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PART I
STRUCTURAL STUDIES IN PORPHYRINS
AND COFACIAL DIPORPHYRINS
PART II
STRUCTURE OF 2-KETO-3-DEOXY-6-PHOSPHOGLUCONATE

ALDOLASE AT 2.8 A RESOLUTION AND ITS
IMPLICATION IN MOLECULAR EVOLUTION

BY

Marcos H. Hatada

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department Of Chemistry

1982

ABSTRACT

PART I
STRUCTURAL STUDIES IN PORPHYRINS AND
COFACIAL DIPORPHYRINS
PART II
STRUCTURE OF 2-KETO-3-DEOXY-6-PHOSPHOGLUCONATE

ALDOLASE AT 2.8 A RESOLUTION AND ITS
IMPLICATION IN MOLECULAR EVOLUTION

BY
Marcos H. Hatada

The structure of the synthetic analog of heme-a,
l,3,5,7-tetramethyl-2,6,-di-n-pentyl-4,8-diformyl
porphyrin (DFP), was determined by X-ray crystallographic
methods. The crystal structure of DFP was solved by
direct methods using the program MULTAN. The porphine
core of DFP is very similar to other free base porphy-
rins. The formyl group does not seem to cause any
significant effect on bond distances and angles except
at or near the point of substitution.

The structure of the cofacial dicopper hexyl dipor-
phyrin-7 (CUZDP-7) was also determined by X-ray
crystallographic techniques. The crystal structure was
solved by use of the Patterson function and the tangent

formula. The two porphyrin rings of Cu DP-7 slip with

2

respect to each other by 3.8 A. The crystals are
composed of d,l enantiomorphs which leads only to
disordered carbonyl 0 atoms.

The structure of CuZDP-7 was redetermined at
-150°C (LT). The parts of the structure that had the
higher thermal parameters at room temperature proved
to be regions with disordered atoms. Except from the
foregoing, the structure of LT-CuzDP-7 is essentially
the same as that at RT.

The 2.8 A resolution structure of 2-keto-3-deoxy-
6-phosphogluconate (KDPG) aldolase has been established.
The chain folding of KDPG aldolase can be described in
terms of an inner cylinder composed of eight B-strands
and an outer coaxial cylinder of a-helices that connect
adjacent B strands. The active Lys residue is located
on a shallow depression on the surface of the molecule
at the end of the a/B-barrel cavity.

The chain folding of KDPG aldolase is very similar
to that of triose phosphate isomerase (TIM) and domain
A of pyruvate kinase (PK). A quantitative comparison
of the geometry of the main chain folding was carried
out by the method described by Rossmann and Argos (1975).

This comparison showed that secondary structural

segments basically correspond in the different enzymes.

This similarity in the folding of KDPG aldolase, TIM

and PK can be a result of divergent evolution from a
common ancestor or convergent evolution to a highly
symmetrical and perhaps highly stable form of the

a/B barrel. Evidence for both hypotheses are examined

and discussed.

ACKNOWLEDGMENTS

To Dr. Alexander Tulinsky, for his constant
guidance, encouragement and friendship throughout this
study, I wish to express my deepest gratitude.

My sincere appreciation is extended to Dr. Lukasz
Lebioda and Dr. Irene Moustakali-Mavridis for I
indispensable contributions to this study and for the
many stimulating discussions.

I am greatly thankful to Dr. Chi K. Chang for his
cooperation in providing the porphyrin and the
diporphyrin‘samples.

I am indebted to Dr. Donald Ward for the use of

a data collection facility, many computer programs and

helpful discussions. Thanks are extended to Dr. David
J. Duchamp and to Ms. Connie Chidester also for the use
of a low temperature data collection facility.

I am grateful to Dr. Willis Wood for useful dis-
cussions and to Mr. Paul Kuipers for cooperation in pro-
viding the aldolase crystals.

I would like to thank Dr. Thomas V. Atkinson for
invaluable technical assistance and Dr. N. V. Raghavan
and Dr. Lawrence Weber for helpful discussions. I am
also indebted to Mrs. Debbie WUethrich for assistance in

typing this dissertation.

ii

Support of the Michigan Heart Association,
National Institutes of Health and Michigan State
University is gratefully acknowledged.

Thanks are also due to Dr. Michael Rossmann for
providing the protein comparison program.

Finally I would like to thank all members of
Dr. A. Tulinsky's laboratory for their general

assistance.

iii

To my parents

iv

TABLE OF CONTENTS

LIST OF TABLES O O O O O O O O I O O 0

LIST OT FIGURES. . . . . . . . . . . .

PART I Structural Studies in Porphyrins and

Cofacial Diporphyrins

1,3,5,7-Tetramethyl-2,6-di-n-pentyl-4,8-diformy1

Porphyrin' I o o o o o o o o o o 0

Introduction . . . . . . . . . .
Experimental . . . . . . . . . .
Structure Solution and Refinement
Results . . . . . . . . . . . . .
Discussion. . . . . . . . . . . .

Cofacial DiCOpper Hexyldiporphyrin . .

Introduction. . . . . . . . . . .
Experimental. . . . . . . . . . .
Structure Solution and Refinement
Results . . . . . . . . . . . . .
Discussion. . . . . . . . ... . .

CuZDP-7 Low Temperature Determination.

Experimental. . . . . . . . . . .
Refinement. . . . . . . . . . . .
Results . . . . . . . . . . . . .
Discussion. . . . . . . . . . . .

Page

vii

(DCDU’IDJI-‘H

24

24
30
34
38
45

56

56
57
62
62

Part II Structure of 2-Keto-3-Deox -6-Phospho-
gluconate Aldolase at 2.8 Resolution
’and Its Implication in Molecular
Evolution A

Introduction . . . . . . . . . . . . . . . . . . .
Measurements of Kendrew Model Coordinates. . . . .
Description of the Molecule of KDPG Aldolase . . .

General . . . . . . . . . . . . . . . . . . .
o/B Barrel Cavity . . . . . . . . . . . . . .
B Bends . . . . . . . . . . . . . . . . . . .
Ion Pairs . . . . . . . . . . . . . . . . . .
Hydrogen Bonds. . . . . . . . . . . . . . . .
Environment of the Residues . . . . . . . . .
The Trimer. . . . . . . . . . . . . . . . . .
Packing of the a-Helices and B-Strands. . . .
Heavy Atom Derivative Sites . . . . . . . . .

Active Site Region of KDPG Aldolase . . . . . . .
Comparison of the Structures of KDPG Aldolase. . .

Qualitative Comparisons . . . . . . . . . . .
Quantitative Comparisons. . . . . . . . . . .
Implications in Protein Evolution . . . . . .

APPENDIX I Details of the Measurement of Kendrew
‘ Model Coordinates With Two Theodolites

APPENDIX II Method for Systematic Comparison of
Two Molecular Structures (Rossmann
and Argos, 1975). . . . . . . . . . .
APPENDIX III Environment and Quality of the
Electron Density of the Residues
of KDPG Aldolase . . . . . . . . . .

REFERENCES 0 O O O O O O O O O O O O O O O O O O 0

vi

Page

74
87
94

94
102
106
108
111
114
119
124
128

132
142

142
145
159

170

176

183
191

LIST OF TABLES

Table . Page
I Final Atomic Parameters of DFP. , ; _ , , , ‘9
II. Final Hydrogen Atom Parameters. _ . . . . , 10
III Deviations of the Atoms of the Pyrroles
of DFP from Their Best Least Squares
Planes O O O O O O O O O O I O O O O O O O O O 12
IV Final Atomic Parameters of Cu2DP-7. . . . 39
V Comparison of the RT and LT Cell
Parameters of CuZDP-7 . . . . . . . . . . . 58
VI Comparison of RT and LT Refinements of
cuZDP-7 o o o o o o o o o o o o o o o o o o 63
VII Final Atomic Parameters.of LT-CUZDP-7 ; . . 54
VIII Comparison of Peak Heights of CuTPrP
at RT and LT-Cu DP-7. 71
2 o o o o o o o o o o 0
IX Comparison of bond distances measured
with two theodolites and those measured
with a surveyor's transit-cathetometer. . 92
X Secondary Structural Elements of KDPG
AldOlase. . g o 0 o o o o o o o o o o o 98
XI Summary of the Quality of the Density

of Side Chains in the Electron Density
Map Of KDPG AldOlase. O O O O O O O O O O O 100

XII(a) Residues Related to a/B Barrel Cavity . . 103

XII(b) Residues at the Amino End of Barrel
Cavity Adjacent to I-helix Residues at
the Carboxyl End of Barrel. . . . . . . . 104

vii

Table Page

XIII B-Bends of KDPG Aldolase . . . . . . . . . 105
XIV Ion Pairs of KDPG Aldolase . . . . . . . . 109
XV Hydrogen Bonds of KDPG Aldolase. . . . . . 113
XVI Summary of the Environment of the

Residues in KDPG Aldolase. . . . . . . . . 116
XVII(a) Residues of KDPG Aldolase on the Surface . 117

XVII(b) Residues of KDPG Aldolase Near the Surface 118

XVII(c) Buried Residues of KDPG Aldolase , . . , . 118
XVIII Trimer Interfaces

(a) Trimer of the First Kind

(b) Trimer of the Second Kind, , , , , , , , , 121

XIX(a) Distance of Closest Approach Between
Axis of Helix and the B-Strands. . . . . . 125

XIx(b) Residues in the Helix-Strand Interface . . 125

XX(a) Distance of Closest Approach Between
Helix Axes O O O O O I O O O O O I O O O O 127

XX(b) Residues in the Helix-Helix Interface. . . 127

XXI Heavy Atom Parameters of the Isomor-
phous Derivatives. . . . . . . . . . . . . 129
XXII Interaction of KDPG Aldolase With Sub-

strate and Substrate Analogs . . . . . . . 136

XXIII Experiments Giving Rise to No Intensity
Changes in KDPG Aldolase , , , , , . , . , 139

XXIV Comparisons of the Structures of KDPG
Aldolase, TIM and PK in Different

Superpositions . . . . . . . . . . . . . . 153

viii

Tables Page

XXV Structural Equivalences Among KDPG
Aldolase, TIM and PK, , , , , , . . . . . 160

ix

Figure

LIST OF FIGURES

Structural formulas of the free base
porphyrins heme-a (l) and of its
synthetic analog l,3,5,7-tetramethyl-

2,6-di-n-pentyl-4,8-diformyl porphyrin (2).

Numbering system of DFP . . . . . . . .

0
Deviations (in A) of the atoms of DFP
from the best least squares plane . . .

Interatomic bond distances (in A) and
angles (in deg) of DFP. . . . . . , . .

Average structure for porphine and DFP
(underlined) with the differences

(A for porphine and 6 for DFP) between
pyrrole rings . . . . . . . . . . . . .

Comparison of the central core of por-
phine (top) octaethylporphyrin (center
and DFP (bottom). . . . . . . . . . . .

Comparison of substituted pyrrole rings

and the formyl-pyrrole with the formyl

group of DFP

a. 3-Ethbxycarbonyl-l,2-dimethyl-4-
pyrrole-carbaldehyde

b. 4-acetyl-3-hydroxymethylpyrrole

c. Ethyl 4-Acety1-3-ethy1-5-methyl-
pyrrole-Z-carboxylate

d. DFP

Packing diagram of DFP. . . . . . . . .

Cofacial diporphyrin-7, , , . , . . . .

Page

Figures

10

ll

12

13

14
15

16

17

18

Page
Cofacial diporphyrin biomimetic models
a. "Special pair" chlorophyl models
reprinted from (I) Katz et a1.,
(1976) and (II) Fong (1974)
b. Cytochrome oxidase, according to
Palmer et a1., (1976)
c. Sterically crowded heme with "bent"
Fe-C-O bond (I) and its synthetic
‘ model (II). . . . . . . . . . . . . . . 27
Hexyl cofacial diporphyrin-7
(a) syn-isomer
(b) anti-isomer . . . . . . . . . . . . . 31

Stepwise development of the structure of

Cu DP-7 with Karle recycling. Atoms

la eled 1,2,3 and 4 were used in the _

nth cycle to produce atoms labeled n+1, , , 35

Flow chart of the course of the
refinement 0f CUZDP'7 o o o o o o o o o o o 36

Numbering scheme of Cu7DP-7 , , ; , , y 1 , 43

Deviations (in A) of the atoms of CuZDP-7 from
the best least squares plane. . . . . . . . 41

Interatomic bond distances (a, in A)
and bond angles (b, in deg) of CuzDP—7, , , 42

Perspective ORTEP drawing of Cu DP-7.

Pyrrole nitrogen atoms are numbered and

the black circles represent disordered

carbonyl oxygen atoms . . . . . . . . . . . 44

Projection of the central core of one
porphyrin of CuZDP-7 onto that of the
other. Distances in A, angles in deg.
(The N -N2 component of the slip is

0.63 A} , ,

O O C O O O I O O O O O O O O O 46

xi

Figures

19

20

21

22

23

24

25

26

27

28

29

Perspective drawing of Cu2(FTF 6-3,2-NH-
diamide) (a) and a packing diagram (b), ,
Stacking of CuzDP-7 along b axis. Views
along ring directions (a) and mutually
perpendicular (b). . . . . . . . . . . . .
Comparison of average bond distances

(in fi)and angles (in deg) of pyrroles

in CuTPrP (a) and CuzDP-7 (b). . . . . . .

Flow chart of the course of the refinement
of LT-Cu DP-7.

2 o o o o o o o o o o o o o o

0
Deviations (in A) of the atoms of LT-CU DP-7

from best least squares plane. . . . . g .

Interatomic bond distances (a, in A)

and bond angles (b, in deg) of LT-CuZDP-7.
Comparison of peak heights (in eA-B) of
RT-CuzDP-7 and LT-CuzDP-7 (underlined)
Broken lines correspond to disorder
observed in LT-CuzDP-7..
Two stages of the glycolytic pathway
(Embden-Meyerhoff), showing the pivotal
position of aldolase.,

Glycolytic pathway (Entner-Doudoroff)

in Pseudomonas. G-3-P is converted to
Py by stage II of the Embden-Meyerhoff
pathway. . . . . . .

Specificity of KDPG aldolase

Proposed mechanism of KDPG aldolase.

xii

Page

48

51

55

60

Q
m

'67

70

76

78
81
83

Figure

'30

31
32
33

34
35
36
37

38

39
40

Arrangement of asymmetric units in the

unit cell of KDPG aldolase.
of the first kind (AAA, BBB,

Trimers

...);

trimers of the second kind (ABC, BCD,
...); three-fold axis (3) is body
diagonal; other three-fold axes pass

through cell edges and cell

faces

(reprinted from Mavridis and Tulinsky

(1976)

Geometry of the measurement of Kendrew
model coordinates. Theodolite (I) is

the origin of the coordinate system.

Ca diagram of KDPG aldolase

Ribbon drawing of KDPG aldolase with
I-helix (drawn by Dr. L. Lebioda).

Type I B—bend in KDPG aldolase.,

Hydrogen bonding scheme of the B-strands

Ca drawing of the trimer of
kind: three-fold axis shown

Ca drawing of the trimer of
kind; three-fold axis shown

Entrance to the active site
KDPG aldolase

the first
approPriately.

the second
appropriately.

region of

Active site region of KDPG aldolase..

Ribbon drawing of KDPG aldolase down
the o/B barrel axis (drawn by Dr. L.

Lebioda). For clarity, the

first 25

residues which are not part of the
barrel have been omitted (region includes

I-helix)

xiii

Page

85

89

96

97
107

112

122

123

133

134

143

Figure

41

42

43

44

45

A1

(a)

(b)

AI

‘priately designated.

Page

Ca backbone structures of KDPG aldolase,

TIM and the A domain of PK. All

viewed down the B-barrel axis and in

best least squares orientation. . , . . , . 144

Distance diagonal plots of KDPG aldolase,

TIM and PK. Contours at 6.0, 11.0 and

16.0 A; secondary structural elements
designated along the diagonal, break

in PK sequence apprOpriately noted. . . . , 145

Structural features of KDPG aldolase
diagonal plot (from Kuntz (1975)) , , , , , 150

Best fit of Ca backbones of KDPG aldo-
lase, TIM and PK. Heavy lines corre-
spond to secondary structural elements;
Lys 144 of KDPG aldolase and Glu 165
of TIM are marked with arrows; break
in PK sequence appropriately designa-

ted. C C O O O C O O O O O O O O O I O O O 154

"Cross" diagonal distance plots of
differences in Ca -positions between
KDPG aldolase—TIM and KDPG aldolase-
PK in their superimposed orientation.
Contours at 6.0, 11.0 and 16.0 A;
secondary structure elements appro-

. O O O O O O O O O O 157

Transformation of spherical coordi-
nates to system in which the second
theodolite has coordinates ¢ = 0,

X = n/Z when viewed from first
theodolite.

Coordinate systems of the two theo-
dolites.

Rotation of the coordinate systems
by an angle 1 around both y axes. , , , , , 171
The Eulerian angles 0 , 02 and 03

relating the rotated Axes x', y', z'

to the original unrotated orthogonal

axes x'Y'z' o o o o o o o o o o o o o o o o 178

xiv

PART I

STRUCTURAL STUDIES IN PORPHYRINS
AND COFACIAL DIPORPHYRINS

l,3,5,7-Tetramethyl-2,6-di-n-pentyl-4,8-diformyl porphyrin
Introduction

Cytochrome c oxidase catalyzes the four electron
reduction of dioxygen to water by using reduced cytochrome
c as the substrate. In this role it bridges the mito-
chondrial electron transport chain with the oxygen
transport.system in aerobic organisms. Cytochrome c
oxidase is equipped with two heme-a bound iron atoms
and two copper atoms. Heme-a differs from protoheme,
the more common hemoprotein prostetic group, in that
the peripheral vinyl and methyl groups of the latter
are replaced by hydroxyfarnesylethyl and formyl groups
respectively (Figure 1). In the protein, one heme-a
and one copper atom are involved in oxygen binding and
reduction, while the second heme-a and possibly the
second copper are involved in the oxidation of
cytochrome c (Palmer, Babcock and Vickery, 1976).

Cytochrome c oxidase possesses several unuSual
characteristics such as high electron affinity, high
oxygen affinity and a heme group which is a poor oxygen
reducing agent when compared to protoheme (Erecinska
and Wilson, 1978; Babcock and Chang, 1979; Chang, 1979a).
Babcock and Chang (1979) and Chang (1979a) suggested

that the strongly electron withdrawing formyl group at

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the periphery of the heme-a may play an important role
in the forementioned properties of cytochrome c oxidase.
Spectral studies (Falk, 1964) indicate that the formyl
group is in conjugation with the w system of the
porphyrin ring and therefore this could

possibly change the dominant resonance structure of

the macrocycle.

The X-ray crystallographic investigation of a
synthetic analog of heme-a, l,3,5,7-tetramethyl-2,6—di-n-
pentyl-4,8-diformyl porphyrin (DFP) (Figure 1),
synthesized by Professor C. K. Chang, of this department,
was undertaken to determine the influence of the formyl
groups on the resonance structure of the porphyrin. An
accurate structure would also show the effect of the
asymmetrical substitution of the pyrroles on the geometry

of the macrocycle.
Experimental

Single crystals of DFP were grown by evaporation
of a toluene solution. The crystal used in the X-ray
diffraction work had dimensions 0.12xo.12xo.96 mm.
Preliminary X-ray diffraction measurements indicated the
crystal system to be monoclinic and systematic absences
of the reflections unambiguously showed the space group

to be P21/c. The lattice parameters Obtained from

diffractometer measurements using MoKa radiation
(A = 0.71069 A) by the least squares fit of 16 reflections
with 26 greater than 35° were a = 12.120(6),
b = 6.677(3), c = 19.49(1) A and e = 99.1°(1). The
calculated density of the crystal on the basis of
two molecules per unit cell is 1.200 gcm-3. Since
there are four equivalent positions in each unit cell
for space group P21/c, the fact that there are only
two molecules per unit cell fixes each molecule of
DFP to be situated on a center of symmetry.

Intensity data were measured using 6/26 scans with
a Picker FACS I diffractometer and graphite monochroma-
tized Mo radiation. Background was measured for 20 s
at the end of each reflection scan. A 26 scan rate of
2° per minute was used. During the course of data
collection three standard reflections, with
24° < 26 < 38°, were measured every 100 reflections.
The deviations of the intensities of these standards
were all within counting statistics, indicating that
there was no X-ray damage to the crystal nor misalignment
of the crystal during data collection.

Intensities of 2903 reflections were measured in
the range 2° < 26 < 50° and of these 2766 were unique.
The intensities of the reflections were corrected for

Lorentz and polarization effects, but not for absorption

(p = 0.410 cm-l). Standard deviations of the

amplitudes (Wei and Ward, 1976) were calculated with an

instrumental instability factor of 0.02.
Structure Solution-and Refinement

The crystal structure of DFP was solved by direct
methods using the program MULTAN (Main et al., 1976).
The positions of 18 of 21 non-hydrogen atoms were
located in the initial E map and the remaining three
in a subsequent electron density map. The 1219
observed reflections with F > 30(IFI) were used in the
ensuing refinement. Three cycles of full matrix least
squares refinement with isotropic thermal parameters
gave R= 0.14, R = ZIIFol-IFcl l/ZIFOI. Two more
cycles with anisotropic thermal parameters for 17 atoms
reduced R to 0.12. A difference electron density map
at this stage revealed some residual density around
the last three carbon atoms in the pentyl side chain
(Figure 2). Slightly different positions for these
three atoms were obtained from an electron density
map and several more cycles of isotropic and anisotropic
refinement were applied lowering R to 0.11. The bond
distances C(9B)-C(9C) = 1.69, C(9C)-C(9D) = 1.25 and
C(9D)-C(9E) = 1.66 A in conjunction with the residual

density around these atoms and their inordinately high

        

  
 

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thermal parameters suggested that these three carbons
were probably disordered. Several models with partially
occupied carbon atoms were tried but all failed in the
process of refinement. The positions of 11 hydrogen
atoms were then located in another difference electron
density map. Isotropic thermal parameters which were
25% larger than the atoms to which they were bonded were
assigned to the hydrogens. Two additional cycles of
refinement with anisotropic thermal parameters for non-
hydrogen atoms gave R = 0.097. The remaining hydrogen
atoms were included at theoretical positions and in
subsequent refinement calculations, all hydrogen atoms
were fixed geometrically. Several additional cycles

of refinement varying non-hydrogen atom parameters

with hydrogen atoms at theoretical positions calculated
from the previous cycle resulted in a R value of 0.072.
At this point, the bond distances between the last three
carbon atoms of the pentyl side chain were restrained

to be 1.54 t 0.02 A.’ Refinement was terminated when

the individual parameter shifts were on the average

of 0.05 of their standard deviations. The final R

value was 0.069.

Results

The final atomic coordinates and anisotropic thermal
parameters of DFP are given in Table I, with the standard
deviation of the significant figure given in parenthesis.
The coordinates of hydrogen atoms and their isotropic tem-
perature factors are listed in Table II. The numbering
system used for the hydrogen atoms labels them after the
carbon or nitrogen atom to which they are bonded.

