Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations

1990 The 5Å esolutr ion crystal structure of adenylosuccinate synthetase from Escherichia coli Michael Alan Serra Iowa State University

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Recommended Citation Serra, Michael Alan, "The 5Å er solution crystal structure of adenylosuccinate synthetase from Escherichia coli " (1990). Retrospective Theses and Dissertations. 11220. https://lib.dr.iastate.edu/rtd/11220

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The 5Â resolution crystal structure of adenylosuccinate synthetase from Escherichia eoli

Serra, Michael Alaji, Ph.D.

Iowa State University, 1990

UMI 300N.ZeebRd. Ann Arbor, MI 48106

The 5Â resolution crystal structure of

adenylosuccinate synthetase

from Escherichia coli

by

Michael Alan Serra

A Dissertation Submitted to the

Graduate Faculty in Partial Fulfillment of the

Requirements for the Degree of

DOCTOR OF PHILOSOPHY

Department: Biochemistry and Biophysics Major; Molecular, Cellular, and Developmental Biology

Approved:

Signature was redacted for privacy.

In Charge of Major Work

Signature was redacted for privacy.

For the Majo^VDepartment

Signature was redacted for privacy. For the Graduate College

Iowa State University Ames, Iowa

1990 i i

TABLE OF CONTENTS

Page

DEFINITIONS iv

ABBREVIATIONS v

INTRODUCTION 1

Properties of the Synthetase from Escherichia coli 3

Mechanism 4

Role in Disease 6

Cancer 6

Hyperuricemia and gout 7

Malaria 8

Inhibitors of Therapeutic Importance 9

Long Range Goals 11

Present Study 12

CRYSTALLIZATION AND CHARACTERIZATION OF THREE CRYSTAL FORMS 13

Enzyme Preparation 13

Growth of the P2i and the P2i2j2]^ Crystal Forms 13

Crystalline Enzyme-Ligand Complexes; Soaking Experiments 16

Crystalline Enzyme-Ligand Complexes: Growth of the P3i21 (P3221) Crystal Form 16

Space Group Determination 18

Determination of the P2i crystal form 18

Determination of the ?2i2i2i crystal form 20

Determination of the P3i21 (P3221) crystal form 21

Results and Discussion 28 i i i

STRUCTURE DETERMINATION OF THE P2i CRYSTAL FORM TO 5.0À RESOLUTION 32

Introduction 32

Phase Problem 36

Isomorphous replacement 37

Anomalous scattering 39

Materials and Methods 43

Crystallization 43

Crystal manipulation 44

Data collection 46

Data processing 49

RESULTS AND DISCUSSION 72

Stabilization Buffer 72

Heavy Atom Derivatives 74

Patterson Map 78

Rotation Function 80

Electron Density Map 87

APPENDIX: STRUCTURE OF l-(p-NITROBENZYLIDINEAMINO) GUANIDINIUM CHLORIDE 102

Abstract 102

Introduction 102

Experimental 104

Discussion 105

REFERENCES 112

ACKNOWLEDGEMENT 118 iv

DEFINITIONS

x,y,z fractional coordinates; for atomic positions a,b,c unit cell edge vectors parallel to the X, Y, and Z axes of a right handed coordinate system a*,b*,c* reciprocal unit cell vectors associated with the X, Y, and Z axes of a right handed coordinate system a,b,c unit cell edges in direct space a*,b*,c* unit cell edges in reciprocal space r direct space vector; r = ax + by + cz h reciprocal space vector; h = ha* + kb* + Ic*

F(h) structure factor for the hth reciprocal space vector referred to one unit cell

F*(h) the conjugate vector of F(h)

F(h) modulus or amplitude of any vector F(h)

f atomic scattering factor

a, (3. Y angles between pairs of unit cell edges be, ac, and ab respectively V

ABBREVIATIONS

AMP adenosine 5'-monophosphate

ATP adenosine 5'-triphosphate

IMP inosine 5'-monophosphate

GMP guanosine 5'-monophosphate

GDP guanosine 5'-diphosphate

GTP guanosine 5'-triphosphate

HEPES N-2-hydroxyethylpiperazine-N'-2- ethanesulfonic acid

MPD 2-methyl-2,4-pentanediol

PEG 3350 polyethylene glycol, approximate molecular weight of 3350 pi isoelectric point 1

INTRODUCTION

Adenylosuccinate synthetase catalyzes the first committed step toward the ^ novo biosynthesis of AMP (Figure 1). Adenylosuccinate is formed from the ligation of IMP and aspartate with the concomitant hydrolysis of GTP to GDP and P^. Adenylosuccinate lyase then cleaves adenylosuccinate releasing fumarate and AMP. Adenylate kinase transfers a high energy phosphate from ATP to AMP to produce two molecules of ADP.

Finally, ATP is produced from ADP and P^ by oxidative phosphorylation in animals and by photophosphorylation in plants.

OOCCHaÇHCOO- NH L-aspartate.

GDP + PI Adenylosuccinate ribose-5'-P ribos6-5'-P synthetase

Adenylosuccinate Inosine 5'-monophosphate

Figure 1. The reaction catalyzed by adenylosuccinate synthetase

Adenylosuccinate synthetase also participates in the purine nucleo­

tide cycle (1,2). This cycle (Figure 2) involves the interconversion

of IMP, adenylosuccinate and AMP and is thought to play a number of

regulatory roles including: 1) the liberation of ammonia from amino

acids via aspartate, 2) regulation of adenine ribonucleotides, 3)

regulation of phosphofructokinase activity and glycolysis via changes in

AMP and ammonia levels, 4) regulation of phosphorylase b which is 2 activated by IMP, and 5) replenishment of citric acid cycle intermediates in tissues that do not have pyruvate carboxylase. " ribose-5'-P IMP

L-aspartate ^ / NH/ Adenylosuccinate synthetase f AMP deaminase

/ ^ GDPGDF + Pi

OOCCHgCHCOO" NH NHg fumarate

6) adenylosuccinate "<ï> lyase ribose-5'-P ribose-S'-P

AMP Adenylosuccinate

Figure 2. The purine nucleotide cycle

The enzyme has been isolated from plant (3), animal (4), and bacterial systems (4). The synthetase is believed to be enzymatically active as a dimer with typical dimeric molecular weights of 90,000 to

110,000 daltons (5-7). The enzyme from all sources requires a divalent cation for activity (7-11). Magnesium is the best activator, but Mn2+ 3 and Ca2+, and in some cases Co2+, Ba2+, and will substitute with decreased activity.

Matsuda et al. (6) reported the isolation of two isozymic forms of adenylosuccinate synthetase. Later studies in chicken (12) and in healthy tissues of rat and rabbit also revealed only two distinct forms

(8,13). They are distinguished by their isoelectric points. The acidic

isozyme (pl=5.9) predominates in the brain, kidney, and spleen (6) and

is believed to be involved primarily with ^ novo biosynthesis. The

basic isozyme (pl=8.9) is found predominantly in skeletal and cardiac

muscle and its primary role appears be the purine nucleotide cycle

(1,2). The liver contains roughly equal amounts of both (6).

This dissertation will concentrate on the structure of the

synthetase isolated from Escherichia coli. A comprehensive review of

the regulation, genetics and properties of the synthetase from various

sources has been published (4).

Properties of the Synthetase from Escherichia coli

The synthetase from E. coli exists as a dimer with a molecular

weight of 96,000 Da (14). The amino acid sequence has been determined

(15). Post translational processing cleaves the N-terminal methionine

leaving 431 amino acids in the polypeptide chain. Little homology

exists between adenylosuccinate synthetase and other GTP binding

proteins. This suggests the possibility of a unique nucleotide fold.

The enzyme from ^ coli most closely resembles the acidic isozyme from

mammalian tissues. 4

Mechanism

COO- 0

fO_H- "OOCCHgCHCOOr B| 0 ^ 09 NH £-L-osp-GTP'IMP^= E-GOP-N'^N^ -L-asp^z^GDPPj-E- N^N.

c R5P , R5P % //h

'OOCCHgÇHCOO" -OOCCHpCHCOO" -O^NH. r., -HO,P., I .ST.. St»-.

ÂSP 5} ' R5P

Figure 3. Three different reaction mechanisms proposed for adenylosuc­ cinate synthetase. This figure is taken from reference 4

Initial rate kinetic studies from a variety of sources (10,12,16-18) are consistent with a sequential mechanism involving the random binding of the three substrates followed by the random release of products.

More recent evidence, which is discussed below, suggests that there may be a preferred, but not strict, order of binding. The details of the mechanism; however, have not been fully described and are a subject of some controversy (Figure 3). Miller and Buchanan (19) suggested a concerted mechanism requiring simultaneously the presence of aspartate,

IMP and GTP (scheme A). In contrast, Lieberman (8) and Fromm (20) proposed the formation of a 6-phosphoryl-IMP intermediate followed by 5 nucleophilic displacement of the phosphate by the amino group of L- aspartate (scheme B). Finally, Markham and Reed (21), on the basis of studies of the enzyme from Azotobacter vinelandii, suggested a 3 step reaction pathway, the first step being the nucleophilic addition of L- aspartate onto the 6 position of IMP (scheme C). The second step in­ volves the phosphorylation of the 6-hydroxyl group of the intermediate from step one. The phosphorylated intermediate then breaks down spontaneously to give adenylosuccinate.

Two lines of experimental evidence support the hypothesis that

6-phosphoryl-IMP is an intermediate in the reaction catalyzed by adenylosuccinate synthetase. With positional isotope exchange Bass et al. (22) observed the exchange of 0^® from the 3 - y bridge position of

GTP to the g nonbridge position in the presence of enzyme and IMP. The

presence of aspartate was not necessary for exchange to occur. Using

the more sensitive technique of equilibrium isotope exchange, Cooper et al. (23) observed slower exchange rates for IMP and GTP. This result suggests a forward binding mechanism containing a preferred path in which the quaternary complex is most often formed by aspartate binding

to the enzyme-GTP-IMP complex. Furthermore, the similar exchange rates of IMP and GTP suggest that such an interaction simultaneously commits

both nucleotides to product formation. This observation supports the

formation of a phosphoryl-IMP intermediate before nucleophilic attack by

aspartate. 6

Role in Disease

Adenylosuccinate synthetase plays a vital role in the metabolism of adenine nucleotides. Altered activity of the enzyme can have deleter­ ious effects on an organism. Also, the synthetase may be used by certain parasites to aid their growth. Extensive studies suggest several possible roles of the synthetase in disease.

Cancer

The activity of adenylosuccinate synthetase increased 1.6 to 3.7 fold in a variety of tumors studied in the rat (24). These changes were not linked with growth rate or with age as activity in regenerating liver was not significantly different from normal liver and neonatal liver showed less activity than did adult liver. Thus, the elevated activity of the synthetase in rat liver and kidney tumors is thought to be linked with neoplastic transformation.

Synthetase from tumor cell li.ies show altered kinetic parameters as compared to the enzyme from healthy cells. Novikoff ascites tumor cells showed a significantly higher for aspartate and an elevated Kj for

AMP as compared to the enzyme from rat liver (25). These changes signal an alternate form of regulation of adenylosuccinate synthetase in the tumor. The altered Kj for AMP indicates the enzyme could operate at a higher flux since AMP is a feedback inhibitor. The physiological sig­ nificance of the high for aspartate is not well understood.

Matsuda et al. (26) were able to distinguish two forms of the syn­ thetase from Yoshida sarcoma ascites tumor cells. One form came from the crude fraction of purification and had an isoelectric point of 5.0. 7

The purified enzyme had an isoelectric point of 5.9. The crude fraction had markedly lower Michaelis constants for aspartate, IMP, and GTP sug­ gesting that the enzyme at this stage of purification should be more efficient at purine production than the purified enzyme. A compound called the pl-converting factor was eventually isolated which could cause the conversion of the pi 5.9 enzyme to the pi 5.0 form. Further characterization of the compound demonstrated it had DNA-like prop­ erties.

Studies were conducted on seven enzymes of the purine ^ novo bio- synthetic pathway using healthy and cancerous tissues of the rat and human kidney (27). The activities of three enzymes, adenylosuccinate synthetase, adenylosuccinate lyase, and adenylosuccinate deaminase, were significantly higher in cancerous versus healthy tissue. The elevated activities appear to be linked to neoplastic transformation as similar changes are not seen in regenerating or fetal liver. The elevated activities are consistent with the need of rapidly growing cells, such as are found in cancerous tissue, for large amounts of adenine nucleo­ tides.

Hyperuricemia and gout

Hyperuricemia in humans results from either diminished renal clear­ ance or excessive purine overproduction (28). Only a few percent of the clinical cases of hyperuricemia and gout can be accounted for by specific enzymes associated with elevated purine production. Mutant T- lymphoma (S49) cells dubbed AU-lOO are 80% deficient in adenylosuccinate synthetase yet they secrete 30-50 fold greater amounts of purine metabo­ 8

lites as compared to wild type cells (29,30). Furthermore, the AU-lOO

cell line overproduces total purines, primarily IMP. The deficiency of

adenylosuccinate synthetase is thought to be the primary reason for

purine overexcretion as a large intracellular concentration of IMP is

needed to maintain ATP levels. Ullman et al. (29) suggest many patients

suffering from hyperuricemia and gout may have defective adenylosuccin­

ate synthetase. Allsop and Watts (31); however, caution against

extrapolating these results as compensatory metabolic pathways in the

whole organism may nullify the deleterious effects of a defective

synthetase.

Malaria

The malaria parasite Plasmoidia does not synthesize purines ^ novo

(32). Mature human erythrocytes lack the enzymes to convert IMP to AMP

(33). Studies with Plasmoidium falciparium grown in continuous erythro­

cyte culture demonstrated the synthesis of adenosine nucleotides from

hypoxanthine via adenylosuccinate (34). Further studies with two inhib­

itors of adenylosuccinate synthetase, hadacidin and alanosine, showed

that only hadacidin prevented the synthesis of adenine nucleotides (35).

