MICHIGAN STATE

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This is to certify that the
dissertation entitled
STRUCTURE OF IVONOCLINI C
KRINGLE 4 FROM HUMAN PLASMINOGEN

presented by
K. G. Ravichandran

has been accepted towards fulfillment
of the requirements for

 

 

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Major proféssor

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MS U i: an Affirmative Action/Equal Opportunity Institution 0— 12771

 

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STRUCTURE OF MONOCLINIC
KRINGLE 4 FROM HUMAN PLASMINOGEN

BY

K. G. Ravichandran

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Chemistry

1989

ABSTRACT

STRUCTURE OF MONOCLINIC
KRINGLE 4 FROM HUMAN PLASMINOGEN

BY

K. G. Ravichandran

Monoclinic crystals of kringle 4 from human plasminogen
were grown from 35% PEG 8000, 0.1 M ammonium sulfate, 0.8%
n-butanol, at pH 6.2 by the hanging drop method. The
crystals contain two molecules of kringle 4 per asymmetric
with a vm - 1.86 A3/dalton. The crystals are twinned along
the c* direction. Three-dimensional intensity data were
collected to 3.5 A resolution for the crystal and 6.0 A
resolution for the twin. The twinned reflections in the
l-O,l,3,4, and 8 layers were untwinned. The structure was
solved by molecular replacement methods. A self rotation
search was carried out to find the orientation of the two
independent molecules in the asymmetric unit. The search
yielded a solution at ¢-0.0°, w-80.0°, and x-180.00° which
corresponds to a non—crystallographic two-fold rotation
approximately parallel to the a* axis of the crystal unit
cell. The orientation and position of the two independent
molecules of kringle 4 were determined using the refined
coordinates of the kringle of prothrombin fragment 1. The
former were then refined using the non-crystallographic
symmetry averaging procedure. The final rotation angles and

the translation vectors for the two molecules are :

a b g TX TY TZ
(de9-) (A)

Molecule A 313.62 142.80 186.88 6.2 0.0 11.3
Molecule B 109.77 149.77 158.77 25.8 48.6 31.8

Phase angles for the structure factor amplitudes were
calculated using the conserved structure of the kringle of
fragment 1 and an electron density map was calculated with
reflections to 2.8 A resolution. In general, the kringle 4
structures of the independent molecules are very similar in
overall conformation to the refined prothrombin fragment 1
kringle. The amino terminal (3 residues) and the carboxy
terminal interkringle tail (5 residues) and most of
non—conserved aromatic side chains were clearly visible in
the electron density. There was even reasonable density in
regions which have a deletion in kringle 4 compared to the
fragment 1 kringle. From an examination of the molecular
arrangement in the crystal lattice, each independent kringle
4 molecule makes close contacts with two other kringles,
giving rise to a three dimensional network. This might be
of relevance in kringle-kringle interactions in plasminogen
which contains 5 kringles and in apolipoprotein(a) which has
37 copies of kringle 4 and one copy of kringle 5. The
molecular packing also gives rise to two different "dimer"
possibilities; it is difficult at this stage to reconcile
these dimeric species to relevant kringle-kringle

interactions in physiological systems.

The lysine binding site of kringle 4 is located on the

surface of one of the oblate faces of the kringle as

reported previously from modelling studies. The binding
site is characterized by an apparent dipolar surface, the
polar parts of which are separated by a hydrophobic region
of highly conserved aromatic residues. Zwitterionic ligands
such as lysine and e—aminocaproic acid can form ion pair
interactions with Asp57 and Asp59 located on the dipolar
surface. The cationic center of kringle 4 is formed by
Arg72. Overall, the lysine binding site, with the exception
of the indole ring of Trp73, which has a different
orientation in the crystal structure, compares well with the

predicted model of the lysine binding site of kringles.

To my parents

ACKNOWLEDGMENTS

It is my great pleasure to sincerely acknowledge
Dr. Alexander Tulinsky for his guidance, support and

inspiration throughout the course of this work.

I would like to express my deep gratitude to Dr. Miguel
Llinas for providing us with an abundant supply of the
material. I would like to thank Anne Mulichak for helping me
with the crystals and the data collection. I would also
like to thank Dr. Manuel Soriano, Dr. K. Padmanabhan, Trevor
M. D'Souza and Tapankumar Nayak for their help in preparing
the figures and tables. I am also grateful to Dr. Ewa
Skrzypczak-Jankun for the many useful discussions regarding
processing the data. My thanks also go to Dr. Pushpa for
proof reading the manuscript. I would like to thank
Dr. Chang H. Park, Dr. James P. Fillers and Timothy J. Rydel

their help and support.

Finally, but not the least, to my family and friends

for their love and support.

Support by the National Institutes of Health is

gratefully acknowledged.

vi

CHAPTER

II

III

IV

VI

VII

VIII

IX

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . .
LIST OF FIGURES . . . . . . . . . . . .
INTRODUCTION . . . . . . . . . . . .
HOLECULAR REPLACEHENT METHOD . . . . . . .

Patterson Function . . . . . . . . . .
Rotation Function . . . . . .
Rossnann and Blow Rotation Function .
Crowther Fast Rotation Function . . .

Lattman Rotation Function . . . . .

Rotation Functions in Direct Space .

Practical Aspects of Rotation Function
Calculations . . . . . . . . . . . .
Translation Function . . . . . . . .
Crowther and Blow Translation Function .
R Value Mapping . . . . . . . . . . . .
Packing Functions . . . . . . . . . . .
BRUTE Translation Function . . . . . . .

Flat-i=3 Q'lll'lUnlfl’

EXPERINENTAL . . . . . . . . . . . .
A. Crystallization . . . . . . . . . . . .
B. Data Collection . . . . . . . . . . . .

DATA REDUCTION . . . .
A. Processing of Twinned Reflections

PATTERSON SEARCH . . . .
A. Self Rotation Function .
B. Cross Rotation Function
C. Translation Function .

SYMMETRY AVERAGING . . . . . . . . . . . .
RESULTS . . . . . . . . . . .
A. General Conformation of Kringle 4 . .
B. Differences Between the Two Independent
Molecules . . . . . . . .
C. Comparison of K4 with K1 . . . . . . . .
LYSINB BINDING SITE OF RRINGLE 4 . . . . . .
CRYSTAL PACKING . . . . . . . . . . . .

LIST 0' REFERENCES 0 I O O O I O O O O O I

PAGE
viii

102
106

108
118
128

TABLE

10

11

12

LIST OF TABLES

Primary structure of homologous kringles aligned
to maximize conservation. . . . . . . . . .

Rotation matrix in terms of Eulerian angles
91,82,930 O O O O O O O 0 O O O O O O O O 0
Symmetry of rotation function when a model
triclinic Patterson is rotated onto the Patterso
of a test molecule with various symmetries.

Summary of crystal data of Monoclinic plasminogen

kringle 4.

Orientation matrices of the crystal (a) and the
twin (b). . . . . . . . . . . . . . . . . .

Fraction of twinned reflections and the average
4 separation of the crystal and the twin
reflections in twinning l-layers. . . .

Self rotation results, both in terms of Eulerian

PAGE

27

n
32

45

63

65

angles e.,ea,e, and spherical polar angles ¢,w,x.

All the symmetry related solutions are listed in
degrees. . . .

Cross rotation results. (a): Polyalanine backbon

69

e

kringle model (387 atoms; 57%). (b): Kringle with

conserved side chains (489 atoms; 72%). (c): All
the kringle atoms (621 atoms; 92%). All models
based on the coordinates of K1 of prothrombin
fragment 1. . . . . . . . . . . . . . . . .

Correlation between the cross rotation and the
self rotation results. . . . . . . . . .

Correlation between the cross rotation and the
self rotation results. . . . . . . .

"BRUTE" translation search solutions for
molecules A and B at various resolution ranges.

"BRUTE" translation search solutions for the two
molecules A and B. (a): Search for molecule B
while molecule A is stationary. (b): Search for
molecule A with stationary B in the correct
position. (c): Final refined rotation and
translation parameters for molecules A and B. .

viii

76

77

78

81

82

TABLE

13

14

15
16

17

18

PAGE

Results of non-crystallographic symmetry

averaging. The spherical polar angles ¢' and w'

are defined according to Rossmann and Blow [47].
Xoffset, Yoffset, and Zoffset refer to the
intersection of the rotation axis with the
crystallographic a, b, and c axes respectively. . 88

Comparison of secondary structural features of
kringle 4. . . . . . . . . . . . . . . . . . . . 98

Secondary structural elements of kringle 4. . . 99

Differences in side chain electron density
between the independent molecules A and B. . . . 107

Intermolecular contacts at the A-B "dimer"
interface (< 3.2 A) and the possible
interaction(s). . . . . . . . . . . . . . . . . 121

Intermolecular contacts at the A-B' "dimer"
interface (< 3.2 A) and the possible

interaction(s). 125

ix

FIGURE

1

10

11

12

LIST OF FIGURES
PAGE

A schematic view of plasminogen kringles,
Kl - KS [12]. o o o o o o o o o o o o o o o o o o 4

Kringle 4 from human plasminogen: outline of

primary structure. Amino acid residues are

labelled according to the conventional one-letter
code. The predominant kringle 4 species terminates
with Ala86 but, depending on the extent of

elastase digestion of plasminogen, the C-terminal
peptide extend two residues further to Va188.

Blanks are deletions with respect to plasminogen
kringle 5. . . . . . . . . . . . . . . . . . . . 6

Kringle ligands [Abbreviations used: eACA,
e-aminocaproic acid; AcLys, Na—acetyl-L-lysine:
AMCHA, trans-amino-methyl(cyclohexane)carboxy-

lic acid; BASA, p-benzylamine sulfonic acid]. . . 8

Stereoview of modeled energy-minimized lysine
binding site of plasminogen kringle 4 (taken
from [30]). . . . . . . . . . . . . . . . . . . 10

Crystallographic (perpendicular to the page) and
non-crystallographic (in the plane of the page)
symmetry operations (taken from [37]). . . . . . 16

The rotations defining the Eulerian angles 91,
82, and 83 (taken from [65]). . . . . . . . . . . 25

Spherical polar angles 4. w, and x with respect
to crystallographic axes. . . . . . . . . . . . . 28

Crystals of Monoclinic kringle 4. . . . . . . . . 44
The reciprocal lattices of the crystal and the

twin. The crystal c*—axis is shown by the solid
line, that of the twin by the dotted line. . . . 47

The principal axial intensity distributions of
kringle 4 Crystal. 0 0 O O O O O O O O O D O O O 48

A schematic drawing of the goniostat of a
four-circle diffractometer. . . . . . . . . . . . 50

The intensity of the kringle 4 monitor
reflections Vs. time of exposure. . . . . . . . . 53

FIGURE

13

14

15

16

17

18

19

20

21

22

23

24

25

26

PAGE

w—profile of (-5,5,5)taken before the 3—D data
collection. Ralf—width ~0.2°. . . . . . . . . . 55

Absorption curve of the (0,-10,0) reflection. . . 57

Schematic of the four molecules in the unit cell.
Non-crystallographic symmetry elements are
indicated by the dotted lines. . . . . . . . . . 71

Sequences of bovine prothrombin fragment 1

kringle (a) and human plasminogen kringle 4 (b):
Residues identical in both sequences are enclosed

by diamond blocks; similar residues are indicated

by asterisks; loop segments designated A, B, C,

and D. . . . . . . . . . . . . . . . . . . . . . 73

A schematic diagram of the non—crystallographic
symmetry elements. The local two-fold axis appro-
ximately parallel to the a* axis is shown by the

dotted lines ( ..... ) and the local two—fold axis
approximately parallel to the c* axis is shown by
the broken lines ( ----- ). The crystallographic

2. screw axis is indicated by the conventional
symbol. . . . . . . . . . . . . . . . . . . . . . 89

Electron density of the side chain of TyrS of
molecule A (contours at 1 a). . . . . . . . . . 91

Electron density of the side chain of Trp73 of
molecule B (contours at 1 c). . . . . . . . . . 92

Electron density of the amino terminal of
molecule 8 (contours at l a). . . . . . . . . . 93

Electron density of the carboxy terminal of
molecule B (contours at l a). . . . . . . . . . 94

Ramachandran angles of kringle 4 (molecule A).
Allowed regions enclosed by the dotted lines.
Circled residues Gly; outlier residues numbered. 96

Graphic representation of the folding of kringle 4
emphasizing secondary structure. The reverse turns
labelled Tl-TlZ; disulfide bridges indicated
appropriately. . . . . . . . . . . . . . . . . . 97

a-carbon drawing of the krigle 4 molecule A (blue)
optimally superimposed on molecule B (amber). . 103

r.m.s deviations between the chemically identical
a-carbon atoms of molecules A and B. . . . . . . 104

Lysine binding site of kringle 4 (molecule B). . 110

xi

FIGURE

27

28

29

30

31

32

33

PAGE

Space-filling view of the lysine binding site of
kringle 4 (molecule B). The following color codes
have been used for the atoms: carbon, light grey;
nitrogen, blue; oxygen, red; sulfur, yellow. . 114

Comparison of the lysine binding sites.

Left: Lysine binding site from the present study.
Right: Lysine binding site from the modelling

study (from [31]). In the model, the ligand
e-aminocaproic acid is also shown (white). . . . 116

Cu, C, N main chain atoms of the two independent
molecules A and B of the A-B "dimer". Non--
crystallographic 2-fold rotation axis indicated. 119

Space-filling view of the two independent
molecules A and B of the A-B "dimer".

Orientation same as Figure 29. . . . . . . . . . 122
Cu, C, N main chain atoms of the two independent
molecules A and B' of the A—B' "dimer". Non--
crystallographic symmetry element (approximate

21 screw axis) indicated. . . . . . . . . . . . 124

Space-filling view of the two independent
molecules A and B' of the A-B' "dimer".
Orientation same as Figure 31. . . . . . . . . . 126

Schematic of crystal packing of kringle 4. Non-
crystallographic symmetry elements are indicated

by the dotted lines. Crystallographic symmetry
elements and positions designated appropriately. 128

xii

I INTRODUCTION

Kringles are autonomous structural and functional
folding domains of molecular weight approximately 10,000,
that serve as protein binding modules of many proteins
involved in blood coagulation and fibrinolysis. They
possess characteristic three disulphide triple loop
structures made up of approximately 80 residues. They are
found singly in urokinase [1,2] and factor XII [3], as pairs
in prothrombin [4] and tissue—plasminogen activator (t-PA)
[S], as five copies in plasminogen [6] and remarkably as 38
copies in apolipoprotein(a) [7], 37 of which display 75-85%
conservation with kringle 4 of plasminogen. It has been
shown recently that type II finger domain structures of
fibronectin also exhibit kringle homology [8,8a]. The
sequences of the kringles in the different proteins

mentioned above are listed in Table l.

The biological roles of the kringles have been
established in many cases. Fibrin binding sites are located
in kringle 1 [9], kringle 4 [10], and miniplasminogen
(kringle 5+light chain of plasminogen), while lysine binding
sites have been localized to kringles 1 and 4 of plasminogen
[11]. Some of the plasminogen kringles are also capable of
binding low molecular weight compounds of the
w-aminocarboxylic acid class at the lysine binding sites
[12] while benzamidine sites reside on kringle 5 and the
light chain of plasminogen [13]. There is good evidence in
the case of plasmin and plasminogen that kringles mediate

l

Primary structure of homologous kringles aligned to maximize conservation.‘

Table 1.