The atomic positions of the porphine nucleus of the
DFP molecule were fitted to a least squares plane accor-
ding to the method described by Shomaker et a1., (1959).
The deviations of the atoms from this plane are given in
Figure 3. The individual pyrrole rings were also fitted
to least squares planes and the atomic deviations from
these planes are listed in Table III. The interatomic
distance and bond angles for DFP are given in Figure 4
along with the errors in these quantities based on the
standard deviations of the atomic coordinates from the

least squares refinement.
Discussion

The structure of the porphine core of DFP is very
similar to other free base porphyrins (Silvers and
Tulinsky, 1967; Chen and Tulinsky, 1972; Codding
and Tulinsky, 1972; Lauher and Ibers, 1973; Little and

Ibers, 1977) and remarkably resembles the average

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.m.m.~ .m.v.n .¢.~.¢ .mvm.c~ .m.~.a .m.~.o .¢.amma. iaacmmaa.~ .m.mm~q.: .mo.o
.~.m. 16.“.H .G.~.- .m.m.m~ .c.o.~e .m.m.a .m.moa°. .me.ccam.~ Aa.aamm.n .ea.o
.m.m. .mVG.Hu 1616.6 .a.p.- .m.°.¢~ .a.q.~H Aecmvma. ioa.aamm.~ .a.ecm~.n .ma.O
.m.m. ...”.n .mcm. .mcm.ca .m.~.m Amco.a .quHma. 1-.mmmp.e .w.o~m~.- .ma.o
Am.a.au Amos. .m.m.: .m.~.m 1¢CS.G .m.H.m .m.~mac. .ca.mcms.~ .m.aana.n .Ha.o
inv~.du .m.o.: imso.d imam.m 1.32.4 Amcm.m inseamo. .a.mcmm.~ ...acao.u .a.o
im1H.H- .~.n.u .m.m. INCm.¢ .m.e.q Amco.o ANVMSSN. 1m.oacm.u Accuses. .Ha.o
.~.m.u lava. .Nca. .m.m.e 1m.m.m 1m.4.4 .memmsa. .m.mqaq.~ xv.moec. .a.o
.mcm. .~.c. 1~.H. .mcu.m .m.a.n .mc5.m iavmaad. .m.v-m.a iccpamo. .a.o
.NVH. Amvm.| vao.u .Nvm.m Amvv.v .mva.m .Nvmova. .m.mmo~.a A¢vnmma. .mvo
.~.~. Lace. .m... .m.m.m .m...m 1~c4.m ANCmcmd. .ocmaac.a .ecqqma. 1m.o
.mea. inem.au lava. 1m.c.m recv.m in.~.v .msqc-. .ca.~qam. .mcmmsn. 1H¢.O
LNVN. .Nvm.| vam. .m.~.v Amvm.n A~.o.m vamwma. Amvoomm. .cvmwmm. .vvu
.m.a.: .m.p.au .m.m.a Accd.a .m.a.v .mvm.m .mommwa. .a.aqam. .e.oaan. .ano
.mvm. .~.a.- .m.~.a .m.h.v .m.~.e .m.v.m .m.mv-. .m.oama. .¢.w~am. .m.O
.mem. .~.H.u imam. .m...e .m.o.q 1~.m.~ Anemone. incamma. .e.~mo~. .~.O
.m.m.~- .~.~.~- .~.c.a .NVS.G .m.~.a .~.o.m .uvman~. .p.m~m~.a .m.cdam. o
.m.~.» .m.a.n .m.m.e Inc~.¢. .m.m.v .m.v.v .Neooac. .m.ac~m. .¢.Hmma. 1H.o
m~m man man mmm «Na Ham s u x saga
.H manna

mhfl MO WHUUQEMHQQ Own—00¢ HMCHW
*

Table II. Final Hydrogen.Atcm.Parameters

PUIIT

H (1)

H (311)
H (312)
H(313)
II (411)
H (6)

H (811)
H(812)
H (813)
H(911)
H (912)
H(921)
H(922)
H (931)
H (932)
H (941)
H (942)
H (951)
H (952)
H(953)
H (12)

.2360
.3521
.4231
.4482
.4378
.2015
.0735
.1499
.0273
-.1660
-.0874
-.2059

-.2872 '

-.2317
-.3328
-.4124
-.3162
-.4669
-.3707
-.4795
-.0020

10

Y

.4866
.4648
.5810
.6269
.9080
1.2662
1.5212
1.6462
1.7313
1.7936
1.8613
1.6841
1.6374
2.0654
1.9658

'1.8746

2.0019
2.1821
2.3094
2.2259
1.1400

.0173
.1331
.0807
.1640
.2236
.1829
.2494
.2024
.2127
.0460
.1183
.1799
.1064
.1400
.1747
.0688
.0380
.1281
.0973
.0448
.0400

9’

P
coo-000.08
3%

O
qqqqoooooomooHquqquwwm

HHHHHHHEH
emowmmmm rqqmmmemmmmm

337

003 ()

J55

.022 '05“

—.032 028
1021
1046 r“

1008
.1047

H— N -.o11

1060

Figure 3.

1082
1045
'25
.258
4.008
'fl33
1394
1353

Deviations (in A) of the atoms of DFP from

the best least squares plane.

Table III. Deviations of the Atoms of the Pyrroles of

DFP from Their Best Least Squares Planes

Ring with formyl Ring with N-H
Atom 5 (3.) Atom 6 (A)
C(2) -0.0072 C(7) 0.0060
C(3) 0.0043 C(8) -0.0055
C(4) 0.0001 C(9) 0.0062
C(5) -0.0046 C(10) 0.0013
N(11) 0.0074 N(12) -0.0080

o=i0.005 A 0:10.006 A

13

§.Q

.mha MO

.2 .n--

Ammo cHV moamcm paw A< cflv moocmumflp ocon owEODMRUDQH
O

..z 91.“ o

is :3 .n,
a}...

3&- 5N.

 

.v musmwm

14

structure of porphine (Figure 5) proposed by Codding

and Tulinsky (1972). The differences between the two
independent pyrrole rings are small but significant.

In addition, the hydrogen atoms of the core are localized
on the same opposing pyrrole rings as other free base
porphyrins.

The porphyrin core is practically planar and the
deviations of the atoms from the least squares plane
are shown in Figure 3. An examination of the out of
plane displacements from individual pyrrole rings (Table
III) indicates that each pyrrole is planar within
I 0.006 A, while the porphyrin nucleus shows much higher
deviations ranging up to 0.053 A. The standard deviation
of the latter is 0.030 A. Adjacent pyrrole rings are
tilted by 4.1° with respect to each other.

From a comparison of the core region of DFP,
porphine and octaethyporphyrin (Figure 6), it can be
seen that the distortions from square symmetry increase
from porphine to DFP. This is especially true for the
N(i-l)-N(i)-N(i+1) angles and to a lesser extent, for
the angles formed by the methine carbons. These
distortions can be attributed to significant differences
in the conformations of the three molecules which may

be due to the size of the substituents. The transannular

 

 

 

 

 

 

H N 1.380

1.919

 

 

   

A: 0.01 7 A
1.415 6 = 0034‘

L458

 

   

A: 0.015 A
1.345 0: 0.028 I

1.348

 

 

Figure 5. Average structure for porphine and DFP (under-
lined) with the differences (A for porphine and
6 for DFP) between pyrrole rings.

16

 

C5 —4.835 C10
90.00 89.90
l
90.70
4.821 I 4.829
2.911 4'09? 2 99

N22 \8225 —|4.133 -89.05N24

..Z.I><J.><:

 

 

 

 

N23
9001
C20 -4838 C15
CA —4.849 CB
8994 90.00

Yam 4.828
2.910 2.910

N2 8800- 1 - 4.190-

 

 

 

 

 

c1—4.828 C6

90.46 89.54
N I I - l

92.31

 

 

 

 

Figure 6. Comparison of the central core of porphine (top),
octaethylporphyrin (center) and DFP (bottom).

17

separation of the imino hydrogen atoms is 2.44 A in
DFP, slightly longer than that found in octaethyl-
porphyrin (2.36 A) but compares very well with the
corresponding distance in porphine (2.45 A). The
imino hydrogen atoms are localized on the pyrrole

with the pentyl substituent, since the presence of

the electron withdrawing formyl group in the other
pyrrole renders the nitrogen electrophilic. The
deviations from planarity indicate that in octa-
ethylporphyrin the nitrogen atoms of the pyrrole rings
are alternatively tilted above and below the plane;

in porphine the distribution of the deviations from
planarity approximate sz symmetry, with the mirror
planes passing through the methine carbons. In DFP
the nitrogen atoms of the core are practically in the
least squares plane of the molecule but the pyrroles
are tilted in the methine-Ca direction in such a way
that two adjacent methine carbons are tilted downward
while the centrosymmetrically related ones are tilted
upward. In these three free base porphyrins the angles
that the pyrrole rings form with the least squares plane
of the molecule are all small and approximately 2° and

are probably related to packing arrangements.

18

The presence of different substituents on the
pyrrole rings in DFP does not seem to drastically
influence the bond distances and angles in the por-
phyrin macrocycle. As mentioned earlier, the formyl
group could conjugate with the n system of the porphyrin
ring, thus changing the nature of the dominant resonance
structures. However, the formyl group does not seem to
cause any significant effect on bond distances and.
angles except at or near the point of substitution.

The C(3)-C(4)-C(5) angle of 105.9°(5) is about 1°

less than expected (the corresponding angle in the average
structure of porphine is 107.?“ while the C(3A)-C(3)-C(4)
and C(2)-C(3)-C(3A) angles, 129.4°(5) and 123.3°(6)
respectively, suggest a steric repulsion of the methyl
group adjacent to the formyl moiety. The carbonyl
carbon and oxygen atoms are 0.153 and 0.337 A out of

the plane of the porphyrin respectively, so that the
formyl group is rotated by only 4.8° out of the plane

of the pyrrole to which it is attached. The C(4A)-0
bond length of 1.201 A is shorter than most C-O double
bonds found in organic crystals (Birnbaum, 1973;
Dideberg, Campsteyn and Dupont, 1973; Tanimoto et a1.,
1973). The C(4)-C(4A) bond length of 1.453 A is very
short but compares well with corresponding values found

in substituted pyrrole molecules (Figure 7) where there

Figure 7.

19

Comparison of substituted pyrrole rings and* the

formyl pyrrole with the formyl group of DFP*

a. 3- -Ethoxycarbonyl- -l, 2- -dimethyl- 4-pyrrole
carbaldehyde.

b. 4- -Acety1- -3- -hydroxymethylpyrrole.

c. Ethyl 4-Acetyl-3-ethy1-5-methy1-pyrrole-
2-carboxylate.

d. DFP.

* Distances in A, angles in deg.

20

 

21

 

Packing diagram of DFP

Figure 8.

22

is strong evidence for delocalization of the C-0

double bond (Bonnett, Hurtshouse and Neidle, 1972;
Sheldrick, Borkenstein and Engel, 1978b; Conde, Lopez
Castro and Marquez, 1979). Direct correlations are not
possible because in these three examples the carbonyl
is bonded to a single pyrrole ring. In porphyrins, the
pyrrole rings are distorted as a consequence of the
aromatic 2 system. In DFP, the delocalization of the
carbonyl electrons is through the entire 6 system of
the porphyrin ring, so that the distortion of the molecule
should be minimal and generally within experimental
error.

The large values of the C(8)-C(7)-C(6) and
C(1)'-C(10)-C(9) angles, 128.2°(5) and 128.0°(6)
respectively, are probably the result of packing effects
arising from the presence of the pentyl substituent at

C Average values for the corresponding angles are

8'
126.6°(2) in porphine and 127.3°(l) in octaethylporphyrin.
The pentyl side chain is in extended conformation and
produces some short intermolecular contacts such as
O-C(9B), 3.362 A.and C(3l)-C(9E), 3.610 A.

DFP stacks in layers along the b axis in the unit
cell (Figure 8) and when the arrangement is viewed

perpendicular to the molecular planes, one molecule

is displaced almost in the methine-methine direction

23

with respect to the molecule below. The distance
between the least squares plane of adjacent porphyrin

rings is 3.42(3) A corresponding to a normal van der

Waals contact.

Cofacial Dicopper Hexyldiporphyrin-7
Introduction

Dimeric porphyrins linked in a cofacial configuration
(Figure 9) have recently been synthesized (Chang, Kuo
and Wang, 1977a; Chang, 1977b; Chang, 1977c; Collman et
a1., 1977; Kagan, Mauzerall and Merrifield, 1977; Ogoshi,
Sugimoto and Yoshida, 1977; Chang, 1979b). These cofacial
diporphyrins are potentially of multifaceted importance in
chemistry and biochemistry. The binuclear metal complexes
of these molecules can form sandwiched compounds with
several ligands and are ideal systems for studying multi-
electron redox reactions (Chang, 1977c; Chang, 1979b;
Collman et al., 1979). The binuclear metal diporphyrins
may also be developed into a new class of homogeneous
catalysis for molecular transformations that require
the cooperation of more than one catalytic Site. They
may also be used in the design of elaborate biomimetic
models of many essential biological systems such as:
l) the "special pair" chlorophyll model in photosynthetic
units, 2) a cytochrome oxidase model for multielectron
reduction of oxygen and 3) an oxygen carrying hemoglobin
and myoglObin model. All of the forementioned systems
include either two metal centers at selected distances

or a metal center and a ligand with restricted mobility

24

25

 

R='CH2CH2CON (n-BUIKHzCHzCHz‘

Figure 9. Cofacial diporphyrin-7.

26

due to neighboring groups (Figure lOa-c).

Collman and coworkers (1980) used a series of
B-linked cofacial metallo-diporphyrins with amide bridges
of varying lengths to test catalytic activity towards the
electroreduction of oxygen to water in aqueous acidic
electrolytes. The diporphyrins coated the surface of a
graphite electrode and all the molecules examined
exhibited some catalytic activity. The dicobalt dimer
with six atom linkages cause the reduction of oxygen
to proceed primarily to hydrogen peroxide. Dicobalt
dimers with five atom linkages show a greater proportion
of oxygen being reduced directly to water. However,
only the most closely linked cobalt dimer, with bridges
of four atoms, produced a catalyzed reduction almost
exclusively to water. The process seemed to demonstrate
the participation of the two metal centers in controlling
the course of the reduction and was found to be sensitive
to the geometry of the dimers, with the four atom bridge
dimer more active toward the reaction than the five or
six atom bridge dimers.

Chang and coworkers (l977a-c; 1979b) have also shown
that the separation between the metal centers plays an
important role in ligand intercalation. Metal-metal
distances were estimated indirectly by using triplet

EPR parameters and the values proposed were 6.4 A for

Figure 10.

27

Cofacial diporphyrin biomimetic models

a. "Special pair" chlorophyl models
reprinted from (I) Katz et aZ.,(l976)
and (II) Fong (1974).

b. Cytochrome oxidase, according to Palmer
et aZ.(l976).

c. Sterically crowded heme with "bent"
Fe-C-O bond.

28

 

 

x \
CYTOCHROME a
CYTOCHROHE a,
Y

 

X=(CH2)
X=(CH2)2

Fe-Cu-4

Fe-Cu-S

29

a dicopper cofacial diporphyrin with bridges of seven
atoms, 5.4 A for six atom bridges and 4.2 A for dimers
with five atom bridges. These values for the separation
between metal centers are nearly identical to those
obtained from CPK molecular models assembled with the
bridges in extended conformation. These distances were
also assumed to be the intermolecular separation of

the rings of diporphyrin. However, the assumptions need
not be necessarily correct, and in fact other possibili-
ties were also evident, where the rings are in "slipped"
positions with respect to one another. On the other hand,
a most stable or probable structure was not obvious.

The X-ray crystallographic investigation of cofacial
dicopper hexyldiporphyrin-7 (CuzDP-7) was undertaken to
resolve such ambiguities. More importantly, the cofacial
diporphyrins constitute a novel class of porphyrin come
pounds which would also most likely have new structural
principles underlying and governing their behavior.

Thus, an accurate structure for Cu2DP-7 would Show the
effect of the seven atom bridge on the planarity of the
porphyrin ring and possible intramolecular interactions
between the two rings. In addition, new and unantici-

pated principles could be expected from the results.

30

Experimental

The cofacial diporphyrin was synthesized by coupling
of diacid chloride and the dibutyl amine of 2,6-dihexy1-
porphyrin II, followed by copper insertion using COpper
acetate in a chloroform-methanol mixture (Chang, Kuo
and Wang, 1977a).* This procedure statistically yields
two diasteric isomers designated as syn and anti
(Figure 11) and each compound consists of an enantiomeric
pair because of the asymmetry in the carboxyamide linkages.
Attempts to separate the mixture have not been successful
so that it is not known if the syn and anti forms are
produced in equal amount.

Crystals of CuzDP-7 were obtained by slow evapora-
tion of a mixture of toluene and dimethyl sulfoxide. Of
the several diporphyrin crystals examined in this work
X-ray crystallography, all proved to be in the syn
configuratiOn. The crystal used for data collection
was a small prism of 0.30 mm in length with a square
cross section of about 0.08 mm on edge. The crystal
system was determined to be monoclinic with the space
group being the centrosymmetric P21/c. The room

temperature unit cell parameters are: a'= 15.36 (1),

 

* .
carried out by Professor C. K. Chang of this department.

31

1:

 

umEOmwumhsw any
uoEOmwlzmm Adv
racflumnouoofio Hmflommoo Haxom .HH Tasman

. 3331:}: 3
.622. .. cum e

 

32

b = 9.34 (1), c = 31.05 (2) i and s = 111.22° (2). A
subsequent low temperature determination was carried out
which will be described in the next section.

The calculated density of the crystal based on two
molecules of CuZDP-7 per unit cell is 1.208 g cm-3,
which compares favorably with the observed density of
1.19 (2) g cm-3. Since there are four equivalent posi-
tions in each unit cell for space group P21/c, the fact
that there are only two molecules/unit cell fixes each
molecule to be situated at a center of symmetry. CuzDP-7
is asymmetrical (Figure 11) so that the molecule must
be disordered in a manner such that it will appear to
be statistically centrosymmetrical.

The crystals were shown to display an orientational
type twinning and this fact compounded further the
difficulty presented by their relatively small size.
Repeated attempts to grow larger or untwinned crystals
were unsuccessful. However, since the positions of
the reflections in twinned crystals differed by about
0.65° in w and l.0-l.2° in x, the diffraction patterns
of the two crystals could be resolved with our diffracto-
meter (crystal to detector distance of 650 mm). The
intensities of the reflections from the two crystals
were about equal and consequently the effective size

of the crystal used in intensity data collection was

33

half of the morphological size described above
(v = 0.0007 mm3).

The intensity data were collected using CuKa
radiation and a Picker Four Circle Automatic x-ray
Diffractometer controlled by a DEC,4K,PDP-8a computer
(FACS I system) coupled to a DEC 32K Disk File and
equipped with an AMPEX TMZ Digital Tape Memory System.
The intensities were measured by a "wandering" w-step
scan procedure which also utilized balanced Ni/Co
filters (Vandlen and Tulinsky, 1971). During the course
of the data collection three standard reflections
50° < 20 < 60° were measured every 100 reflections. The
deviations of these standards were all within counting
statistics. Data were collected in the range
2° < 20 < 80°, which corresponds to spacings greater
than 1.2 K.

Intensities of 2800 independent reflections were
measured but only 1380 (49%) were greater than 30(I),
where 0(1) was calculated based upon counting statistics.
The intensities of the reflections were corrected for
absorption using a semiempirical method based on the
variation of the relative transmission (1) with the
azimuthal angle 0 (North, Phillips and Mathews, 1968).
The T(¢) curves were constructed by measuring the varia-

tion of the absorption of reflections at x = 90° (b* axis).

34

The maximum absorption ratio for these reflections

(I /I

max ) was about 1.25 and occurred at the i a* axes.

min
The intensity data were then converted to structure
amplitudes by applying Lorentz-polarization and lack of

balance corrections.
Structure Solution and Refinement

The position of the Cu atom, three of the four
coordinating nitrogen atoms and three carbon atoms were
located from the Patterson function of CuzDP-7. This
fragment was used as input to the tangent formula
(Karle recycling) and the development of the structure
proceeded as shown in Figure 12.

The remaining atoms were located by Fourier methods
and the structure was refined by several cycles of
least squares refinement (Sheldrick, 1976) including
isotropic thermal parameters. The course of the
refinement is summarized with a flow chart in
Figure 13. The disorder leading to statistically
centrosymmetrical molecules proved to be basically
that between d,Z enantiomorphs occupying the same
position in the crystal and in a first approximation,
simply led to two positions for the carbonyl oxygen

atoms of the bridge. After the positions of these

two disordered half oxygen atoms were included in the

35

 

 

3 3
4
3 3
2 3
2 4
4 2 4
4 3
4 2
1
3
4 4 3
4 4
4 2 2 3 3
3 3
4
4 4 4

Figure 12. Stepwise development of the structure of
Cu2DP-7 with Karle recycling. Atoms labeled
1,2,3 and 4 were used in the nt cycle to
produce atoms labeled n + l.

36

Figure 13. Flow chart of the course of the refinement

of CuzDP-7*

*0 = electron density map

difference electron density map

A0

LESQ least squares refinement
NA = number of atoms in the calculation

number of atoms that were refined

NR

R = leFnl ' [F011
N T

 

(R = 0.34)

L

 

 

 

o with 31 atoms]

 

 

 

 

 

 

 

'0 with 21 atoms -

 

[A0, hexyl side chain

1

redetermined

 

 

 

(R = 0.32)

p with 39 atoms
(R = 0.28)
LESQ NA = 49

NR = 17
R = 0.25

 

 

 

 

 

LESQ NA = 49
NR 25
R = 0.24

LESQ NH = 43
NR = 41
R = 0.22

l

'00, 2 more atomsJ

LESQ NA = 45'
NR = 44
R = 0.20

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

LESQ' NA = 49
NR = 25
R = 0.20

[—gp, 4 more atoms]

LESQ NA = 51
NR = 24
R = 0.170

 

 

 

 

 

 

 

 

 

 

 

 

LESQ NA = 51
NR = 51
R = 0.160

1

 

 

 

I Ap, 1/2 occupancy OJ

 

 

Ir
LESQ NA = 52
NR = 51
R = 0.150

 

 

 

 

 

LESQ NA = 52
NR = 51
hexyl side chains
constrained
R = 0.137

 

 

 

38

refinement, the bond distances of the atoms in the

hexyl chain still varied from 1.30 to 1.80 A. Two

cycles of least squares refinement with bond distances

of the hexyl side chain restrained to 1.54 a 0.05 A

were performed and the R value decreased from 0.150 to
0.137. The R value for the 1625 reflections with

F > 20(IFI) was 0.148. The refinement became stationary
at this stage; from the least squares standard deviations
in coordinates, the standard deviations in bond distances
are about 1 0.1 A and 1 1-2° in bond angles (Hatada,

Tulinsky and Chang, 1980).
Results

The final atomic coordinates and isotropic
temperature factors of CuzDP-7 are listed in Table IV.
The numbering system is shown in Figure 14. The atomic
positions of the porphyrin ring of CuZDP-7 were fitted
to a least squares plane according to the method by
Shomaker et a1., (1959). The deviations of the atoms
from this plane are given in Figure 15. The inter-
atomic bond distances and angles are presented in
Figure 16. A perspective ORTEP drawing is shown in
Figure 17, where the black circles represent the

disordered half oxygen atoms.