Alanosine relies on an enzyme found in ^ novo biosynthesis to catalyze

the formation of an inhibitory complex (36). Since both human erythro­

cytes and Plasmoidia lack the ^ novo biosynthetic pathway no inhibitory

complex could be formed. Hadacidin inhibits adenylosuccinate synthetase

specifically (37). These results suggest a unique metabolic target for

the design of new drugs against malaria. 9

Inhibitors of Therapeutic Importance

AMP, GDP, GMP, and adenylosuccinate are feedback, inhibitors of the

enzyme. Succinate (an analogue of L-aspartate) and 6-mercaptopurine (an analogue of IMP) are competitive inhibitors of the synthetase (17). An­

ions such as Cl~, Br~, HCOg", and I" are strong competitive inhibitors

with respect to GTP (38), and inhibition of the synthetase by NOg' and

GDP is synergistic (5,39). A variety of other substrate analogues are

interesting for their potential as chemotherapeutic agents (Figure 4).

Two important analogues, which are natural antibiotics, are alano-

sine (L(-)2-amino-3(hydroxynitrosamino)propionic acid), and hadacidin

(N-formyl-N-hydroxyaminoacetic acid). Alanosine was isolated as an ex­

tracellular product of Streptomyces alanosinicus and demonstrates

antibiotic, antitumor, and immunosuppresive activity (AO). Alanosine

has no direct effect on the synthetase (40) but acts through a conjugate

of alanosine and 5-amino-4-imidazolecarboxylic acid to form L-alanosyl-

5-amino-4-imidazole-N-succinocarboxamide ribonucleotide (36) (L-alan-

osyl-AICOR). Alanosyl-AICOR is a potent inhibitor of adenylosuccinate

synthetase with respect to IMP with a reported Kj of 0.2viM (41). Inhi-

biton of the synthetase is the likely effect of the antibiotic. Hada­

cidin was isolated from the fermentation broth of Pénicillium frequen-

tans and was found to have antitumor activity (42). While alanosyl-

AICOR has been shown to also inhibit adenylosuccinate lyase (43) the

only known affect of hadacidin is the inhibition of adenylosuccinate

synthetase (5,2,37) with reported Kjs of 0.3 to 6.3pM (5,25,44).

^ vitro studies using allopurinol have demonstrated antigrowth

activity against several leishmanial parasites (45-47) and Trypanosoma 10

% r» .0 C-C-CHg-C -0 A 'o- "CO :oc) ribose-5'-P ribose-5'-PPP

L-aspartate IMP GTP

Substrates

ON^ % ?" fi HN' G—N—CHg—G N-GH,-CH-COOH / I n \N H HO NHg I Ribose-5'-P

Hadacidin Alanosine Afiopurinol Ribonucleotide

ON^ ^OH

ÇH. O HC-HN-C GOd 1> HgN N rlbose-5'-P

Aianosyl-AIGOR

Substrate analogues

Figure 4. Substrates and several substrate analogues of adenylosuccinate synthetase 11 cruzi (48), a related family member which is the causitive agent of

Chagas' disease (sleeping sickness) in South America. The synthetase from these organisms is capable of selectively aminating allopurinol ribonucleotide to generate 4-aminopyrazolo(3,4-d)pyrimidine. The amin- ated allopurinol ribonucleotide is converted to the triphosphate and is incorporated into the RNA of these parasites where it is thought to have a toxic effect (47,49-51). Mammalian cells do not show this conversion and incorporation (52). The synthetase of the parasites offers a site for chemotherapy. Several clinical trials using allopurinol have met with favorable results (53-55).

Long Range Goals

Detailed structural information of a number of synthetase complexes would give us insight into the variety of roles played by the adenylo­ succinate synthetase. We could better understand the mechanism of catalysis as well as design better therapeutic agents for the treatment of cancer, malaria, and Chagas' disease. Intimate knowledge of the enzymes structure would also be a benefit to those researchers carrying out site specific mutagenesis of the enzyme. These studies in turn will shed more light on the metabolic role of adenylosuccinate synthetase.

With these thoughts in mind the structural studies of eight enzyme complexes have been proposed. Our hope is to more fully characterize and understand the functions of the enzyme. The synthetase complexes are as follows: 1) aspartate and enzyme, 2) IMP and enzyme, 3) OTP,

Mg2+, and enzyme, 4) IMP, GTP, Mg2+, succinate and enzyme , 5) GDP,

P04^~, adenylosuccinate, Mg2+ and enzyme, 6) L-alanosyl-AICOR and 12 enzyme, 7) allopurinol ribonucleotide and enzyme, and 8) hadacidin and enzyme. The first three structures will map out the active site of the enzyme. The fourth and fifth structures are capable of catalytic exchange and they should give us information regarding specific turnover of the enzyme. The last three represent important enzyme-inhibitor complexes with pharmacological value in the treatment of cancer and

Chagas' disease. These structues should give us a much clearer picture of the importance of adenylosuccinate synthetase in metabolism.

Present Study

Adenylosuccinate synthetase has previously been crystallized from rabbit (11,56) and rat (7) skeletal muscle and from ^ coli (57). This dissertation describes conditions used to obtain three suitable crystal forms of the synthetase from ^ coli and the structure of the enzyme- succinate complex to 5Â resolution. 13

CRYSTALLIZATION AND CHARACTERIZATION OF THREE CRYSTAL FORMS

Enzyme Preparation

Adenylosuccinate synthetase used in the crystallization experiments came from a genetically engineered strain of E. coli that exhibits an approximate 40-fold overproduction of the enzyme. Bass et al. describe the procedure for cell growth and enzyme purification (14). Protein concentration was measured by the method of Bradford (58).

Growth of the PZ^ and ?2i2i2i Crystal Forms

Two distinct crystal forms (Figures 5a and 5b) of the synthetase have been grown using the method of hanging drops (59). Prior to its use in crystallization experiments the protein was dialyzed against a solution (pH 7.7) consisting of imidazole (20mM), succinate (75mM), and

2-mercaptoethanol (70yl/l). Crystals grew at 20 to 25°C from 5ul drop­ lets consisting of equal parts PEG 3350 (24%(w/w)) in imidazole (lOOmM,

pH 6.6) and dialyzed protein (19 to 20mg/ml). Water vapor from these droplets equilibrated against 400pls of the polyethylene glycol solution described above. Elongated prisms (belonging to space group PZ^) ap­

peared within four days and grew to approximately 1mm in two weeks.

Crystals also grew at 4°C from droplets consisting of equal parts ammonium sulfate solution (23%(w/w)) in imidazole buffer (100mm, pH 7.0) and dialyzed protein (20mg/ml). These droplets equilibrated against a solution containing 2.5vil of saturated NaCl and 400m1 of the ammonium sulfate solution described above. Crystals (belonging to space group

P2i2i2j) appeared in one to two months and grew to about 1mm. Figure 5. The three different crystal forms of adenylosuccinate synthetase which belong to the following space groups: a) P2i2i2i, grown from ammonium sulfate, b) P2j^, grown from PEG 3350, and c) (P3221) grown from ammonium sulfate in the presence of succinate, IMP, GDP and MgCl2 r 16

Crystalline Enzyme-Ligand Complexes: Soaking Experiments

The ?2i crystal form was soaked with a number of ligands in an effort to obtain enzyme-ligand complexes. The concentrations of the ligands were approximately 100 fold in excess of their reported binding constants. GDP is the sole exception. Soaking solutions were prepared in a mounting buffer consisting of 95 parts PEG 3350 (25%(w/w)) buffered with imidazole (lOOmM, pH 7.0) and 5 parts MPD. The exact conditions and results are in Table 1. Aspartate and hadacidin had no deleterious effect on the crystals. These two ligands probably displace succinate due to their much stronger affinity for the active site (17,37). In contrast, exposure to GDP and GMP caused rapid and severe cracking of

the P2]^ crystal. Crystals did not crack when exposed to nearly 5mM

K4P2O7 or 2mM guanosine. Crystals slowly dissolved in the presence of

IMP. Exposure to adenylosuccinate, a competitive inhibitor with respect

to IMP, caused pitting but not dissolution, as occurred with crystals soaked with IMP. A diffraction photograph taken after a 24 hour soak in

adenylosuccinate did indicate some disordering may have taken place,

however.

Crystalline Enzyme-Ligand Complexes: Growth of the P3i21 (P3221) Crystal Form

In order to study guanosine nucleotide interactions a third crystal

form (Figure 5c) was grown using the method of hanging drops (59).

Protein was dialyzed versus a solution (pH 7.7) consisting of imidazole

(20mM), succinate (75mM) and 2-mercaptoethanol (70yl/l) prior to its use

in crystallization experiments. Dialyzed protein (32mg/ml) was mixed in 17

Table 1. Results of soaks with the ?2i crystal form

Ligand or Kj Soaking conc. Results^

Aspartate 350wMb (17) SO.OmM N

Hadacidin 4.2wM i (37) 0.6mM N

IMP 20mM (17) 2.0mM D

Adenylosuccinate 5pM (17) 0.5mM P

GMP + 5mM MgClg lOyM (16) 1.2mM C,D

GDP + 5mM MgCl2 12yM (17) 0.5mM C,D

Guanosine 2.0mM N

5 no ill effects; D = dissolution; P s pitting; C,D s cracking and dissolution.

^The Kj of GMP is based on the the enzyme isolated from human placenta. All other reported binding constants are based on the synthetase isolated from coli. The numbers in parentheses refers to the references where the Kj or were found.

a 1:1 ratio with a solution (pH 7.0) consisting of IMP (4mM), GDP (AmM),

and MgCl2 (lOmM) buffered with imidazole (lOOmM). This solution was

placed on ice for 15 minutes before being mixed in a 1:1 ratio with an

ammonium sulfate solution (25%(w/w)) buffered with imidazole (lOOmM, pH

7.0). 5yl droplets of the combined ammonium sulfate and enzyme-complex

solution equlibrated at 4°C against wells containing AOOyl of an ammon­

ium sulfate solution (25%(w/w)) plus various amounts of saturated NaCl 18

(10 to 2.5pl). Crystals with well defined trigonal faces appeared with­

in four days and grew to between 0.6 to 0.8mm in two weeks.

Space Group Determination

Space group symmetry for each crystal form was deduced from a series

of precession photographs taken using a fine focus sealed X-ray tube

with a Cu anode powered at 40kV and 20mA. The X-ray beam, shooting down

a 4mm collimator, was passed through a Ni filter before reaching the

crystal. Figure 6 shows the relationship of the unit cell axes to

crystal morphology. The ratio of the volume of the asymmetric unit to

the molecular weight of the asymmetric unit, V^, was calculated for each

crystal form (60). This ratio gives a reasonable estimate of the number

of molecules per asymmetric unit and it also indirectly provides an

estimate of the solvent content of the crystal. Vp^ot» the fractional

volume of protein in a crystal is determined by the relationship Vpj-Qj. =

1.66v/V|^ where v is the partial specific volume of the protein. For

most proteins \i = 0.74cc/g. Unless there is reason to suspect otherwise

this value can be used in the expression for Vp^-Qj, giving Vpj-Qj. =

1.23/V[^. The fractional volume of solvent is then given by = 1 -

Vprof The numbers obtained and their possible significance will be

discussed below.

Determination of the P2i crystal form

Crystals grown from PEG 3350 were mounted using a solution consis­

ting of PEG 3350 and MPD. The mounting buffer is described in greater

detail in the next chapter. Crystals were mounted with their long axis 19

a.

a

b.

b

c

Figure 6. A diagram illustrating the relationship between unit cell axes and crystal morphology: a) the PZj crystal form, b) the P2i2i2i crystal form and c) the PS^Zl (P3221) crystal form 20

(b axis, see Figure 6a) parallel to the length of the capillary. Two precession photographs were taken with the crystal in this orientation

(Figures 7a and 7b). The zones were approximately 71.7° apart indicat­ ing the presence of at least one nonorthogonal interaxial angle (Figure

7c). Both photographs displayed orthogonal nets exhibiting mm or 2/m

Laue symmetry. A zero level photograph displays this symmetry when viewing perpendicular to a two-fold axis. Moreover, alternating reflec­

tions were absent (extinct) along the horizontal axis of the film, thus

the axis was a two-fold screw axis. No other extinctions were present, indicating a primitive lattice. The presence of only one two-fold axis and one nonorthogonal net lead to the assignment of this crystal form to

the monoclinic space group P2]^. Unit cell parameters are a = 73.31(9)Â,

b = 72.23(7)Â, c = 82.87(9)Â, g = 108.59(6)°, and the unit cell volume

is 416,700(1,200)Â^. The numbers in parentheses are the observed standard deviations based on measurements of low resolution reflections

(20 < 14°, Cu radiation) from 5 crystals.

Determination of the P2i2i2i crystal form

The crystals grown from 23%(w/w) ammonium sulfate were mounted with

their long axis (b axis, see Figure 6b) parallel to the length of the

capillary. The mounting buffer consisted of an ammonium sulfate solu­

tion (25%(w/w)) buffered with imidazole (lOOmM, pH 7.0). Two photo­

graphs were needed to determine the space group (Figures 8a and 8b).

The zones were separated by 90°. Both photographs displayed orthogonal

nets with mm Laue symmetry. Identical extinctions were found along each

major axis with alternating reflections being systematically absent. No 21 other absences were found indicating the presence of a primitive lat­ tice. These data support the assignment of the orthorhombic space group

P2i2i2i. Unit cell parameters, measured directly from the film using a

Nikkon Profile Projector, are as follows: a = 79.0(1)Â, b = 70.2(1)Â, and c = 152.6(2)Â. The unit cell volume is 845,900A3

Determination of the P3i21 (P3921) crystal form

Crystals grown in the presence of succinate, IMP, GDP, and MgCl2 were mounted with their long axis (c axis, see Figure 6c) parallel to

the long axis of the capillary. Pictures taken down this axis revealed six-fold symmetry (Figure 9a). A six-fold rotation axis cannot be dis­ tinguished from a three-fold axis in a zero level photograph due to the presence of an inversion center in reciprocal space. An upper level photograph taken along the same axis (Figure 9b) clearly showed that only three-fold symmetry is present. Re-examination of the zero level photograph revealed two reciprocal cell axes having the same dimensions with an interaxial angle of 60°. These reciprocal axes were located at

30 and 90° from the horizontal axis of Figure 9a and defined a primitive net. A rotation of 90° about the spindle (horizontal axis) revealed a second zone (Figure 9c) which displayed mm Laue symmetry indicating the

presence of a two-fold symmetry axis perpendicular to the direction of

the beam. The two-fold symmetry axis must lie along a real space axis given the choices of reciprocal axes above. Furthermore, the photograph of Figure 9c displays systematic absences along the three-fold axis; only every third reflection is present, implying a 3^ or 32 screw axis.

