom T HILhi'Ali

klii,hi‘—j]hi

llo—submatn'x(Al,O,(rows(A1)— I),1,(eols(Al)— 1))

"Regression Analysis: multiple regression statistics:SS(Residual)"

—->
Jlt—(kl-ll)2

for 116 0.. (cols(ll)— l)

mini—”£11“>

T

nlo—ml

"Regression Analysiszmultiple regression statistics: residual standard deviation)"

————)
0114—— _n_]___.
(il+l)-4

107

MathCad Program (continued)

 

"Regression Analysiszmultiple regression statistics: SS(Total)"
for “IE 0.. (cols(.ll)— 1)

<1”)
mnmh'le
il+l
I'lllt—mllT
for 1126 0.. (cols(nll)-— 1)

for 1136 0.. (rows(ll)— l)
mlzmc—Ill

nlzll3,112‘_m]2112

<ll2>
2

.2
"”0,ii2’

113,112-
nl3nzc—an

ml31—n13T

"Regression Analysiszmultiple regression statistics: SS(Regression)"

 

————)
nl4e—(ml3—nl)

"Regression Analysis:multiple regression statistics: coefficient of determination R"2"

‘3 i
n154— Im13— nlI
\ m13 /

"Regression Analysiszmultiple regression statistics: F test statistic calculated"

n161—

 

(i1+1)— 4
"Center of Mass"
for ole 0.. (rows(Al)— l)

 

ph—AIOLO
for ql e 0.. (cols(Gl)— I)

up]

rlqlt—‘I Glo‘ql+Gll’ql-H-Glz'ql-x2+Gl3,ql-x3+(314‘qI-x4 dx
0
0p]

slqlc— x- Glow+G11,qi'x+Glz,qi'x2+GI},qi'x3+Gl4,qi'x4.dx
0
Op]

thlt—I (310m+GILqI-xl-(112.q|~x2+GILqI-x‘i-rGIMII-x4 de
O

 

108

MathCad Program (continued)

"'Center of Mass: x-coordinate"

sl 1
ul 4-—_q_.

q] rl
ql

"Center of Mass: y-coordinate"

tl 1

VI l<—0.5-—q
q r1

ql

 

r11«—submatrix(rl, 1,(r0ws(r1)- l),0,cols(rl)— 1)
ullc—submatrix(u1,1,(r0ws(u1)- l),0,cols(u1)-— 1)
v11«—submatrix(v1,1,(r0ws(v1)— l),0,cols(v1)-— 1)
"End"

"Moment Arm"

for W] e 0.. (rows(ul)— l)

  

xl «—
wl

 

, wl,0
x1k—submatn'x(x1,1,(r0ws(x1)—l),0,cols(xl)—1)
"End"

"Moment of Area"

for yl e 0.. (rows(xl)- 1)

zlyli—rlyl-xlyl

zll<—submatrix(zl,l,(rows(zl)—1),0,cols(zl)-l)
"End"

"Organizing Results"

 

ch— augment(m1, r1 1)

L14— augment(K1, ul 1)

Mlc—augment(Ll, v1 1)

N11—augment( M l , xl l)

011-— augment( N1, 21 1)

PI«— ( "Residual Standard Deviation" "Area" "x" "y" "Moment Arm" "Moment of Area" )
Qlt—stack( P1,0I)

ol 1

 

109

APPENDIX C

DESCRIPTION OF GENES GROUPED ACCORDING TO BIOCHEMICAL
PATHWAY USED TO STUDY RELATIVE GENE EXPRESSION T0 OSMOTIC
SHOCK.

Genes studied in response to osmotic shock are listed in the following
Tables. Description of genes and related information was obtained from the
Saccharomyces cerevisiae genome database (SGD) located at
www.yeastgenome.org. Diagrams for each pathway can be obtained from the

Kyoto encyclopedia of genomes and genes (KEGG) located at
www.genome.ad.jp/kegglkeggz.html.