Table IV.

ATOM

CU
N(1)
N(2)
N(3)
N(4)
C(1)
C(2)
C(3)
C(4)
C(5)
C(6)
C(7)
C(8)
C(9)
C(10)
C(11)
C(12)
C(13)
C(14)
C(15)
C(16)
C(17)
C(18)
C(19)
C(20)
C(ZA)
C(3A)
C(33)
C(3C)
N(BD)
C(38)
C(3F)
C(36)
0(3C)
C(38)
C(81)
C(82)
C(83)
C(84)
C(7A)
C(8A)
C(88)
C(8C)
C(8D)
C(88)
C(88)
C(12A)
C(17A)
C(18A)
C(188)
C(18C)
C(18D)
C(188)
C(18F)

a x 10

0

Final Atomic Parameters

X

1.0035
1.0127
“8966
.9978
1.1055
1.0762
1.0536
.9794
.9536
.8799
.8562
.7816
.7808
.8513
.8736
.9364
.9519
1.0133
1.0501
1.1137
1.1425
1.2198
1.2272
1.1583
1.1467
1.1075
.9306
.8720
.8160
.8090
.8550
.8538
1.0490
.8980
.8810
.7440
.6450
.5650
.4970
.7218
.7127
.6327
.5548
.4687
.4135
.3379
.8955
1.2758
1.2993
1.3840
1.4520
1.5360
1.6238
1.6658

5-45

39

Y

.2352
.2114
.0916
.2572
.3761
.2708
.2240
.1408
.1300
.0418
.0309
.0622
.0516
.0483
.0871
.1938
.2438
.3404
.3534
.4463
.4532
.5429
.5182
.4109
.3666
.2778
.0676
.1500
.3050
.3720
.5020
.6179
.4393
.3480
.4870
.3520
.3590
.3440
.4300
.1560
.1256
.0260
.0087
.0611
.1281
.1650
.1922
.6363
.5905
.4817
.5476
.4485
.4117
.5548

9-81

of Cu DP-7

2

.0270
.0922
.0059
-.0386
.0475
.1309
.1711
.1570
.1059
.0801
.0346
.0038
-.0391
-.0399
-.0776
-.0780
-.1185
-.1050
-.0545
-.0279
.0200
.0495
.0939
.0941
.1325
.2202
.1865
.2060
.1960
.1570
.1760
.1378
-.1346
.2270
.2160
.1080
.1000
.0490
.0600
.0207
-.0842
-.1105
-.0978
-.1423
-.1140
-.1623
-.1691
.0288
.1381
.1559
.2018
.2120
.2550
.2639

2-24

2

Sb

iso

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Figure 17.

44

Perspective ORTEP drawing of Cu DP-7. Pyrrole
nitrogen atoms are numbered and the black
circles represent disordered carbonyl oxygen
atoms.

45

Discussion

CuzDP-7 is the first cofacial diporphyrin to have
its structure determined crystallographically (Hatada,
Tulinsky and Chang, 1980). The two porphyrin rings in
CuzDP-7 do not stack exactly over each other with the
two copper atoms lying on the normal of the planes with
empty space between the two macrocycles. _The manner
with which the rings slip with respect to each other
is depicted schematically in Figure 18 which shows the
projection of the central core of one porphyrin onto
that of the other. The slip of 3.80 A is almost parallel
to the methine-methine direction and gives an intra-
molecular Cu-Cu separation of 5.22 A. we can define a

quantity called slip angle, 8, such that
_--l
s - Sin (m/M-M)

where m is the magnitude of the slip as described above
and M-M is the intrametallo separation or the separation
between the centers of the central nitrogen core of free
base porphyrins. The intramolecular slip angle of
CuzDP-7 is 46.7°. The arrangement of the pyrrolic nitro-
gen atoms proves to be square planar within the errors

of the determination (Figure 18). When viewed perpen-
dicular to the porphyrin ring, the projection of N(2)

coincides closely with the center of the pyrrole below

46

 

 

\ - /
2,02 1.93
\ 90/
2.92 90 CU90 2-79
9o

 

 

 

 

 

 

2.9 . N1.
3400
N1 ‘. N2
9] \‘ 87
Cu
92 9O

 

N4 N3

 

Figure 18. Projection of the central core of one porphyrin
of CuZDP-7 onto that of the other. Distances in

A, angles in deg. (The Nl-N2 component of the
slip is 0.63 A).

47

it while the centrosymmetrically related N(2) projects
near the center of the pyrrole above it. When compared
to the "face to face" dic0pper diporphyrin-6

(Cu2(FTF 6-3,2-NH diamide), Figure 19a (Collman at 02.,
1981), one important similarity is evident: in both
cases, one of the porphyrin rings slips with respect to
the other in order to minimize the distance between ‘
rings and maximize the interaction of the delocalized

fl systems. The intramolecular slip angle of 51.4° for
Cu2(FTF 6-3,2-NH diamide) is considerably larger than

that of Cu DP-7 (46.7°). "The Cu-Cu distance of the

2
former is 6.33 A, even with a smaller six carbon bridge,
while it is 5.22 A for the latter, which has a bridge
with an additional atom.

As expected, the Cu atom in CuzDP-7 is located in
the plane of the porphyrin macrocycle, (Figure 15)
(Mavridis and Tulinsky, 1973; Sheldrick, 1978a). The
r.m.s. error of the least squares plane of the porphyrin
ring is t 0.07 A, with individual pyrrole rings planar
to at least i 0.02 A. Dihedral angles between the
pyrrole rings are all within experimental error. The
interplanar separation between the macrocyclic rings
was calculated to be 3.52 t 0.08 A and it corresponds

closely to a normal van der Waals stacking distance.

An examination of the distribution of the out of plane

48

a a .10. 2000000
cflxomm m can .0. .mpwamwolmzlm.m10 mamvcso mo mcfi3muv m>fluommmumm

.ma magmas

 

49

 

(Cont'd.)

Figure 19.

50

displacements (Figure 15) reveals that the porphyrin
rings might be slightly buckled about a line through
the methine carbons, with the deviations displaying
approximate 4'symmetry. 0n the other hand,

' Cu2(FTF 6-3,2-NH diamide) deviates markedly from plana-
rity with adjacent pyrrole rings tilted up to 23.8°
(Collman et a1., 1981). These distortions from planarity
appear to minimize steric interactions between the
methyl side chains on the adjacent pyrroles and the
meso substituents. The two cofacial porphyrins differ
in that the porphyrin rings of Cu2(FTF 6-3,2-NH diamide)
are linked with bridges through the methine carbons
(meso), whereas CuzDP-7 has bridges through C8 of the
pyrrole rings.

It can be seen from Figure 17 that the n-hexyl
chains of a given ring assume approximately centrically
related extended conformations perpendicular to the ring.
This gives rise to a number of close van der Waals con-
tacts with the n-hexyl chain of the opposite ring. The
n-butyl chain of the carboxyamide group also has an
extended conformation and is perpendicular to the
porphyrin rings. The structure of the aliphatic side
chains together with the crystal packing leads to the
formation of hydrocarbon channels within which the

porphyrin rings are stacked (Figure 20). The interplanar

51

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..QVHMHsowpcmmumm madmsuse was

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so no mdexomum

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52

distance between the dimer molecules of 3.47 i 0.08 A
is also normal van der Waals, but quite surprisingly the
intermolecular Cu-Cu separation is only 4.60 A which

is less than the intramolecular distance. This results
from the fact that there is less intermolecular slip
(3.17 A) between adjacent rings of dimer molecules

(8 = 43.6°). Cu2(FTF 6-3,2-NH diamide) stacks in the
unit cell in a manner such that the closest inter-
molecular Cu-Cu separation is 8.76 A (Figure 19b).
There are numerous van der Waals contacts in both
structures but the packing of CuzDP-7 appears to be
more dominated by aliphatic van der Waals interactions
combined with 0—0 interactions between the porphyrin
rings.

On examination of the seven atom bridge between the
porphyrin rings, it can be seen that each three carbon
atom fragment starting in opposite rings has different
conformations in the same macrocycle. However, these
conformations are centrosymmetrically related in the
dimer, except for the carbonyl oxygen atom. Two oxygen
atoms for each connecting chain, at half peak height, I
were clearly observed in the electron density map.
Moreover, the n-hexyl and n-butyl side chains have
essentially one configuration in CuZDP-7. Therefore

the crystals are composed of d,Z enantiomorphs of the

53

syn isomer (Figure 11a) centered on crystallographic
centers of symmetry giving rise to a statistically
centrosymmetrical molecule. Cu2(FTF 6-3,2-NH diamide)
is also located at a center of symmetry but it has a
six atom bridge (Collman et aZ., 1981). The third atom,
the amide nitrogen, and the fourth atom, the carbonyl
carbon, are related by the center of symmetry and as a
result both atoms, together with the carbonyl oxygen,
are found to be disordered.‘

At room temperature, only the carbonyl oxygen of
the bridge of CuzDP-7 shows disorder. The determination
is not accurate enough to observe the more subtle dis-
order in the carbonyl carbon positions of the bridge.
This is a consequence of two factors: 1) the static
disorder itself should detract from the quality of the
diffraction pattern and 2) the volume of the crystal
used in data collection was very small, especially when
the orientational twinning is considered, making
measurements of weak intensity reflections more
difficult. The effect of the two was to increase
artificially the rate of fall off of the diffraction
pattern.

The slipped configuration of CuzDP-7 may be a gen-
eral feature of other metallo-diporphyrins and free

base diporphyrins. This geometry was observed in

54

Cu2(FTF 6-3,2-NH diamide). The slipped configuration
is certainly of significance for ligand interaction:
for example, dioxygen adducts to Co2DP and FeZDP
could also assume a slipped "trans" geometry. While
direct X-ray structure proof of these complexes is still
lacking, changes in EPR spectra and electrocatalytic
behavior of the dicobalt have been observed as the amide
bridges between the rings were shortened, which limit
the degree of slippage and vary the metal-oxygen bond
geometry (Chang and Wang, 1980; Collman et a1., 1980).
The precision of the room temperature analysis of
the structure of CuzDP-7 is compromised by the apparent
large thermal parameters (Table IV) which are probably
the result of the static disorder. Although there is
not a quantitative correspondence of the bond distances
and angles with other Cu porphyrins (Figure 21)
(Mavridis and Tulinsky, 1973; Sheldrick, 1978a), the
presence of the hexyl side chains and particularly the
seven atom bridge do not appear to distort the pyrrole

rings of the macrocycle to any large degree.

55

 

l.32

 

Figure 21. Comparison of average bond distances (in A)
and angles (in deg.) of the pyrroles in
CuTPrP (a) and CuzDP-7 (b).

Cu DP-7 Low Temperature Determination

2

Experimental

In an effort to circumvent the effects of the dis-
order in the structure at room temperature (RT), a low

temperature (LT) structure determination of Cu DP-7 was

2
also carried out. The crystal used for LT data
collection was the same one used for the RT determina-
tion. The twins of the twinned crystals were accident-
ally separated when the crystal cleaved about halfway
along its long direction resulting in dimensions of
0.15xo.08xo.08 mm. An examination of the X-ray diffrac-
tion pattern showed no evidence that any fragment of

the twin remained.

The intensity data collection was performed at
-150°C on a Syntex P21 diffractometer at the Upjohn
Company, Kalamazoo, Michigan. Graphite monochromated
CuKa radiation was used throughout. A 0/20 scan tech-
nique (Duchamp, 1977) was employed with a scan range of
approximately 3.2° and a variable scan rate of 4-24 min/
reflection depending on the intensity of the reflection
being measured. Accurate cell parameters were deter-
mined with a least squares calculation based on

accurately determined Ka - 20 values for 38 selected

reflections in the range 25° < 20 < 90°. Cell

56

57

parameters at RT and LT are given in Table V. The cell
volume of 4050.2 A3 for LT represents a shrinkage of
about 2.5% compared to RT. 'The largest cell parameter
changes occurred along the a-direction (0.28 A) and as
expected in B (1.44°).

During the course of data collection, nine reflections
were monitored, one every 20 observations. From the
variation of these reflections the standard deviation in

intensity was approximated by

_ 2 2 8
0(1) - (OCS(I) + (0.02881) )

where 0CS(I) is the standard deviation based on counting
statistics and the coefficient of I is calculated
considering fluctuations in intensity above that of
counting statistics.

Data were collected in the range 2° < 20 < 120°,
which corresponds to spacings > 0.9 A. The intensities
of 5455 independent reflections were measured of which
1858 were greater than 20(1) and 2802 were greater than
0(1). The usual Lorentz-polarization and absorption

corrections (1 /I

max = 1-20) were applied to the data.

min
Refinement
As expected, the lattice parameters at LT were

generally shorter and the position of the Cu atom was

slightly different, as determined from the Patterson

58

Table V. Comparison of the RT and LT Cell Parameters

of CuZDP-7
RT LT
a-A. 15.36 (1) 15.080 (1)
b-A. 9.34 (1) 9.254 (1)
c-A. 31.05 (2) 30.844 (3)
B-Deg. 111.22 (2) 109.78 (1)

v-A3. 4152.5 4050.2

59

function of LT-CuzDP-7 (later it became evident that the
entire porphyrin was displaced also). As a result, the
trial structure using the coordinates of the RT deter-
mination could not be refined by the method of least
squares. Therefore, the structure was redetermined
with the aid of the tangent formula and Fourier methods
as described for the RT work. Several cycles of least
squares refinement coupled with examination of electron
density maps were then performed using the program
SHELX76 (Sheldrick, 1976). The thermal parameters of
the atoms remained large so that they cannot be a
consequence of atomic vibrations alone, but must also
have a contribution from static disorder in the
structure. In fact, the refinement proceeded with
more difficulty than the RT work since more atoms
appeared to be positionally disordered and in very
complex ways. A summary of the course of the refine-
ment is shown in Figure 22. The positions of
disordered n-hexyl side chains and the seven atom
bridges were redetermined several times with different
partial occupancy of atoms in attempts to account for
the observed electron density. The hydrogen atoms
were included when observed in difference electron
density maps or at calculated positions for the carbon

atoms of the side chains closest to the porphyrin

' LESQ =

60

22. Flow chart of the course of the refinement
of LT-Cu DP-7*

2
electron density map.
difference electron density map.
least squares refinement:

NT = total number of atoms included in the
calculations.

NR = number of atoms that were refined.

Biso isotropic temperature factors.
Baniso = anisotropic temperature factors.

ring = 24 atoms of the porphine core.

61

 

0, 38 atoms

1

L830 NT I 38
NR I ring
R I 0.35

I A0, 8 more atoms

LESQ NT I 46
NR = ring
R I 0.33

I

I A0, 6 more atoms

1

LESQ NT I 52
NR I ring
R I 0.27

J,

Ap, l more atom

 

 

 

 

 

 

 

 

 

 

 

 

 

k occupancy 0

 

 

 

 

 

LESQ NT I 54
NR = 24

Cu with Baniso
R I 0.23

A0, disordered atoms
in connecting bridge

1

LESQ NT I {4

 

 

 

 

 

 

 

NR I ring
. +6
ring with Baniso
R I 0.23

 

 

 

 

 

LESQ NT I 54
NR I 54
R I 0.21

l

 

 

redetermined

I A0, hexyl side chains F

 

 

LESQ NT I 54
NR I ring

ring with B.
R a 0.25 15°

 

 

 

LESQ NT I 54
NR I ring

Cu with B

l

LESQ NT I 54

aniso

 

 

 

 

 

 

 

 

NR = 36

R I 0.18
LESQ NT I 54
NR I 36

hexyl side chain with
constrained C-C distances
R I 0.16

 

 

 

_4

LESQ NT I 54
NR I 36
ring with 8

l

aniso

 

 

 

A0, hexyl side chains
bridge

 

 

 

 

 

LESQ NT I 54
NR = ring
ring with Baniso
damped shifts
R I 0.21

 

 

 

 

 

LESQ NT I 54
NR I ring
ring with Biso
damped shifts
R I 0.16

1

A0, 14 hydrogen

1

LESQ NT I 68
NR I ring
R I 0.15

 

 

 

 

 

 

 

 

62

skeleton. The final R value is 0.15 and Rw is 0.14,
where Rw =2\/w_ IIFol-IFCH/ZVW [Fol and
w = 1/02(|Fol).

The standard deviations in bond distances are still
about i 0.1 A with the bond angles being about i l-2°.
A comparison of the determination at RT and LT are given

in Table VI.
Results

The final atomic coordinates and thermal parameters
of LT-CuzDP-7 are listed in Table VII. The deviations
of the atoms of the porphyrin ring from the least
squares plane are shown in Figure 23. Interatomic bond

distances and angles are given in Figure 24 where two

configurations of the seven atom bridge are depicted.
Discussion

, The structure of CuzDP-7 did not show any marked
improvement with the lowering of the temperature. In
fact, the parts of the structure that had the higher
thermal parameters at RT proved to be regions with
disordered atoms. Thus, the thermal parameters, B, have

two components

+B

B = Btherm stat

63

Table VI. Comparison of RT and LT Refinements of

CuZDP-7
RT
DMIN 1.2 A
20MX(1Cu) 80°
No. Reflections 2,800
No. Observed 1,380 > 3 x 0

1,780 > 2 x 0

Data Collection "Wandering" 0
step scan (count

7-drop 3)
Temp. factors Isotropic
Disorder Disordered car-

bonyl oxygens

R R = 0.15,IFOI>2xo)

RW = 0.16JFOI>ZXO)

Standard oBond~iO.l A

deviation

oangles~i1-2 deg.

LT

0.9 A

120°

5,455

1,858 > 2 x 0
2,802 > 1 x 0

6/29 scan

Anisotropic por-
phyrin ring,
isotroPic side
chains

Disordered car-
bonyl carbon and
oxygen

R = 0.1sJR|>2xo)

RW = 0.14JFI>2X0)
OBond~io°l A

aangles 1-2 deg.

64

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Table VII

ATOM

C(ZA)
C(3A)
C(381)
C(3CH)
N(3D)
C(81)
C(82
C(83)
C(84)
C(380)
0(3E)
C(382)
C(3C0)
0(3C)
C(3EH)
C(3F)
C(3C)
C(7A)
C(8A)
C(88)
C(8C)
C(80)
C(88)
C(8F)
C(12A)
C(17A)
C(18A)
C(188)
C(18C)
C(18D)
C(1BE)
C(18F)
8(5)
8(10)
H(lS)
H(ZO)
H(3Al)
H(BAZ)
H(8Al)
H(8A2)
8(881)
8(882)
H (8A1)
H(EAZ)
8(881)
8(882)

0 x 104
0 x 101

(cont'd)

1.1002
.9207
.8857
.7895
.7952
.7312
.6234
.5486
.5680
.8386
.8746
.8214
.8174
.8786
.7778
.8495
.9393
.7140
.7163
.6292
.5671
.4745
.4359
.3354
.9026

1.2822

1.2938

1.3840

1.4501

1.5386

1.6096

1.6897
.8315
.8346

1.1467

1.1840
.8610
.9690
.7575
.6908
.5901
.6558

1.3171

1.2611

1.3628

1.4187

20-38

65

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.2326
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.3551
.3843
.3885
.2345
.5060
.4998
.1349
.2969
».3602
.5494
.6286
.5683
-.1577
-.1412
-.0502
-.0050
.1217
.0395
.1490
.1775
.6423
.6038
.4878
.5853
.4768
.6022
.5128
-.0122
.0311
.5162
.4239
.0116
-.1690
-.2387
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.7150
.6786
.6580
.6072
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.6893
.7240
.6600
.6410
.6333
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.4193
.3897
.4109
.3848
.3388
.3378
.3321
.5276
.6344
.6536
.6988
.7161
.7577
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..0 . 0.000.

.em 000000

.2.

69

where Btherm is related to the mean square displacement

(02) from an equilibrium position,

- 2 2
Btherm - 8" u

and Bstat is due to static disorder in atomic positions.
There is a general decrease of B in lowering
the temperature to -150°C (Tables IV and VII). This
fact is illustrated further in Figure 25, where the peak
heights (in electrons A-3) of the atoms of CuzDP-7 at
RT and LT are compared. On the average, the peak
height of the atoms of the porphyrin ring increase by
a factor of 1.75. However, the final peak heights for
the LT determination are still lower than for an ordered
porphyrin such as Cu tetra-n—propyl porphyrin (CuTPrP,
Mavridis and Tulinsky, 1973) at RT (Table VIII). This
applies particularly to the copper atom. The magnitudes
of the peak heights for the porphyrin ring of LT-CuZDP-7
are only comparable to those of CuTPrP at RT. These
observations confirm that there is significant contri-
bution from Bstat to the thermal parameters of CuZDP-7
and consequently, most of the atoms are probably
disordered. The C(38), C(3C) and C(3E) atoms of the
seven atom bridge between the two porphyrin rings, in

addition to the carbonyl oxygen atom have at least

two slightly different positions giving rise to different

70

hlma

ma om>ummno Hmcm
DUIBA 6:8 hlma

 

0..

. N
sumo s I
Oman 0» pcommwuuoo mmcfla cmxoum ..cwnaaumwsww

sunem mo .mnmw as. manage: #000 m0 consummaoo .mm musmam
0.. N.
.0 q.
4.
MM
nu
mm as
s.
«a
e.
an

N.

 

71

Table VIII. Comparison of Peak Heights of CuTPrP at

RT and LT-Cu DP-7

2
Atom Peak Height (eA‘3)
CuTPrP (RT) LT-CuzDP-7

Cu 49.0 34.9
Average of pyrrole N 7.2 7.8
Average of pyrrole Ca 6.0 5.9
Average of pyrrole CB 5.6 5.6
Average of methine C 6.0 5.6

72

bridge conformations (Figure 24a). The hexyl side chains
are also disordered at LT, the last three atoms of the
chains being simply obtained from a difference electron
density map and not refined.

Except from the foregoing differences, the structure
of LT-CuzDP-7 is essentially the same as that at RT
(Hatada, Tulinsky and Chang, 1980). The porphyrin ring
is planar to i 0.06 A and the Cu atom is located in the
least squares plane of the porphyrin ring (Figure 23).
The interplanar separation between the rings is 3.47 i
0.06 A and again is the same within experimental error
for both the intra- and intermolecular cases. The
geometry of the central core of LT-CuzDP-7 is square
planar around the copper atom. The distance between the
metal centers remains the same: 5.17 A for intramolecu-
lar and 4.64 A for intermolecular.

_The N(3D) atom of the 7-atom bridge does not appear
to be disordered, and neither does the n-butyl side
chain. Two configurations of the bridge were proposed
from the electron density: one has the carbonyl group
at position C, C(382)-C(3CO)-N(3D)-C(3EH)-C(3F) and the
second with the carbonyl at position E, C(381)-C(3CH)-
N(3D)-C(3EO)-C(3F) (Figure 24). The two configurations
of the bridge carbon atoms are expected: the center of

symmetry of the crystal requires disordered carbonyl

73

oxygens and since the carbons should have different
hybridizations, sp2 and sp3, consequently different
geometries are expected around these carbon atoms.
At LT these configurations can be resolved and the
positions are such that C(38) is disordered while

C(3F) appears as a single atom.