This crystal form was assigned to the trigonal space group P3i21 or its Figure 7. The three major zones of the crystal form: a) the hkO zone, b) the Okl zone and c) the hOl zone F Figure 8. The two major zones of the P2j^2]^2i crystal form: a) the hkO zone, and b) the Okl zone

Figure 9. Three zones of the PSjZl (P3221) crystal form: a) the hkO zone, b) the hkl zone, and c) the hOl zone

28 enantiomorphic space group P3221. Throughout the rest of this disser­ tation this crystal form will be designated P3i21 (P3221). The unit cell parameters were measured directly from the film using a Nikkon

Profile Projector and are as follows: a = b = 80.8(1)Â, and c = 158.2(1)Â. The unit cell volume is 894,000Â^.

Results and Discussion

The results of the soaking experiments suggest several interesting properties of the crystalline enzyme. The dramatic effects caused by the guanine nucleotides and by IMP indicate that the binding sites are readily available in the ?2i crystal form. Furthermore, the nucleotides probably induce some type of conformational change in the protein which leads to severe cracking of the crystal. These results are consistent with the hypothesis that some type of interaction occurs between IMP and

GTP before any interaction with aspartate (22,23). Soaks with aspartate cause no apparent change in the crystal. These findings are also con­ sistent with the results of Nichol et al. (61) who proposed that the

binding of IMP might lead to a conformational change in the synthetase.

It is interesting to note that the binding of adenylosuccinate does not cause the severe dissolution seen in soaks with IMP. Perhaps the aden­ ylosuccinate binds in a different fashion and does not trigger the same

type of conformational change.

Calculation of gives us information about the number of molecules

per asymmetric unit and leads to an estimate of the solvent content of a

crystal. Both the ?2i and the P2i2i2i crystal forms appear to have a

dimer per asymmetric unit. Based on this assumption, their calculated \

29 ratios are 2.17Â^/Da for the monoclinic form and 2.20Â^/Da for the orthorhombic form. These values are close to the median value of

2.15Â^/Da (60). The solvent content for the monoclinic form is ident­ ical to the median value of 43% (60) while the orthorhombic solvent con­ tent of 44% is very close. Not surprisingly, their diffraction power is also similar. Both crystal forms diffracted well out to 2.8Â. The

P3i21 (P3221) cystal form had a much higher solvent content. Assuming a monomer per asymmetric unit the calculated ratio was 3.10A^/Da which gives the trigonal crystal form a 60% solvent content. This is at the high end of the range normally seen in protein crystals (60). The dif­ fraction power was correspondingly poor. Zones parallel to the c axis diffracted out only to 4Â resolution. However, a photograph of the Okl zone with a crystal measuring 1mm in length diffracted out to 2.8Â reso­ lution.

Information about the molecular symmetry can be had by calculating the ratio of the number of asymmetric units per unit cell to the number of molecules per unit cell. The International Tables for Crystallogra­ phy gives information about the former while calculations of Vf^ supplies information about the latter. A ratio less than unity implies that non- crystallographic symmetry is present in the asymmetric unit. Both the

?2i and the ?2i2iZi form have a ratio of 1/2 suggesting a molecular two­ fold rotation axis is present. A rotation function (discussed in the

RESULTS AND DISCUSSION chapter) indicated the presence of a noncrystal- lographic two-fold axis in the ?2i form. Heretofore crystallographic evidence suggest, but does not guarantee, that the dimer is composed of

two identical monomers. Stronger evidence for identical monomers can be 30 found by examining the unit cell of the P3i21 (P3221) crystal form.

Each asymmetric unit in the unit cell is related to its nearest neighbor by a crystallographic two-fold axis. It appears that the two-fold axis of the dimer coincides with the crystallographic two-fold axis. If this is true than the monomers should be identical in order to satisfy the two-fold symmetry. However, the possibility of disorder still does exist and the two monomers may, indeed, be different.

One intriguing possibility is that the two-fold relationship is simply an accident of crystallization. Perhaps the dimer dissociates in the presence of its nucleotide substrates. This theory runs counter to the evidence which suggests the synthetase is active as a dimer (10).

Another possibility is that the dimer dissociates after the hydrolysis of GTP to GDP and P^. If GDP can cause a conformational change, as sug­ gested by the soaking experiments, it might cause the dissociation of the dimer or at least a structural change to a nonactive form. This alteration would serve as a means of regulation, alternately turning the enzyme on and off with dimer to monomer transitions.

To this point we have discussed the binding of ligands to the crystalline enzyme while actually giving little proof that they can bind ligands in the crystalline state. The strongest evidence for ligand binding can be found by comparing the P2i2i2i and the PSjZl (P3221) crystal forms. Both forms grow under nearly identical conditions of ammonium sulfate concentration, pH, and temperature. Indeed, crystals of the two forms have been seen in the same droplet. Despite the simil­ arities the crystalline habit of the protein is different. In several droplets, which had a 10-fold lower concentration of GDP than described 31 in the crystallization section, a transition from the PSiZI (P3221) crystal form to the P2i2i2i crystal form was seen. It is believed that ammonium, a competitive inhibitor with respect to GDP (38), displaced

GDP from its binding site. This resulted in the breakdown of the trig­ onal crystalline lattice. PZj^ZjZj^ crystals appeared after most of the

P3i21 (P3221) crystals had dissolved away. The concentration of GDP was increased to its present level to prevent dissolution of the crystals from occuring in the future.

Three crystal forms have been obtained to date. The stucture deter­ mination of two of these will be pursued; the PZj form due its rapid and reproducible growth and the PSjZl (P3221) form because of the informa­

tion it should yield regarding enzyme-ligand interactions. 32

STRUCTURE DETERMINATION OF THE CRYSTAL FORM TO 5.0A RESOLUTION

Introduction

In 1912 Freidrich and Knipping, two researchers working in the lab of Max von Laue, obtained the first diffraction photographs of a crys­

tal. In that same year Laue published the results and proposed X-ray diffraction was similar to the diffraction of light from a grating (62).

The basic principles of the theory can be understood by examining diffraction from a one dimensional grating. Let r be the regular inter­

val between slits on the grating (Figure 10). Plane wave, incident

radiation is diffracted by the grating in the direction denoted by the

unit vector S. In order to detect diffracted radiation, rays 1 and 2

must interfere constructively. For constructive interference to occur

d, the path length difference, must be an integral number of wave­

lengths. Stated as a simple equation d = nX. The letter n represents

any integer and X is the wavelength of the incident radiation. The path

length difference can also be expressed in terms of the vectors r and S,

rS = d

and

r S = I r| COS0

where 0 is the angle the diffracted ray makes with the grating. By simple substitution we obtain |r|cos0 = nX.

This simple relationship demonstrates two important principles of

X-ray diffraction. First r, the interval between slits, must be greater

than or equal to the wavelength of the incident radiation. If r is less

than X then |r|cos0 < nX for all n greater than zero and diffraction 33

Plane wave radiation

Grating

Figure 10. Diffraction from a one dimensional grating will not be observed. Second, diffraction will be detected in only discrete directions in space, because only specific values of 0 will satisfy the relationship.

Three dimensions introduces the complication of three conditions which must be satisfied simultaneously. These conditions can be ex­ pressed as follows:

a S = hX

b-S = kX

c-S = IX

The above are the Laue conditions of X-ray diffraction. The vectors a, b, and c define the three dimensional grating or lattice. The magni­

tudes of a, b, and c are the lengths of the unit cell, the smallest unit of volume whose translation in three dimensions reproduces the entire 34 crystal. Finally, h, k, and 1 are integers which represent the order of diffraction.

A crystallographer builds a model of the protein based on the intensity of each reflection signified by the integers h, k, and 1. In general, each part of the molecule will contribute to every part of the diffraction pattern. Scattering contributions from all the atoms in the unit cell are summed for each reflection as shown below,

N P(h) = Z fiexp[2ni(h'ri)]. j=l

P(h) is known as the structure factor and it is calculated for each h, k, and 1 for all atoms j = 1 to N in the unit cell. The atomic scatter­ ing factor, fj, is defined as follows:

fj = (amplitude of the wave scattered by atom j) (amplitude of the wave scattered by a free electron)

The exponential term represents the phase of the scattered wave with respect to a specified origin.

The structure factor is a complex quantity which may be represented by two terms, that is

F(h) = F(h)expia.

F(h) is the amplitude of the scattered wave, F(h), while a is the phase of the scattered wave. This relationship can be graphed on an Argand diagram (Figure 11), a coordinate system containing a real and an imaginary axis. F(h) represents the magnitude of the vector while a can be thought of as the angle through which the vector is rotated counter­ clockwise in the plane. The Argand diagram has proven a useful means to visualize various concepts in X-ray crystallography. 35

Im

F(h)

Real

Figure 11. An Argand diagram of the stucture factor F(h)

The structure factor contains information about the diffracted radiation from the structure. How does one obtain the structure? The answer is integrally linked to Fourier transform theory. The diffrac­

tion pattern is the Fourier transform of the structure. Conversely, the

structure is the Fourier transform of the diffraction pattern.

The structure factor is rewritten in terms of a continuous summation over the volume of the unit cell.

N F(h) = E f^exp[2lli(hTO] j=l

= Jp(r)exp[[2iii(hT^)]. V

Multiplying both sides by exp[-2iii(h*rj)] and integrating over the

volume of the unit cell gives us

p(r) = J'F(h)exp[-2ni(hT-j)]dVs V

where dVg is a small unit of volume in diffraction space.

F(h) assumes nonzero values only at integral values of h, k, and 1.

Hence, 36

p(xyz) = (1/V) Z L Z F(h)exp(-2ni(h*)] h k 1

By knowing the structure factor for all values of h, k, and 1 we can calculate the electron density at all points x, y, and z in the unit cell. A model of the structure is built based on the electron density map generated.

X-ray crystallography would be a straightforward computational process if it were not for one major complication. The intensity of each reflection is the experimentally measured information from which the crystallographer works. Intensity is proportional to the magnitude of the structure factor squared, that is

1(h) « F(h)expia x F(h)exp-ia

oc F(h)2

The phase information has been lost. This is known as the phase problem. Regaining this lost information constitutes the primary task in solving a crystal structure.

Phase Problem

There are two primary methods used by protein crystallographers in their attempt to overcome the phase problem. The oldest method is that of isomorphous replacement. A newer and very promising method is based on the measurement of differences due to anomalous scattering. Each method will be briefly discussed. 37

Isomorphous replacement

The technique of isomorphous replacement was first successfully exploited by Green et al. in their study of sperm whale myoglobin (63).

The efficacy of the method relies on the fact that a typical protein crystal is approximately 50% solvent. A heavy atom such as mercury can flow through solvent channels and interact at specific sites on the

protein without disturbing the overall conformation of the molecule.

Initial phase information can be obtained by locating the position of

the heavy atom in the unit cell.

The scattering from a heavy atom derivative crystal can be thought of as arising from the scattering of the native crystal plus scattering from the heavy atom substructure. In vector notation the relationship is written as

FpH = Fp + Fh where Fpg and Fp are the structure factors for the derivative and native crystals, respectively, while Fg is the structure factor for the heavy atoms alone. Figure 12 depicts this vector equation in an Argand dia­ gram.

Im

Real

Figure 12. An Argand diagram showing the relationship FpH = Fp + Fh 38

The vector representation can be rewritten in polar form giving us,

FpHexp(iapH) = Fpexp(iap) + F^expCio^)

FpH, Fp, and F^ are the magnitudes of the derivative, native, and heavy atom vectors, respectively. The angles oç, and oj^ represent the phases of the scattered wave from the derivative, native, and heavy atom substructure, respectively.

By multiplying both sides by their complex conjugates we obtain

FpQ^ = Fp^ + Fy^ + 2FpF{|COs(oç - o^)

Rearrangement of the above equation gives us an expression for oç, the phase of the native structure:

0Ç = ojj ± cos'^KFpH^ _ Fp2 - Fj^^)]/2FpFfj.

The magnitudes Fpy and Fp are determined from the experiment. Thus

F^ and must be determined in order to generate the native phase oç.

These two parameters are found by correctly interpreting the results of a Patterson synthesis. The Patterson function generates a map of interatomic vectors based on the observed intensities. No phase inform­ ation is necessary. The peak heights of the map are proportional to the product of the atomic numbers of the atoms connected by the vector.

Vectors connecting heavy atoms should correspond to prominent peaks in the map. In searching for heavy atoms a difference Patterson is usually calculated. The difference Patterson uses |Fp - Fp^l^ as coefficients.

The map produced should have only peaks corresponding to the interatomic vectors between heavy atoms.

Once the heavy atoms have been located their contribution to the

total scattering can be found by 39

Fy = EfHexpt2iii(hTH)l H where the summation extends only over the heavy atoms. The parameter fjj is the scattering factor for the heavy atoms.

To better understand how phase information is obtained it would be helpful to use what is known as a Barker diagram. The vector expression

FpH = Fp + Fh is rewritten as

FpH - = Fp

For each reflection we can draw a Barker diagram where the magnitudes of the structure factors describe the radii of circles (Figure 13). -Fjj is drawn with its tail at the origin. The circle described by Fp is centered at the origin. Finally, the circle described by Fp^ is centered at the head of -Fy. The phase corresponds to the points of intersection of the two circles. There are two possible phase values,

and «2» each reflection. This two fold ambiguity can be overcome

by finding another suitable isomorphous derivative or by using the

method of anomalous scattering.

Anomalous scattering

Anomalous scattering occurs when the frequency of the incident rad­

iation falls near the absorption edge of an atom. The result is a

breakdown in Friedel's law; a law which states that the intensities of

inversion related reflections are equal, that is 1(h) = I(-h). By

carefully measuring the differences due to anomalous scattering we can 40

Imaginary axis

-F» Real axis

PH

Figure 13. A Marker diagram displaying the two fold ambiguity of phases determined with single isomorphous replacement

obtain phase information. This method can be used in conjunction with

isomorphous replacement to correctly phase the intensities.

The following analysis is based on the work of Smith and Hendrickson

(64).

In the presence of an anomalous scatterer the atomic scattering

factor, f, takes on the complex form

f = fo + Af' + iAf"

where fg is calculated based on the assumption of free electrons, ûf is

a real valued correction, usually negative, due to the fact that

electrons are not free but are associated with the nucleus, and Af" is a 41 correction due to anomalous scattering. The structure factor now becomes

F(h) = E(fo + ûf' )exp(2ni(h*r) ] + iEûf"exp[2iii(hT)]

= D(h) + i5(h) where D(h) = [(fg + ûf' )exp[2ni(hT) J and 5(h) = EM"exp[2ni(hT)].