110

 

 

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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118

APPENDIX D

GENES EXHIBITING A SIGNIFICANT INCREASE OR DECREASE IN
EXPRESSION STEPPING FROM 1.0 M T0 1.2 M NACL

Genes exhibiting a decrease in relative expression of at least 0.5 and
those genes exhibiting an increase in at least 2-fold expression stepping from 1.0
M to 1.2 M NaCl are displayed in the table below. Relative expression values
were obtained from the ratio of the 1.2 M NaCI data and the 1.0 M NaCl data.
Negative values indicate a decrease in expression stepping from 1.0 M to 1.2 M
NaCI. Positive values indicate an increase in expression stepping from 1.0 M to
1.2 M NaCl. Highlighted genes are discussed in the results section.

119

 

Table 0.1. Genes exhibiting a significant increases or decreases in relative
expression at the time of maximum displacement. Comparison between the 1.0
M and 1.2 M NaCI erturbation ma nitudes.

 
  

        
      
 

     

Systematic Standard Gene Description Pathway *Change in

Name Name Response
from 1.0 M to

1. 2 M NaCI

 

“Genes exhibiting a decrease in relative expression of at least 0.5 stepping from 1.0 M to 1.2 M
NaCI.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

YBR136W MECt 53$? $622313?” '"duced Cell Cycle -o.77
YER173W RAD24 Cell cycle checkpoint protein Cell Cycle -5.04
YGL003C CDH1 figggg'géi‘tsggfifgggvam °‘ APC‘ Cell Cycle -5.os
YGL086W MAD1 Spindle assembly checkpoint component Cell Cycle -9.77
YGR092W DBF2 Serine/threonine protein kinase Cell Cycle -0.77
YGR113W DAM1 Essential mitotic spindle pole protein Cell Cycle -2.13
YGR1 88C BUB1 figzcszlépolnt senne/threonlne-proteln Cell Cycle -2.64
YIL046W MET30 gigjflrfgifgu'ates sum" am'"° ““5 Cell Cycle -1 .35
YJL030W MADZ Spindle-assembly Checkpoint protein Cell Cycle -3.94
YJL074C SMC3 Chromosome segregation protein Cell Cycle -0.99
YJL21OW PEXZ Peroxisomal assembly protein - peroxin Cell Cycle -1.15
YJR053W BFA1 Unknown Cell Cycle -1.58
YJROQOC GRR1 33:32:23? $315332; if?“ and f°' Cell Cycle -2.3a
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YLR21OW CLB4 Cyclin, GZ/M-specific Cell Cycle -1.27
YLR288C MECB GZ-speciflc checkpoint protein Cell Cycle -3.83
YML064C TEM1 GTP-binding protein of the ras superfamily Cell Cycle -5.81
YML065W ORCt gamifiwgmm “mp'ex ”“3"” Cell Cycle -207
YMROOlC cocs gzgfgg‘zmabsfuflfrhxmwms at the Cell Cycle -1 .27
YMROSGC lMlH1 M-phase inducer phosphatase Cell Cycle -3.72
YNL289W PCL1 Cyclin, G1/S—specific Cell Cycle -1.77
YOR368W RAD1? DNA damage checkpoint control protein Cell Cycle -5.94
YPL153C RADS3 serlthr/tyr protein kinase Cell Cycle -2.90
YPL194W 0001 DNA damage checkpoint protein Cell Cycle -37.48
YPR111W DBF20 Cell cycle protein kinase related to DBF2P Cell Cycle -9.62
YAL0540 ACS1 Acetyl-CoA synthetase Glycolysis -5.31
YGR087C PDC6 Pyruvate decarboxylase isozyme 3 Glycolysis -99.94
YLR377C F BP1 Fructose-1 .6-bisphophatase Glycolysis -8.79
YMR1690 ALD3 Aldehyde dehydrogenase (NAD(P)+) Glycolysis 479.33
YMR3030 FKS3 1,3-beta-glucan synthase Glycolysis -1.89
YPL017C YPL017C Dihydrolipoamide dehydrogenase Glycolysis -38.20
YDR147W EKl1 Ethanolamine kinase Glycerolipid -5.46
YGR170W PSDZ Phosphatidylserine decarboxylase Glycerolipid -2.36

 

 

120

 

 

 

 

Table D1. Continued

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

121

 

 