PART II

STRUCTURE OF Z-KETO-3-DEOXY-6-PHOSPHOGLUCONATE
ALDOLASE AT 2.8 A RESOLUTION AND ITS
IMPLICATION IN MOLECULAR EVOLUTION

Structure of 2-Keto-3-Deoxy-6-Phosphogluconate Aldolase
at 2.8 A Resolution and Its Implications in

Molecular Evolution
Introduction

Glycolysis, the anaerobic degradation of glucose
to lactic acid, is one of the several catabolic pathways
known as anaerobic fermentation by which many organisms
extract chemical energy from various organic fuels in
the absence of molecular oxygen. Since living organisms
first arose in an atmosphere lacking oxygen, anaerobic
fermentation is the most ancient type of biological
mechanism for obtaining energy from nutrient molecules.
These pathways occur with only minor variations in most
forms of life, an indication of their evolutionary
survival value. In animals, glycolysis serves as an
important energy mechanism capable of yielding energy
for short periods when oxygen is not available.

Glycolysis is catalyzed by the consecutive action
Of thirteen enzymes, most of which have been crystallized
and their structure solved to some degree or other by
X-ray diffraction analysis. These enzymes are localized
in the soluble portion of the cellular cytoplasm.

All the intermediates of glycolysis between glucose
and pyruvate (Py) are phosphorylated compounds. Their

phosphate group appears to have three functions:

74

75

a) to provide each intermediate with a polar, nega-
tively charged group, which prevents it from leaking
out through cell membranes, b) to serve as binding or
recognition groups in the formation of the enzyme-
substrate complex, and most important c) to conserve
energy since they ultimately become the terminal phos-
phate group of ATP in the course Of glycolysis.

Aldolase plays a central and pivotal role in the
pathway: it divides anaerobic glycolysis into two
major stages (Figure 26). The first stage is a collection
phase, where a number of different hexoses enter the
A glycolytic sequence after phosphorylation by ATP and
are prepared for cleavage to a common product,
glyceraldehyde-3-phosphate (G-3-P). The second stage
is a common pathway for all sugars:l G-3-P is converted
to lactate and ADP is phosphorylated to ATP. The net
yield is two molecules of ATP per molecule of glucose
degraded to lactate.

On the basis of their requirement for metals,
Rutter (1964) defined two classes of aldolases. Class I
aldolases, generally present in animals and higher plants
do not appear to require a metal ion cofactor and form
a Schiff base intermediate with their substrate. These

aldolases are inactivated by reduction with NaBH4 in

76

 

 

 

 

 

Fructose Glycogen, starch
Mannose Glucose Pi
Pentoses
ATP Glucose-l-phosphate
Phosphorilation ’ /
Glucose- -phosphate
Fructose-G-phosphate
ATP
STAGE 1
Fructose-1,6-diphosphate
ALDOLASE
-—------------ \-------------
Dihydroxy acetone phosphate
GI3-P.‘(———
2mm+
H’

 

2P1
3-Phosphoglycmroyl-phosphate

STAGE 1:: 21mp___._..,(

 

 

 

3-Phosphoglycerate 4
2 NADB
2-Phosphoglycerate

Phosphoenol Py

ZADP

2ATP t

 

 

Y
9!

 

ZNAD

Lactate

Figure 26. Two stages of the glycolytic pathway (Embden-Meyerhoff),
showing the pivotal position of aldolase.

77

the presence of the substrate (Grazi, Cheng and Horecker,
1962) and are not inhibited by EDTA (Rutter, 1964).

The Class II aldolases, found in bacteria and molds,

are not inactivated by reduction with NaBH4 in the
presence or absence Of substrate and are inhibited by
EDTA, indicating the requirement for a metal ion
cofactor (Rutter, 1964).

A major variation of the glycolytic pathway was
discovered by Entner and Doudoroff (1952) (Figure 27) in
Pseudomonas saccharophila. It was postulated that
6-phosphogluconate was dehydrated to a new intermediate
2-keto-3-deoxy-6-phosphogluconate (KDPG) which was then
cleaved to yield Py and G-3-P. The latter enters the
second stage of the glycolytic pathway and is converted
to Py. MacGee and Doudoroff (1954) isolated and
characterized KDPG and Kovachevich and WOOd (l955a,b)
separated and partially characterized the enzymes in this
pathway from Pseudomonas putida.

The utilization of a number of sugars by a variety
of organisms is dependent on KDPG aldolase as a result
of the key position that it occupies in this metabolic
pathway. Degradations Of glucose, fructose, mannose,
gluconate, glucosaminate and 2-ketogluconate are
dependent on KDPG aldolase. It also functions in the

utilization of alginic acid via 4-deoxy-1-erythro-5-

78

Mannose Glucose Fructose
P. P. P .
i i i
Mannose-G-phosphate Fructose-6-phosphate
\t
Glucose-6—phosphate /
NADP H20
Gluconate NADPH

6- -Phosphogluconate

KDPG Aldolase

G-3- P

 

Stage II of the glycolytic -
pathway.

Figure 27. Glycolytic pathway (Entner-Doudoroff) in
Pseudomonas. G-3-P is converted to Py by
stage II of the Embden-Meyerhoff pathway.

79

hexosulose uronic acid and 2-keto-3-deoxygluconate
(Smiley and Ashwell, 1960; Cynkin and Ashwell, 1960;
Preiss and Ashwell, 1962). Finally, KDPG aldolase
occurs in eubacteria exclusively. However, 4-hydroxy-a-
ketoglutaric aldolase is found in mammalian liver

(Rosso and Adams, 1967) as well as in bacteria.

KDPG aldolase catalyzes the cleavage of KDPG to
Py and G-3-P via a Class 1 mechanism utilizing a lysine
residue for Schiff base formation (Meloche and Wood,
1964). Extensive chemical and physical studies of
KDPG aldolase (Hammerstedt et a1., 1971; Robertson,
Hammerstedt and Wood, 1971; Mohler, Decker and Wood,
1972) showed that the enzyme is a trimer in solution
of identical 24,000 dalton subunits and that each
subunit possesses a catalytic site. Preliminary X-ray
diffraction data confirmed the trimeric structure in
crystals grown at pH 3.5 (Vandlen et a1., 1973).

KDPG aldolase is known to catalyze four reactions:
cleavage of KDPG, Schiff base formation with carbonyl
compounds, exchange between solvent protons and decar-
boxylation of oxalacetate. The corresponding turnover
rates in moles min-1(mole of aldolase)-1 are: 17,250
(28°C), 38,000 to 45,000, 20,000 to 30,000 and 860,

respectively (WOOd, 1972). Thus, KDPG aldolase has the

highest activity of any aldolase.

80

It has been demonstrated that KDPG aldolase can be
inactivated by treatment with Py plus NaBH4, but not
with NaBH4 alone or G-3-P and NaBH4 (Grazi et aZ.,l963).
Moreover, of a series of analogs of Py (Figure 28), only
hydroxy-Py and dihydroxyacetone did not inactivate. I
Since these two molecules have a hydroxyl group on the
carbon equivalent to the deoxy group of KDPG and other
Py analogs that inactivate have this position substituted,
a nonsteric restraint against the hydroxyl group at
position 3 exists. The analogs of KDPG, 5-keto-4-deoxy-
glucarate, 2-keto-3-deoxygluconate, 2-keto-3-deoxy-6-
AphoSphogalactonate all inactivate but none are cleaved.
Therefore, KDPG aldolase is completely nonspecific in
forming Schiff bases with carbonyl compounds but this
fact alone is not sufficient for cleavage. Consequently,
a six carbon carbohydrate will be a proper substrate
only if it has simultaneously a 3-deoxy position, a 4-
hydroxyl in erythro configuration and a 6-phosphate
group.

A lysine residue in the active site forms a Schiff
base with the carbonyl group of substrates (Ingram and
WOod, 1966). The position of the lysine was originally
located in a hexadecapeptide (Robertson, Hammerstedt
and Wood, 1971) and later in a 50 peptide cyanogen

bromide fragment by derivatization with [14C] Py and

81

a. Analogs of Py CO2 OH

2:0 :C)

00 not OH OH
Inactivate hydroxy-Py dihydroxyacetone

Analogs of Py
OH CO

2 2
Inactivate . 2 O 2 O :O
hydroxyacetone a-keto- .
butyrate a-ketoiso-
valerate'

.ZNonsteric restraint against OH in position 3

b. Analogs of KDPG (All inactivate, but not cleaved)

 

 

 

'— C02 —C02 rCO2

0::0 ' (m=0 «0:0

0 0 0

(>— OH w—OH HO—o
HO—-4) (h—OH (>— OH

— 002' L- OH —OPO3H‘
S-keto-4-deoxy- 2-keto-3-deoxy- 2-keto-3-deoxy-

glucarate gluconate phosphogalactonate

.2 Cleavage requirements
SIMULTANEOUSLY

3-deoxy position 4-hydroxyl in erythro 6-phosphate
configuration

Figure 28. Specificity Of KDPG Aldolase

82

reduction with cyanoborohydride (Tsay and Wood, 1976).
The complete amino acid sequence (Suzuki and Wood, 1980)
shows that the subunit of the trimer consists of 225
residues and that the position of the azomethine forming
lysine is 144. Because Schiff base formatiOn is not a
sufficient condition for cleavage, there has been con-
siderable interest in the identity of an additional base
which would function in catalysis. A second lysine
residue (Barran and Wood, 1971) has been proposed for
the role of the second base but without direct evidence.
The continuing investigations by Meloche and collabora-
tors with the substrate analog BrPy has shown that BrPy
inactivates the enzyme by alkylating a glutamate residue.
The position of this glutamate was located by sequencing
a heptapeptide fragment (Meloche, Monti and Angeletti,
1978) which was identified in the complete sequence to be
at Glu 56. At higher ionic strengths, BrPy was found to
also aklylate an SH of a cysteine residue (Meloche, 1970).
These results have led to a postulated mechanism for
KDPG aldolase action (Wood, 1972) which is shown in Figure
29. The ketamine of KDPG or Py is formed first. The
ketamine-eneamine rearrangement in the case of Py leads
to the observed exchange of methyl hydrogens of Py with

the medium. .The eneamine Schiff base of Py is the

83

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Ous>su>m

a @x m 20.0.? I
m + ... + $1.785 Ir 1mg (“2-7000 AIIN .. umdzumuudm
ermvu<= Al\~oo 9.. 0.7. MOO 9..

0

OO
O...
0....
mumwcmeumucH H0COwuwmcsuB
/ 3
u 00 :
enm10.(.
mamuo.+.
mewnumfioua omox
manoeo Osmodo Osmomo
:0 0~=+ :0 =0
Nam—Inn (luv! :0 VII." :0
--- ..... Own:
a .2145 \® .0130 saw/cu + "unsung.
0 00 O 0 .. O 00 ..

84

common transitional intermediate which condenses with
G-3-P or is the first 3 carbon product formed in the
cleavage of KDPG.

The structure of KDPG aldolase at 3.5 A resolution
was determined by Mavridis and Tulinsky (1976). KDPG
aldolase crystallizes in the cubic space group P213
with a = 103.0 A.~ There are 12 monomeric subunits in
the unit cell and one subunit per asymmetric unit. The
subunits are related to each other by crystallographic
three-fold rotation axes and three mutually perpendicular
non-intersecting twofold screw axes. Since each subunit
has four close contacts, two different trimeric arrange-
ments of monomer arise from the molecular packing (Figure
30) and an ambiguity results in the choice of the trimeric
Oligomer of KDPG aldolase. There are four trimeric
assemblages as a consequence of the arrangement of the
three subunits (AAA,BBB,...) around each of the four
threefold rotation axes. Each of these subunits interacts
with two other subunits, each from a different trimer
to give a second kind of trimeric arrangement (ABC,BCD,...).
Crystallographically, the subunits of the first kind of
trimer are related to the subunits Of the second kind by
the three different non-intersecting mutually perpendicular
twofold screw axes. The trimers of both the first and
second kinds are related to themselves by only one Of

the three twofold screw axes.

85

 

 

 

 

Figure 30. Arrangement of asymmetric units in the unit
cell of KDPG aldolase. Trimers of the first
kind (AAA, BBB, ...); trimers of the second
kind (ABC, BCD, ...); three-fold axis (3) is
body diagonal; other three-fold axes pass
through cell edges and cell faces (reprinted
from Mavridis and Tulinsky (1976)).

86

Since it is impossible to resolve the ambiguity
of the Oligomer from crystallographic considerations
alone, the probable trimeric assemblage in solution
was chosen from a study of the contacts and interactions
in each of the two kinds of trimers. The electron
density map showed that the trimer of the first kind
has many more and closer contacts between subunits than
the trimer of the second kind. As will be seen later,
in the discussion of the 2.8 A resolution model of
KDPG aldolase, the choice appears to be chemically sound.

The 3.5 A resolution electron density map was
extended to 2.8 A (Mavridis et a1., 1982) by multiple
isomorphous replacement methods (MIR) using three heavy
atom derivatives: two Hg and one Pt. The MIR phase
angles were refined with several cycles of density
modification which utilized inverse fast Fourier transform
techniques (Raghavan and Tulinsky, 1979). An electron
density map computed along the cubic axial directions
was used to calculate a map in planes perpendicular to
a threefold axis of the unit cell. This map had a
maximum electron density of 0.9 eA-3 and it was plotted
on a scale of 2 cm per Angstrom. The contours were
drawn starting at 0.25 eA-3[30(0)] with contour intervals
of 0.15 eA-3. The map sections were traced onto plexi-
glass sheets and used in a Richards' box with a parallel

mirror to build a Kendrew model of KDPG aldolaseo

Measurement of Kendrew Model Coordinates

Several methods have been proposed and utilized to
measure the coordinates of a Kendrew model. The use of
a plumb line is imprecise and cumbersome since it requires
physical contact with the model. Coordinates can be
obtained from a calibrated grid inserted in a Richards'
box at the same depth as the atom to be recorded. This
method is also inaccurate and tedious. A computer con-
trolled "ccordinate hunting engine" (Salemme and Fehr,
1972), even though precise and accurate, appears to
involve considerable time in its construction. Frentrup
and Tulinsky (1981) introduced the use of a surveyor's
transit as a coordinate measuring instrument. The
transit in conjunction with a laboratory cathetometer
can be used to measure accurate polar coordinates of a
Kendrew model. The main disadvantage of this method
resides in the fact that large errors are associated
with small values of the inclination angle (x). The
conversion from polar to Cartesian coordinates depends
on l/tan x. Since the derivative of l/tan x becomes
large as the value of x decreases, a small error at
small x will introduce large errors in the calculated
position. Therefore, to minimize this effect, the

transit must be placed at a different height than the

87

88

model, higher or lower, both of which lead to uncomfor-
table positions for the observer. We have used a
different approach here and measured the atomic coordi-
nates of the Kendrew model of KDPG aldolase with two
theodolites, which are essentially improved surveyor's
transits.

The basic geometry of the measurements is shown
in Figure 31. The system of coordinates is conveniently
oriented when the origin is located at one of the
theodolites, the x axis points to the other theodolite,
y is perpendicular to x and in the plane of the level of
the theodolite ("parallel to the surface of the earth")
and z is the cross product of x and y. The direction
of y is defined in a way that the coordinate system is
right handed and 2 points up. Since the orientation of
two of the axes in the theodolites are arbitrary, a a
series of transformations are necessary to result in the
”system shown in Figure 31 (see Appendix I).

All measurements of the Kendrew model of KDPG
aldolase were performed with a system that included
two Keuffel and Esser electronic theodolites, model DT-l,
and a minicomputer that processes the angles and cal-
culates the Cartesian coordinates. This arrangement is
marketed as the Analytical Industrial Measuring System

(AIMS) (the algorithm and coordinate systems actually

89

 

 

 

Figure 31. Geometry of the measurement of Kendrew model
coordinates. Theodolite(1) is the origin of the
coordinate system.

90

used by AIMS may be different from those described
above). The accuracy of the electronic theodolite is
1/1000 grad or about 3 seconds. At a distance of 2 m
this uncertainty corresponds to a deviation of about
i 0.003 cm in the position of a target.

The polar angles measured with the theodolites were
transformed to Cartesian coordinates and an uncertainty
distance was also calculated for each atom. This
distance is based on the two points defined in Eq. 10
(Appendix I) and represents the minimum estimate of the
error in the measurement. Only observations with
uncertainty distances of less than 0.03 cm were
accepted: this value corresponds to an error of
i 0.015 A in atomic positions. The diameter of the
Kendrew model parts is approximately 0.25 cm or at
least 8 x the uncertainty. It is possible to reproduce
the position of the atom to about 1/9 of the diameter
of the rods (more precisely, the midpoint of the segment
defined in Eq. (11) of Appendix 1).

The availability of the uncertainty distance
immediately after measurement eliminated gross errors,
and the immediate conversion to Cartesian coordinates
made the procedure fast and convenient. With this

system, two persons were able to measure all of the

91

1677 atoms in the asymmetric unit Of KDPG aldolase in
four working days (or about 60 atoms/hour).

The Cartesian coordinates obtained from Eq. 11
(Appendix I) are referred to_a system with the origin
at one of the theodolites and in a general orientation
with respect to the axes of the unit cell. The
transformation of the measured coordinates to Cartesian
coordinates based on the unit cell axes was carried out
in three steps: a) measurement of coordinates of eight
standards (tetrahedral Kendrew model parts placed
around the model of the enzyme) with AIMS and also with
a calibrated grid inserted in the Richards' box,

b) use of Rossmann and Argos' comparison program to find
the best rotation-translation transformation from the
laboratory to the unit cell system (Appendix II) and

c) multiplication Of the measured coordinates by the
rotation-translation transformations.

A very accurate set of atomic coordinates of the
Kendrew model of KDPG aldolase was obtained by using the
procedure described above. A summary of the measured
bond lengths and angles of the main chain of the enzyme
is given in Table IX, where they are also compared with
the values of chymotrypsin obtained using a surveyor's

transit and a cathetometer (Frentrup and Tulinsky, 1981).

92

Table IX. Comparison of the bond distances measured
with two theodolites and those measured with
a surveyor's transit-cathetometer.

** # Standard
Distances Theodolite(0) Transit(0) Values
N-Ca l.50(.04) l.50(.08) 1.463
Ca-C 1.56(.04) 1.56(.09) 1.522
C-O l.26(.04) l.24(.10) 1.234
C-N 1.34(.04) 1.32(.09) 1.314

Angles **

N-Ca-C(T) lll.5(6.7) 110.5(5.0) 109.54

Ca(i)-C-N-Ca(i+l)(w) l79.3(9.7) l79.6(6.5) 180.1
* -
Standard deviations calculated as 0 = [£(xi-x)2/(n-l)]3,

where A is the average value and n is the number of
observations. -

** o
Distances in A and angles in deg.

#M.A. Frentrup and A. Tulinsky (1981).

93

From Table IX, it can be seen that although the values
obtained by both methods are in very good agreement and
that the standard deviations Of the present method are
much lower reflecting the inherent higher precision of
the electronic theodolites. These are the coordinates

used in all subsequent calculations and discussions.

Description of the Molecule of KDPG Aldolase

Gammal

The contrast between solvent and protein in the
electron density map of KDPG aldolase is excellent, as is
expected from the composition of the crystals (37% protein,
63% solvent by weight). The protein molecules correspond
to electron density generally greater than 0.4 eA-3,
forming well defined and, with few exceptions, connected
peaks which are surrounded by large regions of electron
density less than 0.3 eA-B, which have no apparent struc-
ture. The molecule of KDPG aldolase is very clearly
outlined with respect to solvent because most of the
exterior of the molecule is composed of a-helices. Each
subunit resembles an oblate ellipsoid of dimensions
25x40x40 A. There are nine a-helices (hereafter referred
to as A through I) ranging from Slightly over one to
four turns and these comprise about a third of the
molecule. The two longest helices are at the terminal
parts of the polypeptide chain; of the two, the carboxy
terminal helix is better formed in the electron density
with prominent and well defined side chains. The helix
begins near Trp 208, which density is so large and

characteristically shaped that it was used as the starting

94

95

point for assigning side chains of known sequence to the
electron density map. The neighboring Trp 196 and Trp
202 residues served nicely to confirm the initial
assignment (the amino acid sequence of KDPG aldolase is
listed in Appendix III).

The tracing of the main chain was facilitated by
the absence of disulfide bridges, and thus absence of
branching, but the detailed interpretation of the elec-
tron density map was possible only because the amino
acid sequence was known. All 225 residues were fixed
in the model at 2.8 A resolution while only 173 residues
were accounted for at 3.5 A resolution (Mavridis and
Tulinsky, 1976). The missing residues were not located
as an appendage to the 173 but rather, they were found
in the interior of the molecule. The complete interior
folds regularly in a manner strikingly similar to that of
triose phosphate isomerase (TIM) (Banner et a1., 1975)
and forms an inner cylinder or B-barrel consisting of
eight strands of parallel chain in more or less
8 conformation (a through h). Adjacent strands are
linked together by the helical segments, A through H,
and structureless lOOps in a regular consecutive manner.
The Ca structure of KDPG aldolase is presented in Figure
32 and as a diagrammatic representation in Figure 33;

the secondary structural elements are listed in Table X.

97

 

 

Figure 33. Ribbon drawing of KDPG aldolase with I-helix
(drawn by Dr. L. Lebioda)

98

Table X. Secondary Structural Elements of KDPG Aldolase

a-helices B-strands

1 - Met 12 - Lys 25 a - Pro 30 - Thr 33
A - Ala 44 - Ile 52 b - Leu 55 - Arg 60
B - Ala 67 - Glu 73 c - Glu 77 - Gly 83
C - Ser 89 - Glu 95 d - Gln 100 - Thr 104
DA- Thr 108 .- Val 116 e - Pro 121 - Leu 123
E - Thr 128 - Met 133 f - Leu 138 - Arg 142
F - Ile 150 -- Ala 156 g - Gly 165 - Cys 170
G - Asn 179 - Ala 185 h*— Val 189 - Leul98
H 4 Ala 209 - Leu 221

There is a small kink at 193-195 in h

99

Domain A of pyruvate kinase (PK) (Stuart et a1., 1979)
and the main domain of Taka amylase (TA) (Matsuura
et aZ., 1980; Kusunoki et.aZ., 1981) also Show a similar
folding. The eight strand a/B-barrel had been proposed
earlier for KDPG aldolase by Richardson (1979) based on
the 3.5 A resolution structure and comparisons with TIM
and PK. It was suggested that four chain reconnections
could introduce four additional B-strands and change
the then proposed folding of KDPG aldolase to resemble
that of these two enzymes. Although Richardson's pro-
posed reconnections are correct topologically to produce
an eight strand a/B-barrel, since the 50 additional
residues found at 2.8 A resolution were mainly in the
interior of the molecule as part of the B-barrel, the
details of the barrel are different and the reconnections
do not apply in detail.

An indication of the clarity or quality of each
residue of KDPG aldolase in the electron density map
is given in Appendix III and Table XI. The helical
regions on the surface of the molecule are generally
described by Significantly higher electron density
than the average and this fact probably had an adverse
effect on the determination of the density of the
interior of the molecule at 3.5 A resolution. Helix-A,

following strand-a, was not apparent in the 3.5 A

100

Table XI. Summary of the Quality of the Density of
Side Chains in the Electron Density Map of
KDPG Aldolase

Good Partial None
Ala 20 1 10
Arg 4 9 l
Asn 2 4 0
Asp 7 4 0
Cys 3 2 0
Gln 3 2 0
Glu 9 5 1
His 1 0 0
Ile 12 4 3
Leu 14 5 2
Lys 0 6 1
Met 2 5 0
Phe 6 l 0
Pro 13 l 0
Ser 6 0 4
Thr 6 1 4
Trp 3 0 0
Tyr 2 1 0
Val 9 2 3

122 53

N
\O

101

resolution map while helix-G is shorter at

2.8 A resolution because a Pro residue terminates the
helix. At lower resolution, the apparent

effect of the Pro residue was to lengthen theSe helices.