Friedel's law is valid under normal circumstances and the structure factor moduli are related by

F(h) = F(-h) = F*(-h) where * denotes the mathematical operation of conjugation. With the introduction of an anomalous scatterer Friedel's law breaks down and the following relationships are true

F(h) = D(h) + i5(h) a D*(-h) - i5*(-h) = F*(h).

Figure 14 shows the vector relationships in an Argand diagram.

Now let Fp(h) be the structure factor for the protein excluding those atoms which contribute to anomalous scattering. Let F^g(h) be the structure factor for the anomalous scatterers. The angle w lies between

Im

-i5*(-h)

D(h) = D*(-h)

Real

F(-h)

Figure 14. An Argand diagram showing the vector relationships for anomalous scattering 42

F^s(h) and Fp(h). By referring to Figure 15 and using the law of co­ sines we obtain

(i) F(h)2 = D(h)2 + S(h)2 + 2D(h)S(h)cos(+ w- a) and

(ii) F*(-h)2 = D*(-h)2 + &*(_h)2 - 2D*(-h) 5*(-h)cos(o^s + w- a).

Im

F(h)

Real

Figure 15. Vector relationships and pertinent angles used to derive phase information from anomalous scattering

Subtracting (i) by (ii) gives us

F(h)2 - F*(-h)2 = 4D(h) S(h)cos( a^s + w - a).

Upon rearrangement we obtain

F(h) - F*(-h) = 4D(h)6(h)cos(aAs + w - a)/(F(h) + F*(-h)).

Similarly, the summation of (i) and (ii) followed by rearrangement gives

D(h) = l0.5(F(h)2 + F*(-h)2 - 5(h)]l/2

If 5(h) « D(h) then D(h) is approximately 0.5(F(h) + F*(h)). Sub­ stitution of this expression into the equation

F(h) - F*(-h) = 4D(h)5(h)cos(o^s + w - a)/(F(h) + F*(-h)).

leads to the following approximation

F(h) - F*(-h) = 25(h)cos(a&g + w - a). 43

The angle a will have a two fold ambiguity with the calculated values being symmetric about + w:

a = o^S + w ± cos-l[(F(h) - F*(-h))/26(h)].

The quantities F(h), F*(-h) and 5(h) are experimentally measured.

The angles a^g and w are obtained from a correct interpretation of the

Patterson synthesis. If there is only one type of anomalous scatterer present then u = it/2. The phase angle a is equivalent to the angle 0%,% obtained from the isomorphous replacement method. The phase otp of the structure factor Fp(h) is gotten through the vector relationship

FpH(h) = Fp(h) + F{j(h).

The anomalous scattering method yields two values of which can be converted to two values of o^. However, only one value from the anomalous scattering method will be consistent with one value of oç from single isomorphous replacement. The phase angle which is consistent with both sets of data will be the correct phase value.

Materials and Methods

Crystallization

Three distinct crystal forms of the synthetase have been grown. A detailed discussion of the growth and charcterization of each crystal form has been presented in Chapter II. The structure solution of the

crystal form is initially being pursued due to its rapid and repro­ ducible growth. P2i crystals were obtained by the method of hanging drops (59). Prior to its use in crystallization experiments the protein was dialyzed against a solution (pH 7.7) consisting of imidazole

(lOOmM), succinate (75mM), and 2-mercaptoethanol (70m1/1). Crystals 44 grew at 20 to 25°C from Syl droplets consisting of equal parts PEG 3350

(24%(w/w)) in imidazole (lOOmM, pH 6.6) and dialyzed protein (19 to 21 mg/ml). Water from these droplets equilibrated against a 400ul solution of polyethlyene glycol described above. Elongated prisms appeared with­ in four days and grew to approximately 1mm in two weeks.

Crystal manipulation

Mounting buffer A suitable buffer was needed to maintain crystal stability outside of the droplet. A solution consisting of 25% (w/w)

PEG 3350 buffered with imidazole (lOOmM, pH7.0), and 2-methyl-

2,4-pentanediol (MPD) in a 95:5 (v/v) ratio proved to be a suitable

buffer. The crystal is stable in this buffer for an indefinite time.

Chloride or acetate was used as a counteranion. Three drops from a

disposable pipet of O.IM sodium azide per 10ml of mounting buffer were

added to inhibit bacterial growth.

Heavy atom derivative soaks Various heavy atom solutions were

screened by soaking ?2i crystals and examination of diffraction photo­

graphs. Two potential derivatives were found based on changes seen in

diffraction photograghs. Yunje Cho discovered the first isomorphous

derivative by soaking crystals in a 2mM solution of K^Hgl^ prepared by

mixing 1 part of a 20mM stock solution of aqueous K^Hgl^ with 9 parts of

a solution consisting of PEG 3350 (27.9% (w/w)) buffered with imidazole

(0.12M, pH 7.0) and MPD in a 94.5:5.5 (v/v) ratio. Crystals were soaked

for two to four days before they were used for data collection. A

solution which was ImM in ErClg and ImM in citrate was prepared by 45 mixing in a 1:1 ratio a solution which was 5mM in both ErClg and citrate and a solution consisting of 52.8% (w/w) PEG 3350 buffered with imidazole (0.2mM, pH 7.0) and MPD in a 90:10 (v/v) ratio. The resulting solution, 2.5mM in ErClg, was then diluted to ImM with the proper amount of mounting buffer. Crystals were soaked in ImM ErClg, citrate solution for three days before data collection.

Use of various PEG 3350, MPD solutions may at first appear a bit confusing. However, greater flexibility can be had by preparing heavy atom solutions with these buffers. The heavy atoms mentioned in the above paragraph are readily soluble in water. Standard solutions of these heavy atoms are prepared in water and then mixed with the PEG

3350, MPD buffers. The buffers are prepared in such a way that dilution by the proper amount gives a solution which has the same makeup as the

95:5 stabilization buffer. Also, small amounts of soaking buffer can be freshly prepared for each experiment which makes for more reproducible results.

Crystal mounting Crystals were mounted in flattened, thin-walled glass capillaries. The b axis was mounted parallel to the long axis of the capillary. Crystals had to be maintained moist in order for adequate diffraction to occur. This leads to a problem of severe slip­ ping of the crystal in its capillary. The problem was alleviated some­ what by sandwiching the crystal between two strips of filter paper with

the crystal resting on the flattened surface of the capillary. Several

problems arose using this procedure. The filter paper increased the

background scatter. Also, the filter paper could draw off mother liquor 46 from around the crystal. The moistness of the crystals was found to have a small effect on the unit cell parameters.

Data collection

Data were collected on a four circle, single-counter diffractometer under the control of a computerized control system developed by Larry W.

Finger and C. G. Hadidiacos of Krisel Control, Inc., Rockville, Mary­ land. X-rays were generated by a sealed tube with a copper anode powered at 40kV and 30mA. A nickel filter was used to screen out the Kg radiation. The incident beam was collimated by two 0.8mm pin holes separated by 12cm. A helium path between the crystal and the detector was used to reduce the absorption and scatter of X-rays by the air.

Diffracted radiation was detected by a Nal scintillation counter.

Figure 16 is a schematic of a four circle diffractometer showing the relevant axes about which the crystal is rotated.

9 Rotation

X Rotation

Incident X-ray -fn Beam trap

beam Counter Diffracted beam

» Rotation

26 Rotation

Figure 16. A schematic of a four circle diffractometer showing the four angles of rotation: 20, w, X» and <#. This figure was taken from the book by Ladd and Palmer (65) 47

Data were collected to a resolution of 5Â (20 = 18°) on the native crystal and two heavy atom derivatives. For the monoclinic space group one quadrant of reciprocal space was collected from -16 to 16 in h, 0 to

16 in k and 0 to 16 in 1. Intensity data were collected from half- height to half-height for each peak using an w scan of 7 steps, 0.05° in

CO, with a 15 second count per step. Shells of approximately 200 to 250 reflections each were collected at a time. An overlap of 0.1° between shells of the same crystal was collected to obtain multiple measurements of a reflection for the purposes of checking reproducibility. Native data were collected with a 0.1° overlap between shells of consecutive crystals. This amount of overlap did not provide enough redundancy for scaling purposes so one crystal was used to collect the hOl data from

2-18° in 29. Derivative data were collected with a 0.3° overlap between shells of consecutive crystals. This amount of overlap provided adequate redundancy for the purposes of scaling. Two check reflections were used throughout data collection to monitor profile alignment and the decay in intensity due to the bombardment by X-rays. Data collec­ tion was halted on a particular crystal when its check reflections showed an approximate 30% decrease from their initially measured inten­ sities. Table 2 lists some of the details of data collection including numbers of crystals used, numbers of reflections and the calculated Rsym values.

The orientation matrix was calculated as described by Hamilton (66) and King and Finger (67). The observed angles for the eight equivalent positions (Table 3) of a reflection were used to determine a set of

"true" angles for the reflection, thus reducing the systematic error in 48

Table 2. Experimental parameters of data collection and processing

No. of Observed Unique crystals Exp.^ Reflections^ Reflections^ ^sym^

Native 5 70-80 hr. 4090 3513 0.044

Hgl2- 7 35-40 hr. 3824 3410 0.080

ErCl] + citrate 8 30 hr. 4176 3208 0.066

&The approximate length of time each crystal was exposed to radia­ tion before the check reflections decayed by 30%.

^The number of reflections observed after the scaling of the indi­ vidual data sets.

CThe number of reflections obtained after scaling all the data sets.

N dRgym = E E 11(h) - I(h)iI h i=l N I Z I(h)i h i=l where I(h)^ is the ith measurement of a reflection h and 1(h) is the average value of the N equivalent reflections. crystal alignment due to unsymmetrical diffraction profiles and optical centering of large crystals. Four reflections with 20 values between

7.6° to 14.6° were used in the calculation of the matrix. The process was repeated whenever the crystal slipped.

Anomalous pairs and data for the native crystal were collected on a

Mark III area detector. X-rays were generated with a rotating anode

powered at 50kV and 100mA. The facilities were graciously provided by

Dr. Martha Ludwig at the University of Michigan. Crystals were mounted 49

Table 3. The 8 equivalent positions of a reflection

Setting No. Indices Angles

1 hkl 20 w X *

2 -(hkl)a 20 CO -X 11+(j)

3 hkl -20 -w rt+X

4 -(hkl) -20 -w n-X 11+4)

5 hkl 20 -0) it-X ii+

6 -(hkl) 20 -w n+X *

7 hkl -20 CO -X n+

8 -(hkl) -20 w X *

&-(hkl) indicates the Friedel mate of (hkl), i.e., -h, -k, -1.

with their crystallographic b axis perpendicular to the long axis of the capillary. This oriention allowed for the collection of the maximum number of reflections. Derivative data to 2.OA (nominal resolution

2.6°) and native data to 2.0° (nominal resolution 2.3°) were collected in about three weeks.

Data processing

Data reduction The intensity data are reduced in a two pass pro­ cedure described by Hanson et al. (68) as modified by Hendrickson. In the first pass step data from the more intense reflections are fit to a double Gaussian function of the form

yi = Ci[exp-((C2 + ki - Xi)/C3)2 + exp-((C2 + ^2 - Xi)/C3)2] 50

where Yi = li - bk (Ij is the count at x^, and bk is the background count). Cj is related to the peak height. C2 is the shift of the peak

from its expected position in the scan range. The constants kj and k2

describe the spectral dispersion due to the copper Ka^, Ka2 doublet.

The parameter x^ describes the relative positon of step i from the cen­

ter of the profile. C3 is proportional to the peak width.

In the first pass only y^ which satisfy three criteria are used.

First, the maximum count rate must not appear before the second step nor

after the second to last step. Second, the step profile must be suc­

cessfully fit by the two Gaussian model. The parameters 0%, C2, C3 are

fit by a nonlinear least squares procedure. The intensity at each step

i is compared to the calculated intensity at step i. The least squares

procedure minimizes the difference (ygj - y^i) where y^^ and y^^ are

respectively the calculated and observed intensity at step i. The

relative intensity of a reflection is given by CiCg. Finally, the

relative intensity determined by the model must be greater than 3 times

a where a is the root mean square deviation of the modeled intensity.

The subset of reflections which satisfy these criteria form the basis

for a six parameter fit of two tensors. One tensor gives the shift of

the peak step of a given reflection from the center of the profile as a

function of h, k, 1. The other tensor describes the width of a reflec­

tion as a function of h, k, 1.

All the data are reduced in the second pass. For each h, k, 1 C3

is calculated from the width tensor, determined from selected data of

the first pass. If a reflection is weak or poorly formed C2 is calcu­

lated from the shift tensor, otherwise the shift based upon the least 51 squares fit of the individual reflection is used. Thus, in the first pass for strong reflections, C^, C2, and C3 are adjustable parameters in the fitting process whereas in the second pass only Cj and C2 are varied. Weak, reflections are rejected in the first pass, but are fit, with Cj being the only adjustable parameter, in the second pass. For strong intensities the value of the intensity is the weighted average of values obtained from pass one and pass two.

Background A seven term expression was used to account for the variation in background in reciprocal space:

= a(h2) + b(k2) + cfl^) + d(hk) + e(kl) + f(hl) + g(sin0)

In the above expression h, k, 1, are the indices of a given reflection, sin0 is a resolution term, and the parameters 'a' through 'g' are ad­ justed by the method of least squares. Data are divided into shells for

which the sin0 dependence on background is nearly linear. For low res­ olution data only one shell is used.

Absorption The incident beam is attenuated as it passes through

the crystal. The amount of attenuation will differ as different pro­

files of the crystal are presented to the beam. The phenomenon, known as absorption, must be adequately taken into account to be assured of an

accurate data set. We have employed the method of North, Phillips, and

Mathews (69) to correct for absorption. A reflection near X of 90° is

rotated about the 4» axis. Intensity measurements are taken at regular

intervals (10° in our case). A transmission profile of relative trans­

mission versus is produced. The transmission of any reflection h, k, 52

1 is approximated by the equation T(hkl) = (T(*i) + T(*r)]/2 where (|>i and <()j- are the azimuthal angles of the incident and reflected beam. The calculation of these two angles is dependent on the geometry of the experiment. The absorption is given by the reciprocal of the transmis­ sion coefficient, T(hkl).