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inserted or deleted relative to KS sequence are indicated with + or -,

t-PAKl, kringle 1 of tissue plasminogen activator, etc.; Uk, urokinase;
(taken from [29]).

respectively. Conserved residues are boxed, homologous conservation is dotted;
factor XII

obvious deviations from conservation are enclosed by diamond blocks. Segments

involved in the fibrin/lysine binding region are underlined with heavy trace.
The abbreviations used are : PT, prothrombin; Pngl, kringle 1 of plasminogen,

Crucial ASp and Arg residues of plasminogen kringle 4 lysine binding site are

designated with asterisks.

etc.;
FXII,

attachment of the protease or its zymogen to the target
fibrin. Moreover, kringle 2 of prothrombin is known to bind
to the heavy chain of membrane-bound factor Va in the
prothrombinase complex [14,15] and kringle 2 of t-PA binds
to fibrin [16]. Thus kringles appear to be involved in
biological recognition and in imparting specificity to
accompanying catalytic domains. On the other hand, there
does not yet appear to be a clear function for the
benzamidine binding site of plasminogen kringle 5, and so
far, for the other kringles of plasminogen, prothrombin and

t-PA and those of urokinase and factor XII.

Plasmin is a blood plasma serine protease primarily
responsible for the dissolution of fibin clots deposited on
the walls of blood vessels. Plasmin is produced by the
enzymatic activation of its zymogen, plasminogen, a single
chain plasma glycoprotein comprised of 791 amino acid
residues [17]. Plasmin , on the other hand, is a
glycoprotein composed of two chains, covalently linked by
two cysteine bridges [6]. The light chain of molecular
weight ~ 25000, carries the catalytic function [18], while
the heavy chain, of MW ~57000, is formed by a tandem array
of five kringles some of which are involved in fibrin
binding [6,19]. A schematic of the heavy chain of the

plasminogen is shown in Figure 1.

As already mentioned, fibrinolysis is the process of
dissolution of the fibrin blood clot of coagulation by an
enzyme system present in blood of all mammalian species.

The fibrinolytic system consists of the plasma zymogen

3 I *4
.. (I) «5

 

 

 

 

Figure 1. A schematic view of Plasminogen Kringles, Kl-KS [12]

5
plasminogen, its activated product, the proteolytic enzyme
plasmin, activators of plasminogen, inhibitors of both
plasmin and plasminogen activators, and fibrinogen and
fibrin. On the basis of various chemical and biochemical
studies, a molecular model for physiological fibrinolysis
has been proposed [20], which explains the restricted action
of plasmin in vivo. According to this model, the system
seems to be regulated at two levels: localized plasminogen
activation at the fibrin surface; and sequestration of the
formed plasmin from circulating plasma. When fibrin is
formed, a small amount of plasminogen is specifically bound
to it by way of its lysine binding sites. t-PA present in
the blood or released from the vascular endothelium is
adsorbed on the fibrin surface and efficiently activates the
adsorbed plasminogen ( t-PA converts plasminogen to plasmin
by cleaving two bonds, Lys76-Lys77 and ArgS60-Va1561). The
formed plasmin has its lysine binding sites occupied in
complex formation with fibrin and is also involved in fibrin
degradation by way of its active site, and therefore reacts
only very slowly with antiplasmin. In contrast, plasmin
which is released from digested fibrin is rapidly and

irreversibly neutralized by antiplasmin in the circulation.

Kringles 1 and 4 of plasminogen can be isolated in
vitro by the controlled digestion of the zymogen [6]. The
amino acid sequence and the disulfide crosslinks of kringle
4 from human plasminogen are illustrated in Figure 2 with
the bridge between Cys4 and CysBl bringing the N-terminus in

the proximity of the C—terminus. It should be

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7
noted,however, that the end product of elastase digestion of
plasminogen is a heterogeneous mixture of ~70% C-terminal

Ala86 and 30% C-terminal Va188 [21].

Studies carried out on the lysine binding of kringle 4
of plasminogen and other kringles have been successful in
characterising the various residues involved in ligand
binding. The binding of various aminocarboxylic acids, of
~6.8 A dipolar distance, to human plasminogen and its
proteolytic fragments has been studied extensively, examples
of which are the antifibrinolytic agent trans-
4(aminomethyl) cyclohexane carboxylic acid, p-benzylamine
sulfonic acid and linear aliphatic ligands like

Na-acetyl-L-Lysine and c-aminocaproic acid (Figure 3).

Chemical modification of plasminogen with
tetranitromethane has revealed that Tyr43 and TyrSZ are not
essential for the maintenance of the w-aminocarboxylic acid
binding site of the protein [22]. Crosslinking of Lys 38
and Tyr43 shows that although these two residues are not
directly involved in ligand binding, they are probably close
to this site. It has also been shown that the core
structure of the kringle-fold and the lysine binding site
are unaltered when the disulfide bridge between Cys4 and
CysBl is selectively reduced and alkylated. Modification of
kringle 4 with 1,2-cyclohexanedione or l—ethyl-3-(3-dimethyl
aminopropyl)-carbodiamide has shown that Arg72 and Asp59 are
essential for ligand binding [9]; the complementary charges

on these residues provide the dipolar ends necessary for the

CO; CO; CO,’
('ZH2 CH3-CO-NH—(lIH
C'Hz cu.
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in, in,
CH2 (IZ'Hz CH2
11,113. | 3. 3,,
eACA AcLys AMCHA
SO,"
0 O
:11: mm
BASA Benzamidine

Figure 3. Kringle ligands
[Abbreviations used: eACA, e-aminocaproic acid:
AcLys, W-acetyl-L-lysine: AMCHA, trans-amino-
methyl(cyclohexane)carboxylic acid:
BASA, p-benzylamine sulfonic acid]

ligand binding [9]. Highfield NMR experiments carried out
on kringles 1 and 4 have shown that aromatic residues are
significant components of ligand binding probably due to the
lipophilic interaction between the ligand and the aromatic
side chains [21,23-27]. One of the aromatic residues which
has been shown to be involved in the binding is Trp73 [28]

with Trp63 and Phe65 probably close to this site.

Based on the three dimensional structure of the kringle
of prothrombin fragment 1 [29,30] and NMR experiments, a
model has been proposed for the lysine binding site of
kringle 4 of plasminogen [31,32]. According to this model,
the central loop CysSB to Cys76 supports or carries the
binding site. The binding site can be defined as a
relatively open depression that extends from the ProSG—LysGO
peptide stretch which contains Asp57 and Asp59 to a short
segment where Arg72 neighbors H1531 (Figure 4). The
depression is lined by Tyr75 and by Trp63 near the Asp57-
Asp59 stretch. The side chain of Trp63 is also close to the
Trp73 aromatic ring which interacts with another aromatic
residue, Phe65. The three side chains, Trp63, Phe65, and
Trp73, thus expose a lipophilic surface which separates the
protruding anionic and cationic centers defined by residues
AspS7/Asp59 and Arg71, respectively. The two ionic centers
thus form complementary polar ends at a distance of about
6.8 A. It is also apparent that the lysine binding site
interacts with a number of other aromatic residues, such as
Hi534, Tyr43, and Trp28, which neighbor the Leu48 side

chain. The side chain of Leu48 has been shown earlier to

10

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mo mufim mcflccfin mcfim>a omufiewcfisammumco cmaocos mo 3ma>oouuum .v musmfim

\
i

 

f
O

K A‘.

ll
lie close to the binding site [33]. The model of the
binding site given above is relatively open and exposed

allowing for facile ligand access.

The lysine binding site on kringle l of plasminogen, on
the other hand, may have a different arrangement of the
aromatic residues. While in the case of kringle 4 all the
residues implicated in lysine binding are present in the
inner loop 51 to 75, there is evidence for the participation
of Phe36 in kringle l, which is extraneous to this loop
[11,34]. Chemical modification of Arg34 with
1,2-cyclohexanedione abolishes the binding capability of
kringle l to w-aminocarboxylic acids (Arg34 immediately
preceeds Phe36 in the primary sequence due to a deletion).
On the other hand, glycosylation of Asn34 in kringle 4 of
chicken plasminogen seems to have no effect on ligand
binding [35]. A model has also been proposed for the
lysine binding site of the kringle 1 based on the kringle
structure of prothrombin fragment 1 , NMR experiments and

energy minimization [31,34].

The initial aim of the present study was to determine
the three dimensional structure of the kringle 4 of human
plasminogen by the molecular replacement method, using as a
model the known structure of the kringle of prothrombin
fragment 1, to establish the exact nature of lysine binding
site. The diffusion of small molecular substrates to the
site in crystals will then provide a precise model for the
interaction of plasminogen and fibrin and the role kringles,

in general, play in biological recognition. Since

12
apolipoprotein(a) carries 37 copies of the kringle 4 of
plasminogen and since the amino acid homology of some is
close to 85%, it should be possible to confidently model
such kringles based on the kringle 4 structure determined
here. However, since the onset of the work a fortunate
unexpected development has broadened the scope of the
project considerably. This development was the
crystallization of kringle 4 in two different crystal
modifications, one of which contained two molecules or a
"dimer" of kringle 4 in the asymmetric unit. This structure
might also prove to be an excellent approximation and basis
for discussing all-important kringle-kringle interactions of

blood proteins.

II MOLECULAR REPLACEMENT METHOD

The large and continually growing number of three
dimensional protein structures that have been determined
(approximately 350 so far) increases the possibility that
some new protein being investigated will have features in
common with one or more of the known structures. In
addition, there is growing interest among many biochemists
and protein crystallographers in determining the changes in
protein folding and/or side chain structures caused by site
specific modifications of the amino acid sequence. In these
cases, the application of the g: 2212 multiple isomorphous
replacement technique [36] to determine the phase angles of
the diffraction pattern may not be the fastest or most
economical way to achieve the ultimate goal. A more direct
approach is to utilize information from a closely related
protein of known structure by application of the molecular
replacement technique [37]. If successful, this approach
can dramatically decrease the time required to determine a
protein structure and can render heavy—atom derivative

preparation unnecessary.

The term molecular replacement method has been used to
describe several techniques. These can be classified
broadly into two categories. In the first, involving more
than one copy per asymmetric unit, the orientation of non—
crystallographic symmetry elements is searched for within an
asymmetric unit of the crystallographic unit cell. This
kind of molecular replacement has many applications. It can

13

14
be used in combination with multiple isomorphous replacement
to improve the refinement of heavy atom parameters [38].
The method has also been used to improve the quality of an
electron density map by averaging around the local symmetry
elements. These techniques have been critical in the
evaluation of virus structures, which generally contain many

copies of a subunit and are initially poorly phased [39-46].

The second category of molecular replacement methods
involves an attempt to model an unknown structure by
orienting and positioning a closely related molecule of
known structure in the unit cell of the unknown. These are
in general six-dimensional searches comprising the determi-
nation of three orientation angles and three positional
parameters. In practice, the six dimensional problem is
evaluated in two three dimensional parts: angles are deter-
mined using a 'rotation function' and positional parameters
with a 'translation function' or some other positioning
technique. Most of the methods mentioned below apply to
macromolecular structures but they are equally valid for

small molecules as well.

The occurrence of many identical structures not related
by the crystal symmetry has given rise to the concept of
"non-crystallographic symmetry". Crystallographic and
non-crystallographic symmetries are differentiated by the
property that an operator applies throughout the whole
infinite crystal for the former, whereas a
non-crystallographic symmetry element relates only to a

localized volume within the crystal. The difference between

15
the two classes of the symmetry elements is shown in

Figure 5.

The molecular replacement method essentially consists

of three stages. These are :

a). Determination of the relative orientation of the
independent molecules or subunits of molecules within one
crystal or subunits of molecules within one crystal lattice
or between different crystal forms. This may be
accomplished by analyzing the convoluted Patterson function
of the unknown structure and the closely related known model
protein. In case of more than one molecule in the
asymmetric unit of the crystal, the relative orientation
between the crystallographically independent molecules can
be determined by an analysis of the Patterson function of
the protein convoluted with itself. In practice, this is
achieved by calculating a "rotation function" [47], to be

described below.

b). Once the relative orientation of the protein molecule
is known with respect to a closely related model, the next
stage is to position the molecule in the unit cell in the
correct orientation. This is accomplished by calculating a
special function of the Patterson function called
"translation function" [48,49]. At the completion of stage
a and b, the exact equivalence between point X' in the
unknown structure and the point X in the model will be known

and can be expressed by

X‘ = [CIX + d ....(1)

 

Figure 5. Crystallographic (perpendicular to the page) and
non-crystallographic (in the plane of the page)
symmetry operations (taken from [37]).

17
where [C] is the rotation matrix determined in stage a and d

is the translation vector determined in stage b.

c). In the third stage, the structural information of the
model protein is used to calculate a set of phase angles of
structural amplitudes of the unknown protein; these phases
are then combined with the measured amplitudes to calculate
the electron density of the unknown protein to obtain a

trial structure.

There are numerous examples of successful applications
of the molecular replacement methods some of the examples of
which are various virus structures [39-46], lysozyme [50),
insulin [51], myoglobin [52], serine proteases [53-55],
phospholipase A2 [56], immunoglobin fragment [57],
phycocyanin [58], etc. The procedure is relatively
straightforward in the case of a rigid molecule and success
depends on how well the model approximates the unknown
protein. Proteins that are relatively flexible or which
deviate considerably from spherical shape pose special
difficulties in the application of molecular replacement
method. Even in the case of rigid globular proteins, the
success depends on the careful choice of the various

parameters in the calculation.

A. PATTERSON FUNCTION

Since the concept of both the rotation function and the
translation function involves the Patterson function, a

brief description of the latter follows. The Patterson

 

18
function is a Fourier series for which only the indices of
diffraction and the intensity of the diffracted beam are
required as coefficients, quantities that are directly

obtained from the experiment [59]. It is given by

2

P(uvw) - (l/V) 2 |r| Cos(2n(hu+kv+lw)) ....(2)

where V is the volume of the unit cell, [Fl2 is proportional
to the intensity of the diffracted beam corrected for
absorption and other factors, and u, v, w are the
coordinates of a point within the unit cell. No phase
information is required for this function as no origin for

the unit cell is implied, only the relative positions of the

atoms.

The Patterson map is the sum of the appearances of the
structure when viewed from each atom. A peak in the map, at
a position related to the origin of the map by a certain
vector, implies that at least one position of that
particular vector in the corresponding structure has atomic
positions at both ends. If there are many pairs of atomic
positions related to a particular peak in the function or if
there are only a few but the atoms involved have many
electrons, then the function will have a relatively large
peak height at that position. The heights of the peaks in
the Patterson function are approximately proportional to the
product zizj' where 21 is the atomic number of an atom at
one end of the vector and Zj that of the atom at the other
end. A difference Patterson between a native and an

isomorphous heavy atom derivative of a protein crystal

19
yields valuable information in the form of the positions of
the heavy atom which may then be used to determine the phase
angles of all the diffracted beams, as in the multiple

isomorphous replacement method.

Patterson space can be thought of as made up of two
types of vectors: intramolecular vectors and intermolecular
vectors. The former are vectors that are characteristic of
the distance between atoms within one molecule. These are
the vectors that are important in rotation function
calculation. The latter are vectors that reflect the
distance between atoms in different molecules, whether
symmetry related or independent. The translation function

is calculated based on these vectors.