Only four of the B—strands consist of large and
continuous electron density while the other four are
weaker. Strands-d, -e, -f and part of -g were in the
lower resolution model as well as strand-a but the
latter was not recognized as such because there were
no matching adjacent strands. The h-strand lies on
disconnected electron density at 2.8 A resolution and
was completely absent at lower resolution. Except for
this region (192-195) the main chain density can be
considered generally good.

Of the side chains (Table X1), 122 residues occur
ingood electron density, 53 residues have only partial
and 29 residues have no side chain density (21 additional
residues are Gly). The electron density of the aromatic
side groups varies somewhat in clarity. The three Trp
residues (196, 202, 208) are unmistakable as well as
Tyr 140 and 183. The direction of the phenyl ring in
Phe and Tyr side chains is very clear but their orienta-
tion around the CBICY bond is usually ambiguous. Packing
considerations were taken into account in deciding the
latter. The side chain definition is somewhat more

poorly defined for the surface residues, especially for

102

Lys and Arg. The fourteen Pro residues are well defined
and most appear to serve a structural function;q nine of
the Pro either terminate a helix or a B-strand (30, 42,
105, 121, 124, 129, 163, 171, 187), three are in loops
connecting B-strands and helices, and two occur at the
beginning of the N-terminal pentapeptide tail which
(extends into the solvent. The Gly residues lie in turns
of the main chain both on the surface and in the interior.
In the case of the latter, there is usually not enough
space to accommodate an amino acid residue with a side
chain. The electron density of Gly residues is not

well defined and in some regions, even disconnected.
Three of the GlyGly sequences are in sharp turns, and one

occurs at the beginning of the F-helix.

a/B Barrel Cavity

Residues related to the central cavity of the
O/B-barrel are given in Tables X 11 (a,b). The cavity
of the barrel is about 8-9 A in diameter from atom cen-
ters of about 6 A if van der Waals radii are considered
and it is about 20 A long. From the electron density,
the side chains of several amino acids forming the
center of the barrel extend into the cavity: Ile 32,
Ala 35, Glu 56, Arg 141, Asp 166 and Cys 170. The
charged residues interact with partial neutralization

(Table X.IY). The remaining side chains point away from

103

Table XII. (a) Residues Related to 0/8 Barrel Cavity*

Pro 30 i-I Pro 121 e 1
Val 31 i I Leu 122 i I
Ile 32 i E Leu 123 i I
Thr 33 i I Pro 124 e PL
Ile 34 i PL Leu 138 e E
Ala 35 i E Gly 139 i
Arg 36 e E Tyr 140 i 1
Leu 55 e E Arg 141 i E
Glu 56 i E Arg 142 i I
Val 57 i PL Phe 143 e PL
Thr 58 i PL Pro 163 e PL
Leu 59 e PL Phe 164 i I
Arg 60 e E Gly 165

Ser 61 e E Asp 166 i E
Gln 62 e E Ile 167 i 1
His 63 e E Arg 168 i I
Glu 77 e PL Phe 169 i 1
Leu 78 e I Cys 170 i E
Cys 79 e E Pro 171 e PL
Val 80 i 1 Val 189 e PL
Gly 81 i Met 190 e PL
Ala 82 i PL Cys 191 e E
Gly 83 i Val 192 i PL
Thr 84 e PL Gly 193 i
Gln 100 e E Thr 194 i I
Phe 101 e E Gly 195 i
Val 102 i I Trp 196 e E
Val 103 i I Met 197 e PL
Thr 104 e PL Leu 198 e PL

*
e = entrance of the cavity

i = internal surface of cavity

Table XII.

(b)

Arg
Leu
Glu
Leu
Cys
Gln
Phe

Leu
AIS
Ser
G1

His
Thr
Thr

104

Residues at the Amino End of Barrel

Cavity Adjacent to I-Helix

36
55
77
78
79
100
101

MMMHMMM

Pro 121 1
Leu 138 E
Pro 163 PL
Val 189 PL
Met 190 PL
Cys 191 E

Residues at the Carboxyl End of Barrel

Cavity

59
60
61
62
63
84
104

PL
E
E
E
E
PL
PL

Pro 124 PL
Phe 143 PL
Pro 171 PL
Trp 196 E

Met 197 PL
Leu 198 PL

105

Table XIII. B-Bends of KDPG Aldolase

Residues Location
Lys 25 - Ala 26 - Arg 27 - Ile 28 from “I to Ba
Leu. 41 - Pro 42 - Leu 43 - Ala 44 'before “A
Arg 60 - Ser 61 - Gln 62 - His 63 after 8b
Leu 86 - Asp 87 - Arg 88 - Ser 89 before 0C
Ala 96 - Ala 97 - Gly 98 - Ala 99 from ac to 8d
Arg 142 - Phe 143 - Lys 144 - Leu 145 after 8f
Ile 157 - Lys 158 - Ala 159 - Phe 160 after 0F
Pro 177 - Ala 178 - Asn 179 - Val 180 before a

G

106

the cavity toward the bulk of the molecule. The

central portion of the barrel not related to any entrance
is about 71% non-polar. The entrance of the carboxyl

end of the barrel Table X 11 (b), is surrounded with
positively charged and polar residues (46%). However,
the amino end of the barrel cavity is essentially non-
polar (80%) (Table X II(b)) probably because the

close proximity of the I-helix prevents the interaction
of these residues with solvent. The non-polar residues
at this end extend into the cavity. However, the 1-helix
introduces some negatively charged side chains in the

vicinity (Asp 14, Asp 20, Glu 24 and Asp 117).
B-Bends

In several places the peptide chain folds upon
itself by forming a hydrogen bond frOm the amino group
of one amino acid to the carbonyl group in the third
residue back along the chain, making a hydrogen bonded
loop of ten atoms. In KDPG aldolase, there are eight
of these reverse turns or B-bends which are listed in
Table XIII and all are of Type I as described by
Venkatachalam (1968) (Figure 34). Because of the
topological constraints imposed by the a/B-barrel, the
B-bends are located near the juncture between helices
and strands. In fact, the B-bends are the complete

connections between helix-1 and strand-a, and between

107

Figure 34. Type I B bend in KDPG aldolase.

108

helix-C and strand-d. A search for reverse turns in
globular proteins shows that they are very abundant,
comprising about one quarter of all residues (Crawford
et a1., 1973; Chou and Fasman, 1974). When surveying
the location of the B-bends in proteins Kuntz (1972)
found that they are concentrated at the surface, with
mostly hydrophilic residues. In KDPG aldolase, except
for residues 142 to 145, all of the reverse turns are
located on the surface. Of the identifiable secondary
structure elements, a-helices account for 35%, B-strands

for 20% and B-bends for 14% of the molecule.

Ion Pairs

There are twelve conspicuous ion pair interactions
in KDPG aldolase, some of which appear to be structurally
important (Table XIV). The Lys 15 residue occurs at
the beginning of the I-helix, and its interaction with
Glu 113 serves to bring the I-helix into close proximity
of the 0/8 barrel. The I-helix extends approximately
across the non-polar biased end of the barrel (amino
end) (Figure 33), and partially blocks the entrance to
the barrier cavity. The other end of the I-helix is
hinged to strand-a. The Arg 53 - Glu 212 ion pair
essentially closes the barrel. The former residue is

at the end of helix-A, beginning the barrel, and the

Table XIV.
Residues
Glu 4 Arg
Lys 15 Glu
Arg 27 Glu
Glu 37 Lys
Asp 45 Arg
Arg ~53 Glu
Glu 56 Arg
Arg 60 Glu
Arg 75 Glu
Arg 75 Asp
Asp 166 Arg
Arg 181 Asn
Arg 181 Asp
Asp 207 Arg

109

*
Ion Pairs Of KDPG Aldolase

2

113

77
66
72
212
141
95
77
223'
141
225
223
210'

Density
1 2
N G
P G
P P
G P
G P
G G
N N
P: P
G ‘ P
G G
G N
P G
P N
G P

Comments

holds 1 helix close to
bulk of molecule

between helices A and B
between helices A and 8
between helices A and H

inter-subunit interaction

between helices G and H
between helices G and H
inter-subunit interaction

* prime (') denotes another subunit

110

latter residue occurs near the beginning.of the final
helix-H. The ion pair thus formed helps maintain the
barrel closure in a most obvious way. The ion pairs

Arg 181 - Asn 225 C0; and Arg 181 - Asp 223 appear to
have a Similar function to that of Lys 15 - Glu 113 in
that the interaction keeps the long H-helix close to the
barrel by virtue of the interactions of the carboxyl
groups of the C—terminal with Asp 223 and Arg 181, and
the latter is located at the beginning of the G-helix.
The ion pairs Glu 37 - Lys 66 and Asp 45 - Arg 72 help

to preserve the integrity of the barrel by connecting
helices-A and -8. There is a network of charged residues
on the surface, near the interface of trimer: Arg 27,
Arg 75, Glu 77 and Asp 223, the latter from another sub-
unit. These residues, along with the Asp 207 - Arg 210
ion pair, help maintain the trimers in the crystal struc-
ture. The side chains of Glu 56, Arg 141 and Asp 166
point toward the cavity of the a/B-barrel. There is no
electron density corresponding to the side chains of the
first two, probably due to the lack of isomorphism of
this part of the structure in the native and heavy atom
derivative protein structures (positions oftwo Hg atoms,
Hg 1 and Hg 5, are relatively close) so that the arrange-
ment of the side chains of these residues is speculative.

The location of Glu 56 is of particular interest Since

111

the reactivity of this residue has been implicated in
catalysis through studies with BrPy (Meloche, 1970;
Meloche et 01., 1978). The importance of this residue
will be discussed in more detail in the description

of the active site Of the molecule.

Hydrogen Bonds

The hydrogen bonding interactions in the a-helices
are generally as expected, but the same is not true of
the eight strand B-barrel. To begin, the barrel
possesses a fairly severe twist about its cylindrical
axis. Moreover, the strands are not strictly parallel
to each other and tend to diverge as they approach the
helices connecting them together on the outside of the
molecule. This can be clearly seen in Figure 35, where
a schematic representation of the hydrogen bonding
between the B-strands is shown. Except in the mid-
section of the twisted barrel, the hydrogen bonding-
between the strands is basically poor (and apparently
non-existent between strands-a and -b). Nonetheless,
the parallel eight strand cylindrical arrangement is
strikingly obvious. A

A summary of the hydrogen bonding in the barrel
and other positions that have structural significance is

listed in Table XV. Again, the I-helix is held close

112

,_/.M_//././/.//

.mwcmuumum was NO mamnom mcfltcon cwmoucw: .mm musmam

0m. 00. 8.. cm. 00 . .
...».\mm. 00.. u... \-«.\M0..\8..m\n .0» .
. an. ..m.\...\0.. \ ..n. .m. «0. «0 W4 .8. .
mm \mm. 00..\0.z .o_. v 4.... . «n .

.m «m.\nw.. 8.. 00.. 00 . 8 . .n .

0m .0.\ on. 2. . a... 0m
0m. 2. .
. t.

Table XV.

Donor

Arg

Val
Ile
Leu
Gly
Gln
Val
Leu

18 NnH
31-NH

34-NH

59-NH

81-NH
lOO-NH
103-NH
122-NH

123-NH
141-NH
142-N
142-NA

162-NH
166INH

188-N6H
191-NH
192INH

194-NH
205-N6

113

Acceptor

Glu

Gly
Gly
Ala
Val
Val
Gly
Val
Arg
Glu
Pro
Pro
Asp
Val
Tyr
Asp

Phe
Gly
Ile
Asn

100-0e

193-CO
195-co
82-CO
57-00
80—CO
83-CO
103-co
141-co
119-OE

121-CO.

124-CO
166-CO
192-CO

140-CO.

164-CO
165-CO
167-CO
205-06

Hydrogen Bonds of KDPG Aldolase

Comment

holds I-helix close to
molecule

barrel
barrel
barrel
barrel
barrel
barrel
barrel
barrel
strand e
8 barrel
strand-e
8 barrel
8 barrel
8 barrel

mmmmuom‘mm

(strands
(strands
(strands
(strands
(strands
(strands
(strands
(strands

.a-h)

a-h)
b-c)
c-b)
d-c)
d-c)
e-d)
e-f)

and strand f .

(strands

f-e)

and strand-f

(strands
(strands
(strands

f-g)
g-h)
f-g)

holds I-helix close to

molecule
8 barrel (strands h-g)
8 barrel (strands h-g)
8 barrel (strands h-g)

three-fold intermolecular

interaction

114

to the molecule through the interactions Of Arg 18 Nn-H

with Os of Gln 100 and Asn 188 N -H with O of Asp 20.

0 6
Of special importance is the interaction Of Asn 205 of
three different subunits in the interface of trimer
molecules. These hydrogen'bonds together with the

ion pairs Arg 75 - Asp 223 and Asp 207 - Arg 210, fix

the three fold intermolecular interactions.
Environment of the Residues

The environment of the main polypeptide chain is
classified in Appendix 111 according to whether it is
on the surface of the molecule (S), near the surface
in cavities (NS), in the interior (1), related to the
barrel cavity (B), in the interface of the subunits of
the trimer (FT), or in the intermolecular interface
between trimer molecules (ST). Side chains of amino
acids on the surface or related to the cavity of the
a/B-barrel are classified as: extending into solvent
or the cavity of the barrel (E), parallel to or forming
the surface (PL), or pointing into the protein, away
from the surface or the cavity of the 0/8 barrel (1).
In addition, an indication of the clarity or quality
of the electron density of each residue is given:
good (G), partial (P) and non-existent (N). A summary

of the environment of the residues of KDPG aldolase is

115

given in Table XVI, from which it can be seen that
charged and polar residues generally concentrate on the
surface, while the non-polar aromatic and aliphatic
residues tend to be located in the interior, away from
the solvent. A basic difference exists between the
intra- and intermolecular interactions: the interactions
are mainly between non-polar residues in the former while
in the latter, the interaCtions are between polar and
charged groups. The amino acid composition of KDPG
aldolase indicates that 63% of the residues are non-
polar and only 37% are charged or polar (His and Tyr
classified with the latter). In a study of 22 protein
structures with a total of 5221 residues, Janin (1979)
found that 67% of residues accessible to the solvent
are polar while 72% of buried residues are non-polar.
Residues on the surface, near the surface and in
the interior are given in Tables XVII (a-c) along with
the direction of their side chains using the same con-
ventions as in Appendix III. The majority of the charged
and polar amino acids are located on the surface, and
they constitute about 48% of the residue in contact with
the solvent. Most of the polar residues extend into
the solvent where they probably interact with or are
neutralized by solvent ions. Many of these side chains

are ill defined, probably indicating a fair degree of

116

.mflmmnucmumm Ca HmHOQ 0cm HmHomlcos .Hmuou mo chHuomum
¥

ma. NN. Hm. mm. NN. we. Nm. Hmuou\umHom
mm. me. me. so. me. Nm. me. HmuouxumHodneod
.NH..OH .0H..NH .NN..NH .ee..m .Ne..e .ee..mm mm .0mmudeouusHod
.Ne..NH .mN..mm .NN..ee .No..oH .HH..GH .oe..em NeH «umHodusod
.OH..NN .NN..Ne .0N..Nm .No..mH .eH..NN .ae..oHH mNN .Hmuou
o m N N N N eH H8>
o . o H o H H N use
H H H o o H N mas
o m m H o m HH use
0 m H H H 8 0H 000
N m m o e 0 HH one
o m e o o o A one
o N N o m H N 002
o N o H H e N mNH
H m N N N OH HN 00H
H e m H e 8 NH 0HH
0 o H o o H H 8H0
0 e e o N HH HN NH0
H H N N H N mH 0H0
H H N H H N m 0H0
H H m o H H. m 0N0
m H H o H a. HH ems
N o e e o e e ems
m N m e e oH 4H 004
e m N e N NH Hm 8H4.
Em Bm HTHHMQIm wUflmGH GOMHHSm Townhfim HMUOB
Hmmz
mmmaocafi.wmax cw mmscwmmm may no usmEGOHw>cfl msu mo hnmfifiom .H>x manna

Table XVII.

Thr
Thr
Leu
Glu
Arq
Pro
Gln
Pro
Lys
Leu
Ser
Met
Ala
Asp

Alag

Arg
Asp
Ala
Glu
Lys
Ala

Glu
Asp
Ile
Leu
Pro
Ala

Hta
Hommqmmewmw
til

Ht‘
saw
H'UMM’UMMMDIMMMMMMMHNH

0101010101

"U’U'U
Ut‘t“

l'."

I."

(a)

117

Residues of KDPG Aldolase on the

Surface
Asp 45 PL
Ala 46 PL
Ala 49 E
Gly 50
Gly 51
Ile 52 PL
Arg 53 E
Thr 54 PL
Leu 59 PL
Arg 60 E
Ser 61 E
Gln 62 E
His 63 E
Gly 64
Leu 65 E
Ala 67 PL
Ile 68 PL
Leu 71 E
Arg 72 E
Glu 73 PL
Gln 74 PL
Arg 75 PL
Pro 76 PL
Asp 87 E
Arg 88 E
Ser 89 E
Val 94 PL
Glu 95 E

Gly
Ala
Thr
Asp
Ile
Glu
Ala
Gly
Ile
Gly
Tyr
Ala
Glu
Ser
Lys
Gly
Gly
Gly
Thr
Asn
Pro
Ala
Asn
Val
Al'g
Asn
Ala
Leu

98

99
108
110
111
113
114
115
120
135
136
137
149
151
158
161
162
165
172
176
177
178
179
180
181
182
185
186

PL
PL
PL
PL
PL
PL
E

E

PL
E

Pro
Asn
Leu
Asp
Ser
Ser
Ile
Lys
Asn
Gly
Asp
Trp
Ala
Arg
Glu
Ala
Cys
Ala
Glu
Ala
Ala
Leu
Leu
Asp
Ala
Asn

187 E
188 PL
198 PL
199 E
200 E
201 PL
203 PL_
204 PL
205 E
206
207 E
208 PL
209 E
210 E
212 PL
213 E
214 PL
216 PL
217 E
218 PL
220 PL
221 PL
222 I
223 E
224 E
225 E

118

Table XVII. (b) Residues of KDPG Aldolase Near the

Surface

Lys 15 E Asp 117 E
Ala 16 E Gly 173
Ile 19 1 Gly 174
Ile 22 1 Val 175 PL
Cys 23 I Tyr 183 PL
Ile 28 I Met 184 PL
Leu 29 E Val 189 PL
Leu 43 PL Met 190 PL
Ala 97 PL Met 197 PL
Gln 100 8 Ser 215 I
Glu 109 I Ile 219 I

(c) Buried Residues of KDPG Aldolase

Glu 37 Ala 96
Leu 47 Leu 112
Ala 48 Val 116
Lys 66 Ser 118
Gln 69 Glu 119
Val 70 Trp 202
Ala 92 Ile 211

Ala 93

119

mobility. On the other hand, the hydrophobic residues
are generally either part of the surface (PL) or extend
inSide the protein (1). There are some small non-polar
regions composed of NS residues, where the interaction
with the solvent is somewhat restricted."

There is a non-polar region which involves a cluster
of aromatic residues. This is in the form of a surface
cavity involving Met 133, Tyr 140, Phe 160, Pro 163 and
Phe 164. The presence of the Met sulfur atom in the
cavity is noteworthy since precedence has been set for
the interaction of aromatic residues with sulfur atoms
of Cys in the study of the interaction of the fluoree
scence probe ANS with a-chymotrypsin (Weber et a1., 1979).

All charged residues that are located in environments
inacceSsible to the solvent are neutralized as ion pairs

(Glu 37 - Lys 66) or form a hydrogen bond (Glu 119 08 with

Tyr 136 On-H) so that 80% of the residues in the interior

are non-polar.

The Trimer

The molecular packing consists of arrangements of
trimers which make a close contact with surrounding
trimers: each subunit possesses intermolecular contacts
with four others and in this way they form a network
throughout the crystal. This gives rise to two kinds

of likely trimeric arrangements of subunits in the

120

crystal: the trimer of the first kind, the one presumed
on the basis of number and closeness of contacts to be
the trimer of KDPG aldolase in solution (Mavridis and
Tulinsky, 1976); and the trimer of the second kind,

with much fewer contacts, and considered to be an
intermolecular interaction of trimeric molecules. With
a knowledge of the amino acid sequence the interfaces of
both trimers can be examined (Table XVIII). The inter-
faces Of trimers of the first kind (Figure 36) are
composed largely of residues with non-polar side chains.
These amino acids form 75% of the contact region, which
proves to be as hydrophobic as the regions of the poly-
peptide chain buried in the protein not accessible to
the solvent. The majority of the polar residues are
located at the periphery of the contact with possible
hydrogen bond interactions. The contact region de*
scribed is typical of interfaces of oligomeric proteins.
Chothia and Janin (1975) found that in several Oligomeric
proteins, more than two thirds of the interfaces between
subunits are non-polar. On the other hand, 45% of the
residues of the interface of the trimer of the second
kind (Figure 37) are polar, and the side chains of the
amino acids in contact also interact with the solvent.
In fact, the trimeric interactions have been fixed to

be simply: a) ion pairs of Arg 75 - Asp 223' and

Asp 207 - Arg 210' from three different subunits arranged

Table XVIII.

Ile
Ala
Ser
Gln
Thr
Val
Leu
Ser
Met
Phe
Val
Thr
Pro
Gly
Ile
Thr
Leu
Pro
Gly
Ile
Ser
Thr
Pro
Ser
Glu

Asp
Ala
Ala
Arg
Gln
Arg
Pro
Asn
Pro
Ala
Ile

32
35
61
62
84
85
86
89
90
91
103
104
105
106
107
108
123
124
125
126
127
128
129
130
131

45
46
49
72
74
75
76
176
177
178
203

Trimer Interfaces
(a) Trimer of the First Kind

E Ile 132 PL
E Met 133 PL
E Met 134 PL
E Arg 142 I
PL Phe 143 E
PL Lys 144 E
E Leu 145 PL
E Phe 146 PL
E Pro 147 PL
PL Ala 148 PL
1 Ile 150 1
PL Gly 152
PL ' Gly 153
Val 154 I
E Ala 155 PL
PL Ala 156 PL
I Ile 157 PL
PL Lys 158 PL
Ala 159 E
E Phe 160 E
E Arg 168 E
PL Phe 169 I
PL Cys 170 E
PL Pro 171 PL
E Trp 196 E
Asp 199 E

(b) Trimer of the Second Kind

PL Asn 205 E
PL Asp 207 E
E Trp 208 PL
E Ala 209 8
PL Arg 210 E
PL Ala 213 E
PL Cys 214 PL
PL Glu 217 E
PL Ala 220 PL
PL Leu 221 PL
PL Asp 223 E

122

 

Figure 36. Ca drawing of the trimer of the first kind;
three-fold axis shown appropriately.