Lorentz and polarization factors The polarization factor, p,

is dependent on 0 only and is given by (1 + cos^29)/2. The Lorentz

factor accounts for the relative velocity of each reflection as it

passes through the diffraction condition. The Lorentz factor is

dependent on the geometry of data collection. For a four circle

diffractometer in the Symmetrical A Setting (70), the Lorentz factor, L,

is given by l/sin20. The polarization and Lorentz factors are applied

to the data as (Lp)~^.

Decay X-ray radiation damages crystals through a dual process of

thermal decay and the production of free radicals. Blake and Phillips

(71) proposed a model describing the possible transitions of irradiated

protein crystals. From the undamaged crystal, Aj, there are two paths.

One pathway involves the direct transition to an amorphous, nondif-

racting species, A3. This decay proceeds with a rate constant kg. The

second pathway is a two step transition. The first step involves the

the transition of A^ to a partially damaged crystal A2 which contrib­

utes to diffraction only at low resolution. The rate constant for this

process is k%. Continued decay leads to the formation of the totally a-

morphous state A3 at a rate governed by the constant k2. 53

Hendrickson (72) used the Blake and Phillips' model to calculate a radiation damage factor R which relates the intensity of a reflection at time t (I(t)) to its initially measured intensity (Iq)- R is dependent on the time and on the resolution of the reflection, s = sin0/X. The general expression for radiation damage is given by

I(t)/lQ = exp[-(ki + k3)t] + [(ki/(ki + k2 + kg)] x

exp(-k2t){l-exp-(ki + kg - k2)t}exp(-Ds2).

The parameters k^, k2, kg are the rate constants of the Blake and

Phillips' model. D is equal to Siru^ where u is the root mean square displacement of an atom.

Hendrickson tested several variations by fitting each model to the radiation damage on myoglobin. The models differ by the rate constants applied in the general expression. The best fit of the data for low to moderate damage occurred when kg was set equal to zero. No model fit the data well at a decay of 72% or greater. When s^ is approximately zero, as is the case at low resolution, the rate constants kj and k2 are not linearly independent; therefore, k2 is set equal to kj. Another problem with low resolution data is that a meaningful value of the parameter D cannot be fit by the least squares procedure due to the lack of high angle data. For the 5Â data the value of D was set equal to zero. The radiation damage factor now assumes the form

R(t,s) = exp(-kit)(l + kjt).

This model suggests that decay is governed by the initial state of

the molecule and is agent independent or dependent on only one agent.

Also the fact that kg has been set equal to zero suggests that direct 54

transition from fully ordered to the totally disordered state is insig­ nificant.

Reflections on lines lOh, hlO, and Oil from 2 to 18° in 20 were col­ lected at the beginning of data collection and approximately every 24 hours thereafter for the purpose of calculating the rate of decay.

Identical reflections from each set of decay reflections are fit by the

procedure of Hanson et al. (68). An observed ratio, RQ, is calculated

by dividing the intensity of a reflection at time t by its initially

measured intensity. R^ is the calculated ratio based on the Hendrickson model. The rate constant is fit by a least squares procedure which

minimizes the difference between RQ and R^,. The final values of k^ for

the native and two heavy atom derivatives are given in Table 4.

Scaling A full data set typically involves collecting data from several crystals which will differ in such properties as size, absorp­

tion characteristics, and diffraction power. Data sets of isomorphous derivatives will also differ from the native crystal in scattering due

to the presence of one or more heavy atoms in the asymmetric unit.

These data sets must be placed on a common scale as we obtain phase

information based upon the differences in the amplitudes of the struc­

ture factors. Scaling is an instrumental part of data processing as an

error of 2% or greater in the scale factor can destroy the signal in the

difference Patterson map.

Four types of scaling have been employed. Crystals comprising one

full data set are placed on a common scale based on the multiple

measurement of the same reflection. An absolute scale factor is then 55

Table 4. Calculated k^s for the native and derivative crystals

Native 317a 417 517 617 717 kl 0.02106 0.01878 0.01281 0.02086 0.01587

GOpb 0.12209 0.12933 0.17300 0.06987 0.14584

HglA^- Mil MI2 MI3 MI4 MI5 MI6 MI7 kl 0.02974 0.01402 0.03901 0.03920 0.02448 0.03364 0.04016

GOF 0.13134 0.27149 0.17688 0.15843 0.28538 0.09073 0.30416

ErCl3+ citrate ECTl ECT3 ECT4 ECT5 ECT9 ECTIO ECTll kl 0.02133 0.02931 0.02797 0.02888 0.02386 0.02921 0.01942

GOF 0.11855 0.10969 0.14346 0.17451 0.28510 0.15560 0.12235

ECT12 kl 0.02699

GOF 0.10949

^Crystals were labeled with an alphanumeric code. The number rep­ resents the order the crystal was used for data collection. In some cases the data from certain crystals were not used due to its poor quality. In the case of the native data 17 stands for the use of an imidazole-acetate buffer at pH 7. MI stands for the K^Hgl^ crystals and ECT stands for ErClg-citrate derivative crystals.

^Goodness of fit which is defined by: Z wi(Rq - Rc)2/E wj where w^ is l/(sin0/X)^. RQ and R^ are defined in the text. 56 calculated by the means of a Wilson plot. Native and derivative data are placed on the same scale by applying an absolute scale factor to the derivative data. Finally, a process of local scaling based on the method developed by Matthews and Czerwinski (73) was applied to the derivative data to limit the effects of systematic errors.

Scaling of data sets Scaling of data sets from several crystals is carried out by comparing multiple measurments of the same

reflection. The method of Hamilton et al. (74) was employed. The observational equation assumes the form

$(h)i = (w(h)i)l/2(F(h)i2 - GiF(h)2).

where F(h)i is the ith independent observation of the reflection h, Gj

is the scale factor for the ith observation and (w(h)i)l/2 is the weight

for the ith observation and is proportional to the estimated standard

deviation of F(h)j2. The function to be minimized is

N „ xp = Z E $(h)i2 h i=l

where N is the number of independent observations for reflection h.

The best least squares value for F(h)2 is given by

9^ = 0 9F(h)2

Taking the derivative readily gives the value of F(h)^.

F(h)2 = E w(h)iGiF(h)i2/E w(h)iGiZ i=l i=l 57

Introducing the above expression in for F(h)j2 causes $(h)j to be nonlinear in Gj. A standard nonlinear least squares procedure is adopted in which $(h)i is approximated by

N $(h)i = (w(h)i)l/2(F(h)i2 - GiF(h)2) + Z (9$(h)i/aGk)AGk i=l

An initial value of 1.0 is used for Gj, the partial derivatives are evaluated and the resulting linear equations are solved for ûGj by the usual least squares method. One of the parameters is fixed during re­ finement as the complete set of Gj comprise a linearly dependent set.

The correct the Gj and the process is repeated until the ratio of

ÙGi to the standard deviation of G^ is insignificant.

Absolute scale factor An approximate value of the scale factor is obtained from a Wilson plot. Wilson (75) proposed that the probability of obtaining a reflection between I and I + dl is given by

P(I) = (1/Zfj2)exp(-I/Efj2).

The Zfj2 is the summation of the squares of the scattering factors for atom j. The mean value of the intensity can be expressed as

= EfjZ.

A scale factor, K, is introduced which adjusts the value of the average intensity to best fit the equation

K = Efj2exp(-2Bsin2e/x2) the exponential term accounts for the thermal vibration of the atoms.

Taking the natural logarithm of both sides and rearranging leads to the expression

ln(/Efj2) = -ln(K) - 2B(sin2e/x2) 58

A plot of ln(/Zfj2) versus sin^0/X^ gives a line with slope -2B and y intercept -ln(K).

This derivation is based on the assumption of a random arrangement of atoms in the unit cell. This assumption is only partially true at high resolution where the best estimate of the absolute scale factor is obtained between 3 to 1.5Â resolution. However, this assumption does not hold true at low resolution and the values obtained from a plot of low angle data may be greatly in error. A meaningful value for the temperature factor cannot be obtained. Consequently B in the exponen­ tial term is set equal to zero for low resolution work. The scale factor is then given by

(1/K) = /Zfj2.

The values of and Efj^ are calculated in resolution ranges of sin0/X. Five ranges between 3 and 18° in 20 were used for the native and derivative data sets. The scattering factor contribution was calculated based on the amino acid composition of the protein and the number of polypeptide chains in the unit cell. The contribution of heavy atoms for the isomorphous derivatives was calculated using an assumed number of heavy atoms per unit cell. The scale factor was cal­ culated as 1/K by dividing the multiplicity corrected intensities by the corresponding scattering factor for the proper range of sin0/X and then taking the average value of this ratio by dividing by the total number of reflections in the range.

Scaling of native and derivative data Scaling of native and derivative data is carried out by adjusting the terms to compensate 59 for the extra scattering due to the heavy atoms. The following relation holds in general, defining Kpjj, the scale factor in terms of Fy, Fpy and

Fp:

The native data must be on absolute scale. An estimate of F^^ must be obtained as its value is still unknown at this point of data processing.

For centric zones disregarding "cross-over" conditions where Ffj and

Fp have a phase difference of Ji, Ffj is given by Kp^Fp^ - Fp. Substitu­

tion of this approximation in for Fpj in the initial equation yields

KpH%FpHFp = %Fp^ which can be readily rearranged to give

KpH = SFp^/ZFpjjFp.

The scaling of native and derivative data was carried out using centric reflections from 4.4 to 18.0° in 20. The maximum value of Fy^ was calculated using a nine component expansion of the scattering fac­

tor. An estimated number of heavy atoms per unit cell was used in the

calculation. This estimated value of Fjj^ is used to screen out poten­

tial cross-overs, i.e., values where F^ > KpjjFpfj + Fp, which occur when

Fpfj and Fp are small. The initial value of Kp^ is unity. Thus, when

KpH is calculated from selected centric data, the search for potential

crossover terms must be repeated. Cycles of search and calculation of

Kpfi are performed until a stable set of reflections are retained. Usu­

ally two to three cycles of the above process results in a stable set.

An initial estimate for Kpjj was obtained from the expression

ZFp^/EFpfjFp calculated from the centric reflections. A better value for

the scale factor is obtained from the acentric data by replacing F^ with 60

Ffj(est), an estimated value of F^.

EFH^Cest) = KpH^ZFpH^ - EFp? so that Kpjj can be obtained as follows

KpH^ = (EFn^Cest) + 5:Fp2)/EFpn^.

Ffj(est) is estimated from isomorphous data as - Fp)l/2.

If anomalous scattering data are available, then Ffj(est) is given by

Fhle> the heavy-atom lower estimate;

FHLE^ = + Fp2 - 2[FM2fp2 _ {(k/4)(M)}2]l/2

where

Fm2 = (KpH/2)[F(h)2 + F*(-h)2], M = KpH[F(h)2 _ F*(-h)2|, and k = kemp/2. k-emp is an estimate of the relative errors in the

measurement of isomorphous and anomalous differences. Only acentric

reflections are used in the calculation, which involves the ratio of the

real and imaginary parts of the heavy atom structure factor, kg^p is

given by

2[(E(Kph2FPH2)1/2 _ Fp2)2/j;{(Kpj^2F(h)2)l/2 _ (KpH2F*(-h)2))l/2)2]l/2

An initial estimate of Kpjj must be known before Ffj(est) can be calculat­

ed. The scale calculated from the centric data was used. An improved

value of the derivative scale factor is obtained using FjjCest). The

process is repeated until convergence is reached, i.e., when the newly

calculated scale factor is within 0.1% of the previously calculated

scale factor.

Local scaling Systematic errors may arise in a given data

set due to a number of problems including absorption and misalignment

errors. The method of local scaling (73) is used to eliminate these 61 errors as much as possible. Scale factors are calculated for local regions of reciprocal space instead of the whole of reciprocal space as is usually done. These local scale factors are more sensitive to sys­ tematic errors which vary as a function of h, k, and 1. On the other hand, local scale factors are calculated with far fewer reflections so they have larger statistical uncertainty. A balance must therefore be achieved between the sensitivity of the factor and the number of reflec­ tions used in the calculation of the factor.

Assume and I2 represent two intensities from two sets of data which are to be compared. For example, I2 might correspond to the intensity as measured from a native crystal and I2 would correspond to the same reflection measured in an isomorphous derivative.

The local scale factor, K^, should minimize the sum

Zwidi - IcKi)2 where the summation is over a local region of reciprocal space. Ig is a calculated intensity based on weighted values of and I2 and is calcu­ lated for each pair. The w^ are weighting factors for each intensity and are proportional to the inverse of the standard deviation for the measurement of that reflection. The scale factor, Kj, for the reference data set, Ij, is set equal to one as and K2 are not both linearly independent. Some of the local scale factors, which are calculated for each h, k, 1, may be subject to large statistical uncertainty due to the small number of common reflections in reciprocal space. The statistical uncertainties are removed by a smoothing algorithm involving either the

7 or 27 nearest neighbors in reciprocal space. 62

Local scaling has been applied to both the Hgl^^" and the ErClg,

citrate derivative data sets. The native data must be on absolute scale

before applying local scaling. Local regions consisted of blocks of 10

to 125 reflections with a 20 of 3° or greater. The scale factor for a

block of reflections was calculated by the method of Hamilton et al.

(74) discussed previously. In order to reduce the statistical variation

in the scale factor amongst the various blocks a 27-point smoothing

algorithm was employed.

Location of heavy atoms The Hgl^^- heavy atom positions were

located in a difference Patterson map employing coefficients (PpQ - Fp)^

obtained from the scaling of native and derivative data sets. The use

of local scaling greatly improved the signal-to-noise ratio of the heavy

atom vectors. The improvement seen with local scaling suggests that

systematic errors may be present. This will be discussed in the fol­

lowing chapter.