Systematic Standard Gene Description Pathway *Change in
Name Name Response
from 1.0 M to
1.2 M NaCI
YHL032C GUT1 Glycerol kinase Glycerolipid -0.69
YlL155C GUT 2 Glycerol-3-phosphate dehydrogenase Glycerolipid -2.74
YKR031C SPO14 Phospholipase D Glycerolipid -3.71
YML07OW DAK1 Dihydroxyacetone kinase Glycerolipid ~28.28
YOR374W ALD4 Aldehyde dehydrogenase Glycerolipid -5.54
YBR200W BEM1 Bud emergence mediator MAPK -1 .33
Two-component phosphorelay MAPK
YDL235C YPD1 intermediate -6.46
serine/threonine protein kinase of the MAPK
YGRO40W KSS1 MEKK family -1.41
YGR088W CTT1 Catalase MAPK -626.33
Cuanine nucleotide-binding protein alpha- MAPK
YHR005C GPA1 1 subunit -2.13
Tyrosine protein kinase of the MAP MAPK
YJL128C PBSZ kinase kinase family -o_53
YKR095W MLP1 MLosin-like protein MAPK -1.19
Osomolarity two-component system MAPK
YLROOBC SSK1 protein -0.73
Ser/T hr protein kinase involved in the MAPK
YLR362W STE11 mating signalling pathway -1.60
YMR037C MSN2 Stress responsive regulatory protein MAPK -2.32
Putative transcriptional activator of alpha- MAPK
YMR043W MCM1 specific genes -0.76
"Genes exhibiting an increase in relative expression of at least 2-fold stepping from 1.0 M to
1.2 M NaCI.
YBL016W Fuss m::g;n'a°"va‘ed pm‘e'" “"359 (MAP Cell Cycle 32.46
YBR093C PH05 :RPespgfssible acid phosphatase precursor Cell Cycle 1.05
YBR135W CKSt Eggflggtdepewem kinase 'egu'am'y Cell Cycle 10.33
YDR507C GIN4 serine/threonine-protein kinase Cell Cycle 0.43
Phosphate system positive regulatory
YFR0340 PHO4 protein PHO4 Cell Cycle 2.78
YGL201 C MCMB Involved in replication Cell Cycle 0.83
YJL076W NET1 Establishes silent chromatin Cell Cycle 25.82
YBR196C 23211 Phosphatidate cytidylyltransferase Glycolysis 0.58
. 1-acyl-sn-glycerol-3-phosphate .
YDROSOC SLC1 acyltransferase Glycolysrs 2.35
YDR380W PH08 Repressible alkaline phosphatase Glycolysis 12.34
YER178W MNTZ Alpha-1 ,3-mannosyltransferase Glycolysis 0.58
YGR24OC MUQl Choline-phosphate cytidylyltransferase Glycolysis 1.20
Ethanolaminephosphotransferase .
YKL0600 EPT1 (ETHPD GlycolySls 2.43
YBROZQC GPP1 Glycerol biosynthesis Glycerolipid 0.35
YDL05ZC PGl1 Glucose-G-phosphate isomerase Glycerolipid 0.30
YDR481C TPl1 Triosephosphate isomerase (TIM) Glycerolipid 1.44
YGL257C AR010 Pyruvate decarboxylase Glycerolipid 0.54
Pyruvate dehydrogenase E1 component, . .
YGR007W PDA1 al ha subunit Glycerollpld 7.87

 

      

 

 

 

 

 

 

 

 

 

 

 

 

Systematic Gene Description Pathway *Change in
Name Name Response
from 1.0 M to
1.2 M NaCI
YHR123W PFK1 6-phosphofructokinase Glycerolipid 1 .69
YlL053W FBA1 Fructose-bisphosphate aldolase Glycerolipid 1.57
MA...
YFL026W STE2 Pheromone alpha factor receptor MAPK 11.29
YKL178C STE3 Pheromone A factor receptor MAPK 1.05
YPL089C RLM1 Serum response factor-like protein MAPK 0.40
YPR165W RHO1 giggl'ifig‘fio‘t’gg?" °f "'8 "‘° SUDfam'” MAPK 11.38

 

*The Change in response is the difference between the relative expression for the 1.0 M and 1.2
M NaCI perturbations. Negative values indicate a decrease in the response.

“Relative expression values were obtained from the ratio of the 1.2 M NaCI data and the 1.0 M
NaCI data.

122

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