123

 

opriat

124

approximately in a plane perpendicular to the three-

fold rotation axis giving rise to a cyclic arrangement

of alternating positive and negative charges and,

b) a trigonal hydrogen bonding arrangement involving

Asn 205 from three different subunits. Coincidently or
by design, the axes of the a/B-barrels lie approximately
parallel to this three fold direction. A conical opening
is formed in the three fold region by the terminal
H-helices of the three subunits. These helices make a
close approach with the Asp 207 - Arg 210' ion pair near
the apex. The opening of the cone is fairly spacious

at about 15 A in diameter. From the foregOing, the
trimer of the first kind emerges as the more likely
candidate for the oligomeric arrangement of KDPG aldolase

in solution.

Packing of the a-Helices and B-Strands

The distances of closest approach between the axes
of the a-helices and the inner surface of the barrel are
listed in TabLe XIX (a).

Except for helix-A, which is 11 A from the B-strands,
all helices have residues that interact with the surface
of the barrel (Table XIX (b)). The interface is shielded
from solvent and is composed mainly of non-polar residues
(69%), 39% of which are either Ile or Val. Janin and

Chothia (1980) found a marked preference for Ile/Val

Table XIX.

Table XIX.

125

(a) Distance of Closest Approach Between
Axis of Helix and the 8 Strands.

Helix

EQWEIUOCU

Distance (A)

11.
9.
7.
9.
9.
8.
7.
8.

0
0
0
0
0
O
5
5

(b) Residues in the Helix-Strand Interface

Residues of Helix

A

MOON

'11

not in contact with

strands

Val
Ala
Leu

Pro
Met

Ile

Tyr

Ile
Ile

70,
93,
112,

129,
133

150,

183,

211,
219

Glu 73

Glu 95
Val 116
Ser 130,

Val 154

Met 184
Ser 215,

Strands
b,c Thr
c Ala
d Val
e,f Leu
f,g,h Arg
Val
h Met
a,h Met
Pro

Residues of Strand

58, Arg 60, Val 80
82

102

123, Tyr 140

142, Ile 167,
189

190, Val 192

197, Leu 198,
30

126

residues (35%) in the helix sheet interface of eight
proteins. The number of residues making contact is not
very large because of the short length of the B-strands
and the twisted nature of the inner surface of the
barrel. The closest approach distances of axes of
consecutive helices are given in Table XX (a). These
distances vary more because of the nature of the packing
of the helices around the barrel which does not produce
many contacts (Table XX (b)). Of special interest are
the ion pairs of Asp 45 - Arg 72 between helices -A and
-B and Arg 53 - Glu 212 between helix-A and the beginning
of helix-H which help maintain the barrel closure.
Several vacant pockets or cavities are formed because
of the twisted nature of the B-strands. The most
striking of these is an ellipsoidal cavity of about 11 A
in diameter and 20.3 long between helix-A and the surface
of the barrel. This surface cavity is formed by helix-A,
part of helices -B and -H, strands-a and -b and part of
strand-c. The side chains of Val 31, Thr 33, Ile 34,
Ala 44, Ala 48, Val 57, Gln 69 and Val 80 extend into
the cavity. The residues Glu 37 and Lys 66 form an
ion pair at one end of the ellipsoid. Smaller pockets,
with diameters of about 7 A or less, are formed at the
interfaces of helices-C, -F and -H and the B strands

that form the barrel. In general, side chains of

Table XX.

Table XX.

omwonmawzv

Helices

Helix-l

Leu 47, Gly 50, Gly 51

(a)

(b)

127

Distance of Closest.Approach Between

Helix Axes.

H-A
A-B
B-C
C-D
D-E
E-F
F-G
G-H

Distance (A)

7.5
10.0
13.5

9.5
12.0
11.0
10.0
13.5

Residues in the Helix-Helix Interface.

Ala 44, Asp 45

None

Met 90, Ala 93, Val 94

None
None
Ile 150
None

SOMEIUDCDE

Helix-2

Ala 209, Ile 211, Glu 212
Gln 69, Arg 72

None

Thr 108, Ile lll, Leu 112
None

None

Tyr 183

None

128

hydrophobic residues extend into such cavities while
the side chains of polar residues that line these
pockets extend toward the solvent. The amino acids
that form some of these regions are given in Table

XVI (b).

Heavy Atom Derivative Sites

Sites 1-4 (Table XXI) of the mercury heavy atom
derivatives correspond to mercury binding at sufhydryl
groups of four of the five Cys residues of the KDPG ~
aldolase monomer. Site 1 is only 1 A from the OS‘Of
Asp 166 and 2 A from SY of Cys 23 suggesting that these
residues move slightly in derivative formation; this
site is also close to SY of Cys 191 (5 A), 08 of Glu 56

(5 A) and C of Arg 141 (6 A) and is located in the in-

C
ternal cavity of the d/B-barrel. Mercury site 2 is
located on the surface of the subunit very close to

SY of Cys 79 (N l A) and the Ne of Lys 25 (5 A). Both
these sites occur near the onset of B-strands (c and h)
whereas sites 3 and 4 are near the terminal helical
regions (H and I). Site 3 is 2.5 A from SY of Cys 23
and is located on the surface near the center of the
entrance to the cavity of the a/B-barrel. Site 4 is

located about 2.A from SY of Cys 214 in the conical

three fold cavity mentioned previously. Lastly, mercury

129

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131

site 5 occurs at about 3 A from 06 of Asp 166 and only
5 A from site 1. The low occupancy of the site in one
of the mercury derivatives and its absence in the other
suggest that this was probably a movement of the
carboxylate group of Asp 166 rather than a mercury
binding site.

Two of the Pt(CN)i- binding sites are near
positively charged side chains and appear to be ion pair
interactions. Site 8 is about 4 A from Ne of Lys 144‘
while site 9 is only 2 A from CC of Arg 168 and nearly
equidistant from N8 of Lys 144 and the center of the
ring of His 63 (m 6 A). It should be noted that both
sites are located in the active site region at the
interface of the trimers of the first kind. On the
other hand, the remaining Pt(CN)i- of significant
occupancy occurs in a depression formed by the main
chain near SY of Cys 214, Trp 208 and Gly 50 at the

contact region of trimers of the second kind.

Active Site Region of KDPG Aldolase

The position of the Schiff base forming Lys residue
of KDPG aldolase was originally established within a 50
peptide cyanogen bromide proteolysis fragment (Tsay and
Wood, 1976), and was subsequently located within the total
sequence at position 144 (Suzuki and Wood, 1980).

The LYS 144 residue resides on a shallow depression
at the surface of the subunit at the end of the a/B barrel
cavity opposite to the I-helix. The presence of another
subunit in the oligomer related by three fold symmetry
transforms this region to correspond to a cavity of about
25 A in length, 20 A in width and 9 A deep. The entrance
of the cavity is lined with the residues Leu 145, Pro 147,
Phe 169 and Pro 171 from one subunit and Gly 152, Gly 153
and Ala 155 from another, giving it an Opening of about-
7.5 A in diameter (Figure 38). There are about fourteen
residues in the immediate vicinity of Lys 144 with side
chains that are in contact with each other. These are
His 63, Arg 142, Phe 143, Pro 147, Arg 168, Phe 169,

Cys 170, Pro 171 and Trp 196 from one subunit and Ala 155,
Ala 156, Ile 157, Lys 158 and Phe 160 from a three-fold
related subunit. These residues more or less form an
ellipsoid of 9 B. by 14 A by 14 11 around Lys 144 (Figure 39) .
There is little or no electron density corresponding to

the side chains of Lys 144 and Arg 168; however the Ca

132

133

 

 

 

 

 

Figure 38. Entrance to the active site region of
KDPG aldolase.

134

 

 

 

% ARG I 68
IflSSS

CYS|7O

TRPISG

 

 

Figure 39. Active site region of KDPG aldolase.

135

positions of these residues are about 8 A apart. Side
chains of His 63 and Cys 170 are located in regions with
better electron density, both about 11 A from the Ca
position of Lys 144 (Figure 39). The active site region
of the molecule occurs at the loop between strand-b and
helix-B (His 63), the carboxyl end of strands-f,-g, and
-h (Arg 142, Phe 143, Arg 168, Phe 169, Cys 170, Pro 171,
Trp 196) and the loop between strand—f and helix-F (Pro
147) (Table X) of one of the subunits. All the residues
from a three-fold related subunit (155-160) occur in the
loop between helix-F and strand-g. Most of these residues
lie at the carboxyl end of the barrel and corresponds to
the general observation that active sites tend to occur
at the carboxyl end of B-strands.

We have tried to confirm the Lys 144 active region
in an independent way by diffusing a series of substrate
analogs into crystals of KDPG aldolase. All X-ray
crystallographic measurements utilized an automated
Picker FACS I four circle diffractometer. Details of
intensity data collection, and treatment of enzyme
derivative data are described elsewhere (weber, 1978).
The difference electron density peaks of four such_
derivatives are listed in Table XXII.

Intensity changes from crystals soaked in Py were

small and the corresponding difference electron density

136

Table XXII. Interaction of KDPG Aldolase with Substrate
and Substrate Analogs.#

_ (SOuM) (250uM; (30uM)
Sites py+BH4 Br-Py KDPGal FDP+
Pt 8
close to - g.%8 — g.39
Lys 144 ‘ '
H 1 0.08 0.16 0.19 0.32
g 4 5 7 l 6.6 8.2
Close to
Leu 65 - g'és - -
Lys 66 '
Close to _ 0.12 0.15 -
Cys 214 5.1 5.2
Pt 9
close to g°g7 - - 2'17
Arg 168 ° '
Interface of
trimer of the - - 3'30 g.§1
first kind '
0.18
H9 2 " ' ' 4.7

peak height in e A-3

ratio of the peak height to the
rms difference electron density.

# upper number

lower number

* P.J. Stankiewicz, unpublished results of this
laboratory.

f M.F. Frentrup, unpublished results of this
laboratory.

137

map showed no significant features. The probable
reasons for such a result are: a) inaccessibility of
the active site region in crystals, b) inactivity of
KDPG aldolase at pH 3.5 (Optimal activity at pH 7-8) and
high ionic strength or c) Py is simply too small to
observe, especially since < B >, the average isotropic
temperature factor of the native enzyme is about 50 A2.
On the other hand, crystals grown from enzyme inactiva-
ted in a solution with Py, at high pH, followed by
reduction with NaBH4 also led to inconclusive results
(Table XXII) implying that the e-N(l-carboxyethyl)Lys 144
is too small or the side chain is too disordered to
observe.

A Glu residue has also been implicated in catalysis
as a base assisting Lys 144 (Meloche, 1970). The posi-
tion of the residue has been established as 56 by
locating a heptapeptide of known sequence containing
the Glu (Meloche, Monti and Angeletti, 1978) in the
complete sequence of KDPG aldolase (Suzuki and Wood, 1980).
However, Glu 56 is located about 25 A from Lys 144.

This is an untenable contradiction because Br-Py can
crosslink a Glu residue and the Schiff base forming
Lys (Meloche, 1973). Moreover, at high ionic strength
the alkylation of a Cys residue is preferred over the

esterification of Glu (Meloche, 1970).

138

Although Glu 56 is located within the central
cavity of the a/B-barrel, access to it does not appear
to be excluded, especially by smaller molecules such as
Br-Py. Therefore, crystals of KDPG aldolase were soaked
with Br-Py even though the pH was 3.5 and the ammonium
sulfate concentration was 1.5 M. The difference electron
density map showed three very significant positive regions
of density (Table XXII), none of which were near Glu 56
corresponding to ester formation.. The largest peak
occurred at the Pt 8 position, near Lys 144, Cys 170 and
Pro 171. The next largest peak was in the cavity of the
barrel near the Hg 1 binding site. The other peak
appeared to be due to a shift in position of Lys 66.
Although high ionic strength favors SH alkylation of Cys
at the expense of esterification of Glu (Meloche, 1970),
the peak heights of the largest difference density fea-
tures suggest the presence of a much heavier atom such
as bromine. The largest density in the 2.8 A resolution
native enzyme map is only 0.9 eA-3 while the difference
density in a map at 3.5 A resolution based on native
phases produced a peak of 0.18 eA-3. Thus the largest
difference peak of the Br-Py derivative, located in the
vicinity of Lys 144, could readily correSpond to a

Schiff base adduct of Br-Py.

139

Table XXIII. Experiments Giving Rise to No Intensity

0'11 FIDO

Changes in KDPG Aldolase

Phosphate ions

a. with 0.1 M citrate buffer
b. no buffer

Arsenate'ions

a. with 0.1 M KHZPO4

b. with 0.1 M citrate buffer
c. no buffer
Phosphoglycollate
5-Phospho-2-deoxyribose

FDP

KDPG

Pyridoxal phosphate
(photosensitive)

140

The difference electron density of crystals soaked
in 0.25 M 2-keto-3-deoxy-6-phosphogalactonate (KDPGal)
suggested that the active site region is probably not
accessible to a six carbon sugar in the crystal or that
Schiff base formation was negligible-at pH 3.5. The
largest peak occurred near the three-fold axis in the
active site cavity, but near the exposed surface of the
protein. When fructose-1,6-diphosphate (FDP) is added
to the mother liquor of KDPG aldolase crystals, it
causes the pH to increase to 4.6. Therefore, the majority
of the numerous peaks that result in the difference
electron density map are due to pH dependent conforma-
tional changes. This is further supported by the fact
that crystals of KDPG aldolase shatter at pH > 5.0.
Crystals soaked in solutions of FOP at pH 3.5 show no
changes in intensity (Table XXIII).

Experiments in which no intensity changes occurred
are listed in Table XXIII. Unless otherwise noted, all
experiments were carried out at 1.5 M ammonium sulfate,
pH 3.5. KDPG aldolase does not seem to be affected by
either phosphate or arsenate (the enzyme can conceivably
already have a bound phosphate group after purification
and crystallization). Five and six carbon sugars do not
seem to bind, probably for the reasons similar to those
outlined previously. Pyridoxal phosphate causes intensity

changes but the complex with the enzyme appears to be

141

photosensitive. Changes in the diffraction pattern

disappeared upon standing overnight. Attempts were
also made to grow crystals inactivated with KDPGal

at higher pH and reduced with NaBH4, but invariably,

the protein crystallizes in a different space group.

Comparison of the Structures of KDPG Aldolase, Triose

Phosphate Isomerase and Pyruvate Kinase

Qualitative Comparisons

The folding of a subunit of KDPG aldolase which
accounts for all 225 residues is shown in Figure 32 and
33; Table X describes the secondary structural features.
This folding can be easily idealized to an eightfold
singly-wound a/B barrel by omitting a small kink between
strands hl and h2 and the helix designated I. The
result is shown in Figure 40. As can be seen from the
Ca-backbone structures of Figure 41, such a folding is
also very similar to that of TIM and the A domain of PK.
However, it should be noted that the amount of regular
secondary structure in KDPG aldolase (36% helix, 20%
B-structure) is considerably less than that in these
two enzymes. This is especially so in the case of TIM
(55% helix, 22% B-structure), which has 23 more residues.
Preliminary results indicate that the structure of yeast
TIM, like avian TIM, is also an eight-fold a/B barrel
(Alber et a1., 1981).

The main domain of Taka-amylase (TA) has also been
reported to be an eight-fold a/B barrel (Matsuura et a1.,

1980; aKusunoki et a1., 1981) and it should prove to be

143

 

Figure 40. Ribbon drawing of KDPG aldolase down the
a/B barrel axis (drawn by Dr. L. Lebioda).
For clarity, the first 25 residues which
are not part of the barrel have been omitted
(region includes l-helix).

144

 

KDPG Aldolase

 

 

Figure 41. Ca backbone structures of KDPG aldolase,
TIM and the A domain of PK. A11 viewed .

down the B-barrel axis and in best least
squares orientation.

145

of significant interest in further comparisons of these
enzymes when coordinates become available. In addition,.
a recent low resolution structure determination of
spinach glycolate oxidase (GLOX) (Lindqvist and Branden,
1980) suggests that a domain of this enzyme also has

an eight-fold a/B barrel, thus increasing the multipli-
city of this class of folding to include five function—

ally very different enzyme molecules.
Quantitative Comparisons

The quantitative comparisons of the structures of
KDPG aldolase, TIM* and PK* began by examining the
distance diagonal plots of the three enzymes (Figure 42).
Distance diagonal plots are graphs of Ca-Ca distances
plotted against residue number, with contours drawn at
fixed interatomic distances. Secondary structure
features are revealed by characteristic patterns near
the diagonal in the distance map (Kuntz, 1975). Helical
regions give rise to contour lines very near and parallel
to the diagonal; B strands yield contours parallel and
perpendicular to the diagonal. The pattern of a distance
plot is characteristic of a chain fold and therefore
useful for chain fold comparisons. The structural

elements found in the KDPG aldolase diagonal distance

 

*
The coordinates were obtained from the Protein Data
Bank File, Brookhaven National Laboratory, Upton, NY.

146

 

\

.~~ s- ...“) “2.5 f
. .(é. i 3%; 6

 

60 120 160

   

 

ae'dé I‘... I"--.

 

 

 

 

 

 

 

 

 

 

 

Figure 42. Distance diagonal plots of KDPG aldolase,

TIM and PK. Contours at 6. 0, 11.0, 16.0 A;
secondary structural elements designated
along the diagonal, break in PK sequence
appropriately noted.

147

 

 

 

 

 

Figure 42. (Cont'd.)

148

 

 

 

 

 

 

 

 

 

... ......... .. ....... . .................. . .................. .............. G. .1... 262

 

 

Figure 42. (Cont'd.)

149

plot are shown schematically in Figure 43 (Kuntz, 1975).
Turns appear as simple line elements that depict contour
lines that intersect the diagonal. Features of this
type represent adjacent segments of residues that come
close together in space in an antiparallel manner. The
slope of the line will depend on the secondary structures
involved because the slope is determined by the ratio

of the number of residues per unit length for the seg-
ments a and b (Figure 43). This ratio is 2 if segment

a is helical and segment b is a B strand. A strand-
helix arrangement will have a slope of 0.5 and if both
segments are of the same secondary structure, the slope
is unity (Kuntz, 1975).

Four sided patterns such as squares and trapezoids
represent the interactions among three segments that
come closer together in space (Figure 43). Segments
a and b are antiparallel as are b and c; however a and
c are parallel to each other. Trapezoidal forms are
found whenever turns link helix to extended segments or
vice versa and represent the smallest units of tertiary
structure that can form parallel spacial arrangements
of the polypeptide chain. These patterns are also
indicative of compact packing of the chain (Kuntz, 1975).

The characteristic eightfold interactions of the
B-barrel give rise to the combination of the trapezoidal

forms designated a-b, a-c, etc. in Figure 42, with those

150

Structure Idealized feature Backbone conformation

9’ N a helix

Turns ”,o' _ b strand
' 5. (solid line)

a strand
b = helix
(dotted line)

helix
strand
helix

N_
Three strand 5 C 6 -
-Loops c

OU‘D’
llllll

strand
helix
strand

00'!”
"Ill!

strand
helix
strand
helix
strand

Multi strand
loop

(000 UN
II II II II II

 

Figure 43. Structural features of KDPG aldolase diagonal
plot (from Kuntz(l975)).

151

of KDPG aldolase being the most pronounced and regular,
although a change in the contour interval would enhance
these interactions in TIM and PK. It can be seen from
Figure 42, that the amount of secondary structure of
TIM and PK is considerably greater than that of KDPG
aldolase and that the Class B three strand a-B-a and
B-a-B loops (Kuntz, 1975) increase in length in TIM

in going from the N to the C-terminal. It can also be
seen from Figure 42 that the lengths of the helices and
the B-strands of KDPG aldolase and PK are more uniform,
particularly those of the former. Some of the addition-
al secondary structure of TIM is doubtless due to the

23 additional residues of that enzyme. Lastly, all
three enzymes show characteristic barrel closure features
in the upper, right-hand corners of their respective
diagonal plots. Thus, it is clear that there are more
than qualitative relationships among the folding
structures of these three enzymes.

A quantitative comparison of the geometry of the
main chain folding of KDPG aldolase, TIM and PK has been
carried out by the method described by Rossmann and
Argos (1975) (Appendix II). The method searches for
the best fit between two structures by the method of
least squares starting with a set of assigned equiva-

lences. These are then expanded and the process is

152

reiterated until convergence is attained and no
additional equivalences determined. This particular
method also has the added advantage of allowing for
insertions and deletions in sequence which applies in
the present comparisons.

In order to assure the validity of the equivalences
at convergence, several different starting sets of
equivalences were investigated. The final best fit
orientations of the three Ca-backbone structures to
each other viewed down the B-barrel axis are presented
in Figure 41 which clearly shows that appropriate
secondary structural segments basically correspond in
the different enzymes. This is shown diagramatically
in Figure 44 and given quantitatively in Table XXIV.
The non-equivalent areas of Figure 44 generally result
from different lengths of a/B elements or they reside
in connecting loops between these elements. However,
even some of the connecting loops are closely related,
especially those between heliceSsD and-F of KDPG aldo-
lase and PK (Figure 44). Most significantly, this
region of the molecule occurs in the active site of
KDPG aldolase. We shall return to this point in the

next section.

153

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Since the B-barrel has pseudo-eight-fold symmetry,
equivalences in structure can be produced by 45° rota-
tions about the eight-fold axis. The results of such
comparisons are summarized in Table XXIV from.which
it can be seen that although a quantitative assessment
of the fitting is not possible, since the distributions
of the deviations are not normal, there is no obvious
superiority of the A-A superposition over any of the
others. Although Stuart et a1., (1979) report 160
equivalences between TIM and PK with a r.m.s. distance
of 3.0 A, which appears to be a better fit than that
listed in Table XXIV, the method of comparison used by
Stuart et al., was slightly different from the present
one and permitted omissions of single residues in one
structure only (H. Muirhead, personal communication).

It can also be seen from Table XXIV that there is
no sequence homology between KDPG aldolase and TIM
(the sequence of PK is unkonwn). The minimal base
change (MBC) per codon, which measures the sequence
relatedness of the various superpositions of KDPG
aldolase and TIM proved to be quite similar and only
slightly lower than the random value of 1.54. The
lower values probably result from the correspondence

of hydrophobic and hydrOphilic residues in the proteins

156

and the correlation of the second base of the codon
with hydrophobicity. Such a view is further supported
by similar values of the NBC obtained in the auto-
correlation comparisons of KDPG aldolase (Table XXIV).
Thus, there is no amino acid sequence homology between
these two enzymes. The Ca backbone drawings of the
enzymes shown in Figure 40 are in the orientation of
a-a, A-A, etc. and correspond to the least squares fit
of KDPG aldolase, TIM and PK. The eight-fold pseudo-
symmetry of the molecules corresponding to the (oz/B)8
structure is strikingly apparent as is the similarity
of the three folding structures.