A Patterson map is refered to the a, b, and c reference frame of the

unit cell. By convention the coordinates of a peak in the Patterson are

assigned the triple (u, v, w) whereas coordinates of atoms in the cor­

responding electron density map are assigned the triple (x, y, z). A

useful property of the Patterson map is the concentration of vectors in

well defined regions of u, v, w space due to the symmetry of the space

group. These concentrations of peaks, known as Marker planes or lines,

correspond to unusually high average intensity regions of reciprocal

space. Marker peaks can be used to locate heavy atoms in (x, y, z)

space. The two-fold screw axis of space group P2;j^ produces a Marker 63 section at u, 1/2, w where u = 2x, w = 2z and y is undefined. Locating a heavy atom vector on the Marker plane assigns a value to x and z with the y coordinate being arbitrary and specifies the origin of the unit cell. The heavy atom related by the two-fold screw axis can be found at

-X, y + 1/2, -2.

The presence of two or more atoms requires more careful study to insure that all assigned coordinates relate to the same unit cell origin. The y coordinate is assigned by finding cross vectors at u, v, and w which connect two heavy atoms. Two heavy atoms in the unit cell at (xyz)i and (xyz)2 give rise to a cross vector,

(xyz)i - (xyz)2 = (uvw).

Due to the periodic nature of the Patterson function, a peak at u 1/2 w is equivalent to a vector of length u+1, 1/2, w or u, 1/2, w+1 or u+1,

1/2, w+1. The first heavy atom is chosen as (x, z) = (u/2, w/2). The second heavy atom may be located at any one of the following four (x, z) locations:

(u/2, w/2)

(u/2 + 1/2, w/2)

(u/2, w/2 + 1/2)

(u/2 + 1/2, w/2 + 1/2)

All cross vectors which can occur between atom one and atom two and

their space group equivalents are calculated and the Patterson map is searched for peaks corresponding to these cross vectors. Since y is

unassigned, the y value of one of the heavy atom peaks is set equal to zero. The y coordinate for the second atom is assigned the v value of

the cross vector. 64

If phase information for the protein structure has been obtained from a previous derivative, then this information can be used to locate the heavy atom positions of other derivatives by the method of differ­ ence Fourier techniques. The coefficients used in the calculation take the form (76)

(FpH - Fp)exp(iap)

The Fourier synthesis is dominated by the phases and not the magnitudes of the structure factors. Therefore, care should be used in the inter­ pretation of difference maps which depend on derived from only one heavy atom derivative. "Ghosts", peaks (both negative and positive) corresponding to heavy atom positions upon which the phases are based, may appear in the difference map of a new derivative. Sites common to the new and the old derivative should be treated with a great deal of skepticism.

Phases calculated with the derivative were used in the dif­ ference Fourier synthesis of the ErClg derivative. Peaks located in the difference Fourier were checked against the isomorphous difference Pat­ terson map calculated from the ErClg data. Local scaling of the ErClg data against native data resulted in a noticeable improvement in the difference Patterson.

Refinement of heavy atom positions The locations of heavy atoms in a Patterson map are only approximate positions. These positions can be defined more precisely through a process of least squares refinement.

At this stage of data processing values of Fpjj and Fp have been measured and an estimate of Fy can be calculated from positions of heavy atoms. 65

If the estimate of Fjj is correct and the amplitudes have been measured correctly then the vector triangle should close (see Figure 12). How­ ever, due to errors the triangle will not close. This lack of closure, ej, of the jth derivative, is defined as

Gj = FpH(obs) - FpH(calc) where

FpH(calc) = |Fp(calc) + Fj^Ccalc)!

With each refinement cycle the sum over all reflections of

Zw(FpH(obs) - FpH(calc))2 is minimized. Conventional least squares techniques are employed to calculate the shifts of the scale factor and the positional and thermal parameters of heavy atoms. The weight, w, is taken as 1/E where E =

2, the r.m.s. lack of closure error over all derivatives used in the calculation of oç for the reflection in question. Table 5 lists the occupancies and isotropic thermal parameters for the two site mercury derivative based on isomorphous and anomalous differences.

Phase calculation Blow and Crick (77) described the calculation of phases from an isomorphous heavy atom derivative as a probability distribution function based on a "lack of closure" error defined by

Gj = Fppj(obs) - Fp{j(calc).

This relationship has been discussed previously in regard to heavy atom

refinement. It is assumed in both cases that Fy is small in comparison

to Fp and Fpjj.

The probability that a phase is correct is related to the "lack of

closure" of the phase triangle for the angle otp and is given by 66

Table 5. Heavy atom parameters for the mercury derivative

Atom Site x y z O^so^ Og^o'' B(A2)C

Hg 1 0.1728 0.0000 0.3442 2.9 5.6 71.75

2 0.2831 0.2329 0.1053 2.4 4.6 55.92

&The occupancy based on isomorphous differences.

^The occupancy based on anomalous differences.

is the isotropic thermal parameter and is equal to 8n^w^ where y represents the r. m. s. atomic displacement.

Pj(oç) = exp[-ej(op)2/2Ej2] where Ej is the total error assigned to reflection j. If several heavy atoms are used simultaneously, then the total probability is given by the product of the individual probabilities:

P(oç) = n Pj(oç) = exp[-E(Gj(ap)2/2Ej2].

Two possible transforms arise from these considerations.

The most obvious case would be to simply use the o^s with the high­ est probabilities for each value of F(h). This results in the "most probable" Fourier. Indeed, this would be a reasonable thing to do for a nearly unimodal distribution, but P(o^) tends to be bimodal. Serious errors can arise if the incorrect value of oç is chosen.

Selecting the centroid of the probability distribution represents a

better choice. This can be demonstrated by examining the error in electron density arising from errors in one reflection. An initial 67 value Fo(h) is chosen for this reflection. F'p(h) represents the true value. The calculation of the Fourier synthesis introduces an error given by Ap:

Aph =

2 = (2/V2)(Fo - Ft)2.

Fip is not known precisely and must be estimated in the form of the probability distribution function. A weighted mean is taken over all possible values to give,

2rt 2n <6ph> =2 J" (Fq - Fexpiop)2p(ap)dap/f P(oç)doç V2 06=0 cx=0 where Fexpia = F-p. The numerator in this expression is equivalent to the moment of inertia of a ring, mass P(cxp) and radius Fexpio^, about an axis which is perpendicular to its plane and which passes through the

end of vector FQ. By the parallel axis theory, this integral has a min­

imum value when FQ is at the center of gravity of the ring, i.e.,

2 It 2%

Fgfbest) = FQJ (expioç)P(oç)doç/J P(oç)doç ot=0 0^0

By introducing the term m where

2n 2 It m = J (expioç)P(oç)doç/J" P(cq))do^ ot=0 ofcO we obtain

FQ(best) = mFQexp(io(best))

m is the figure of merit and is effectively a weighting scheme for the calculated phases. The sharper the probability distribution the closer 68 m is to unity. A Fourier synthesis calculated with mF and a(best) is expected to have the minimum mean square difference from the Fourier transform of the true F's when calculated over the whole unit cell and is known as the "best Fourier".

The inclusion of anomalous scattering data in the phase probability calculations was first discussed by Blow and Rossman (78) and expanded by North (79) and Matthews (80). Matthews (80) has shown that the lack of closure terms for anomalous scattering may be written as

+ e_2 ^ 0.5{(e+ + e_)2 + (e+ - e_)2} where and e_ represent the lack of closure for a reflection and its inverse, respectively.

Im

Real

Figure 17a. Vector relationships for anomalous scattering and the error vectors G+ and e_

Figure 17a is an Argand diagram displaying the vector relation­ ships for anomalous scattering and the error terms and e_. D(h) is the resultant vector of Fp(h) + F^g(h). The mean of anomalous pairs,

Fpjj', is equal to (F(h) + F*(-h))/2. If there were no anomalous scat- 69

tering D(h) and Fp^' would be equal, but in the presence of anomalous scattering they are unequal. Their difference can be used to assess the lack of closure terms for isomorphous scattering. The anomalous pairs are used to estimate the error terms for anomalous scattering.

If E and E' are defined as the estimated total r.m.s. error in determining (e+ + e_) and(- s_) respectively, then P(oç), which is

the overall probability of a phase being correct, is given by

• f(e++E_)2 (e+ - s_)2y P(«p) = exp - + — L I 2E2 2E'2 J. P(oç) can be rewritten as

P(cq)) = Piso(^ ^ano^®?"^

PisoCoç) represents the phase probability distribution using isomorphous

replacement and is given by

Piso(«p) = exp{-2(D(h) - Fph')2/e2}

where (G+ + e_) is equal to 2(D(h) - Fpfj') and is known as the 'total

isomorphous lack of closure'. Pano^^ï") is the probability distribution

obtained from anomalous scattering and is dependent on the types of

anomalous scatterers present in the structure.

We shall only treat the case where all the anomalous scatterers are

of the same type. In this case W must be it/2. - E_, the 'anomalous scattering lack of closure', is given by

E+ - E_ = -F(h) + F*(-h) + 2S(h)cos(oi^s - a + n/2)

= -F(h) + F*(-h) - 25(h)sin(o(fts - a)

From Figure 17b we use the Law of Sines to show that 70

Im

D(hX

Fp(h)

Real

Figure 17b. The vector relationship D(h) = Fp(h) + FAg(h) and pertinent angles

sin(o%g - a) = [Fp(h)/D(h)]sin(~

For the case where all the anomalous scatterers are the heavy atoms of

the derivative o^g = ay. By substitution we obtain

- e_ - -F(h) + F*(-h) - [2Fp(h)6(h)/D(h)]sin(oH - op).

The probability distribution for the phase of Pp derived from anomalous scattering measurements arising from crystals containing only one kind of heavy atom derivative is; therefore, given by

PanoW) = exp[-(E+ - E_)2/2E'2].

Phase probabilities were calculated based on isomorphous and anoma­

lous differences from the derivative. The probability function was calculated in 10° of around the phase circle for each reflection.

The components of the Fourier synthesis are given by

mcosa(best) = EP(oti)cosai/21P(cxi)

and

msina(best) = EP(a^)sina^/ZP(oq^) 71

The error in the phase angle for a given otj is defined as ûot^ = a(best) - . By a proper shift in the origin a(best) = 0 so that |oj |

= 1 ûoj I . Under these conditions the figure of merit is given by

m = EP(a^)cosa^/ZP(a^)

= . m represents the mean value of the cosine of the error in phase angle for the reflection.

Phase refinement was done in sets consisting of ten cycles each.

The first set refined a scale factor, which is applied to the derivative data, and an overall temperature factor which represents the difference between native and derivative temperature factors. The second set of ten cycles refined the atomic positions. Finally, the third and following sets included the refinement of the occupancy and isotropic thermal parameters. Due to the high degree of correlation of these two parameters at low resolution, they were refined on alternate cycles. 72

RESULTS AND DISCUSSION

Three different crystal forms of adenylosuccinate synthetase from a

mutant strain of coli have been grown. The structure determination of the 22^ crystal form was pursued due to its rapid and reproducible growth. Phasing was accomplished with isomorphous and anomalous differ­ ences obtained from a single heavy atom derivative.

Crystallization of the 22^ form was influenced by several factors.

Growth of this crystal form occurred more readily if the protein solu­

tion was concentrated first to at least 25mg/ml or more than diluted

with an imidazole, succinate, 2-mercaptoethanol buffer to the proper

concentration. The presence of succinate and 2-mercaptoethanol was re­

quired for the growth of the P2i crystal. In the absence of succinate

crystals did not grow. Crystallization attempts using protein dialyzed

against imidazole (lOOmM, pH7.7), succinate (75mM) and dithiothreitol

(ImM), in place of 2-mercaptoethanol, resulted in the formation of an

amorphous precipitate. When protein solution from the same purification

batch was dialyzed against imidazole (lOOmM, pH7.7), succinate (75mM),

and 2-mercaptoethanol (70wl/l), crystals grew in approximately one

week.

Stabilization Buffer

Finding a suitable stabilization buffer was problematic. Crystals

were sensitive to the type of buffer and to pH. The types of ions in

solution were also a concern, especially in regard to their potential to

interfere with heavy atom reagents. Buffers with elevated concentra- 73 tions of PEG 3350, mixtures of enzyme (~ 4mg/ml) and 40% (w/w) PEG 3350, and 100% MPD all proved unsatisfactory as stabilization buffers.

Solutions of PEG 3350 and MPD in various ratios stabilized the cystals nicely. A solution consisting of PEG 3350 at 25% (w/w) and MPD in a

95:5 (v/v) ratio was used as the stabilization buffer.

Imidazole (lOOmM, pH 6.6) and HEPES (50 and lOOmM, pH 7.7) were em­ ployed initially as buffering agents. It was originally assumed that solutions prepared with either imidazole or HEPES could be used inter­ changeably. However, problems arose when large discrepancies in inten­ sity measurements were seen in the first native data set. Data sets from two of the crystals, though agreeing with each other, deviated sig­ nificantly from data sets collected from other crystals. The results from a systematic study suggested that these differences resulted from the use of imidazole as a buffering agent for two of these crystals and the use of HEPES buffer for the others. Evidently the crystalline synthetase is sensitive to the buffer or to pH. Potassium phosphate was also tried as a buffering agent. Initially, a stabilization buffer pre­ pared with O.IM potassium phosphate was used. Crystals mounted with the

O.IM potassium phosphate buffer diffracted poorly. In retrospect this result is not surprising as phosphate inhibits the enzyme at a concen­ tration of approximately lOmM (81). A solution prepared with lOmM potassium phosphate did not disrupt the crystal as diffraction was not affected. Imidazole (O.IM, pH 7) was chosen as the buffer for the re­ mainder of the experiments in order to avoid further difficulties.

Our final concern involved the use of the proper counterions. Ace­ tate was first used as other ions are known to inhibit the enzyme (38). 74

However, acetate could complex the lanthanides preventing their inter­ action with the protein. Chloride, which is known to inhibit the syn­ thetase (38), was then tried as a counteranion. No differences were seen in the diffraction patterns between crystals mounted with the imidazole-acetate buffer and crystals mounted with the imidazole-HCl buffer. We concluded that the use of Cl~ as a counteranion posed no problems. The imidazole-HCl buffered solution was used for experiments involving the lanthanides, 002(^03)2, and platinum compounds. The imidazole-acetate solution was used for the native data and for crystals soaked with mercurials.