B. ROTATION FUNCTION

The rotation function can be defined as an integral
over a spherical region of the product of the given
Patterson function P1 with rotated version of either itself

or the Patterson P2 of a closely related model protein [60]:
R(C) - I P1(x).U(x).P2(x) dv ....(3)

where C is a variable rotation operator and U is a shape
function that is used. to limit the evaluation of the
function to a smaller spherical region centered on the
origin of the Patterson space. In general, such a region
will be rich in intramolecular Patterson vectors, but will

contain relatively few intermolecular Patterson vectors.

20
The rotation function thus measures the degree of
coincidence between the two Patterson functions at various
values of the rotation matrix C. At certain value of the
matrix, this rotation function will have a large value; this
rotation will correspond to a transformation where the
vector set relating electrons within the model coincides

with the corresponding vector set from the unknown molecule.
C. ROSSHANN AND BLOW ROTATION FUNCTION

A number of methods have been proposed for the
evaluation of the rotation function, either in reciprocal
space or in direct space. Rossmann and Blow expanded the

rotation function in the form of a Fourier series [47]:

2 2

R(C) = 22 F (p).Fl (h).G(h+h‘) ....(4>

2

where F12(h) and F22(p) represent the intensities of the
crystal and the model, h‘ is a non-integral reciprocal
lattice point created by the operation of rotation matrix C‘
on h, C‘ is the transpose of the matrix C, and G is an
interference function which is the transform of U. The

quantities h‘ and p are related by the expression
h‘ s Cp ....(5)

This method, though historically very important as it
was the first attempt to evaluate the rotation function, has
very little practical application. It is extremely
cumbersome and lengthy to evaluate. The length and expense

of the computation usually forces the use of only the most

 

21
intense reflections in the calculation. Furthermore, the
interpolation function G is usually truncated to speed up
the process; this introduces serious errors in the rotation

function results.

D. CROWTHER FAST ROTATION FUNCTION

Since rotation functions deal with the rotation of
spherical volume of Patterson density, a natural form for
the Patterson function would be an expansion in terms of
spherical harmonics and spherical Bessel functions, as
suggested by Crowther and Blow [49]. By using expansion
functions appropriate to the rotation group, the rotation

function can be broken down into two parts:
R(C) = C ' D ' (C) ....(6)

where the coefficients Clmn' refer to a particular pair of
Patterson densities and are independent of the rotation
part. The coefficients, Dm'm(C), which contain the whole
rotational part of the problem, refer to rotations of

spherical harmonics and are independent of the particular

Patterson densities.

This formulation of the rotation function has been
coded into a computer program called the Fast Rotation
Function and is one of the most widely used rotation
programs today. It is much more accurate than the rotation
program of Rossmann and Blow and at least 100 times faster

since the summation is reduced to a series of two

22
dimensional Fourier series that can be evaluated with fast
Fourier transform algorithms. Moreover, any amount of data
can generally be used. However, the program has some
limitations. There is a limit to the maximum radius of
integration that be used for a given data set resolution.
Sampling of rotation space is also restricted by the
symmetry of the Patterson of the model and the unknown.
Another potential problem is with respect to monoclinic
space groups, where the program reindexes the data to align

the crystal system to the reference coordinate system.

E. LATTHAN ROTATION FUNCTION

Lattman used the property that the Patterson function
of a model placed in a sufficiently large artificial cell is
self bounded to eliminate the shape function U from the

rotation function which then takes the form [60]:

R(C) - I I1(hkl).C.I (h‘k‘l‘) ....(7)

2

where Il(hkl) is the intensity of the unknown structure,
12(h'k'l') is the squared transform of the model and C is a
rotation matrix. When R is large, the matrix C will rotate
the model structure into alignment with some element of the
unknown structure. In general, the rotated reciprocal point
h'k'l' will not lie near the unrotated reciprocal point hkl.
This problem is resolved by using a very finely sampled
transform of the known structure. No hkl will then be far

from a rotated h'k'l' and the value of 12 at hkl can be

 

23

obtained by interpolation from the eight nearest points of

rotated h'k'l'.

The greatest difference between Crowther's and
Lattman's formulation of the rotation function is that there
is no radius of integration limit in the latter, a limit
that is present in the former due to mathematics of the
formulation [61]. Lattman's version is also more flexible,
especially in regard to the sampling of rotation space. The
sampling can be as fine as the user desires. Crowther's
program, on the other hand, samples the angles alpha and
gamma in a specific way depending on the symmetry of the
unit cell of the unknown and the model ; this limits the
precision with which the positions of the peak maxima can be
determined. The disadvantage of Lattman's method is that
the program is slow. The strategy that one usually follows
is to determine the approximate positions of the peak maxima
using Crowther's program and use Lattman's program, sampling
on a fine grid around those maxima, to determine the precise

location of the maxima.

F. ROTATION FUNCTIONS IN DIRECT SPACE

Another variation of the rotation function is using the
vectors in the model Patterson limited to the relatively
large peak heights. This requires carrying out the
calculation in direct space [62,63]. There are many other
methods which use the same principles and evaluate the

rotation function in direct space. The advantages are that

 

24
one can modify the search vector set in physically

reasonable ways to enhance the search procedure.

In the case of macromolecular structures, the number of
vectors required depends on the number of atoms in the model
and the unknown. For a typical protein, with 150 residues,
choosing the 3000 highest peaks from the Patterson has been
shown to be more than adequate [55]. The Patterson vectors
are then rotated and interpolated to the nearest grid in the
Patterson of the unknown molecule and a product function
calculated. This process is repeated for each set of the
angles. The angles or the rotation matrix corresponding to
the highest value of the product function corresponds to the
transformation needed to bring the model and unknown to same
orientation. The SEARCH routine in the program "PROTEIN"
[64], makes use of this principle. Other major advantages
of the SEARCH program is that very fine sampling in rotation
space is possible and peaks close to the origin can be

removed.

G. PRACTICAL ASPECTS OF ROTATION FUNCTION CALCULATIONS

The matrix C is usually expressed in one of two systems
of angular variables. One way is in terms of the three

Eulerian angles 81,82,e as described by Goldstein [65].

3!
This is illustrated in Figure 6. The rotation operation
consists of (a) a rotation of Cartesian axes by 81 about the
z axis; (b) a rotation of 82 about the new position of the X

axis; (c) a rotation 83 about the new position of the Z

25

 

(a) z

 

 

 

(b) (C)

Figure 6. The rotations defining the Eulerian angles 91,
82, and 83 (taken from [65]).

26
axis. These angles are positive if they are clockwise when
viewed along the relevant axes towards the origin, as in the
usual right-handed convention. This system of angle
definition is difficult to visualize; however, it reveals
the symmetry of the rotation function in a convenient way
[47]. The rotation matrix in terms of the Eulerian angles

is given in Table 2.

The second angular system makes use of the theorem that
an arbitrary rotation can be accomplished by an appropriate
spin about a properly chosen axis [66]. The spherical polar
angles ¢ and w specify the longitude and co-latitude of
this axis, and the azimuthal angle x, the spin about it.
This is illustrated in Figure 7. In this representation, it
is easy to visualize the direction and order of rotation
axis with respect to the crystallographic unit cell. This
is the preferred system when the rotation matrix relates two

molecules in one asymmetric unit of the unit cell.

In eqn. (3), if P1 and P2 refer to the Patterson of
the same crystal, then the resulting rotation function is
called the self-rotation function and if P2 represents the
Patterson of the model, the rotation function is called the
cross-rotation function. Thus the self-rotation function
describes the relative orientation of two or more molecules
within one asymmetric unit of a crystallographic unit cell.
Cross-rotation,on the other hand, relates the orientation of
the model and the unknown or one crystal structure to

another.

27

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amewmlmmoo - ammooammooamcwm-

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e1 x_eaae eacsesae .N algae

28

 

 

Figure 7.

 

Spherical polar angles ¢,
to crystallographic axes.

 

W,

and x with respect

29

Since the origin of a Patterson function is always an
enormous number being the sum of all vectors and since it
does not contain much useful information as far as the
atomic arrangement is concerned, many of the rotation
programs have a provision to remove the origin. Removing
the origin of the Patterson function helps to increase the
signal to noise ratio of the true solutions. The volume
over which the integration is carried out depends on the
molecular size of the model or the size of the unknown
protein, predicted by some experiments like radius of
gyration experiments. Usually, the upperlimit on Patterson
vectors is chosen so as to include as many of the
intramolecular vectors as possible and to cut off the
unwanted intermolecular vectors. This is required by the
fact that in the crystal lattice there are thousands of
molecules and the measured intensity corresponds to all
these molecules. The rotation function, on the other hand,
assumes that the vectors in the Patterson function represent
the atomic arrangement within a single molecule. For a
typical protein of dimension 25 x 25 x 25 A, the best
results are obtained if only Patterson vectors between 4 and

20 A are used.

Another parameter in rotation function calculation is
the resolution of the data used to calculate the function.
The low order reflections usually have a large contribution
from the solvent which may be either disordered or even if
ordered may be different in the model and the unknown

protein. Very high angle reflections , on the other hand,

30
contain fine details of the structure which again may be
different in the model and the unknown. It has been found
that using reflections between 10.0 A and 3.5 A gives the
best result and good signal to noise ratio for many protein
molecules. Rejecting reflections based on individual
statistics and intensities is also found to enhance the

overall success of the method.

The first step in a cross-rotation function calculation
is to calculate a set of structure factors, to a suitable
resolution, of the model in a triclinic unit cell. The size
of the cell chosen is two to three times the size of the
model molecule. The choice of an extra large triclinic unit
cell produces a calculated Patterson function of the model
that corresponds to a single molecule. The number of atoms
of the model that are used to calculate the structure
factors depends on the extent of homology of the primary
sequences between the model and the unknown protein and how
well the side chains of the model are defined in the
electron density. The use of only the main chain protein
atoms and the conserved side chains gives good results. The
thermal parameters of the model are adjusted so as to
correspond to the average fall off in intensity of the

reflections of the unknown protein.

A model Patterson is then computed with the calculated
structure factors. It is this Patterson which is rotated
onto the Patterson of the unknown. There are a number of
parameters which have to be optimized in order to get a

reasonably good solution. These parameters may be different

 

31
for different proteins and different crystal systems.
Initially, one proceeds by sampling on a coarse grid in
rotation space. Rotation peaks are generally quite broad
and it has been found that sampling at five degree
increments is more than adequate. This is followed by a
fine sampling around the approximate solution obtained in

the first step.

The cross-rotation results are best expressed in terms
of the Eulerian angles 91,82,93 for this allows one to see
the symmetry in the rotation function clearly. Part of the
symmetry in the rotation function arises from the definition
of the Eulerian angles themselves; the crystal symmetry of
the unknown also contributes to it [67,68]. The symmetry
expected in the rotation function when a triclinic Patterson
is rotated onto various crystal systems and the size of the
asymmetric unit for the rotation function calculation is
listed in Table 3. Instead of expressing the results in
91,82,83, frequently another set of angles is used with a

simple relationship between the two sets of angles:

61 = a + 90 ; 62 = B ; 9 = y—90 ....(8)

3

H . TRANS LAT I ON FUNC T I ON

The second stage in molecular replacement method is the
determination of the position of molecule with respect to
the crystallographic symmetry elements. Several different
methods have been proposed for this stage of the molecular

replacement method, which is usually referred to as the

32

Table 3. Symmetry of rotation function when a model triclinic
Patterson is rotated onto the Patterson of a test molecule
with various symmetries.

 

 

 

CRYSTAL LATTICE PATTERSON SYMMETRY OF ASYMMETRIC UNIT
SYMMETRY ROTATION FUNCTION FOR ROT. FUN.

8,, 8,, 8, 8, : 0 — 360

Triclinic 1 u+8,, -8,, n+8, 8, : 0 - 360

, 0 - 180

9,, 9,, e, e, :o - 360

Monoclinic 2/m n+8,, ~8,, n+8, 8, : 0 - 180
(b axis unique) n-8,, n+8,, 8, 8, : 0 - 180

'61: “’92: “+93

 

9,, 9,, e, e, :o - 180
Monoclinic 2/m n+8,, -8,, n+8, 8, : 0 - 360
(c axis unique) u+8,, 8,, 8, 8, : 0 - 180

9:: '92: "93

 

9,, 9,, 9,

n+8,, 9,, 9,

u-8,, l+9,, 8, 8, : 0 - 180
Orthorhombic [mun ~8,, 1+8,, 8, , : 0 - 180

u-8,, I-8,, n+8, 8, : 0 - 180

-9,, I-9,, 1+9,
9!, “9:! 1+9,

1+8,, -8,, 1+8,

 

 

33
translation function. In some of the earlier methods, the
position of the molecule is independently determined
relative to each of the space-group symmetry elements either
in reciprocal space or in direct space [49,62,69-71]. This
affords the possibility of reducing the dimensionality of
the problem from three to one or two dimensions. A more
direct but computationally more demanding approach is a
search for a minimum of an agreement index or correlation
coefficient between the observed structure factor amplitudes

and those calculated from the model [72-78].

I. CROWTHER AND BLOW TRANSLATION FUNCTION

One of the earliest methods, which is widely used even
now, is a formulation due to Crowther and Blow [49].
Consider the problem of positioning a known molecule
relative to a particular crystallographic symmetry
element.The term 'known molecule' here implies that not only
do we know the atomic coordinates relative to some local
region, O, fixed in the molecule, but also that the molecule
is in the same orientation as one of the molecules in the
unknown crystal structure. We wish to determine the
position of the local origin with respect to the chosen
crystallographic symmetry element. If the known molecule is
placed at an arbitrary position in the unit cell, the
position of symmetry related molecule is fixed and it is
possible to calculate the set of Patterson vectors from the
known molecule to the symmetry related molecule. As the

position of the known molecule varies, the relative

 

34
configuration of these Patterson vector sets is unchanged
but the set moves bodily to a position characterized by the
vector joining the local origins of the known molecule and
the symmetry related molecule. This set of vectors are
referred to as the cross-Patterson of the model structure
and is a function of two variables, namely position in
Patterson space and also position of the local origin of the

known molecule in the model structure.

A well known method of finding the position of the
local origin is to move this set of cross-Patterson vectors
over the observed Patterson function of the crystal, using a
mimimum function or similar measure of fit to determine the
correct solution. In the case of molecules with thousands
of atoms as in proteins, this can be achieved by the
convolution of the observed Patterson function with the
cross-Patterson function set of the model structure. This
convolution may be carried out by multiplying the Fourier
coefficients of the two functions and performing a Fourier
summation with the coefficients so obtained. The resulting
function should have a prominent peak corresponding to the
vector set between the two origins. Mathematically the

translation function can be defined as

*

T(t) . £|Fobs(h)|2.FM(h).FM (hA).exp(-2ni.h.t) ....(9)

where IFobs (h)| is the observed amplitude, FM(h) is the
structure factor of the known molecule calculated relative

to the local origin, F *(hA), the complex conjucate of the

M
strucutre factor amplitude of a symmetry related molecule,

 

35
related by the symmetry operator A, and t is the translation
vector. In crystals having n crystallographic symmetry
elements, there will be n such expressions for translation
function, each solution representing the position of a
molecule with respect to one symmetry element; thus the
position of the known molecule can be overdetermined with

respect to the symmetry elements.

The observed Patterson function of the crystal contains

both intramolecular and intermolecular Patterson verctors.

In translation function determination, unlike in the
rotation function, we are interested in fitting the
intermolecular vectors ; the intramolecular vectors in fact
only serve to increase the background noise in the

summation. However, since the molecular structure is known,
it is possible to remove the intramolecular vectors from the
observed Patterson function, provided the observed
intensities can be put on an appropriate scale. Suppose
that there are n molecules in the unit cell and that the ith
molecule is related to the known molecule by a symmetry
operator, whose rotational part is represented by A , where
A , the matrix relating the known molecule to itself, is the
identity matrix. Then the modified translation function can
be expressed as

*(hA).exp(-2ni.h.t)

TM(t)-£(|F (h)|2- XIFM(hAi)I2)*FM(h).F

obs M

....(10)

where FObs and PM are assumed to be on an absolute scale.