The "cross" diagonal distance plots of KDPG
alddlase-TIM and KDPG aldolase-PK corresponding to the
differences in Ca positions in their a-a, A-A, etc.
superimposed orientations are shown in Figure 45. After
an initial translation of approximately 25 in sequence,
it is clearly evident from the "diagonal" nature of the
plot that there is a high degree of homology between
these enzymes. The "diagonal" is not straight and is
bowed because of insertions/deletions in one or the
other enzyme. It can be seen from Figure 45 that there
are more insertions with TIM than with PK. The gaps
in the "diagonal" correspond to non-equivalent regions

between the two enzymes and it can be seen that most

157

TIM

 

 

 

Figure 45. "Cross" diagonal distance plots of differ-
ences in Ca-positions between KDPG aldolase
aldolase-TIM and KDPG aldolase-PK in their
superimposed orientation. Contours at 6.0,
11.0 and 16.0 A; secondary structural
elements appropriately designated.

158

 

 

 

 

-Figure 45. (Cont'd.)

159

of the differences reside in or near the loop regions
between a and 8 structures. In the KDPG aldolase-TIM
comparison, the differences occur more often in the
middle of the sequence whereas the opposite tends to
happen in the PK comparison. At this stage, it is
difficult to attach significance to such behavior.
Finally, the satellite "diagonal" peaks of both com-
parisons correspond to the interactions of the first
element of the pseudo-eight-fold symmetry (e.g. a-b,
ArB, etc.) Although the extent of such display is
again dependent upon the contouring intervals, it is
nonetheless most dependent upon the fidelity of the
symmetry. A detailed tabulation of the equivalences
between KDPG aldolase, TIM and PK is given in Table

XXV.
Implications in Protein Evolution

Evolution in proteins involves changes of single
residues, insertions and deletions of several residues,
gene doubling and gene fusion. The change of an amino
acid residue in the polypeptide chain is the basic step
in the process of protein evolution. Such changes
accumulate during the course of time, so that eventually
all similarities between initial and resultant amino

acid sequences might be erased. But even after all

113C)

Table XXV.

Structural Equivalences bong KDPG Aldolase. rm and PK".f

PK ’ 6*-

at.

T

D
L
A

di.

Mu
T

M

3J92J9J‘JSJ ‘6924849 55902933 610421 aazclnsaoo ‘33
o o o o o o o o

 

 

 

 

 

 

o I
| T3; “I... 11 I. I‘ll.
7 9 2 5 ‘23 5 7 90‘23‘56 7 7 ‘2
4MSWfl6flflfifi 666“6“6“ 67777777 $M8wmm M%%9%”m mom
|||||||| |||||||| |||||| |||||| 2
‘3“oo2o|oolu‘os 5“3322o|o‘|02|u|uoo|oo|oo|oolu ‘2LLOL0|||3LLL‘33L‘
D‘xIVAAQ"c Y‘VISP‘HAIIGA‘HVIL GQ‘VAuAI-AEGLHVIIACHG
7 9 2 5 7 989 7 9 2 o 23‘56789 ‘
|||||||||||n||n|u||
c c d D .
6789 5 7 23 7 3 5 7 o. 23‘567890123‘5
||||||1||||||||||||||||||||
Ont-867736] gsgsoJJazasoJ ||44 °00¢|8|79
....... O O C . . . C . . . C . .
‘5322242‘ 2330cu|oolu2nlmm|oasazo 2|3|||220243
1|" 1‘2222 222 3 33333 “‘ 4‘
C C C . C C . . . . . .
13130 1‘23} 222L2020L22L3 12233 3.30G‘o20‘n2301h‘
vesnuKnnsK R‘SLGELIHTL VCG‘P SI'LDFQ‘L
890123‘567 9 34567 0 23 5 7 9 3 5
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ARILPV|T|AREEDILPLADALIAGG|RTLEVTLRSOHBLKA|QVLREQR

nvnflwnunufiuvnnwnz uwnmnwflunflfifiw fimflflaflfififl wwnnnnn

161

Table XXV. (Cont'd.)

 

 

 

 

126 1 143 1 3.0 287 3.2 176 u 214 6 4.1
127 s 144 r 1.8 288 2.8 177 11 215 6 1 4.3 266
128 1 14s 8 2.8 289 3.1 178 A 216 11 4.9 267
129 11 146 E 3.1 218 5.4 179 11 228 L 1 2.9 268
138 s E 147 1 0 2.4 188 v 221 A 6 3.9 269
131 2 148 1: 3.6 211 1.7 181 11 222 s l 2.5 278
132 1 149 A 4.6 212 1. 1.2 182 11 G 223 8 1.9 271
133 11 158 1 5.1 213 3.1 183 1 ° 272
134 11 151 A 4.2 214 5.2 184 11 1 27:1
135 6 155 11 2.8 215 3.6 185 A 274
136 1 156 8 3.1 216 1, 2.6 186 L 275
1:11 :1; 12 1:1:
139 6 I 161 1 3.8 189 v 276
148 1 f 162 1. I 1.1 219 1 1.6 198 11 226 v 2.7 277
141 11 ' 163 A 2.1 228 1.6 191 c a 111 227 8 2.2 278
142 11 l 164 1 ' 3.2 221 3 3.5 192 1 1 228 G' 1.9 279
143 r 222 J 4.9 193 6 229 r 6 3.6 288
144 11 165 I 3.4 223 4.9 194 1 230 1 l 2.8 281
145 L 166 9 2.9 224 4.7 195 6 231 1 3.2 282
146 1' 167 1 4.1 225 3.4 196 11 11 112 232 6 1 3.3 283
147 11 226 5.2 197 11 1 23:1 6 6 3.4 284
148 A 227 3.0 198 L 234 A 1 4.1 285
149 E 228 5.9 199 8
158 1 181 A 3.6 230 3.9 288 s
151 s 182 11 2.1 231 2.9 281 s
152 6 18:1 1: 8.6 232 9.7 282 11
15:1 6 184 1 1.7 233 2.3 203 1
154 v r 185 11 1.1 234 1.8 284 11
1222 I 135’ ‘ ° 5": 33‘ H £2

‘ e 6 B e
1211 12:" 2-2 a" m

K e h
159 9 194 1 I 3.2 , 383: n
68
161 6 282 v 1'. 4.1 248 1 2.7 211 1 287
162 6 283 8 l 5.4 241 2.5 212 E 237 11 11 3.8 288
163 11 284 s 8.1 246 4.8 213 A 238 11 9.7 289
164 r 285 11 3.3 247 11 3.2 214 c 39 _E 4.4 298
16s 6 1 286 1 1 3.7 248 2.1 215 s 1 11 48 r 3.9 291
166 o 287 1 11 3.4 249 3 3.8 216 A 241 1 2.5 292
167 1 9 286 1 l 3.5 258 J, 1.9 217 E 242 8 6 3.0 293
168 11 289 6 3.2 251 2.9 218 A 24:1 1 3.1 294
169 1' 218 6 3.8 219 1 244 1 3.0 296
178 c 228 A 245 11 2.8 297
171 11 221 i. 11 246 A 11 3.7 298
172 1 222.1 247 x 2.4 299
173 6 211 s 3.9 252 4.9 223 8 248 11 2.8 381
174 6 212 1 3.6 253 3.4 224 A 382
175 v 213 1 41 4.1 254 4.2 225 11 38:1

i'i'iI-st 25 residues of KDPG Aldolase do not have equivalences
.0

distance between emivalent 111-carbons in_ L

’aeino-acid semence of PK is not known.

fTotai length of secondary structure elaents indicated by arrow heads.
Deletions indicated by " or by absence of arrow heads.

oobh~bommo

HN-‘d-‘OOO‘HN
e e e e e e

 

e—u-O
O O O I O 0 O O
dN-‘MNOOb&O

N.N-‘N.dtflm~

e e e e e e e e e e
“N‘GUO.G~.HQNVN

NN.-'NN-'—'NUN-‘NUPJ

e——h———r¢———a

162

sequence similarities between two homologous proteins
have vanished the conformation of the backbone might

be conserved. In many circumstances, where sequence
relationship is not readily apparent, structural
relatedness can be used successfully to find insertions
and deletions in sequence and to detect amino acid
homology (Dickerson, 1981). Very gross changes result
from gene duplication which can lead to a doubling in
length of the polypeptide chain (McLachlan, 1980).
Furthermore, cases of fusion of different structural
genes are known (Yourno, Kohno and Roth, 1970), which
implies that one or more genes have been translocated

to a different position in the genome. Proteins evolving
divergently may retain their function, active site and
mechanism of action even when their sequences become
non-homologous, as with hen egg-white and bacteriophage
T4 lysozymes (Rossmann and Argos, 1976; Matthews et al.,
1981a; Matthews et al., 1981b). 0n the other hand, there
are families of proteins related in structure and sequence
in a way which implies their evolutionary relationship
while divergence of their biological function has ren-
dered them either specialized, as with serine proteases,
or completely diversified, as in the insulin family
which also includes somatomedins (growth factors) (Blun-

dell and Humbel, 1980).

163

The number of possible amino acid sequences and
chain folds is so large that similarity is not
expected to occur by chance but to reflect protein
_ differentiation. However, the vast number of structural
options does not exclude the possibility that certain
structures are strongly favored and that several
evolutionary processes may converge to such structures.
Clear examples of convergent evolution are the catalytic
sites of serine proteases and subtilisin (Kraut et a1.,
1971; Argos et a1., 1981). In both cases an incoming
substrate would encounter the same active site geometry,
but the enzymes are completely unrelated with respect
to amino acid sequence and backbOne conformation. The
catalytic mechanism of the protease papain and of
G-3-P-dehydrogenase, an enzyme of the glycolytic pathway
may be analogous to that of serine proteases (Argos
et aZ., 1981). Even proteins diverging from a common
ancestor in their overall architecture can also exhibit
aspects of convergent evolution (Edmundson et al., 1976).
However, at present there are no proven examples of
proteins which have converged to a similar overall
backbone structure and it is often assumed that similar-
ity in folding indicates divergent evolution from a
common ancestor.

The most obvious question that surfaces from the

results of the present structural comparisons is whether

164

the folding of KDPG aldolase, TIM and PK is the result
of divergent evolution from a common ancestor or
rather, a result of convergent evolution to a highly
symmetrical and possibly highly stable form of an

a/B barrel structure (Hol, Halie and Sander, 1981).
Although convergence of proteins to a complicated
structure is very unlikely (Schulz, 1981), this might
not be particularly so for an exceptionally symmetrical
structure as a barrel of repetitive a/B units which
appears to be so natural and reasonable. The overall
organization is simple, symmetrical and under extremely
stringent topological and packing constraints. The
connections between the a/B structural elements must

be righthanded and on the outside of the barrel.
Moreover, the elements must form a well packed B-barrel
with relatively tightly packed helices around the out-
side of the barrel. It is thus conceivable that the
number of possibilities for satisfying such conditions
is quite limited and center about an eight-fold singly
wound barrel structure. In the folding process,
d-helices would be formed first (Ptitsyn and Finkelstein,
1981) with righthanded turns at the a/B connections
(Richardson, 1976) establishing a similar conformation
for all a/B units. As the B-strands form a larger

parallel sheet, the more bulky a-helices could force

165

it upon itself. If the number of a/B units is suffici-
ently large, an a/B barrel could result. The quaternary
structure of a domain of Japanese quail ovomucoid
corresponds to a similar arrangement: four parallel
B-strands from different molecules form a hydrogen bond-
ed channel in the center of the oligomer while the bulky
parts of the subunits are found on the outside at the
surface (Weber et a1., 1981). Steric hindrance apparent-
ly limits the channel to four strands and leads to hydro-
gen bonds of unfavorable geometry. Nevertheless, a four-
fold barrel structure is formed.

Comparisons of KDPG aldolase, TIM and PK in super-
positions related by the exceptional eight-fold pseudo-
symmetry could also lead to convincing arguments in
favor of divergent evolution. Of the eight possible
superpositions, A-A, A-B, ..., A-H, only the A-A corre-
Spondence is consistent with a linear gene because it
does not match a protein with transposed fragments of
the other. Thus, a best fit for the A-A superposition
would be expected if there is a common precursor for
the three enzymes. If the evolution is convergent,
there should be no preference for any particular super-
position. Results of all of the comparisons are
summarized in Table XXIV from which it can be seen that

there is no obvious superiority of the A-A fit over the

166

others. This is an indication of convergent evolution
although another possibility is that it could represent
divergence from a very symmetrical ancestral protein.

The consequence of gene duplication in evolution
was also considered (McLachlan, 1980). In the case of
TIM, there are no indications suggesting duplication.

If KDPG aldolase were to show evidence for gene dupli-
cation, it would strongly suggest that these enzymes
arrived at the eight-fold a/B barrel by convergent means.
The A-E superposition corresponds to the two—fold
symmetry of the molecule and it proves to be of no better
quality than the overall eight-fold symmetry shown by
other superpositions (Table XXIV). Thus there is no
preference for the (on/B)8 structure by gene duplication
of an (oz/B)4 structure. It should be noted, however,
that since glycolysis is one of the oldest biochemical
processes such relationships could have been erased

by evolution. It will be interesting to see the results
that TA and GLOX show in this respect.

The strongest argument for divergent evolution of
these three enzymes comes from a consideration of the
similarity of their function rather than any other
aspect: all activate a C-H bond adjacent to a carbonyl
group (Rose, 1981). In fact, even GLOX is similar in

that it activates a C-H next to a carboxylate group.

167

Moreover, the active sites of these enzymes, including
TA, are located as expected at the carboxylic ends of
the B-strands of the barrel. In the case of KDPG
aldolase, Lys 144 is the Schiff base forming residue
which leads to an azomethine intermediate (Meloche and
Wood, 1964; Suzuki and Wood, 1980) characteristic of
'Class I aldolytic cleavage. The superposition of KDPG
aldolase and TIM in the A-A mode indicates structural
equivalence between Lys 144 and Glu 165 of TIM (Figure
44 and Table XXV). Although there appears to be some
uncertainty about the exact nature of the active site
of TIM (Phillips et al., 1977), nonetheless, Glu 165

is considered the most likely candidate for the
catalytic base of TIM in the interconversion of
dihydroxyacetonephosphate to G-3-P. Moreover, the
active site region of PK has been shown to be located
in a similar region to that of TIM (Levine, et a1., 1978).
Such congruence must be considered more than fortuitive
and a highly meaningful and important factor in favor
of the divergent evolution of these enzymes from a com-
mon precursor. On the other hand, such suggestive
indications do not present themselves when the phosphate
binding region of TIM is compared with equivalent
residues of KDPG aldolase. However, Gly 233 of TIM,
which is said to hydrogen bond to phosphate (Phillips

et a1., 1977), corresponds approximately to Gly 193

168

Thr 194 Gly 195 of KDPG aldolase. This particular triad
has been implicated in phosphate binding in other enzymes
(Schulz and Schirmer, 1979).

In conclusion, if divergent evolution prevails it
has certain remarkable consequences in the present
example. It implies the existence of a family of
different enzymes with unrelated amino acid sequences
which originated from a common ancestral protein with
a very symmetrical structure. Furthermore, this pro-
tein activated a C-H bond adjacent to a carbonyl and
should be thought to have been neither very specific
nor efficient. Notwithstanding the foregoing, it
should be noted that the occurrence of five enzymes of
widely differing function, from widely differing sources
(mammalian (PK), avian (TIM), plant (GLOX), fungal (TA)
as well as bacterial (KDPG aldolase)), with the same
eight-fold a/B barrel structure could also be taken
to support the view that enzymes can converge to a
common, limited number of stable protein folds which
are also probably convenient to many catalytic functions.
This would advocate protein taxonomy based on struc—
tural principles. Decisive evidence for divergence
can still come from sequence homology between KDPG
aldolase or TIM and PK, TA or GLOX, or yet some other

protein which would be a link between the amino acid

169

sequences. On the other hand, evidence of gene
duplication in either TA or GLOX would be fairly

decisive for convergence to a stable fold.

APPENDICES

APPENDIX I

Details of the Measurement of Kendrew Model

Coordinates With Two Theodolites

The coordinate systems of the two theodolites (I and
II) are shown in Fig. la, where z; and z; are parallel
since by definition they are normal to the level of the
instruments. When the theodolites are pointing at each
other, the angles measured will be denoted by the super-
script t (¢§, x: and ¢§, x; and will correspond to the
first (1) or the second (2) theodolite. The point P
is characterized by the angles ¢;, x; and ¢;, x3. The
coordinate systems can be made to be parallel to each other
by rotations around the z" axes. Therefore the

polar angles of the point P will be transformed to:

X = X X
l l 2 2

.— II_ t l "_ t o
¢l - ¢l $1 ¢2 ¢l ¢l + 180 (1)

ll
X

Both coordinate systems have to be rotated by an
angle T = x: - 90° around both y: axes in order to arrive
at the system defined in Fig. 31. This rotation is shown
schematically in Fig. lb, where x and ¢ have to be
determined (since the procedure is valid for both theo—

dolites, the subscripts have been omitted).

170

171

A F’(¢1,>q'.<ag.x2

Xi'

 

 

 

 

Figure Al. Transformation of spherical coordinates to

system in which the second theodolite has
coordinates ¢ = 0, x = “/2 when viewed from
first theodolite.

(a) Coordinate systems of the two theodolites.

(b) Rotation of the coordinate systems by an
angle T around both y axes.

172

 

 

 

 

 

 

Figure Al. (Cont'd.)

173

From Fig. lb,
¢ = 180° - A (2)

and from Napier's analogies of spherical trigonometry

we have:

sin8(XfT) ' tank(A-B)
sink(x+1) cot8¢'

 

 

and

‘cos%(er) =‘tan%(A-B)
cosk(x+¥) cot8¢7 (3)

 

 

Rearranging these equations,

sink(xrr) )

B = A - 2 arc tan(cot%¢' sin%(x+1)

(4)

2 are tan(cot%¢":g::E§;:; ) - A

U1
fl

 

the angle A can be obtained from (4); after substitution

into (2), we have:

¢ a 180° - arctan (cot 8 ¢' sing '[L )-arctan(cot ' cos%( '7) 5
sink(x+r) 8 O cos§(x+r)) ( )

From the law of cosines for sides,

x = arc cos(cosx'cosr + sinx'sintcos¢') (6)
and by the use of Eqs. (1), (5) and (6), the polar angles
measured in arbitrarily oriented coordinate systems

can be transformed to the convenient system defined in

174

Fig. 31 of the text. In this system, the Cartesian
coordinates of the point P will be the intersection of the

lines described by the parametric equations:

x1 = (cos¢lsinxl)u = alu
yl =(sin¢lsinx1).1 = blu (7)
21 = (cosxflu = clu

_x2 =(cos¢231nxéw+£=a2w+£

y1 = Sin¢zsinx2w (8)

II

0'
k)

2:

22 =(cosx3w

In practice, however, these lines rarely intersect
because of experimental error in setting but the minimum

distance between them (d) can be calculated:

2 _ 2 2 2
d - (xl-xz) + (yl-yz) + (21-22)
2 _ 2' 2 2 _
3d /8u - u(al+b1+c1)-w(a1a2+blb2+clc2)-al£-0
2 _ _ - 2 2 2 _
8d /3w - u(ala2+b1b2+clc2)+w(a2+b2+c2)+a2£-O
2 2 2 2 2

but a +b +c = cos ¢sin x+sin2¢sin2x+coszx=l
a1a2+b1b2+c1c2=s

so we have,
u-sw-a12=0

-su+w+a22=0

which results in

u = l (al-sa2)/(l-sz) and w = i (sal-a2)/(l-sz) (9)

175

'Substituting the values of u and w of (9) into Eqs.

(7) and (8), two new points P1(Xl, Y Z1) and P2(X2, Y

1' 2'

22) result:

X1 = a12(al—sa 2)/(l-s: ) X2 = alz-Msal a2)/(l- s :)+£

_1 = b1£(al -sa:)/(l-s2 2) Y2 = b2£(sal -a2)/(l-s:)

zl = c12(a1-sa2 )/(l- s 2) 22 = c2£(sa1-a2)/(l-s )
(10)

The Cartesian coordinates of P are taken as the midpoint

of the segment defined by these two points:

X1+X2 .Y 1+)!2 Z 1+2 2 l l
I T: 2 ) ( )

 

 

P(X,Y,Z) = P(

The coordinates of P are linear homogeneous functions
of l, the distance between the two theodolites. The
value of i need not be measured directly; 2 can be
obtained from the coordinates of two points of very

accurately known separation (machinist's scale).

APPENDIX II

Method for Systematic Comparison of Two Molecular

Structures (Rossmann and Argos, 1975)

To orient the second molecule (identified by the
subscript 2) with the first molecule (identified by the
subscript 1), an initial rotation matrix [g] and a
translocation vector d are devised. The new position

I I I I . ’ .
x2(xi,y2,zz) of a p01nt x2(x2,y2,zz) in the second mole

‘gule is given by the following transformation:

x = c x + c y + c z + d
2 11 2 12 2 13 2 1
I
y = c x + c y .+ c z + d (l)
2 21 2 22 2 23 2 2
z' = c x + c y + c z + d
2 31 2 32 2 33 2 3

or x. = [C]x +61
2 m 2

A number of positions in the second molecule are presumed
to be roughly equivalent to corresponding ones in the
first molecule. These positions are used to linearly
evaluate the nine elements of [S] and the three of d

by minimizing the condition

2

s = (x -x') (2)
1 1 2

where the summation is over at least four equivalent

positions. For instance,

176

177

,BS

1
3c = Z (x - c x + c y + c z - d )x
11 1 11 2 12 2 13 2 1 2

and setting asl/Bc11 = 0.
Zxx=c (sz)+c (£xy)+c (sz)+d(2x).
1 2 11 2 12 2 2 13 2 2 2 2

Similarly, we can set asl/ac12 = 0, asl/ac13 = 0 and
asl/ad1 = 0 and this procedure will give rise to three

sets of four simultaneous linear equations given by

the coefficients

Ex: szyz 2x222 2x2 C11 c21 C31 Zx‘xz Zy‘xz . Ezlx2
szyz 2y: I:yzzz 2y: c12 C22 Caz leyz zy1Y2 £21Y2
)3sz2 Zyzz2 22: 822 C13 c2) c3, Xxiz2 2y):z {2‘22 (3)
2x2 Zy2 222 n d1 d2 d3 le 2yl £2l
Equation set 1 2 3 l 2 3

A rotation can also be specified by the three
Eulerian angles 61, 62 and 63 as shown in Figure I.
The rotation operation consists of: 1) a rotation of
the Cartesian axes by 91 about 2, 2) a rotation 62 about
the new position of the x axis and 3) a rotation 63
about the new 2 axis. Using the Eulerian rotation matrix

given by Rossmann and Blow (1962), it can be shown that

178

 

 

 

 

Figure Al. The Eulerian angles 61, e , and 9 relating the
rotated axes x', y', 2' go the original
unrotated orthogonal axes x,y,z.

179

6 = tan (c /c ),
1 31 32
-1
6 = cos c (4)
2 33
and I - 1
e =

tan (c /c ),
l3 2

3 3

where 62 is defined to be in the range 0 < 62 < n. A

special case occurs when cos 6 = 1; then
2
-1
6 + 6 = cos c
l 3 11
and (5)
-1 >
6 - 6 = cos c .

Equations (4) and (5) are used to find initial
values of the Eulerian angles. These can be refined by

minimizing
.3‘ 3
_ _ 2
82 - 21 Z [013- (0138) Cij (C31C)] (6)
i=1 j=1

The observed values refer to the nine linearly determined
coefficients (Equations 3) while the calculated values
depend upon the evaluation of 61, 62 and 63 (Equations

4 and 5). The three normal equations (i = l to 3) of
Equation (6) can be derived from the nine observational
equations and shifts A6j (j = l to 3) may be computed.