Heavy Atom Derivatives

The search for heavy atom derivatives (Table 6) initially focused on the use of mercury. Previous work demonstrated that the synthetase from rabbit skeletal muscle is inhibited by mercurials (11). Our own experi­ ments demonstrated that the Ej^ coli synthetase is inhibited within three hours by a wide variety of mercurials, including Hgl^^", HgCl2» CHgHgCl, p-Hydroxymercuribenzoate, Hg(N03)2» and Hg^CN)^^-. Striking evidence of mercurial binding was obtained with the bright yellow derivative

2-chlororomercuri-4-nitrophenol (82). Crystals of the synthetase turned bright yellow at concentrations as low as 0.2mM in 2-chlororomercuri-

4-nitrophenol, but no changes were seen in the diffraction pattern which would have indicated a suitable heavy atom derivative. Higher concentrations only weakened the diffraction power of the crystal. This was seen with the majority of mercurials. Differences were seen in the diffraction pattern upon soaking with CHgHgCl, but the diffraction was 75

Table 6. Heavy atom soaks of crystals

Heavy Atom Concentration Length of soak Result^

Lanthanides

ErCl] 2.5mM 15 minutes C l.OmM 8 hours C O.SmM 2 weeks N

GdCl] 2.5mM 15 minutes C l.OmM 8 hours C

LaCl] 2.5mM 15 minutes c l.OmM 8 hours c 0.5mM 6 days N

LaClg+citrate 2.5mM in both 8 hours c

SmClg+citrate 2.5mM in both 8 hours c

ErClg+citrate 2.5mM in both 3 days D 2.0mM in both 2,.5 days D l.OmM in both 3 days D

LUCI3+C itrate 2.0mM in both 1 hour C l.OmM in both 1 hour C

ErClg+K^POy a. 2.25mM in ErCl] 2.0 mM in K4PO7 4 days N b. 4.75mM in ErCl] 5.0 mM in K4PO7 16 days F,N

LaClg+K^POy 2.25mM in LaClg 2.0 mM in K4PO7 7 days F,N

Uranyl

U02(N03)2 1.75mM 2 days U,N 1.0 mM 5 days W,N

U02(N03)2+citrate 2.5 mM in both 5 days C

5 cracking; D 3 derivative; F = fragile, cracks easily; N = not a derivative; ND 2 no diffraction; W s weak diffraction. 76

Table 6. (continued)

Heavy Atom Concentration Length of soak Result

Mercurials

CHgHgCl l.OmM 3 days W,D 0.ImM 6 days N

CHgHgCl + 2-mercaptoethanol l.OmM in both 10.5 days ND

Hg(CN)42- l.OmM 2-8 days W,N

2-chloromercuri- 4-nitrophenol 0.05mM 8.5 days N O.lmM 24 hours N 0.2mM 3 days N 0.5mM 5 days W,N

K2Hgl4 2.0mM 4 days

Platinum

K2PtCl4 lO.OmM 2.5 days W,N

K2Ptl4 2.0mM 11 days W,N l.OmM 11 days W,N 1. OmM 5 days W,N 0.5mM 2 days W,N

[Pt(trpy)Cl)-b 2.5mM 2 days ND

bchloro(2,2';6',2"-terpyridine)platinum(II).

weak and the crystals rapidly decayed upon exposure to X-rays. Longer

soaks with CHgHgCl destroyed diffraction altogether. Weakened diffrac­

tion was also a characteristic with the platinum soaked crystals. In

all cases the probable site of binding is the sulfhydryl of cysteine.

There are four cysteines per monomer (15) and at least one, cysteine 77

291, is readily available (Dr. Herbert Fromm, personal communication;

Dept. of Biochem. and Biophys., Iowa State Univ.). Apparently binding to cysteine may disrupt the crystalline protein.

One exception to the pattern was found by Yunje Cho. The mercurial,

K^Hgl^, forms an excellent derivative demonstrating significant changes throughout the diffraction pattern. K^Hgl^ may be binding electrostat­ ically as Hgl^Z" or Hglg". In addition Hgl^^- may bind as Hglg" or Hgl2 to hydrophobic regions of the protein. For instance, the Hglg" ion was bound in a hydrophobic pocket next to the heme of sperm whale myoglobin

(83). With this in mind the search for heavy atoms turned to possibil­ ities which would form electrostatic interactions.

A number of lanthanides and U02(N03)2 were tried and gave rather curious results. The lanthanides ErClg, GdClg, and LaClg caused severe cracking at concentrations between 2.5 and ImM. Crystals did not crack when exposed to 0.5mM solutions of ErCl] and LaClj, but they showed no apparent changes in their diffraction pattern. Soaks with 1 and l,75mM

U02(N03)2 gave only weak diffraction and no apparent changes. Lanthan­ ides form stable complexes with chelating oxygen ligands (84). With the failure of the lanthanides to work alone they were tried in a 1:1 com­

plex with citric acid. Solutions of SmClg-citrate, and LaClg-citrate caused severe cracking of the crystal. Curiously, ErClg-citrate gave a derivative, causing intensity changes in the diffraction pattern at con­ centrations ranging from 2.5 to ImM. However, there appears to be a

problem with mosaic spread at higher concentrations. The difference in

reactivity was assumed to be due to the difference in ionic radii.

Perhaps the erbium-citrate complex is binding to the same site as Mg2+ 78

(atomic radius of 0.66À (85)). Er3+ has a much smaller radius (0.881Â

(85) then does La^"*" (1.016Â (85)) or Sm3+ (0.964À (85)) which would

allow it to squeeze into sites where the others could not fit. If this

were the case than a smaller atom should also bind and reduce the

problems of mosaic spread. The Lu^* ion has an atomic radius of 0.85Â

(85); however, use of a LuClg-citrate solution at two different concen­

trations (1 and 2mM) severely cracked the crystal. The reason for the

difference in reactivity of the erbium-citrate complex and that of the

other lanthanide-citrate complexes remains unclear.

Patterson Map

The Patterson map was divided into 40 sections along each axis of

the unit cell. Due to the centrosymmetry of the Patterson function and

the symmetry of the space group only sections from 0-20 in u, 0-20 in v,

and 0-39 in w were examined (an asymmetric unit of the space group

P2/m). A Patterson map, based on isomorphous differences, was calculat­

ed (Figure 18a). Two prominent vector peaks corresponding to heavy

atoms were found on the Barker plane u, 1/2, w. The signal-to-noise

ratio of the peaks was improved by applying local scale factors to the

derivative data. The unrefined atomic coordinates for the four mercury

sites (two sites plus screw related positions) are as follows:

x^ = 0.174 y^ = 0.000 = 0.344

xi'= 0.826 yi'= 0.500 zi'= 0.656

X2 = 0.288 y2 = 0.238 Z2 = 0.106

X2'= 0.712 y2'= 0.738 ^2'~ 0.894. 19

SECTION 20

Z-axis

SECTION 20

Z-axis 80

An anomalous difference Patterson map was also calculated (Figure

18b). The map is excellent and contains less noise than does then iso- morphous difference map. This result runs contrary to what is usually seen in the calculation of Patterson maps. An anomalous difference map generally contains more noise and has weaker signals than does an iso- morphous difference map.

A likely cause for the poorer quality of the isomorphous Patterson map is the presence of nonisomorphism. Binding of Hgl^^" may be dis­ torting the synthetase. Anomalous differences are not sensitive to changes due to nonisomorphism, whereas isomorphous differences will be affected by nonisomorphic changes resulting in a noisy Patterson map.

Rotation Function

A self-rotation function was calculated in order to locate the posi­ tion of the noncrystallographic two-fold axis. According to Rossman and

Blow (87) the function that will relate one subunit to another is given by [C]x + t. [CJ is a matrix which represents the rotation of a set of coordinates, x, about the origin, and t is a translation vector. The rotation matrix is given by [C] = [a][p][g]. The [ g] matrix trans­ forms oblique crystallographic coordinates to Cartesian coordinates, [p] is a rotation matrix written in terms of the three Eulerian angles 0]^,

02, and 63 (Figure 19), and the [a| matrix transforms the rotated coordinates back to the oblique system. Crowther (88), whose rotation function program we used, employs the Eulerian angles ot, g, and y, related to the angles of Rossman and Blow by the relationships a = Sj -

11/2, p = 02, and y = 0% + R/2. 81

Z

Figure 19. A diagram demonstrating the three Eulerian angles 0^, % and 63. This diagram was taken from a paper by Eaton Lattman (86)

The four highest peaks, including the origin peak, are listed in

Table 7. Peak heights are relative to the height of the origin peak.

The highest, nonorigin peak was found at a = 100°, P = 180° and y = 0

Table 7. Eulerian angles (°) for peak positions obtained from the self-rotation function

Relative a (%) g = 82 Y (63) Peak Height

0 (90) 0 0 (-90) 1.00 100 (190) 180 0 (-90) 0.58 10 (100) 180 0 (-90) 0.40 40 (130) 0 50 (-40) 0.28 82

The [p) matrix given by Rossman and Blow (87) can be reduced when ©2 is either 0° or 180°. The highest, nonorigin peak was found on section

02 = 180°. Under this constraint (p] reduces to

-cos(a - Y) -sin(a - Y) 0

[ p] = -sin(a - Y) -cos(a - Y) 0

0 0-1

The rotation is dependent on the angle a - y- ot - y for the highest, nonorigin peak is 100°. The explicit form of the [p] matrix for the monoclinic crystal form of adenylosuccinate synthetase is obtained by substituting 100° in for a - y. This substitution yields

" 0.1736 -0.9848 0

[p] = -0.9848 -0.1736 0

0 0-1

[ PJ will convert fractional coordinates in the crystallographic frame to coordinates in an orthogonal frame. The orthogonal frame is specified by Crowther. For the monoclinic crystal system, b axis unique, the axes lie as follows: b along Z, c along X, and a* along Y.

X, Y, and Z are orthogonal vectors of a right handed system. For a monoclinic crystal system [ g] has the general form

• acosg 0 c

[P] = asing 0 0

. 0 b 0

The [a] matrix is the transpose of (P]~^ and will transform the orthogonal coordinates back to the crystallographic frame. For a monoclinic crystal system the matrix has the general form 83

0 1/asinP c

[a] = 0 0 1/b

1/c -cosg/csing 0

The explicit forms of [ P] and [a] for the 22^ crystal form of adenylosuccinate synthetase can be obtained by inserting the proper unit cell parameters found in the chapter on crystallization, page 20. Per­ forming the substitutions gives the following matrices:

0 0.01439 0 -23.37 0 82.87 la] = 0 0 0.01384 and [ g] = 69.48 0 0

L 0.01207 0.004059 0 0 72.23 0

The orientation of the noncrystallographic two-fold axis is gotten from the three matrices [a], [p], and [g] and the coordinates of the heavy atoms obtained from the Patterson map. We first calculate which pair of heavy atoms are related by the two-fold axis. We can then use this information to calculate the translational vector, thereby fully characterizing the rotational and translational components which will superimpose one subunit onto another.

We wish to know if two heavy atoms are related by the noncrystallo­ graphic two-fold axis. It would at first appear to be a simple matter of applying the rotation matrix [p] to one set of coordinates to see if they produce the second set; however, there might also be a translation­ al component involved which we have no way of describing at the present time. We must; therefore, reduce the problem to one of strict rotation.

The translational component disappears if we translate the origin of the coordinate frame to a point on the rotation axis (Figure 20). The vector DC, terminating at the mid-point between sites Xj and X2, is 84

A 9. &

Figure 20. A diagram dislaying the vectors used to calculate which heavy atom pairs were related by the noncrystallographic two-fold axis. Heavy atom positions were projected onto sections 12-17 and are shown as dark circles. Some elec­ tron density has been removed for clarity given by l/2(Xi + X2). The vectors Xj' and X2' can be calculated since

Xi' = Xi - OC and X2' = X2 - OC. We can now apply [ p] to either X^' or

X2'. If a pair of heavy atoms are related by the noncrystallographic

two-fold axis than the rotation matrix applied to one set of coordinates should generate the second. For example, the pair of coordinates

(-0.174, 0.500, -0.344) and (0.288, 0.238, 0.106) 85 were compared. Orthogonalization and translation through OC produced

the vectors

1) <-13.24, -16.05, 9.46> and 2) <13.25, 16.05, -9.47>.

Applying the rotation operation to the second vector gave the following:

<-13.50, -15.83, 9.47>.

While this is not identical to vector number one, being separated by a distance of 0.34Â, it is certainly close, and the error can be attributed to the crudeness of the coordinates we obtained from the

Patterson map. This process, combined with a careful study of the electron density map, revealed that the heavy atom pairs (0.174, 0.000,

0.344) and (0.712, 0.738, 0.894); (0.826, 0.500, 0.656) and (0.288,

0.238, 0.106) are related by the noncrystallographic two-fold axis.

The translational vector can be calculated with regard to two dif­

ferent reference frames. For the crystallographic reference frame we

have t = X2 - [Cjxi. (C] is the rotation matrix described previously.

For the monoclinic system of the P2]^ crystal form of adenylosuccinate synthetase [C] takes the form

• 0.1576 0 -1.174 •

(C] = 0 -0.9997 0

.-0.8318 0 -0.1576.

X2 and x^ correspond to the fractional coordinates for the heavy atoms

related by the two-fold axis. For the orthogonal frame, the transla­

tional vector T is given by T = X2 - [ p) is the rotation matrix

previously described, X]^ and X2 correspond to .the orthogonalized coor­

dinates of the heavy atoms related by the two-fold rotation. Using a

suitable pair of heavy atoms we find that the translational vectors are 86

t = <-0.088, 0.738, -0.094> and T = <-5.61, -6.16, 53.31>.

We have now fully described the rotational and translational components for the monoclinic crystal form of adenylosuccinate synthetase in both

the orthogonal and crystallographic reference frames. Y

X Figure 21. A diagram displaying spherical polar angles X» This figure is taken from a paper by Eaton Lattman (86)

In order to better visualize the orientation of the noncrystallo- graphic axis relative to the unit cell axes, we convert Eulerian angles

to spherical polar angles X> 4», ^ (Figure 21). The spherical polar

angles are related to the Eulerian angles by the following relation­

ships:

cos(X/2) = cos(02/2)cos[(©I + 02^/2]

tan* = -cot(02/2)sin[(0i + 63)/21sec((Gj - Qt,)/?.]

cos

Utilizing the values %, 02» and 83 of the highest nonorigin peak in the

self-rotation function we find that X = 180°, <{> = 180° and = 50°.

This tells us that the molecular two-fold lies perpendicular to the b 87 axis, and is inclined approximately 40° in a clockwise direction with respect to the negative c axis (Figure 22c).