36
The translation function results invariably appear on a
Harker section or on an axis. This can be illustrated by an
example. Let us take the space group P212121 with one
molecule in the asymmetric unit. There are 3

non-intersecting 21 screw axes in this space group and the

corresponding equivalent positions are

Molecule 1 : x y 2
Molecule 2 : 1/2-x -y 1/2+z
Molecule 3 : 1/2+x l/2—y -z
Molecule 4 : -x l/2+y 1/2-z

The independent intermolecular translation vectors are then

M01. 2 to M01. 1 : 2x-1/2 2y 1/2

M01. 3 to M01. 1 : 1/2 2y—1/2 22

M01. 4 to M01. 1 : 2x 1/2 22-1/2
..... (11)

Each of the vectors is required to lie on a Harker
section. Calculating all the three Harker sections will
give multiple determinations of each value and these should
all be consistent. In P212121, there is an eightfold
ambiquity in the choice of the origin, with each value being
equally well expressed as T or T + 0.5. However, this

problem arises only if we have more than one molecule in the

asymmetric unit of the unit cell.

One of the modifications that have been suggested to
the translation function of eqn. (1) is due to Langs [70]..

In his formulation, the terms FM(h) and F *(h) which contain

M
both amplitude and phase components of the model structure

 

37
factor, are replaced by terms containing only the phase
component. The magnitude of spurious peaks produced by this
modified translation function is almost half of that

produced by original translation function.

J. R VALUE MAPPING

Another commonly used procedure in place of the

translation function is to calculate the R factor :
R - z ( IIFoI - ch||)/ 2 IFoI ....(12)

where |Fo| and |Fc| are the observed and calculated
structure factor amplitudes respectively as the model is
translated in the unit cell. One simply calculates R values
on a grid covering all potential molecular positions, and
investigates those positions that give minimum R values.
The computation is not very efficient since the fast Fourier
transform (FFT) cannot be used to compute the whole
translation function. Another major drawback of this
approach is that the method is very sensitive to errors in
the relative scale of |Fo| and chl. This is very
important when high resolution data are not available and
especially if only part of the known structure is used for
the translation search ; in such cases an accurate scale
factor cannot be determined. Neverthless, many structures

have been solved by the method [79].

38

K. PACKING FUNCTIONS

There is another method for determining the translation
function which makes use of the fact that the correct
translation solution should result in the fewest
unacceptable intermolecular contacts in the crystal lattice
or the molecules should not interpenetrate each other in the
lattice [80,81]. In this method, one samples the
translation space and for each possible position calculates
the number of "bad" intermolecular contacts. This is a
relatively powerful method for macromolecules, where
crystals contain large solvent space and limited regions of
intermolecular contact. Bott and Sharma [80] have proposed
a modification which speeds up the process considerably.
One of the modifications that has been suggested is to
abandon a particular solution as untenable when a certain
number of "bad" contacts is encountered [81]. Even with the
simplification, the packing program is an extremely slow
process and the method cannot be used in cases having more

than one molecule in the asymmetric unit.

Many of the methods mentioned above have been compiled
in the form of a program package called "MERLOT" by Paula
Fitzgerald [61]. The Merlot package in addition has many
small utilities programs also, such as a program for
calculation of the structure factor of a model, refinement
of the rotation and translation solutions in Patterson

space, etc.

 

39

L. BRUTE TRANSLATION FUNCTION

Another of the methods that been suggested recently and
have been widely used is a translation function that uses a
linear correlation coefficient to determine the correct
position of the oriented molecule in the unit cell. The
method has been implemented in a computer program called
"BRUTE" [77]. In this method a linear correlation
coefficient is calculated between two sets of origin removed

Patterson functions or intensities

c - [p ' p 'du [I P 2 du [p 2 am”1 (13)
O. C O. C

where Po and Pc represent the origin removed Patterson
functions of the unknown and the model. The expression
given above can be represented in a form which is a general

expression of a correlation coefficient

(3 - z:(|Fo|2-|F—o|2).(IFclz-I-FTE'IZH
[ u[ea|2—|fi|2)2.z<[Fe|2-r—re|2)21‘*’

....(14)

Like the R factor, the correlation coefficient is basically
a measure of the agreement between observed ,lFoI. and
calculated quantities, IFcI. But unlike the R factor, the
correlation coefficient is scale insensitive, as replacement
of IFoI by kIFol, where k is an arbitrary scale constant,
gives the same value for C. The only drawback of the method

is it is a real number cruncher calculation and the

 

40
correlation coefficient for each solution must be evaluated

separately.

In many cases the translation function fails to give a
consistent solution. This is often a stumbling block in
molecular replacement calculations. Success in this stage
usually depends on the accuracy of the rotation results. In
case none of the translation function programs mentioned
above gives a consistent solution, one goes back to the
rotation function calculation, in the hope that a better

starting rotation matrix can be obtained.

It is important to refine the orientations and
positions obtained from molecular replacement before
proceeding with the structure analysis. One technique
proposed for doing this involves local minimization of the R
value [82]. One varies all independent parameters (angles
and translations) in small increments around their current
values. R values are calculated for each parameter value.
The parameter values are shifted to those that give the
lowest R value and used as input to another cycle until

convergence is obtained.

Several criteria of the validity of a potential
solution have been used. These include: (a) low residual
(b) non-interpenetration of molecules (c) consistency
between replacement solution and any non-crystallographic
symmetry elements that are present (d) phasing power of the
solution. The last criterion is by far the most powerful.

"Omit maps" are calculated by removing a part of the

 

 

41
structure and analyzed to see whether it returns in

subsequent calculations.

III EXPERIMENTAL

The kringle 4 sample from human plasminogen was kindly
provided to us by Prof. M. Llinas; it was generated from
plasminogen by elastase digestion and affinity
chromatography on lysine-Sepharose [6] as described by Winn
et. al. [83]. The product is a heterogeneous mixture of
approximately 70% C-terminal Ala86 and about 30% C-terminal
Ala86-Ser87-Va188. The kringle 4 used for crystallization
was in the form of a lyophilized solid stored at freezer

temperatures in a dry enviornment.

Kringle 4 crystallizes in two different crystal systems
and in some cases, from very similar conditions. One form
is monoclinic P21, with two molecules per asymmetric unit
while the other is orthorhombic, spacegroup P212121, with
one molecule per asymmetric unit. The structure of
monoclinic kringle 4 with two molecules might be relevant to
intact cassette domain structure molecules such as
plasminogen. The crystals diffract x-rays well and are
relatively stable with respect to degradation upon radiation

exposure.

A. CRYSTALLIZATION

Monoclinic kringle 4 crystals were first obtained by
Dr. Chang Park in our laboratory [84]. The kringle 4 was
dissolved in distilled water at a protein concentration of
approximately 10 mg/ml. Tris-saline buffer was added to

42

43
adjust the pH to 7.4. Crystals were grown by the hanging
drop method using 45% saturated ammonium sulfate (pH 7.4) as
the precipitant. Numerous small hair-like rosettes appeared
within a week. These small crystals were then used in a
repetitive seeding process to obtain large crystals in a
sitting drop set up. Crystals with dimensions of 1.0 x 0.2

x 0.2 mm were obtained in this fashion.

Under slightly different conditions, monoclinic
crystals were also obtained by Anne Mulichak of our
laboratory [84]. Hanging drop experiments were set up with
10 #1 drops consisting of 1:1 ratio of well solution and 10
mg/ml of kringle 4, where the well solution was 0.1 M
ammonium sulfate, 35% PEG 8000, 0.8% n-butanol at pH 6.2.
Needle-like crystals appeared within a few days, sometimes
along with thin plates in small clusters, and reached their
maximum dimensions in two weeks. The small crystals were
later used as seed crystals in a sitting drop set up to
produce crystals of dimensions 1.0 x 0.25 x 0.20 mm. These
crystals exhibit identical space group symmetry and lattice
parameters and similar gross morphology (some crystals
display striations) as the crystals obtained by Dr. Park
and by a different method (Figure 8). The unit cell
parameters and the relevant crystal data are shown in

Table 4.

Crystals of kringle 4 belong to the space group P21.
They contain four molecules in the unit cell, with two
molecules per asymmetric unit. Assuming a protein specific

volume of 0.74 cm3/gram, a protein fraction of 66% , with

44

 

Figure 8. Crystals of Monoclinic kringle 4.

 

45

Table 4. Summary of crystal data of Monoclinic plasminogen

kringle 4.

Space group 921

Num. of molecules

per unit cell 4

Molecular weight 9819

(daltons)

Crystal size (mm) 1.0 x 0.25 x 0.20
a (A) 32.75
b (A) 49.19
c (A) 46.20
8 (deg.) 100.6

Solvent fraction 34%

Matthews number 1.86

(Vm; Ag/dalton)

Unique reflections 3785

Num. of observed 2801

reflections

46
Vm - 1.86, was calculated. The very large protein fraction
is consistent with the excellent extent of diffraction from
relatively small crystals. The small Vm value compares well

with other low molecular weight proteins [85].

A characteristic feature of the monoclinic kringle 4
crystals is the tendency to form twinned crystals. The
crystals are twinned along the c* direction in a manner
similar to a—chymotrypsin [86]. The relative orientation of

the crystal and the twin are shown in Figure 9.

B . DATA COLLECTION

The crystal used for data collection was of dimensions
1.0 x 0.25 x 0.20 mm. The crystal was mounted with the b*
axis along the long axis of the capillary which becomes
coincident with the phi axis of the diffractometer when the
crystal is aligned. Crystals were mounted in capillary
tubes of common glass and diameter 1.5 mm. After a crystal
had been oriented properly with drOps of mother liquor above
and below it, the tube was sealed in a low flame. The
crystal is held to the wall of the capillary by the surface

tension of a drop of mother liquor.

Preliminary x-ray examination of the crystal included
the recording of the diffraction pattern along the three
principal axes of the crystal. The principal axial
intensity distributions are shown in Figure 10. The axial
runouts show that the crystals scatter x—rays well beyond

2.0 A resolution (28-45.3°).

47

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49

Reflection intensities were measured by using Cu Ke
radiation (1.5418 A) with a graphite monochromator on a
Nicolet P3/F four-circle diffractometer controlled by a Data
General Nova/4 minicomputer. A schematic drawing of the
goniostat of this diffractometer is shown in Figure 11. The
goniostat orients the crystal and detector with respect to
the stationary x-ray beam and brings Bragg planes
sequentially into reflection position. The four circles of
the goniostat refer to the three circles swept out by
rotation of the crystal about the w,¢, and x axes, and the
circle swept out by the arm of the detector through rotation
about the phi axis( which is coincident with the axis).
To measure the intensity of a diffracted beam, the
diffractometer is driven to the appropriate angular
positions for each of the diffracted beam to satisfy the

Bragg condition
2d sin 8 = k ....(15)

where d is the interplanar spacing of the reflection and k

is the wavelength of the x—ray radiation.

The 28,w,¢, and x angles which the goniostat drove to
in the course of making an intensity measurement resulted
from the unit cell parameters and the orientation matrix of
the crystal. The information about both the orientation and
the unit cell parameters of the crystal is contained in the
orientation matrix A, which describes the reciprocal vectors
a*,b*, and c* in terms of their components in the instrument

coordinate system.

50

 

 

 

 

Figure 11. A schematic drawing of the goniostat of a
four-circle diffractometer.

 

A a a y b y c y ..... (16)

The orientation matrix is first calculated from the
indices and angular positions of three strong reflections.
Later, a better orientation matrix is obtained by finding
another 8 or 9 strong reflections of high 28, distributed
uniformly in the part of the reciprocal space to be used for
intensity measurements. These reflections constitute the
'reflection array'. The unit cell parameters are obtained
by performing a least squares calculation between the
calculated and observed angles of the reflection in the
reflection array. Usually two or three reflections with
relatively high x value are included in the reflection array

to insure reliability of the calculated orientation angles.

In this data collection, there were eleven reflections
in the reflection array, the 28 of which ranged between
17.0° and 25.0°. Since the x range of data collection was
from 0-90°, three reflections had x between 0 and 40°, five
reflections had 30<x<65°, and three reflections had
65<x<90°. Each time the least squares calculation was

performed, the cell dimensions of the crystal were updated.

The alignment and deterioration of the crystal was
monitored by measuring the intensity of three standard
reflections periodically every 60 reflections (about 70
minutes). Because the crystals are mounted in glass

capillaries with only a drop of moisture adhering the

52
crystal to the walls of the capillary, most crystals tend to
undergo some small orientational motions. If the intensity
of these monitor reflections decreased by more than 20%, the
crystal was considered misaligned. This triggered the
re—measurement of the positions of the eleven reflections in
the reflection array, followed by the calculation of a new
orientation matrix and cell parameters by the least squares
method. The three check reflections used for this purpose
and their corresponding 28 values were : (0,-10,0) (28
-18.02°); (-l,-7,9) (28-21.48°); and (1,0,8) (28-16.36°).
The intensities of these reflections were plotted versus
exposure time of the crystal and the resulting slopes were

used to obtain decay corrections for the data (Figure 12).

The reflection intensities were measured by the Wyckoff
w-step procedure [87]. In this method, data were collected
by holding the detector arm (28) fixed and scanning w.
Usually this method of data collection is used when the
reflections are spaced closely as in a macromolecular
crystal or when it is desirable to collect data quickly to
avoid the danger of x-ray damage fo the crystal. In this
method, the top of the peak is sampled instead of the
profile from background to background. If the peak maximum
is too close to one edge of the scan range, the computer
program is made to collect additional steps. Thus, slight

errors in crystal orientation can be compensated.

Using the Wyckoff method, each peak was scanned 0.09°
on either side of the calculated value for the reflection

in 7 steps, performed in 0.03° increments. Each step was

INTENSITY(Coun]:/Second)

 

S3

 

 

700- (0.40.0) (20:18-02 ’)
4 ° 0
600‘ o o o o
500"
7000, o (-1.-7.9)(2e=21-so’)
° 0
600" o o o
O
500" 0 ° 0
1.0.0) (29:15.30’)
900... (
‘ o o o o
800‘ ° 0 o
o o M
700"
Y 40 ' 8'0 120 150
TIME (hours)
Figure 12. The intensity of the kringle 4 monitor

reflections Vs. time of exposure.

54
measured for a duration of 8 seconds and the five largest
measurements were summed to calculate the integrated
intensity of the reflection. Background measurements were
made , on either side of the peak, for each reflection for a
total duration of 11 seconds while the time spent in
scanning the peak was 54 seconds. The maximum number of

additional steps allowed was 3.

Several measurement procedures preceded and followed
the actual intensity data collection. These included: the
w-profile of a reflection (-5,5,5), the intensity profile
versus angle (absorption) for the reflections (0,—2,0) and
(0,-10,0), and the (h01) zone of reflections to 6.0 A
resolution. The w-profile of a reflection assesses the
quality of a crystal for 3—D data collection from which
information is used to set the Wyckoff step scanning
parameters. The profile of (-5,5,5) was obtained by
measuring the intensity of the reflection at m values i
0.65° from its calculated value in 0.05° intervals of m
(Figure 13). The width of the peak at half the maximum
height defines the region of the peak to be scanned. From
this plot, an offset value can also be obtained to measure
the background. For kringle 4, a scan range of 0.18° and an

offset of 0.2° was used.