The ith normal equation will be of the form

190

3 9
3c..(calc) 3c..(calc)
£2 _13__ _u__ A9j=
3:1 k=1 391 an
‘3‘ ac (c l )
..ac
£_, (cij(obs)-cij(calc)) ——il———-—— (7)

38i

x
1.1

This procedure is applied iteratively until values A6.
are less than a preset value (e.g. 0.0l°). Good values
of the Eulerian angles and the three translational
components are now available. In order to minimize the

sum of the squares of the distances between equivalenced

atoms, Equation (2),

' 2 ' 2
N

must be minimized with respect to 61, 62, 6 , d1, d2,
3

and d3 where N represents the number of equivalenced

, 2
+ (z - z ) ]
1 2

atoms. Successive cycles of non-linear least squares
are then performed to refine the shifts in the six
parameters ¢i° The ith normal equation has the form

6
a I a I I g I I
x2 x2 3y Byz az2 322

. +__2__+_._ A¢j=

3 1 N 3¢i 3¢j 3¢i 3¢j 3¢i 3¢j

gfi ' 3x; , 6y. . 82;

‘J(x‘ - x2) ——— + (yl - y ) -—1 + (z - z ) -—— (8)

331 2 a¢. 1 2 a¢

181

When the best rotation angles and translation com-
ponents have been determined with respect to the pre-
sumed equivalent atoms, it is essential to determine
whether other atoms or residues can be equivalenced and
whether the previous set of equivalences was the most
reasonable. This can be accomplished by calculating
the probability, P, of the possible equivalences between

two given residues. P is dependent on:

1. The distancedij between Cu atoms i and j in the

first and the second molecule. This gives rise to
2 2

where E: is the root mean square value of dij’

2. The scatter SM' given by the root mean square

deviation from the mean of the distances di-l j-l'
I

d.; , , ,
13 and di+1,3+l

main chain in the two molecules is in a similar

When this scatter is small, the

orientation. If

dmean = (di-l,j-l + dij + di+l,j+l)/3
_ _ 2
then SM - ( .2 (dmean dij) /3)
1:3
Thus P a ex (-Sz/2E2)- (10)
2 P M 2 ' -

similarly, E2 is the root mean square of SM.

182

3. The scatter SR given by the root mean square
deviation from the mean of the distances dk between
corresponding atoms in equivalenced residues

_ _ 2
SM - Z (dmean dk) /k'
R

Therefore, P3 0 exp (-S§/2E§). (11)
The joint probability will then be given by

P = P P P

1 2 3'

Values of El’ E2 and E3 were used as input and recal-
culated after each cycle.

Every equivalenced residue j in the first molecule
which is adjacent to residue j - l or j + l in the second
molecule is retained. This gives rise to series of
ascending sequences of equivalenced residues. These
series are extended at either end using the largest
available probabilities among the largest five
probabilities found in series. The extensions are
terminated when no further acceptable probabilities
can be found or when the downward extension of one

series meets the upward extension of another.

APPENDIX I I I

Environment and Quality of the Electron Density of

the Residues of KDPG Aldolase

The environment of the main polypeptide chain is
classified as:
S = at the surface of the molecule

NS = near the surface

I = in the interior

B = related to the barrel cavity

FT = in the interface of the subunits of the trimer
(trimer of the first kind)

ST = in the intermolecular interface between trimer

molecules (trimer of the second kind).

Side chains of amino acids on the surface or related
to the cavity of the a/B-barrel are classified as:
E = extending into the solvent or the cavity of the
barrel
PL = parallel to or forming the surface
I = pointing into the protein, away from the surface

or the cavity of the a/B-barrel

183

184

The quality of the electron density of the residue

is given as:

G = good density
P = partial density
N = little or no density

185

Environment Density
Main Side Main Side
A.A.Residue Chain Chain? Chain Chain

1 Thr S E G= G

2 Thr S E G G

3 Leu S E P P
4 Glu S E P P

5 Arg S E P P
6 Pro S PL G G

7 Gln S PL . G G

8 Pro S PL G G
9 Lys S E G P
10 Leu S I G P
11 Ser S E G G
12 Met S I G G
13 Ala S E G N
14 Asp S E G G
15 Lys NS E G P
16 Ala NS E G G
1? Ala S E G N
18 Arg S E G P
19 Ile NS I G G
20 Asp S E G G
21 Ala S E G G
22 Ile -NS I G G
23 Cys NS I G G
24 Glu S E G G
25 Lys S E G P
26 Ala S E N N
27 Arg' S E G P
28 Ile NS I P N
29 Leu NS E; G G
30 Pro 1,8 I. G G
31 Val I,B I G N
32 Ile FT,B E G G
33 Thr 1,3 I N N
34 Ile I,B PL G G
35 Ala FT,B E G G
36 Arg FT,B E G P
37 Glu I G G
38 Glu S E G G
39 Asp S PL G P
40 Ile S E G G
41 Leu S E G G
42 Pro S PL G G
43 Leu S PL P P
44 Ala S I G G

A.A. Residue

45
46
47
48
49
50
51
52
53
54
55
56
57
58

Asp
Ala

.Leu

Ala
Ala
Gly
Gly
Ile
A139
Thr
Leu
Glu
Val
Thr
Leu
Mg
Ser
Gln
His
Gly
Leu
Lys
Ala
Ile
Gln
Val
Leu
Arg
Glu
Gln
Arg
Pro
Glu
Leu
Cys
Val
Gly
Ala
Gly
Thr
Val
Leu
Asp

186

Environment
Main Side
Chain Chain
ST PL
ST PL
I
I
ST E
S
S
S PL
S E
S PL
S,B E
I,B E
I,B PL
I,B PL
S,B PL
S,B E
FT, B E
FT,B E
FT,B E
S
S E
I
S PL
S PL
I
I
S E
ST E
S PL
ST PL
ST PL
ST . PL
S,B. PL
8,3 I
S,B E
I,B I
I,B -
I,B PL
I,B
FT,B PL
FT PL
FT E
FT E

Density

Main
Chain

0000'6000000000000000000000'U0000000000000000

Side
Chain

00000

'U’U00 0 000'00000'U00'UZO'U0 0'UZ'U000Z0000

. 187

Environment
Main Side
A.A.Residue Chain Chain
88 Arg FT E
89 Ser FT E
90 Met FT E
91 Phe FT PL
92 Ala I
93 Ala I
94 Val 8 PL
95 Glu S E
96 Ala I
97 Ala NS PL
98 Gly S
99 Ala S I
100 Gln NS,B E
101 Phe S,B E
102 Val I,B I
103 Val FT,B I
104 Thr FT,B PL
105 Pro FT .PL
106 Gly FT
107 Ile FT E
108 Thr FT PL
109 Glu NS I
110 Asp S E
111 Ile S PL
112 Leu I
113 Glu S E
114 Ala S E
115 Gly S
116 Val I
117 Asp NS E
118 Ser I
119 Glu I
120 Ile 8 PL
121 Pro S,B I
122 Leu I,B I
123 Leu FT,B I
124 Pro FT PL
125 Gly FT
126 Ile FT E
127 Ser FT E
128 Thr FT PL
129 Pro FT PL
130 Ser FT PL
131 Glu FT E
132 Ile FT PL

Density

Main
Chain

000000'U”10000000000000000000'11000000000'60000000

Side
Chain

0000'UZO 00002’6000 00000020 'UZO'UO0Z 0Z'UZ000'U00

188

Environment
Main Side
A.A.Residue Chain Chain
133 Met FT PL
134 Met FT PL
135 Gly S
136 Tyr S I
137 Ala S E
138 Leu S,B E
139 Gly I,B
140 Tyr I,B I
141 Arg I,B E
142 Arg FT,B I
143 Phe FT E
144 Lys FT E
145 Leu FT PL
146 Phe FT PL
147 Pro FT PL
148 Ala FT PL
149 Glu FT PL
150 Ile FT I
151 Ser FT PL
152 Gly FT
153 Gly FT
154 Val FT I
155 Ala FT PL
156 Ala FT PL
157 Ile FT PL
158 Lys FT PL
159 Ala FT E ,
160 Phe FT E
161 Gly S
162 Gly S
163 Pro S,B PL
164 Phe I,B I
165 Gly S,B
166 Asp I,B E
167 Ile I,B I
168 Arg I,B I
169 Phe FT,B I
170 Cys FT,B E
171 Pro FT,B PL
172 Thr 8 PL
173 Gly NS
174 Gly NS
175 Val' NS PL
Asn ST PL

176

Density

Main
Chain

00000000000000000000000000000000000'U0000000'U

Side
Chain

0'U'U00'UOZO0Z0 0Z'U "U'U

0'6'6'1'1000

.00'U0'U'U0 00

00

1m;

Environment Density
Main Side Main Side

A.A.Residue Chain Chain Chain Chain
177 Pro ST PL G G
178 Ala ST PL G G
179 Asn S PL P P
180 Val S PL G G
181 Arg S E G P
182 Asn S E G P
183 Tyr NS PL G G
184 Met NS PL G P
185 Ala S PL G N
186 Leu S E G N
187 Pro S E G G
188 Asn S PL G P
189 Val NS,B PL G P
190 Met NS,B PL G G
191 Cys I,B E G P
192 Val I,B PL P N
193 Gly I,B P

194 Thr I,B I P N
195 Gly I,B P

196 Trp FT,B E G G
197 Met NS,B PL G P
198 Leu S,B. PL G G
199 Asp S E P P
200 Ser S I E G N
201 Ser S ’ PL G G
202 Trp I G G
203 Ile S PL G G
204 Lys S PL G P
205 Asn ST E N P
206 Gly S G

207 Asp ST E G G
208 Trp ST PL G G
209 Ala ST E N N
210 Arg ST E P P
211 Ile I G P
212 Glu S PL G G
213 Ala ST E G G
214 Cys ST PL P G
215 Ser NS I G N
216 Ala S PL G N
217 Glu ST E G G
218 Ala S PL G G
219 Ile NS: I G G

190

Environment Density

Main Side Main Side
A.A.Residue Chain Chain Chain Chain
220 Ala ST PL G N
221 Leu 8 PL G N
222 Leu S I G P
223 Asp S E G P
224 Ala S E G G
225 Asn S E G G

*
The environment of the side chains in the interior

are omitted.

REFERENCES

REFERENCES

T. Alber, D.W. Banner, A.C. Bloomer, G.A. Petsko,
D. Phillips, P.S. Rivers and I.A. Wilson, Phil. Trans.
R. Soc. Lond. B293, 159-171 (1981).

P. Argos, R.M. Garavito, W. Eventoff and M.G. Rossmann,
Biomolecular Structure, Conformation, Function and
Evolution, Vol. 1, ed. R. Srinivasan, 205-225, Perga-
mon, Oxford, 1981.

G.T. Babcock and C.K. Chang, FEBS Lett. _5, 358-362
(1979).

D.W. Banner, A.C. Bloomer, G.A. Petsko, D.C. Phillips,
C.I. Pogson, I.A. Wilson, P.H. Corran, A.I. Furth,
J.D. Milman, R.E. Offord, J.D. Priddle and S.G. Waley,
Nature 255, 609-614 (1975).

L.R. Barran and W.A. WOod, J. Biol. Chem. 246, 4028-
4035 (1971).

G.I. Birnbaum, Acta Cryst. B29, 54-60 (1973).

T.L. Blundell and R.E. Hummel, Nature 287; 781-787
(1980).

R. Bonnett, M.B. Hursthouse and S. Neidle, J. Chem.
Soc. Perkin II, 902-906 (1972).

C.K. Chang, M.S. Kuo and C.G. Wang, J. Heterocycl.
Chem. 14, 943-945 (l977a).

C.K. Chang, J. Heterocycl. Chem. 14, 1285-1288
(1977b).

C.K. Chang, J. Chem. Soc., Chem. Comm., 800-801
(l977c).

C.K. Chang, "Biochemical and Clinical Aspects of
Oxygen, W. Caughey ed., 437-453, Acad. Press, New
York, 1979a.

C.K. Chang, Adv. Chem. Ser. No. 173, 162-177 (1979b).
C.K. Chang and C.B. Wang, Airlie House Symposium on

”Interaction between Iron and Proteins in Oxygen and
Electron TransportJ'Airlie House, VA, April 1980.

191

192

B.M. Chen and A. Tulinsky, J. Am. Chem. Soc. 24,
4144-4151 (1972).

C. Chothia and J. Janin, Nature 256, 705-708 (1975).

P.Y. Chou and G.G. Fasman, Biochemistry 13, 211-222
(1974).

P.W. Codding and A. Tulinsky, J. Am. Chem. Soc. 24,
4151-4157 (1972).

J.P. Collman, C.M. Elliott, T.R. Halbert and S.B.
Tovrog, Proc. Natl. Acad. Sci. USA 14, 18-22 (1977).

J.P. Collman, M. Marrocco, P. Denisevich, C. Koval
and F.C. Anson, J. Electroanal. Chem. 101, 117-122
(1979). ""

J.P. Collman, P. Donisevich, Y. Konai, M. Marrocco,
C. Koval and F.C. Anson, J. Am. Chem. Soc. 102,
6027-6036 (1980).

J.P. Collman, A.O. Chong, G.B. Jameson, R.T. Oakley,
E. Rose, E.R. Schmittou and J.A. Ibers, J. Am. Chem.
Soc. 103, 516-533 (1981).

A. Conde, A. Lopez Castro and R. Marquez, Acta Cryst.
B35, 2228-2229 (1979).

M.A. Cynkin and G. Ashwell, J. Biol. Chem. 235,
1576-1579 (1960).

J.L. Crawford, W.N. Lipscomb and C.G. Schellman,
Proc. Nat. Acad. Sci. USA 12' 538-542 (1973).

R.E. Dickerson, Biomolecular Structure, Conformation,
Function and Evolution, Vol. 1, ed. R. Srinivasan,
227-249, Pergamon, Oxford, 1981.

O. Dideberg, H. Campsteyn and L. Dupont, Acta Cryst.
B29, 103-112 (1973).

D.J. Duchamp, ACS Symp. Ser. No. 46, 98-121'(1977).
A.B. Edmundson, K.R. Ely, E.E. Abola, M. Schiffer,

N. Panagiotopoulos and H.F. Deutsch, Fed. Proc.'§§,
2119-2123 (1976).

193

N. Entner and M. Doudoroff, J. Biol. Chem. 196,
853-862 (1952).

M. Erecinska and D.F. Wilson, Arch. Biochem. Biophys.

J.E. Falk, Porphyrins and Meta110porphyrins, 78-80,
Elsevier, Amsterdam, 1964.

F.Kt Fong, Proc. Nat. Acad. Sci. USA‘Zl, 3692-3695
(1974).

M.A. Frentrup and A. Tulinsky, (1981) J. Appl. Cryst.
14, 439-443 (1981).

E. Grazi, T. Cheng and B.L. Horecker, Biochem. BiOph.
Res. Comm. 1, 250-253 (1962).

E. Grazi, H.P. Meloche, G. Martinez, W.A. Wood and
B.L. Horecker, Biochem. Biophys. Res. Comm. 10, 4-10
(1963).

R.H. Hammerstedt, H. Mohler, K.A. Decker and W.A.
WOod, J. Biol. Chem. 246, 2069-2074 (1971).

M.H. Hatada, A. Tulinsky and C.K. Chang, J. Am. Chem.
Soc. 102, 7115-7116 (1980).

W.G.J. Hol, L.M. Halie and C. Sander, Nature 294,
532-536 (1981).

J.M. Ingram and W.A. WOod, J. Biol. Chem. 241,
3256-3261 (1966).

J. Janin, Nature 277, 491-492 (1979).

J. Janin and C. Chothia, J. Mol. Biol.‘143, 95-128
(19801.

N.E. Kagan, D. Mauzerall and R.E. Merrifield, J. Am.
Chem. Soc. 92, 5484-5486 (1977).

J.J. Katz, W. Oettmeier and J.R. Norris, Phil. Trans.

R. Kovachevich and W.A. Wood, J. Biol. Chem. 213,
745-756 (1955a).

 

194

R. Kovachevich and W.A. Wood, J. Biol. Chem. 213,
757-767 (1955b).

J. Kraut, J.D. Robertus, J.J. Biktoft, R.A. Alden,
P.E. Wilcox and J.C. Powers, Cold Spring Harbor
Symp. Quant. Biol. 36, 117-123 (1971).

I.D. Kuntz, J. Amer. Chem. Soc.‘24, 4009-4012 (1972).
I.D. Kuntz, J. Amer. Chem. Soc. 21, 4362-4366 (1975).

M. Kusunoki, W. Harada, N. Tanaka and M. Kakudo,
Twelfth International Congress of Crystallography,
Ottawa, Canada, 1981, Abstract 02.1-32.

J.W. Lauher and J.A. Ibers, J. Am. Chem. Soc. 95,
5148-5152 (1973).

M. Levine, M. Muirhead, D.K. Stammers and D.I. Stuart,
Nature 271, 626-630 (1978).

Lindqvist and C.I. Branden, J. Mol. Biol. 143, 201-
211 (1980).

R.G. Little and J.A. Ibers, J. Am. Chem. Soc. 21,
5364-5369 (1975).

J. MacGee and M. Doudoroff, J. Biol. Chem. 210,
617-626 (1954).

A.D. McLachlan. Protein Folding, ed. R. Jaenicke:
79-99, Elsevier, Amsterdam, 1980.

P. Main, L. Lessinger, M. Woolfson, G. Germain and
J.P. Declercq, MULTAN 76, Univs. of York, UK and
Louvain, Belgium, 1976.

Y. Matsuura, M. Kusunoki, W. Harada, N. Tanaka: 3"
Iga, N. Yasuoka, H. Toda, K. Narita and M. Kakudo'
J. Biochem. El, 1555-1558 (1980).

B.W. Matthews, M.G. Grutter, W.F. Andersor: auad 5-3‘
Remington, Nature 290, 334-335 (1981a).

B.W. Matthews, S.J. Remington, M.G. Grutter and
W.F. Anderson, J. Mol. Biol. '147, 545-558 (1981b)-

 

195

I. Mavridis and A. Tulinsky, J. Am. Chem. Soc. 25,
6811-6815 (1973).

I.M. Mavridis and A. Tulinsky, Biochem;11§, 4410-4417
(1976).

I. Mavridis, M.H. Hatada, A. Tulinsky, and L. Lebioda,
(1982) J. Mol. Biol., submitted for publication.

H.P. Meloche and W.A. Wood, J. Biol. Chem.'239, 3511-
3514 (1964). '

H.P. Meloche, Biochemistry 9 5050-5055 (1970).
H.P. Meloche, J. Biol. Chem. 248, 6945-6951 (1973).

H.P. Meloche, C.T. Monti and R.A. Angeletti, Biochem.
Biophys. Res. Comm. 84, 589-594 (1978).

H. Mohler, K.A. Decker and W.A. Wood, Arch. Biochem.
Biophys. 151, 251-260 (1972).

A.C.T. North, D.C. Phillips and P.S. Mathews, Acta

H. Ogoshi, H. Sugimoto and Z. Yoshida, Tetrahedron
Lett., 169-172 (1977).

G. Palmer, G.T. Babcock and L.E. Vickery, Proc. Natl.
Acad. Sci. USA 13, 2206-2210 (1976).

D.C. Phillips, P.S. Rivers, M.J.E. Sternberg, J.M.
Thornton and I.A. Wilson, Biochem. Soc. Trans. 2,
642-647 (1977).

J. Preiss and G. Ashwell, J. Biol. Chem. 237,
309-316 (1962).

0.3. Ptitsyn and A.V. Finkelstein. Biomolecular
Structure, Conformation, Function and Evolution, Vol.
1, ed. R. Srinivasan, 119-132, Pergamon, Oxford, 1981.

N.V. Raghavan and A. Tulinsky, Acta Cryst. B35,
1776-1785 (1979).

J.S. Richardson, Proc. Nat. Acad. Sci. USA 13, 2619-
2623 (1976).

196

J.S. Richardson, Biochem. Biophys. Res. Comm. 99,
285-290 (1979).

D.C. Robertson, R.H. Hammerstedt and W.A. Wood,
J. Biol. Chem. 246, 2075-2083 (1971).

I.A. Rose, Trans. R. Soc. Lond.'BZ93, 131-143 (1981).

M.G. Rossmann and D.M. Blow, Acta Cryst 12, 24-31
(1962).

M.G. Rossmann and P. Argos, J. Biol. Chem. 250,
7525-7532 (1975). -

M.G. Rossmann and P. Argos, J. Mol. Biol.‘105, 75-95
(1976).

R.G. Rosso and E. Adams, J. Biol. Chem. 242, 5524-‘
5534 (1967).

W.J. Rutter, Federation Proc. 33, 1248-1257 (1964).

F.R. Salemme and D.G. Fehr, J. Mol. Biol. 12, 697-
700 (1972).

G.B. Schulz and R.H. Schirmer, Principles of Protein
Structure, 224-226, Springer, New York, 1979.

G.E. Schulz, Angew. Chem. Int. Ed. Engl. 22, 143-151
(1981).

G.M. Sheldrick, SHELX76, Univ. of Cambridge, UK, 1976.
W.S. Sheldrick, Acta Cryst. B34, 663-665 (1978a).

W.S. Sheldrick, A. Borkenstein and J. Engel, Acta
Cryst. B34, 1248-1253 (1978b).

V. Shomaker, J. Waber, R.E. Marsh and G. Bergman,
Acta Cryst. 12, 600-604 (1959).

S.J. Silvers and A. Tulinsky, J. Am. Chem. Soc. 89,
3331-3337 (1967).

J.D. Smiley and G. Ashwell, J. Biol. Chem. 235, 1571-
1575 (1960).

197

D.J. Stuart, M. Levine, H. Muirhead and D.K. Stammers,
J. Mol. Biol. 134, 109-142 (1979).

N. Suzuki and W.A. Wood, J. Biol. Chem. 255, 3427-
3435 (1980).

Y. Tanimoto, H. Kobayashi, S. Nagakura and Y. Saito,
Acta Cryst 329, 1822-1826 (1973).

D.D. Tsay and W.A. Wood, Arch. Biochem. Biophys.

R.L. Vandlen and A. Tulinsky, Acta Cryst. B27, 437-
442 (1971).

R.L. Vandlen, D.L. Ersfeld, A. Tulinsky and W.A. Wood,
J. Biol. Chem. 248, 2251-2253 (1973).

C.M. Venkatachalam, Biopolymers 6, 1425-1436 (1968).

E. Weber, E. Papamokos, W. Bode and R. Huber, J. Mol.
Biol. 149, 109-123 (1981).

L.D. Weber, Ph.D. Dissertation, Michigan State Univer-
sity, 1978.

L.D. Weber, A. Tulinsky, J.D. Johnson and M.A. E1-
Bayoumi, Biochemistry 18, 1297-1303 (1979).

R.T. Wei and D.L. Ward, Acta CrySt. B32, 2768-2773
(1976).

W.A. Wood, The Enzymes, Vol. III, 281-302, Acad.
Press, New York, 1972.

J. Yourno, T. Kohno and J.R. Roth, Nature 228, 820-
824 (1970).