The intensity of absorption versus 0—angle was measured
for reflections (0,-2,0) and (0,-10,0) to find the region in
0 of low x-ray absorption so the data collection could be
carried out over this 0 range, and so that an absorption

correction could ultimately be applied to the measured

480‘

Y

 

400‘

I

L»:
N
O

lNTENS]TY(Counts/Second)
r»
A
O

160..

80--

 

Figure 13.

55

 

A A
v

8 '6 8-8 9'0 92 9.4

1}

1
4b
1?

w (°)

w—profile of (-5,5,S) taken before the 3-D data
collection. Half-width ~ 0.2°*.

 

56
intensities. The b* axis reflections were used because in
kringle 4, the b* direction is coincident with the 0 axis so
that the (0,1,0) Bragg planes are always in the reflecting
position for all values of 0 at x-90°. Intensity
measurements were made every 10 degrees in 0 over a 200
degree range for both reflections. A plot of Imax/I, where
Imax is the maximum intensity of the measured reflection and
I the intensity of the same reflection at any other 0 angle,

is shown in Figure 14.

The intensities of the (h01) reflections to 6.0 A
resolution (28 < 15°) were measured before and after the
data collection to assess the decay due to radiation damage
to the reflections in the 2.5<8<15.0° range. As mentioned
earlier, the monoclinic crystals are twinned along the c*
direction. By virtue of the unit cell parameters , certain
reflections from the crystal and the twin with l-0,1,3,4,
and 8 overlap so closely that they cannot be resolved with
intensity data collection diffractometer conditions(4° x-ray
take-off angle, detector slit size, etc.). Therefore a
6.0 A resolution set of twin intensity data also was
collected and used to determine a crystal/twin ratio (~1.60)
which was then used to correct the twinned measurements to

the corresponding individual reflection intensities from the

crystal and the twin.

Approximately 3800 reflections were measured to 2.8 V
resolution during the data collection for the crystal and
450 reflections for the twin. The 3-D data to 2.8 V

resolution was collected in two shells of 28 in the

57

24V

1-sv '
'MIM 0

W '

Mo '

 

270 310 330 30 7o :10

(1)0)

Figure 14. Absorption curve of the (0,—10,0) reflection.

58
following order ; 25.0°— 32.0° and 2.0° - 25.0°. It took
approximately 110 hours of x-ray exposure to measure all of
the intensities. Of these 3800 crystal reflections, about
2900 were considered observed (~76%). The observation limit
was defined from the average negative intensity of the

accidentally unobserved reflections.

IV DATA REDUCTION

The first step in processing protein intensity data is
to reduce the measurement for each reflection (hkl) to its
corresponding structure factor modulus, |F(hkl)|. The data
was reduced using a program called P-DATA, written by
C.D.Buck , of our laboratory. The program calculates the
structure factor amplitude from the diffraction intensities

by means of the equation
|F(hkl)|2 - CONST x ABS x DECAY x LORPOL x I(HKL), ....(17)

where CONST is a scale constant, ABS is the correction
factor due to absorption, DEC is the decay correction to
compensate for the loss of intensity due to crystal
deterioration from x-ray exposure, LORPOL is the
Lorentz-polarization factor which is a geometrical factor,
and I(hkl) is the background—corrected intensity of a

reflection (hkl).

The absorption correction applied in the P-DATA program
was based on the method proposed by North, Phillips, and
Mathews [88]. The program uses the absorption curve of
Imax/1(0) versus 0 to apply the absorption correction
(Figure 14). The decay correction factor DECAY corrects the
intensity deterioration of a reflection as a function of
exposure time and it is usually 2 dependent. DECAY factor

has the form :

I°(t) = I(t) * {l/(l-St)} ....(18)

where S--s/I°CR where s is the lepe of the intensity versus

59

60

time of exposure curve of the monitor reflections
(Figure 12) and I°CR is the intensity of the monitor
reflections at zero time. From the three monitor

reflections, an average value of 0.00248 was obtained for S,
which corresponds to 40% decay at the end of 162 hours of
x-ray exposure. A decay correction can also be calculated
from a comparision of the (h01) projection Patterson before
and after the data collection. This value (36% at the end
of 162 hours of exposure ) was in good agreement with the

decay factor from the monitor reflections.

Before applying the P-DATA program, the background of
the intensity data was averaged in shells of 28. Background
measurements made at the left and right side of a reflection
peak and the total intensity measured are used to calculate
the integrated intensity from the equation

sum of background counts

I - [total scan - bacngSund to scan time ratio] * scan rate
....(l9)

 

Averaging of background measurements is usually carried out
in shells of 28 and in shells of 0 if there is a 0
dependence. For kringle 4, there was no variation of

background measurements with 0—ang1e.

A. PROCESSING OF TWINNED REFLECTIONS

By virtue of the unit cell parameters and the relative
orientation of the crystal and the twin, certain reflections

of the crystal with l=0,4,7,8,11, and 15 overlap very

61
closely with the corresponding reflections from the twin.
The reflections with 1-0 from the crystal and the twin
overlap exactly. For the other overlapping reflections, the
background was systematically higher. Hence they were
excluded from the background averaging procedure. Their
background was corrected based on the average background of

the non-overlapping reflections in the appropriate 28 range.

To untwin the overlapping reflections from the crystal
and the twin, the crystal to twin ratio must be known. As
mentioned in the previous Chapter, a 6.0 A data set of the
twin was collected as part of the data collection. The twin
data set was corrected with the appropriate background
measurements from the crystal data set and using the program
P-DATA, the corrected intensities were reduced to structure
factor moduli, |F(hkl)|. A systematic comparision of
|F(hkl)| of the crystal and the twin was made to obtain a
crystal to twin ratio of 1.24. This corresponds to a
crystal to twin ratio of 1.55 based on intensity, which
agrees very well with the previous estimate of 1.6.
Approximately 200 observed reflections were used for this

comparision.

When a crystal lattice possess a rotational symmetry
axis which is not a symmetry element of the space group of
the crystal, crystal specimens may grow as twins [89]. In
such cases, the reciprocal lattices of the different crystal
twin domains of the specimen overlap. The resulting
diffraction intensities are given by linear combinations of

the true untwinned intensities of the reflections which are

62
related by the twinning operation. In order to extract the
true intensities from the observed intensities, one must be
able to determine the crystal to twin ratio or twinning
fraction. Several methods have been proposed for untwinning
or resolving the measured intensities into their individual

components [89-93].

In the case of kringle 4, the overlap of the reciprocal
lattices of the crystal and twin are not exact; this implies
that only a fraction of the measured diffraction intensities
need to be untwinned. This is very clear from Figure 9 ,
which shows the reciprocal lattices of the crystal and the
twin. In the Figure, the c* axis of the crystal is shown by
the solid line, that of the twin by the dotted line. The a*
and b* axis of the crystal and the twin are almost
coincident. From the drawing it appears as if all the
reflections of the crystal with l-0,4,7,8,11, and 15
overlap with reflections from the twin. Since the crystal
is mounted with b* axis along the goniometer axis, the 0
value of a reflection is related to the w value directly.
Thus, a comparision of the 0 values of the crystal and the
twin reflections will establish whether any reflection is
twinned. Since the scan range used in the Wyckoff w-scan
was 0.18°, from the w-profile (Figure 13) any two
reflections with a 0 separation of greater than 0.4° will be

clearly resolved.

Before untwinning the measured intensities, the
reflections that are twinned must be identified. From the

orientation matrices of the crystal and the twin (Table 5),

63

Table 5. Orientation matrices of the crystal (a)
and the twin (b).

a. crystal

0.03014 0.00001 0.00500
-0.00136 -0.00001 0.02145
0.00004 -0.02033 0.00006

b. twin
~0.03116 -0.00004 -0.00312
0.00136 0.00000 0.02182

-0.00003 0.02033 0.00000

64
the angles 28,w,¢, and x were calculated for all the
reflections for the crystal and the twin. Those reflections
of the twinning layers with a 0 seperation of less than 0.4°
were considered twinned. A systematic examination of all
the reciprocal points to 2.8 A revealed that out of about
2800 observed reflections, 500 were twinned (~18%). The
fraction of the twinned reflections and the average 0
separation between the crystal and the twin reflection in

each layer of l are listed in Table 6.

Aspects of twinning in Figure 9 can be somewhat
misleading. For example, it appears as if all the
reflections in l=15 layer are twinned. But none of the

reflections in 1:15 layer are twinned (Table 6). The reason
for this is that the Figure was drawn on the assumption that
the b* axis of the crystal and the twin overlap exactly.
But the orientation matrices of the crystal and the twin
reveal a small angular separation between the two. The
separation increases as the distance from the origin of the

reciprocal lattice increases.

As mentioned earlier, for the twinned reflections the
measured intensity is a linear combination of the
intensities which would be observed if there were no
twinning. Let 11 and 12 be the measured intensities of
reflections which are related by the twinning operation and
J1 and J2 represent the true intensities of the reflections
(in the absense of twinning). Also, let the crystal to twin

ratio be K and its inverse by Ki Then the following

t
relations hold :

nv

65

Table 6. Fraction of twinned reflections and the average
0 separation of the crystal and the twin
reflections in twinning l—layers.

1 Number of Number of twinned % of twinned Average 0
reflections reflections reflections seperation

(deg.)
0 324 324 100 0.05
l 323 139 43 1.48
2 316 0 0 3.47
3 314 61 19 1.78
4 308 231 75 0.27
S 295 0 0 2.45
6 279 O 0 2.93
7 264 0 0 1.15
8 252 71 28 0.54
9 225 0 0 2.32
10 202 0 0 2.38
11 182 0 0 0.73
12 156 0 0 0.80
13 126 0 0 2.20
14 88 0 0 1.88
15 58 0 0 0.44
l6 l6 0 0 0.90
total 3785 826 22 1.57

66
Il - J1 + Kinv x J2 ....(20)

12 - J2 + Kinv x J1

These are two simultanious equations in two unknowns, J1 and

J2 which solve to :

2
J1 - (Il - Kinv x I2)/(l-(Kinv) ) ....(21)

2
J2 - (I2 - Kinv x I1)/(l-(Kinv) )

If both 11 and 12 are unobserved reflections, J1 and J2 are
considered to be unobserved. If 11 is observed and 12 is
unobserved, then Jl-Il and J2-0 ; on the otherhand if I1 is
unobserved and I2 is observed, then Jl=0 and J2=12. In the
case of reflections with l=0, where the overlapping
reflections of the crystal and the twin are Friedel mates
with the same magnitude for h (with opposite signs), there

is a special relatioship

J1 - J2 a (Il+lZ)/2(1+Kinv) ....(22)

The set of simultanious equations (Equation 20 ) were solved
for approximately 700 reflections to resolve the measured
diffraction intensities to the individual reflections. Of
these, close to 200 reflections were unoberved after
untwinning. Thus only 18% of the observed reflections out

of a total data set of 2800 are twin-corrected.

V PATTERSON SEARCH

A. SELF ROTATION FUNCTION

As mentioned in Chapter III, monoclinic kringle 4
crystals contain two molecules in the asymmetric unit. To
find the non-crystallographic symmetry element or operation
which relates the independent molecules with respect to one
another, a self rotation search was carried out by Patterson
search methods [64]. The Patterson function was calculated
with a 1.0 A grid using reflections from 9.0 A to 3.5 A
resolution. For the rotation search, the grid points
representing the 1500 highest Patterson peak heights within
a radial shell between 6.0 and 23.0 A were selected to
represent the Patterson. The self rotation search was
carried out, using the SEARCH routine in Steigeman's PROTEIN
pacakge [64], in the angular range 81: 0°to 360°, 82- 0° to
180°, and 83 a 0 to 90° for the three Eulerian angles in
steps of 5°. The lower limit of 6.0 A was chosen to
eliminate the Patterson origin ripple effects; the higher
limit of 23.0 A, on the other hand, was chosen with a view
to eliminate the intermolecular vectors from the rotation
calculation. The molecular dimension of the kringle as
measured from the prothrombin kringle is 20x28x30 A [29].
The product correlation function was calculated as a

function of the orientation angles 81,82, and 83.

The rotation search yielded a correlation peak of 14.3

standard deviations (12.3 0 above the mean) at 81=90.0°,

67

68
82-160.0°, and 83-90.0°. The next highest peak was only 5.2
standard deviations. Then a finer grid scan was carried out
in steps of 0.3A around the peak of highest correlation.
The fine scan increased the value of the highest peak to
14.5 standard deviations, yielding an optimal fit at

91-90.0°, 82-161.1°, and 83:90.0°.

The self rotation calculation was repeated with a
different set of Patterson vectors. This time the Patterson
was calculated with reflections from 12.0 A to 3.5 A
resolution. The grid points representing 1000 highest
function values within a radial shell between 5.0 and 15.0 A
were selected to represent the Patterson function. The
highest solution appeared at the same set of Eulerian angles
but with a peak height of 15.3 a (9.0 a above the mean
value). The next highest peak had a correlation of 9.5 a.
The subsequent refinement of the rotation angles in steps of
0.3° around the highest peak yielded basically the same
[angles obtained previously with the different set of vectors
and other parameters and the peak height increased to

15.5 a.

The rotation angles can also be expressed in a set of
spherical polar angles where it is easier to visualize the
orientation of the rotation axis with respect to the
cryStallographic symmetry elements (Figure 7). In terms of
the polar angles, the self rotation is at 0 =0.0°, w =80.0°,
and x -180.0° (Table 7). This corresponds to a two-fold
rotation approximately parallel to the crystallographic a*

axis. Thus the two independent molecules in the asymmetric

69

Table 7. Self rotation results, both in terms of Eulerian
angles 8,,84,8, and spherical polar angles ¢,w,x.
All the symmetry related solutions are listed in

degrees.

91 92 83 0 w X
1 90.0 60.0 90.0 0.0 80.0 180.0
2 270.0 200.0 270.0 0.0 80.0 180.0
3 90.0 340.0 90.0 180.0 10.0 180.0

4 270.0 20.0 270.0 180.0 10.0 180.0

70
unit are related by a non-crystallographic two-fold rotation
approximately parallel to a* axis, similar to the

non-crystallographic symmetry observed in a-chymotrypsin

[86].

When the Patterson search is carried out over the
entire angular range, the rotation function shows additional
solutions which are symmetry related to the first solution.
This arises from the symmetry of the Patterson and the
definition of the Eulerian angles, as described in
Chapter II. The symmetry related solutions are given in
Table 7, both in terms of the Eulerian angles and the polar
angles. The solution at 0-180.0°, w-10.0°, and x-180.0°
corresponds to a non-crystallographic two-fold rotation
approximately parallel to the c axis. Thus, depending on
how one chooses the crystallographic asymmetric unit, the
non-crystallographic symmetry can be considered as a
two-fold rotation parallel to either the a* or c* axis.
This can be seen from Figure 15. The molecules marked A and
B are the independent molecules and those marked A' and B'
refer to the symmetry mates related by the crystallographic
21 screw parallel to the b axis. The relationship between
A and B is a two-fold rotation parallel to a* axis whereas
8' and A are related by a non-crystallographic two-fold
rotation parallel to the c* axis. Thus there are two
posssible "dimer" solutions for kringle 4. These will be

elaborated upon later in Chapter IX.

71

 

 

 

 

(I
" A :' B
5 3' 5 A'
/ 1 ; 7 b

 

 

Figure 15. Schematic of the four molecules in the unit
cell. Non-crystallographic symmetry elements

are indicated by the dotted lines.

72

B. CROSS ROTATION FUNCTION

The next stage of the molecular replacement analysis
was to determine the relative orientation of the kringle 4
molecules with respect to the crystallographic coordinate
system using a model based on a known kringle structure.
The only kringle structure that has been solved so far is
that of kringle 1 (K1) of prothrombin fragment 1, carried
out in our laboratory [29,30]. The primary sequences of
kringle 4 of plasminogen (K4) and K1 are shown in Figure 16.
Thus, from Figure 16, of a total of 80 residues in the
kringle, 36 are identical and 5 are very similar. This
amounts to a homology of 51% between the two primary
sequences. It is also clear from Figure 16 that the highest
degree of conservation in the kringle sequences occurs in
the region of the inner loop residues (C and D) near the

disulfide bridges CysSB-Cys76 and CysZS-Cys64.

A cross rotation search was carried out with the
coordinates of K1 with many different sets of cross rotation
caluculations being performed with different model
structures. Initially, a simple polyalanine backbone of K1
was used as the model. This contains 387 atoms and
corresponds to a little more than 50% of the K4 structure.
Later, the conserved side chain atoms were also included in
the calculation, increasing the total number of atoms to
489 (~72%). Finally all the atoms in K1 were used in the

calculation.

73

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so nouoodocfi one «monsoon unflassm 1mxooan ocosodo so ommodoco

moo neocosoom soon as ”coaucoofl mmoosmmu "1n1 v mamcaux comocssmmaa
cuss: can 1m1 mflmcaux H ucmsmmuu censouzuoum mcfi>oo uo mmocmoomm .mH magmas

 

74

The model structure was based on a 2.8 A refined
structure of K1 , with 178 water molecules, refined to a R
value of 18% (T. P. Seshadri, unpublished results of this
laboratory). The average thermal parameter (B) at this
stage was 39.8 A2. On the other hand, K4 scatters x-rays
well and does not decay very much on long x-ray exposure.
Hence, a B value of 20 A2 was applied instead for the

structure factor calculations.

Each model of K4 was placed in a triclinic cell with
orthogonal axes of length 75 A. Triclinic structure factors
were calculated from 9.0 A to 3.5 A with an overall
temperature factor of 20 A2. A 3.5 A model Patterson with
grid spacings of 1.0 A was then calculated. The Patterson
synthesis of the crystal was calculated similarly using all
observed refelctions from 9.0 A to 3.5 A resolution with
1.0 A grid spacings. The product correlation of the crystal
and the model Patterson maps was calculated as function of
the Eulerian angles in steps of 5° in the angular range 81-0
to 360°, 82-0 to 180°, 8320 to 180°, and subsequently in
smaller steps of 0.3° around high correlation peaks. All
the rotation searches were performed using the SEARCH

routine in PROTEIN package [64].

The various Kl models were used separately in the
rotational searches to determine the orientation of the
independent molecules A and B within the crystal. Each of
these rotational searches yielded two practically

indistinguishable highest correlation peaks in general

75
positions with their height corresponding to about

7 a (Table 8).

The non-crystallographic two—fold rotation found in the
self rotation calculation could now be compared with the
solutions of the cross rotational search [56]. Let K4A and
K4B represent the two independent kringle 4 molecules in the
asymmetric unit of the monoclinic crystal and [S], the self
rotation matrix relating these two molecules. If [CR1] and
[CR2] are the rotation matrix solutions 1 and 2 of the cross

rotation search, then the following relation hold good

K4B = [S] x K4A
K4A = [CR1] x K1 ....(23)
K4B = [CR2] x Kl
[CR2] = [S] x [CR1]
Using [CR1] and [CR2] from the cross rotation, [S] was

calculated. The various matrices used are listed in Table 9
from which it is very clear that there is excellent
agreement between the self rotation matrix calculated from
the cross rotation results and the observed self rotation

matrix.

As in the case of self rotation, the cross rotation
calculation also revealed the symmetry of the Patterson
function, when the search was extended to the whole range of
the Eulerian angles. Four solutions were obtained which
correspond to the four molecules in the unit cell. The
relationship among the four solutions can be calculated as
before and are listed in Table 10 from which the agreement
between the self rotation and the cross rotation is clearly

evident.

76

Table 8. Cross rotation results. (a): Polyalanine backbone
kringle model (387 atoms; 57%). (b): Kringle with
conserved side chains (489 atoms; 72%). (c): All
the kringle atoms (621 atoms; 92%). All models
based on the coordinates of K1 of prothrombin
fragment 1.

Model Two highest Peak height Height above
correlation (a) the mean value
peaks (deg.) (a)
81 82 83
a 202 152 68 7.0 5.1
46 142 100 6.5 4.6
b 200 149 71 6.2 4.6
44 142 99 6.8 5.2
c 199 149 66 5.9 4.1

45 145 98 5.6 3.9

Table 9.

Cross rotation matrix 1

Correlation between the cross rotation and the
self rotation results.

Cross rotation matrix 2

(a-313.62°,8-142.80°,v-186.88°)(a-70.23°,8a30.30°,y-338.77°)

0.45883 -0.78454 0.41710

~0.65512 -0.61583 —0.43769

0.60025 -0.07243 -0.79653
Predicted self

rotation matrix

(4-0.15°,w=81.63°,X-182.43°)

0.95766 -0.00120 0.28789
0.01115 -0.99909 —0.04124
0.28768 0.04271 -0.95678

0.61299 -0.77144 0.17065
0.63488 —0.60951 0.47479
-0.47029 -0.18270 0.86340

Observed self
rotation matrix

(0a0.00°,w-80.55°,x-180.00°)

0.94609 0.00000 0.32392
0.00000 —l.00000 0.00000
0.32392 0.00000 -0.94609

78

Table 10. Correlation between cross rotation and self
rotation results.

a. Symmetry related cross rotation angles.
(deg.)
a B Y

1 313.62 142.80 186.88
2 109.77 149.70 158.77
3 70.23 30.30 338.77
4 46.38 322.80 186.88

b. Self rotation angles and the related cross rotation
angles.
Related cross Predicted self Observed self
rotations rotation rotation
(deg.) (deg.)
v 0 X 4 W X
l - 2 188.30 8.45 180.29 180.0 9.45 180.00
1 - 3 0.15 81.63 182.43 0.0 80.55 180.00
1 - 4 90.00 90.00 180.00 Crystallographic

2l screw axis

79

C. TRANSLATION FUNCTION

The location of the two correctly oriented molecules in
the unit cell was determined using the program BRUTE written
by Fujinaga and Reed [77] to calculate the translation
function. In this phase, only the K4 model with the
conserved side chains was used for the search. The unit
cell of K4 contains two crystallographically symmetrical
molecules of type A (A and A') and two crystallographically
symmetrical molecules of type B (B and B'). First,
molecules A and B were correctly oriented corresponding to
the solutions of the cross rotation search. BRUTE
translation function were then calculated to position A and
B separately. Later, one of them (molecule A) was fixed at
the correct position and a search was carried out for the
other molecule (molecule B). This was followed by another
calculation where molecule B was fixed and a search

performed for the position of A.

The results of BRUTE translation function calculation
are expressed in terms of a correlation coefficient between
the observed structure factor |Fo| and the calculated
structure |Fc|, as given by equation 14 of Chapter II. The
calculation was repeated using reflections in various
resolution ranges. In all cases, the calculation intially
was performed in steps of 0.5 A translation and in steps of
0.1 A subsequently around the solutions of highest
correlation. For the independent search of the molecules A

and B, the search could be restricted to two dimensions,

80
since in monoclinic space group P21, the origin along the y

axis is arbitrary.

The results of the translation function calculation for
the independent searches of molecule A and B are listed in
Table 11 which shows very good agreement between the
calculations performed at various resolution ranges. The
best correlation coefficient is obtained at low resoltion
(9.0 A to 5.0 A). The heighest peak has a correlation
coefficient of 8.9 a (about 3.8 a above the mean) for
molecule A while it is 8.0 a and 4.1 a respectively for
molecule B (with 7.0 — 3.5 A data set). The rotation and
translation parameters for molecules A and B after

refinement in steps of 0.1 A are listed in Table 12.

To determine the relative positions of molecules A and
B, molecule A was fixed in the unit cell at the position
given in Table 12 and a translation search was carried out
for molecule B. This time the search was extended to three
dimension since the origin along the y axis has already been
fixed by specifying the position of molecule A. Only
reflections in the resolution range 5.0 A to 3.5 A were used
for this search. The maximum correlation coefficient was
obtained at TXB-0.80, TYB-1.00, TZB=0.70 and has a
correlation coefficient of 0.41. The correlation
coefficient is about 11 o(~6.0 a above the mean). The
search was repeated by fixing molecule B and searching for
molecule A. Essentially the same results were obtained,

confirming the relative positions of molecules A and B. The

81
Table 11. "BRUTE" translation search solutions for

molecules A and and B at various resolution
ranges.

Molecule A.

TX - 6.0 A; TZ - 11.0 A

Resolution Correlation Height Height above
range (A) coefficient (a) the mean value

9.0 - 5.0 0.32 6.8 2.6

5.0 - 4.0 0.25 6.2 2.8

7.0 - 3.5 0.22 8.9 3.8

9.0 - 3.5 0.21 8.6 3.7

Molecule B.

TX - 9.8 A; TZ - 9.3 A

Resolution Correlation Height Height above
range (A) coefficient (a) the mean value
(a)
9.0 — 5.0 0.31 6.6 2.9
7.0 - 3.5 0.22 8.0 4.1
5.0 - 4.0 0.21 5.8 3.8

9.0 - 3.5 0.20 7.8 4.0

82

Table 12. "BRUTE" translation search solutions for the two
molecules A and B. (a): Search for molecule B
while molecule A is stationary. (b): Search for
molecule A with stationary B in the correct
position. (c): Final refined rotation and
translation parameters for molecules A and B.

a.

Highest correlation Correlation Peak height Height above

peaks (A) coefficient (0) the mean value

TX TY* TZ (a)
25.8 48.6 31.8 0.43 11.5 6.5
20.3 28.5 26.0 0.36 9.6 4.7

1.1 47.3 38.2 0.33 8.9 3.9

b.

6 2 49 0 11.3 0 42 ll 0 6 0
21.2 15.2 9.0 0.34 8.9 4.0
12.0 25.1 20.3 0.33 8.7 3.8

c.
Rotation angles Translation vectors
(deg.) (A)
o a y TX TY* TZ
Molecule A 313.62 142.80 186.88 6.2 0.0 11.3
Molecule B 109.77 149.77 158.77 25.8 48.6 31.8

* Only relative separation important due to arbitrary
nature of origin along the 21 screw axis in P21.

83
final refined rotation and translation parameters for

molecules A and B are listed in Table 12.

To verify the correctness of the rotation and
translation solutions, the two molecules were positioned
properly in the unit cell and displayed on an Evans and
Sutherland PS390 interactive computer graphics system
equipped with a stereographic screen using the program FRODO
[94]. All the symmetry related molecules within a radius of
40.0 A of the center of the unit cell were generated to
examine whether there was any unacceptable contact or
interaction between the moleucles. In practice, this is
equivalent to the packing function program used frequently
to determine the translation solution [80—81]. There were
very few short van der Waals contacts between neighboring
molecules, thus confirming the correctnes of the molecular
replacement solutions. The packing arrangement in the
crystal is described in Chapter IX. The molecules pack very
tightly which agrees with the excellent x-ray scattering
power of the crystal and its Vm value. Based on crystal
packing criterion alone, there would be exceptionally few
allowed molecular replacement solutions because of the

limited space availabe for the solvent (34%).

VI SYMMETRY AVERAGING

Using the refined orientational and positional
parameters, molecule A and B of kringle 4 were placed in the
monoclinic crystal. The non-conserved side chain atoms were
removed from the model of kringle l of prothrombin fragment
1 so as not to bias the starting model of K4. A set of
phases were calculated using the model. For the structure
factor calculation, 978 atoms were used of a total of 1352
atoms that are present in two molecules of kringle 4 (~72%)
with an overall temparature factor of 20 2. The
discrepancy index (R factor), between the observed structure

factor modulus, IFol, and the calculated structure factor

modulus, IFcI, at this stage was 45%.

A modified Wilson distribution was plotted to obtain
the overall scale factor (K) and the difference in
temparature factor (DB) between the observed and calculated
structure factor moduli. A. J. C. Wilson [95] had derived

the following equation
1n(Z|Fc|/£|Fo|) - an - AB (Sin28)/k2 ....(25)

where A is the wavelength of the x—ray radiation. If the
left hand side of the equation is evaluated for shells of 28
and the values plotted against sinze/kz, the result should
be a straight line in which the extrapolated intercept at
sin28 - 0.0 is In K and the slope is -AB. Since protein
crystals contain large amounts of mother liquor, and since

84

85
the low 28 reflections are influenced by the solvent, the
low angle reflections were excluded from the Wilson plot.
From the Wilson plot, the scale factor was found to be 77.4
and the AB value - -1.4 A2, thus confirming the overall B

value that was used for the structure factor calculation.

The crystallographic asymmetric unit of kringle 4
contains two molecules in intimate association with one
another. The transformation between the two molceulces can

be expressed as

X2

[C]X1 + d ....(26)

where each point X1 in molecule A is related to the point X2
in molecule B by a rotation matrix [C] and a translation
vector d. The rotation matrix [C] specifies the direction
of the rotation axis and translation vector d contains
information about the position of the rotation axis in the

unit cell.

In non-crystallographic symmetry averaging, which has
been used extensively in the structure analyses of virus
particles, the value of C and d are sought which minimize

the quantity
2

where p1 and p2 are the electron density values at the
points X1 and X2, respectively. The rotation matrix and the
translation vector were determined using the rotation

function and the translation function, as described in

86
Chapter V. These values were refined by the least squares

minimization of the equation 27.

Refinement of the transformation parameters between the
two molecules of kringle 4 in the asymmetric unit was
performed using a computer program written by Wayne
Hendrickson and Janet Smith. The 2.8 A resolution electron
density map calculated using the trial phases was used as
the starting map for refinement. An approximate molecular
boundary was defined so that during the refinement, only
those portions of the electron density which lie within a
radius of 15 A centered on the center of mass of molecule A
were used. The intermolecular solvent regions and portions
of the electron density associated with neighboring
molecules were thus partially excluded during the refinement

process.

The measure of agreement between the electron densities
of the two molecules was assessed in terms of a correlation

coefficient which can be expressed as
cc- 8( -' > < -‘ >/[2< —’ )2 2< -' )21‘5 (28)
pl p1 - 92 92 pl pl 0 92 92 00--

where pl and o2 are the electron densities of molecules A
and B, 51 and 52 are the average electron densities , with
the summations being taken over all points within the
molecular boundary defined above. For the case where the
two electron densities are exactly the same, CC would have a
value of 1.0. The correlation coefficient between the two

molecules using the initial transformation parameters was

87
0.77. The coefficient increased to 0.80 after five cycles

of refinement. The initial and final parameters are listed

in Table 13.

The position of the local two-fold axis can be derived
from these parameters and is shown in Figure 17. The
rotation axis intersects the Y axis at 0.74 and z axis at
0.23, given in fractional units of the crystallographic unit

cell.

88

Table 13. Results of non-crystallographic symmetry
averaging. The spherical polar angles 0, 0, and x
are defined according to Rossmann and Blow [47].
Xoffset, Yoffset, and Zoffset refer to the inter-
section of the rotation axis with the crystallo-
graphic a, b, and c axes respectively.

Initial parameters Final parameters
4' (deg.) -9.45 -8.49
w’ (deg.) 90.00 89.53
X (deg.) 180.00 180.00
Xoffset (A) 0.00 —0.12
Yoffset (A) 36.82 36.78
Zoffset (A) 11.55 11.62

Correlation
coefficient 0.767 0.797

89

 

 

 

Figure 17. A schematic diagram of the non—crystallographic

symmetry elements. The local two-fold axis
approximately parallel to the a* axis is shown
by dotted lines b‘-----) and the local two—fold
axis approximately parallel to the c* axis is
shown by broken lines ( ------ ). The crystallo—

graphic 2 screw axis is indicated by the
conventional symbol.

VII RESULTS

The building of a model of K4 structure started with
the symmetry averaged 2.8 A electron density map. The
unaveraged 2.8 A and 3.5 A maps were examined closely where
the averaged map had weak density and in the interkringle
tail regions of the molecule which are involved in crystal
packing interactions with neighboring molecules. The
modelling of the electron density maps was performed on an
Evans and Sutherland P5390 computer graphics using the
program FRODO. All the maps were contoured at l a level and
the amino acid residues were adjusted to fit the electron

density as well as possible.

Most of the residues have well defined side chains.
This was especially true for the larger side chains like
Tyr5, His6, Trp73, Met50, Tyr43, LysZ3, LysZ4, Tyr75 etc.,
(Figure 16) which are different from the smaller side chains
of the fragment 1 kringle. The electron density of the side
chains of Tyr5 and Trp73 are shown in Figures 18 and 19.
The presence of very good electron density for most of the
non-conserved side chains was another good indication of the
correctness of molecular replacement solutions. There was
reasonable density even in regions which have a deletion in
kringle 4 compared to fragment 1 kringle. The amino
terminal (3 residues) and the carboxy terminal (5 residues)
also have strong density though it is difficult to fit all
the side chains in these regions (Figures 20 and 21). The
carboxy terminal corresponds to density for only five
residues. Thus, it appears that only the fraction with the

90

91

 

Figure 18. Electron density of the side chain of Tyr5 of
molecule A ( contours at 1 a).

92

 

Figure 19. Electron density of the side chain of Trp73 of
molecule 8 (contours at 1 a).

93

R‘.
‘

-
‘
’I.
.0
. I

 

Figure 20. Electron density of the amino terminal of
molecule A (contours at 1 a).

Figure 21.

‘-
r

:1
.
' I
,
, .‘

vi."
’3‘

a‘ 'r ‘3 '
«aw

..v
.

Electron density of the carboxy terminal of
molecule B (contours at 1 a).

94

 

95
shorter interkringle tail which ends with Ala86
crystallizes; this fraction constitutes ~ 70% of the

kringle 4 mixture used in crystallization.

The Ramachandran plot of kringle 4 molecule A is shown
in Figure 22 from which it is very clear that the structure
conforms satisfactorily to the allowed conformational
regions. The Ramachandran plot of molecule B is very
similar to that of molecule A. A graphic illustration of
the structure emphasizing the secondary structural elements
of kringle 4 is shown in Figure 23. The structure is in
good agreement with the Chou-Fasman calculations of
secondary structure [96] which predict no helix, 37%
B-structure, and a high percentage of 8-turns(49%).
However, the implications of the ultraviolet circular
dichroism spectra of kringle 4 [96] does not agree with the
Chou-Fasman predictions and the structure observed
crystallographically. A comparision of the secondary
features as predicted by Chou-Fasman calculations, CD

spectra and the crystal structure is summarized in Table 14.

A. GENERAL CONFORMATION OF KRINGLE 4

The overall conformation of the polypeptide chain of
kringle 4 is very similar to that of prothrombin fragment 1
kringle [29,30]. The secondary structural features of
kringle 4 are listed in Table 15. The closed interkringle
loops (C and D, Figure 16) form two distinct antiparallel

chain segments due to the close contact of two disulfide

96

 

 

 

 

 

 

 

 

 

 

 

-:ao 90 0. 9a 180
I ,. 0r . 0 fl}\
'.. ..O ‘7 _
’I ' o' 3
‘ / ..e )‘|
'0 ' I
.1. l O. . '. '—
I l . _ I
' _J ' x;
eo.—« "'96
| u. I” I l
_,| I I I 1.
. ' I I I
l | I
.dk\ . I . ' II ' -
\ I . A \\ 'I
:3 'x- ‘l '5' \’
Q. 9 \( . . ‘\\ 9
e \_ ... \\
'— I) O ' ~—
P_- I I.
—-4' ' L—
F—_.o_-._-.J_.&_.a-.J (D
-50.-I G ---90.
._ G (9 __
_._._.__.. ...... L1
"9": ‘ I I I I I I I I I I I "39°
- I” '98. O. 30. I 80.
PHI

Figure 22. Ramachandran angles of kringle 4 (molecule A).
Allowed regions enclosed by dotted lines.
Circled residues Gly; outlier residues numbered.

97

 

 

Figure 23. Graphic representation of the folding of
kringle 4 emphasizing secondary structure.
The reverse turns labelled Tl-TlZ;
disulfide bridges indicated appropriately.

98

Table 14. Comparison of secondary structural features
of kringle 4.

Secondary Chou-Fasman CD spectra Crystal
structure prediction structure
(%) (%) (%)
a-helix 0 O 0
B-sheat 37 64 35
B-turns 49 30 50

random coil 14 6 15

Table 15.

99

Secondary structural elements of kringle 4.

A.

81

83

T1
T2
T3
T4
T5
T6
T7
T8
T9
T10
T11

C.

T12

B-structure

Ser17 CysZS
Thr18 LysZ4 82
Thrl9 Ly523
Arg54 Trp63 B4
Asn55 Pro62

Kringle B-turns

His6-Gly7-Asp8-Gly9

Gln36
Ser27
Trp28

Trp63
Cys64
Phe65
Thr66

Thr19-Thr20-Thr21-Gly22-Lys23

Ser27-Trp28-Ser29-Ser30
Thr32—Pr033-His34-Arg35
His36-Gln37-Lys38-Thr39
Thr39-Pro40-Glu4l-Asn42
Tyr43-Pro44-Asn45-Ala46
Thr49-Met50-Asn51-Tyr52

Asn55-ProS6-Asp57-Ala58-Asp59

Asp59-Lys60—Gly61-Pro62
Asp68-Pro69-Ser70-Val7l

Other B-turns

Ser82—Gly83-Thr84-Glu85

AsnSl
Met50
Thr49

Tyr75
Glu74
Trp73
Arg72

100
bridges in the folded state; one produces a short stretch of
two—strand antiparallel B-structure in the D loop (84,
Table 15) linked to a strand of the C loop (83, Table 15).
A more liberal assignment of B—structure could expand the
regions to include : Tyr52-Asn55, Pro62-Thr66, Trp73-Asn77
(Figure 23). These surround CysZS-Cys64 and CysS3—Cys76 and
display practically absolute residue conservation among 11
kringle sequences (Table l). The sulfur atoms of disulfide
bridges CysZS-Cys64 and CysSB-Cys76 make unusually close
van der Waals contacts, which produce a sulfur cluster not
far removed from the center of gravity of the kringle
structure (Figure 23) [30]. The two loop structures (C and
D) appear to provide the nucleus of the kringle folded
structure [30] which is also consistent with the aerobic
restoration of these disulfide bridges in reduced kringle 4

with concomitant refolding [97].

The segments A and B of the outer kringle sequence,
which differ in length by seven peptide units, display a
similar three-dimensional conformation. The A and 8
segments each fold into two antiparallel open loops. The
initial residues of segment A (near Cys4-Cys81) appear to
mimic the folding of the antiparallel inner loop C and stack
adjacent to it while those of B (near CysZS-Cys64) copy D
and stack with it (Figure 23). This gives rise to a pair of
stacked duplex loop structures that are approximately
related to each other by two independent 90 rotations and a
translation. Thus the overall three-dimensional structure

of the kringle appears to be the result of an intricately

101
duplicated folding pattern [30]. The overall shape of the
kringle structure resembles that of a highly eccentric

oblate ellipsoid of approximate dimensions 20 x 28 x 30 A

[29].

The kringle structure appears to contain about 11
reverse turns (Table 15) of varying degrees of sharpness.
Of these, four make up two larger, slower turns (T6-T7, and
T9-T10). In addition, the carboxy terminal has a sharp turn
(T12, Table 15). Thus it appears that about half of the
kringle residues concern themselves with turns, of which
one-third are conserved among 11 kringle sequences
(Table 1). The relatively small fraction of the
B-structural features of the kringle fold may be due to the

large number of turns [29].

The path of the main chain in the kringle structure
starts with a turn from His6 to Gly9 (T1), similar to the
prothrombin fragment 1 kringle structure [29]. A 15 A
stretch of more or less extended chain follows from
Serll-Ser17 and runs approximately parallel to Asn45-Asn51
at a seperation of about 6.0 A. The structure then forms 81
from Ser17 to Cys24 (Table 15), which was interpreted as two
antiparallel strands with T2 at the turn. A short
antiparallel contact is made at b2 (Table 15) immediately
followed‘ by T3 which leads to a large loop. The latter
extends from Trp28-Gln37 with T4 effecting the turn. The
main chain then enters into a complicated curve region (T5,
T6, and T7). Of these the curves T6 and T7 are sharp and

similar to the curves T5 and T6 of fragment 1 kringle [29].

102
This part of the structure embodies most of the 8 segment of
the kringle sequence, which is the longest of the four
segments. A short piece of chain (Ala46-Thr49) runs
antiparallel to Tyr52-Pro56 at about 7.0 A seperation in
this region with a turn T8 in between. This is followed by
the curves T9 and T10 which carry some of the residues
implicated in lysine binding. The structure then enters
into the B3 and 84 regions (Table 15) which contain super
conserved residues many of which are aromatic. The T11 turn
produces the 84 structure. Finally the kringle 4 structure
concludes with another sharp turn (T12) in the carboxy

terminal interkringle tail.

B. DIFFERENCES BETWEEN THE TWO INDEPENDENT MOLECULES

The crystallographically independent kringle 4
molecules are engaged in quite different molecular contacts.
The transformation giving the optimal superposition of

molecule B (X2,Y2,ZZ) on molecule A (Xl,Yl,Zl) is

X2 - 1.0117 0.0142 -0.0702 X1 0.589
Y2 - 0.0138 -O.9999 0.0005 Y1 + 73.683 ....(29)
22 - 0.3018 0.0021 -l.0105 21 23.652

In Figure 24, the Ca structures of molecules A and B
are optimally superimposed and presented in the orientation
originally used to discuss the prothrombin fragment 1
kringle [30]. The the r.m.s deviations of homologous
a-carbon atoms of molecules A and B are plotted against the

residue number in Figure 25.

103

 

Figure 24. a-carbon drawing of the kringle 4 molecule A
(blue) optimally superimposed on molecule B
(amber).

104

.m can < measuoaos mo
meoum conumolo Hmoaucmnfi >Hamoflsmco ecu coosuon accuuod>oc m.e.u .mm musmfim

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106

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105

From Figure 24 the similarity of the independent
kringle 4 molecules is clearly evident. Only four segments,
from H156 to Asp8 (b-turn Tl, Table 15), Thr21 to Ly524,
Thr32 to Tyr43, and Val71 to Trp73 show considerable
deviations of their main chain atoms. In addition, there
are some differences between the two molecules in the amino
terminal and carboxy terminals. The r.m.s deviation of the
homologous main chain atoms of the two molecules is 0.70 A.
For all the atoms except the two terminal segments
(Vall-Asp3 and Gly83-Ala86), which are different in the two
molecules, the r.m.s deviation is 1.90 A. Residues Thr21,
LysZ4, Thr32, His36, Gln37, Asp59, and Arg72 exhibit the
largest deviations. The conformational differences of the
main chain segments in both the kringle 4 molecules must be
due to different crystal contacts, since most of the residue
segments described above are involved in intermolecular
contacts. The packing of the molecules in the crystal

lattice is described in Chapter IX.

Relatively large deviations are found near Tyr43,
probably caused by different intermolecular contacts. As a
consequence, Tyr43 is well defined from the electron density
in molecule A, but only partially in molecule B. It is
interesting to note that this residue is part of the B
segment (Figure 16) where insertions or deletions occur
frequently in kringle sequences (Table 1), thus suggesting a

'soft' property.

The side chains of the two molecules exhibit more

differences. A qualitative comparision of the electron

106
density around some of the side chains which show
differences between the two molecules is listed in Table 16
while Vall, Lys79, and Ser82 are not well defined in either
of the two molecules. Apart from this and those in
Table 16, all other side chains have good density in both

the molecules.

C. COMPARISON OF K4 WITH K1

In general, the kringle 4 models are very similar in
overall conformation to the refined prothrombin fragment 1
kringle [29]. The largest main chain deviations are
observed in the segment Ala58-Gly61. It is interesting to
note that in kringle 4 there is a deletion in this region
compared to the fragment 1 kringle. This region embodies
Asp59 which has been implicated in lysine binding of
kringle 4 [9]. Relatively large deviations also occur in
the segment HisB6-Thr39. Further, main chain deviations
between the K4 molcule A and K1 occur around residues
His6-Arg13, Hi534, Gln41-Tyr43, Trp73, and Lys79-Lys80 while
molecule B differ largely around the residues Thr32, Asn45,
Asp57, and Ser70. The carboxy terminal interkringle tail of
kringle 4 folds similar to the folding of the interkringle
tail of fragment 1 structure [29]. The overall r.m.s.
deviation of all main chain atoms, excluding the segment
58-61, between K4 and K1 is 0.95 A and 0.83 A for molecules

A and B respectively.

107

Table 16. Differences in side chain electron density

between the independent molecules A and B.

Side chain Molecule A Molecule B
Gan No density Good
Asp3 Good No density
His6 Good Weak
Arng Weak Good
Thr20 No density Good
Gln26 Weak Good
Ser29 Weak Good
Ser30 Weak Good
Pr033 Good Weak
Gln37 Good Weak
Glu4l No density Good
Tyr43 Good Weak
Asn55 Good Weak
Asp59 Weak Good
Lys60 Good No density
Ser70 No density Good
Trp73 Weak Fair
Thr84 No density Fair
Glu85 No density Fair

VIII LYSINE BINDING SITE OF KRINGLE 4

It has been postulated that plasmin(ogen) and some of
the kringles attach to blood clots by interacting with
lysine side chains exposed in the polymerized fibrin
matrix [13,20]. This is based on affinity chromatography
studies which show that plasminogen and at least some of its
kringle containing proteolytic fragments bind strongly to
lysine-conjucated support gels and can be efficiently eluted
with lysine and with other w-amino carboxylic acid lysine
analogs [6,98-99]. It has also been shown that the
w-aminocarboxylic acid binding sites of plasminogen are
involved in fibrin binding since fibrin-plasminogen

interaction is decreased by w-aminocarboxylic acids [13].

The three main elastase fragments of plasminogen,
kringle 1+2+3, kringle 4 and miniplasminogen(kringle 5+
light chain) were all shown to have affinity for fibrin
polymer [6]; the strongest fibrin binding site was located
on the kringle 1+2+3 fragment [6]. The fibrin-binding of
all three fragments was decreased by 6-aminohexanoic
acid [13]. This decrease was most pronounced with
kringle 1+2+3 [13]. Later, it was shown that the fibrin
binding site of the kringle 1+2+3 fragment resides on the
kringle 1 domain [6] which also binds very strongly to
plasminogen activation peptide, a potential effector of
fibrinolysis activity. The fibrin-binding of kringle 4, on
the other hand, is relatively weak, though it binds very
strongly to lysine analogs [13]. Kringle 4 also has a
relatively weak anti-plasmin binding site [13].

108

109

Because of their apparent roles in the regulation of
fibrinolysis, the lysine binding sites have been the subject
of a number of studies in recent years. Several
investigations of the ligand specificity of the lysine
binding sites have revealed the nature of the various
residues involved in ligand binding. In the case of
kringle 4, it has been shown that the residues Asp57, Asp59,
Trp63, Phe65,Arg71, and Trp73 are either involved in ligand

binding or are close to the binding site [9,24,27,32].

The lysine binding region is located on the surface of
one of the oblate faces of the kringle, bounded by the
residues 34-38,56-60,62-65, and 72-76 (Figure 26) [31-32].
This region essentially corresponds to the inner loop of the
kringle sequence (Figure 16). The site is below the three
dimensional loop formed by the C segment of the inner
kringle loop and runs parallel to the antiparallel B-strand

loop formed by the D segment [31].

The binding site can be described as a relatively
shallow depression, with cationic and anionic centers that
extends from the Pro56-Ly560 peptide stretch which contains
the A5p57 and Asp59, to a short segment where Arg72
neighbors Hi534 (Figure 26) [32]. The depression is lined
by Trp63 near the Asp57-Asp59 stretch, which is consistent
with the observed acid/base titrability of the Trp63 indole
H2 singlet [25]. The depression is lined with Phe65 near
the Arg72/Hi534 positively charged end. The indole ring of
Trp73 is very close to the site on one side of the

depression and is in a very favorable position to interact

110

 

Figure 26. Lysine binding site of kringle 4 (molecule B).

111

with the hydrophobic part of the ligand [32]. It is
interesting to note that the 0G of the side chain of Tyr75
points towards the negatively charged end of the binding
site, as shown previously by high field NMR experiments
[32]. The three side chains Trp63, Phe65, and Trp73, thus
expose a lipophilic surface which seperates the protruding
anionic and cationic centers defined by residue pairs
Asp57/Asp59 and HisB4/Arg72, respectively (Figure 26).
These cationic and anionic centers can bind to the
complementary polar end groups of the w-aminoacid ligand
[9,100]. The distance between the charges is consistent
with a ligand of dipole length ~6.8 A being optimal in terms
of ligand binding [98].

It has been shown by NMR experiments that the presence
of aromatic or aliphatic ligands induce large shifts in the
ring resonances of several aromatic residues
[23-24,101-102]. In the case of kringle 4, Trp63, Phe65,
and Trp73 are the most perturbed by ligand presence [32].
This is in excellent agreement with the crystal structure;
these are the aromatic residues which form the lipophilic
surface in ligand binding (Figure 26). The ligand can be
visualized as lying on the depression in an extended
conformation [32]. Then it can interact very closely with
the aromatic side chains mentioned above. It has been shown
that the side chain of Hi534 which is very near Arg72 in the
crystal structure also undergoes significant perturbation on

ligand binding [32].

112

Somewhat removed from the center, but still an integral
part of the binding pocket are Trp27 and Tyr75. The side
chain of Trp28, besides lying proximal to Trp63, also
establishes good contact with Leu48. It has been proposed
that Leu48 centers at a hydrophobic core which is adjacent
to, but not directly a part of the lysine-binding site
[23,101]. It is very clear that the Trp28 indole group
seperates Leu48 from the rest of the aromatic side chains at
the binding site. The aromatic residues Tyr52 and Tyr43 are
at the periphery of the binding site and this is in
agreement with NOE experiments where it was shown that the
resonances of these two residues are perturbed only slightly
in presence of ligands [32]. These two aromatic residues
also interact with Leu48, again in agreement with NOE
experiments [23]. Residues Gln37, Lys38, and ProS6 are also
in the vicinity of the binding site. The aromatic residues
Tyr5, His6, and Tyr12 are further removed from the binding
site. This has been suggested earlier based on NMR studies
where the spectra of these residues are practically

insensitive to ligand binding [32].

The binding site is relatively open and exposed,
allowing for facile ligand access [32]. The feature is
consistent with recent estimates of association rate
constants for linear and cyclic ligands, suggesting that the
kringle 4 complexation kinetics are essentially diffusion
controlled [102]. This picture of the kringle 4
lysine-binding site is in agreement with a model of ligand

binding to kringle 1 [34]. In kringle 1, the residues

113
Trp73,His34, and Hi536 are replaced by Tyr73, Arg34, and
Phe36 respectively. Based on NMR experiments, and the
crystal structure of the kringle of prothrombin fragment 1,
it has been suggested that all three residues mentioned
above participate in ligand binding in kringle 1 [34]. Thus
it appears that in kringle 1, residues outside the inner
loop segment also participate in ligand binding, unlike
kringle 4. This suggests that although the binding site is
conformed by a fixed set of residues, there appears to be
some flexibility in ligand binding. The ligand binding
affinity of kringle 1 is about twice as large as that for
kringle 4 [21,100,103]. This could be due to the presence
of ArgB4 in kringle 1 which, along with Arg72, can provide a
stronger cationic center towards various ligands [34]. The
evidence for the participation of ArgB4 in kringle 1 comes
from chemical modification studies where it has been shown
that modification of Ar934 with 1,2 cyclohexanediol
abolishes both fibrin and lysine binding [11]. The area
centered around His34 in kringle 4 may not be very important
for lysine binding as glycosylation of Asn34 in kringle 4 of
chicken plasminogen seems to have no effect on ligand

binding [34-35].

A space-filling representation of the fibrin/lysine
binding site of kringle 4 is shown in Figure 27. In this
drawing, carbon atoms are a light grey color, oxygen atoms
red, nitrogen atoms blue, and the sulfur atoms yellow. The
most conspicuous aspect of this drawing is the segregation

and apparent immiscibility of oxygen and nitrogen atoms

114

 

Figure 27. Space-filling view of the lysine binding site
of kringle 4 (molecule B). The following color
codes have been used for the atoms: carbon,
light grey; nitrogen, blue; oxygen, red;
sulfur, yellow.

115
surrounding the binding site on the surface [31]. The
carboxylate group of the ligand can interact with the
electropositive portion of this dipolar surface near the
guanidinium group while the amino terminal of the ligand is
near the negatively charged carboxylate groups Asp57/A5p59
of the protein [31]. The aromatic side chains of kringle 4
can then interact with the neutral methylene groups of the
ligand. The dipolar surface could be of functional
significance in recognizing at long range the marker of the
fibrin ligand site and in aiding in the approximate
orientation and alignment of the kringle [31]. This would
lead to a better defined interaction upon close approach to
fibrin and could also be a major contributing factor to the
resultant stability of interaction of the docked

fibrin-kringle complex.

As described in Chapter I, a model has been proposed
for the lysine binding site of kringle 4 based on the three
dimensional structure of kringle l of prothrombin fragment
1, high field NMR experiments and enery minimization [31].
The lysine binding site of the modeled kringle 4 and the
binding site from the crystal structure are shown in
Figure 28. It can be clearly seen that there is very good
agreement between the model and the actual structure as
observed crystallographically. The largest difference is in
the orientation of Trp73. The side chain of Trp73 in the
predicted model lies with the aromatic ring flat in the
depression while in the crystal structure it is towards one

side of the binding site. Apart from this Trp73, most of

116

 

Figure 28.

Comparision of the lysine binding sites.
Left: Lysine binding site from the present
study. Right: Lysine binding site from the
modelling study (from [31]). In the model,
the ligand e-aminocaproic acid is also
shown (white).

117
the other side chains near the binding site are in the same
orientation and position in the predicted model and in the
crystal structure. This is especially true for the residues
Trp63, Phe65, Asp57, Asp59, Arg72, Tyr75, and Hi534, which
have been implicated in lysine-binding. The residues ArgBZ,
LysGO, and Lys35 which are away from the model also seem to
have a different orientation in the model and the crystal

structure.

IX CRYSTAL PACKING

The monoclinic crystal form of kringle 4 contains four
molecules per unit cell or two crystallographically
independent molecules per asymmetric unit. A schematic
drawing of the four molecules in the unit cell is shown in
Figure 15. The crystallographic 21 screw axis is shown by
the conventional symbol and the non-crystallographic
symmetry elements are indicated by the dotted lines. From
an examination of the molecular arrangement in the crystal
lattice (Figure 15), each independent kringle 4 molecule
makes close contact with two other kringles giving rise to a
three dimensional net work. This might be of relevance in
kringle-kringle interactions in plasminogen which contains
five kringles [4] and in apolipoprotein(a) which has 37
copies of kringle 4 and one copy of kringle 5 [5]. The
molecular packing also gives rise to two "dimer"

possibilities.

As described earlier in Chapter V, the choice of the
asymmetric unit is quite arbitrary and since each kringle is
in contact with two others, two different kinds of "dimers"
are possible (Figure 15). Molecules A and B are related to
one another by a non-crystallographic two fold axis. The
axis is approximately parallel to the a* axis. These two
molecules are shown in Figure 29, viewed perpendicular to

the non-crystallographic two fold axis.

In this "dimer", the maximal interaction between the
two independent molecule involves the interkringle tail

118

Figure 29.

 

Ca, C, N main chain atoms of the two
independent molecules A and B of the
A—B "dimer". Non—crystallographic
2-fold rotation axis indicated.

120
portion and the segment GlnlO-ThrlS. The latter segment of
molecule A participates in interactions with the
corresponding residues of molecule B at the dimer interface.
These residues are part of the flexible outer A segment of
the kringle fold (Figure 16). This is very similar to the
crystal packing of the kringle of fragment 1 where the
majority of close contacts with neighboring molecules in the
crystal involve the A loop [29]. In kringle 4, the amino
terminal of molecule A is also involved in interactions with
the amino terminal and the A loop of molecule B. The
intermolecular contacts (less than 3.2 A) at this dimer
interface are listed in Table 17. The close packing of the
two molecules can be seen from the space-filling

representation shown in Figure 30.

Another kind of "dimer" is also possible. In this
"dimer", the two molecules A and B' are related by an
approximate rotation of 180 degrees, followed by a
translation of about 22.0 A along the c axis (Figure 15).
This pseudo-screw axis runs almost parallel to the c axis
of the crystal cell and intersects xy plane at x-
15.5/32.8 A and y- 25.5/49.2 A. The translational component
of 22.0 A is slightly less than one-half of the length of
the c axis (0.48). Thus the packing of kringle molecules in
the monoclinic crystals is of psuedo orthorhombic P22121.
The intensity of the reflections with l-odd along the c axis
is generally weak compared to the even integer reflections,

as expected from such a packing arrangement described above.

 

121
Table 17. Intermolecular contacts at the A-B "dimer"

interface (< 3.2 A) and the possible
interaction(s).

Molecule A Molecule B Distance Possible

(A)
Vall N Glu10 O 2.81 H-bond
Vall CB Asn45 NDZ 3.12
Glu2 N Serll CA 2.99
Glu2 O Serll O 2.90 H-bond
Glu2 CB Serll CB 2.81
Serll CA Vall C62 3.16
Arg13 O Arg13 O 2.79 H-bond/local
2-fold interaction
Arng 0 Glu14 CA 2.53 local 2-fold
interaction
Arg13 CB Asp3 N 3.02
Argl3 NHl Thr15 O 2.40 H-bond
Glul4 CA Argl3 O 2.53 local 2-fold
interaction
Glul4 C Arng 0 2.93
Thr15 OGl Arg54 NHZ 3.11 H-bond
Met50 CE Tyr52 OH 3.03
Tyr52 OH Tyr52 OH 2.74 H-bond/local

2-fold interaction

122

 

Figure 30. Space-filling view of the two independent
molecules A and B of the A-B "dimer".
Orientation same as Figure 29.

 

 

123

The "dimer" between A and B' is shown in Figure 31 from
which it can be seen that it is the outerloop segment B and
the innerloop segment D which are involved in intermolecular
interactions. There are very few short contacts involving
the A and C segments of the kringles (Figure 16). The
segment Ser29-Pro33 of the B loop of molecule A is involved
in interactions with Gly22-Ly523 (A loop), Thr67-Asp68 (D
loop), and Pro40-Asn42 (B loop) of molecule B'. All these
residues belong to 8-turns of the kringle structure
(Table 15). The residues Thr67-Asp68 of the D loop of
molecule A are also involved in interactions with the
segment Thr39-Pro40 of the 8 loop of molecule B'. All
intermolecular contacts at this dimer-interface which are
less than 3.2 A are listed in Table 18. A space-filling
representation of this "dimer" is shown in Figure 32. The
very tight packing of the molecules (66% protein fraction)

can be clearly seen from Figure 32.

From the Tables 17 and 18 and the Figures 30 and 32, it
is clear that in both the "dimeric species", there are many
close contacts. Some of these interactions involve atoms
which usually participate in hydrogen bonding. From Tables
17 and 18, it would suggest that the "dimer" A-B would have
a better binding energy as it involves many more such
interactions and the non-crystallographic relationship is a
prOper two-fold rotation which is fairly well known. On the
other hand, the arrangement of kringles with a translation
component in addition to a two-fold rotation might afford

very efficient packing and favorable interactions in large

 

Figure 31.

124

Cu, C, N main chain atoms of the two
independent molecules A and B' of the
A-B’ "dimer". Non-crystallographic
symmetry element (approximate 21 screw
axis) indicated.

 

 

Table 18.

125

Intermolecular contacts at the A-B' "dimer"
interface (< 3.2 A) and the possible
interaction(s).

Molecule A Molecule B' Disiance Possible
Thr21 O Ser30 OG 3.19 H-bond
Gly22 O Ser29 O 2.99 H-bond
LysZ3 N Ser29 O 2.73 H-bond
Ly523 CA Ser29 O 2.30
LysZB CA Ser29 C 2.92
Lys23 CB Ser29 CB 3.01
Ly523 CB Ser29 OG 3.20
LysZ3 CG Ser29 CO 2.60
Ly524 NZ His36 O 3.10 H-bond
LysZ4 NZ Glu4l 0E2 3.60 ion pair
Ser27 OG Glu4l OEl 2.50 H-bond

Thr67 O Pro40 CG 2.60

 

126

 

Figure 32. Space-filling view of the two independent
molecules A and B’ of the A-B' "dimer".
Orientation same as Figure 31.

 

127
multi-kringle arrays such as occurs in apolipoprotein(a).
At this stage, however, it is still difficult to reconcile
the dimeric species described above to relevant
kringle-kringle interactions in physiological systems. On
the other hand, it is clear that the "dimers" will serve as
models for the latter until a multi-kringle structure is

determined.

In addition to the dimer interactions, there are a
large number of contacts with neighboring molecules in the
three dimensional crystal lattice. A schematic of the
crystal packing is shown in Figure 33 with the symmetry
elements and their positions indicated appropriately. In
the case of molecule A, all the four loop segments (A,B,C,
and D; Figure 16) are involved in interactions with
neighboring molecules and the carboxy terminal of molecule A
is also involved in packing interactions. In the case of
molecule B, the residues from the outer loop segment B are
involved in most of the interactions. In addition, other
contacts occur between molecules A and 82, A' and B, A' and

A2, A and A2 and B and B'.

128

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1:02 .v mamcoux no mooxoma Hmum>uu uo owumsmoom .mm ossmom

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b

 

 

 

 

 

 

 

 

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