Electron Density Map

The statistics of phasing based on isomorphous and anomalous differ­ ences are found in Table 8. The figure of merit of 0.75 is fairly

typical at this resolution, and indicates an average error of approxi­ mately 41° in the calculated phase angles.

The electron density map was divided into 40 sections along each axis in x, y, and z. Sections of the electron density map as viewed down the crystallographic b axis are shown in Figure 22a-e. These sec­

tions display the density of four unit cells (see Figure 22c). The

molecular envelope of the dimer is centrally located in the map and its density is outlined. Density related by a translation along a unit cell edge is also outlined. Electron density which is not outlined corre­ sponds to molecular dimers related by the two-fold screw axis. The

interface between proteins along the b axis is found on sections 34 and

35. Little density belonging to the dimer is found on these sections

and they have been omitted.

Figure 22c displays a slab of density approximately 11Â thick and

reveals the overall shape of the dimer. These slabs are symmetrically

displaced about the molecular two-fold axis (arrow). The envelope of

the dimer displays two-fold symmetry consistent with the results of the

self-rotation function. The dimer envelope measures approximately 70Â

along the b axis and has a maximum radius of 42Â in the plane defined by

the a and c axis of the unit cell. Table 8. Statistics of phasing based on isomorphous and anomalous differences

Resolution in À

14.55 11.43 9.41 8.00 6.96 6.15 5.52 5.00 Total

a 0.85 0.80 0.79 0.75 0.75 0.72 0.75 0.73 0.75

Isomorphous Differences

No. Refl. 58 122 186 248 368 465 566 665 2678

r.m.s.Fgb 400.45 387.20 358.64 342.35 310.96 283.80 255.98 224.37 289.33

R modulus^ 11.53 10.27 12.07 14.34 16.25 17.40 16.13 15.30 15.03

R (gen. 12.81 11.12 12.70 15.22 17.44 18.87 17.85 16.92 16.03

IT • m • S • LOIso® 170.02 150.30 170.39 174.30 163.05 154.09 147.01 153.81 157.17

Anomalous Differences

No. Refl. 58 122 185 245 360 456 551 656 2633

r.m.s. Dgf 74.62 72.11 64.87 64.90 56.34 52.11 49.41 45.91 54.69 r.m.s. DyS 87.12 81.64 72.20 72.07 61.24 57.03 53.71 54.38 61.43

R (gen.)h 33.38 30.08 27.98 26.39 23.65 34.08 28.76 34.01 30.02 IT• m •s • LOIsoi 30.91 28.63 22.20 20.45 16.28 20.53 17.55 19.91 20.12

^Figure of merit: mean value of the cosine of the error in the phase angle.

br.m.s. Ffj = where fg is the amplitude of the heavy atom structure factor, and n is the total number of reflections.

modulus = 100[ j;(FpH°-FpH^)/EFpH°]. Fpjj° and Fpjj^ correspond to amplitudes of the observed and calculated derivative structure factors respectively.

^Generalized R = 100[Zw^CFpH^-FpH^^)^/Zw2FpH°^]and W2 are weighting factors.

®r.m.s. lack, of isomorphism = ( E| Fpu°-Fpjj^| The absolute value of the lack of closure is divided by the number of reflections, n.

^Calculated r.m.s. difference = where AD^ is the calculated vo anomalous difference.

^Weighted r.m.s. difference = (wiZADg2/n)l/2 y^ere ADq is the observed anomalous difference and w^ is a weighting factor.

^Generalized R = 100(wj(ADq-AD(,)^/w2ADo^)^''^. wj and W2 are weighting factors.

ir.m.s. lack of isomorphism = (2(ADQ-ADc)2/n)l/2. 90

Examination of the envelope reveals density which corresponds to two small domains of the dimer separated from a large, central domain

(Figure 22d). Moreover, the two crevices created by the interface of

the small and large domains serve as sites for the binding of Hgl^^"

(Figures 22b and 22d). Mercury inactivates the synthetase from rabbit skeletal muscle (11) and the enzyme from E^ coli (unpublished results;

Dept. of Biochem. and Biophys., Iowa State Univ.). Inhibtion may be caused by the binding of mercury to the active site, thus identifying

the crevice between the small and large domain as the active site.

Furthermore, the formation of this recess may require the dimerization

of inactive monomers (10).

Comparison of the right and left hand of the dimer revealed possible

asymmetry about the molecular two-fold axis. The packing environment

about the small domains appears to be different. The small domain of

the left hand monomer comes into close contact with neighboring

molecules (Figures 22c and 22d). These protein-protein interactions

apparently alter the conformation of the small domain as suggested by

the lack of a prominent crevice in the electron density map between the

large and small domains of the left hand monmomer. Tight protein-

protein contacts would serve to explain why these crystals crack in the

presence of certain ligands. If the crevice is the active site, and if

a conformational change is occurring as suggested by Nichol et al. (61)

and by our own soaking experiments, then binding of a ligand would cause

a conformational change leading to the movement of domains. This move­

ment would disrupt the protein-protein contacts. The resulting stress

would then lead to the cracking of the crystal. 91

It is interesting to speculate about the possibility of conforma­

tional change and what this might suggest about the mechanism. The

three different mechanisms (see Figure 3) all incorporate the formation of a 6-phosphoryl IMP intermediate. They differ in the proposed role of aspartate. Aspartate has been suggested to participate in the reac­

tion before (21), during (19) or after (8,20) the formation of the

6-phosphoryl IMP intermediate. The equilibrium isotope exchange experi­ ments by Cooper et al. (23) suggest that aspartate binds most often to an IMP-GTP-enzyme complex. In our soaking experiments we have noticed

that only IMP and guanine nucleotides cause apparent changes in the crystal. Perhaps the conformational change brings the IMP and GTP sites closer together to allow for the formation of the 6-phosphoryl IMP intermediate and to position the intermediate in such a way as to allow for the nucleophilic attack by aspartate on the six position.

The 5Â electron density map was calculated based on isomorphous and anomalous differences. The map is not of sufficient resolution to

permit a chain trace; however, the map does clearly reveal the molecular envelope of the dimer. Each monomer appears to consist of a large and small domain. The derivative, Hgl^^-, binds in the crevice created by

the interface of the small and large domains. Since mercury is known to inhibit the synthetase the interface may correspond to the active site.

Clarification of the domain and active site structure must wait for the high resolution structure and additional studies of enzyme-inhibitor complexes. Figure 22a. Electron density corresponding to sections -4 to 3. The refined positions of the heavy atom sites are indicated with an arrow and marked by a filled circle SIXV-X Figure 22b. Electron density corresponding to sections 4 to 11. The refined positions of the heavy atom sites are indicated with an arrow and marked by a filled circle

Figure 22c. An IIÂ thick slab of density (sections 12 to 17) which is symmetrical about the molecular two-fold axis (arrow). Four unit cells are shown. The molecular envelope displays two-fold symmetry consistent with the results of the self- rotation function

Figure 22d. Electron density corresponding to sections 18 to 24. The cleft is most evident in this section of density. An arm of density spans the region between the large and small domain (right). The derivative, Hgl^^", which is known to inhibit the enzyme, binds in the interface between the large and small domain. The refined positions of the heavy atom sites are indicated with an arrow and marked by a filled circle 99 Figure 22e. Electron density corresponding to sections 25 to 33. The refined positions of the heavy atoms are indicated with an arrow and marked with a filled circle

102

APPENDIX: STRUCTURE OF l-(p-NITROBENZYLIDINEAMINO)GUANIDINIUM CHLORIDEl'2

Abstract

CgHjQN502'''.Cl~, Mj. = ,243.67, monoclinic, P2i/c, a = 8.406(2),

b = 11.490(4), c = 11.510(2)Â, g = 101.89(2)°, V = 1087.7(5)Â3, Z = 4,

Dy = 1.49g cm-3, X(MoKai) = 0.70926Â, u = 3.48cm-l, T = 293K, F(OOO) =

504, final R = 0.056 for 1965 observations. Ionic/hydrogen bonds be­

tween the chloride ion and the guanidinium groups as well as stacking

interactions involving the guanidinium and phenyl groups maintain the

crystalline structure. The separation of planes of stacked guanidinium

groups is 3.72(14)A, and of phenyl planes is 3.46(26)A.

Introduction

ADP-ribosylation is an enzyme-mediated transfer of the ADP-ribose

group of NAD+ to an appropriate acceptor. Reactions of ADP-ribosylation

fall into two broad categories:

DNA Acceptor(ADP-ribose) + (1) Acceptor + nNAD+ poly(ADP-ribose) nNicotinamide + H+ polymerase

Acceptor(ADP-ribose) + (2) Acceptor + nNAD+ ADP-ribosyl Nicotinamide + H+ transferase

^Michael A. Serra and Richard B. Honzatko from the Dept. of Biochem. and Biophys., Iowa State Univ., Ames, lA. 50011.

^We thank Robert Jacobson of the Ames National Laboratory for the use of his facilities and the NIH (GM33828), CNR (N00014-84-G-0094) and FRF (1669-G4) for monetary support. 103

Poly-ADP-ribosylation (reaction 1) may play a role in the synthesis, transcription and repair of DNA. The polymerase for poly-ADP-ribosyl- ation requires DNA for activity. In fact, breaks in single- or double- stranded DNA enhance polymerase activity (for a review see reference number 89). Mono-ADP-ribosylation (reaction 2) is involved in the mechanism of cholera toxin, diptheria toxin, and heat-labile enterotoxin from Escherichia coli. The A^ subunit of cholera toxin, for instance, catalyzes the ADP-ribosylation of L-arginine (90). Cassel and Pfeuffer

(91) have evidence for the ADP-ribosylation by cholera toxin of the GTP binding protein from a preparation of solubilized adenylate cyclase.

Finally, Goff (92) has demonstrated ADP-ribosylation of an arginine residue in RNA polymerase of E. coli following infection with T4 phage.

The mechanism of transfer reactions involving the title compound is of interest to investigators studying the broader problem of ADP-ri­

bosylation of macromolecules. Soman, Tomer, and Graves (93) assayed for

the activity of ADP-ribosyl transferases by using l-(p-nitrobenzylidine- amino)guanidinium chloride as an acceptor of the ADP-ribosyl group. The kinetics of the transfer reaction could be sensitive to the tautomeric form of the guanidinium group as well as to its state of protonation.

Structures of the title compound under conditons of high and low pH will

provide information relevant to current speculation on the mechanism of

transfer reactions. We report, here, the structure determination of the salt l-(p-nitrobenzylidineamino)guanidinium chloride. 104

Experimental

Crystals of the title compound (provided by Dr, Soman, Department of

Biochemistry and Biophysics, Iowa State University) grew as yellow prisms from a yellow solution of HCl/ethanol. The specimen for data collection measured 0.70 x 0.68 x 0.35 mm. Unit cell parameters derived from setting angles of 15 reflections with 30 < 20 < 35°. Data over one quadrant (-13 < h < 13, 0 < k < 17, 0 < 1 < 17) were collected on a

Syntex diffractometer to 20 = 60° [(sin0/X)^^^ = 0.704Â~^] using

26-0 scans. Of the total 3481 reflections, 162 were extinct, 139 were redundant (Rint = 0.049), 1412 had intensities with I < 3a(I), leaving

1768 reflections with intensities above three standard deviations. In­ tensities of six standard reflections (20 < 20 < 56°) indicated no measurable decay. The transmission factors based on an empirical ab­ sorption correction (94) varied from 0.975 to 1.000. MULTAN80 (95) gave

the location of all non-H atoms. The H atoms were located in a differ­ ence map. We used 1965 structure factors to 0.6Â~^ in sin0/X in the weighted refinement [w = 1/o^(F)] of the positions and thermal tensors of non-H atoms. Scattering factors came from the International Tables for X-ray Crystallography (96). The highest and lowest peaks in the final difference map were 0.26 and -0.24 eÂ~^. The final statistics of refinement were (A/a)max ~ 0.03, R = 0.056, wR = 0.051 and S = 1.3018.

All calculations were done on a VAX 11/780 computer using programs

developed by Karcher (97), Powell and Jacobson (98), and Lapp and

Jacobson (99). 105

Discussion

Fractional coordinates and average isotropic temperature factors are

in Table Al; Figure A1 shows the atom-numbering scheme, and Figure A2 a

stereoview along the b axis. The near equivalence of bond lengths

(Table A2) of N to C of the guanidinium group [average length 1.320(2)Â|

and the near equivalence of bond lengths of C to C of the phenyl ring

[average length, 1.379(1)Â] indicate an extensive electronic resonance

in these moieties. Atoms fall into either the plane of the phenyl ring

[C(6), C(7), C(8), C(9), C(10), C(ll), C(12), N(13); root-mean-square

deviation from planarity, 0.0067Â] or the plane of the guanidinium group

[N(l), N(2), C(3), N(4), N(5); root-mean-square deviation from

planarity, 0.0015Â]. Guanidinium groups stack along the a axis with a

planar separation of 3.72(1A)Â. Even stronger stacking interactions

occur between C(10)-C(12^), C(ll)-C(ll^) and C(12)-C(10^)^ of the phenyl

groups. The separation of planes of stacked phenyl groups is 3.46(26)Â.

the chloride ion, Cl(16), binds to four H atoms of three molecules of

l-(p-nitrobenzylidineamino)guanidinium chloride (Table A3); the second

and third molecules are related respectively to the first by the glide

operation [atom H(18^^)] and by the symmetry operation (3/2) - x, -1/2 +

y, 2 - z [atom H(21^^^)]. Crystals of the title compound slowly decom­

pose into an amorphous powder upon exposure to the air. In view of the

proximity of four exchangeable protons to each chloride ion and the

anomalously low pKg (approximately 7.0; personal communication: D. J.

Graves; Dept. of Biochem. and Biophys., Iowa State Univ.) of the guani-

^The symmetry operations are as follows: (i) 2 - x, -1 - y, 1 - z; (ii) X - (1/2), y - (1/2), z; (iii) (3/2) - x, -(1/2) + y, 2 - z. 106 dinium group, deterioration of crystals may be a consequence of the for­

mation and volitilization of HCl from the crystal. 107

Table Al. Atom coordinates (x 10^) with e.s.d.s in parentheses and average temperature factors (À2 X 103)

Atom X y z Uav&

N(l) 8181(3) -2296(2) 10587(2) 53 N(2) 8171(3) -3938(2) 9459(2) 54 C(3) 8546(3) -2838(2) 9673(2) 40 N(4) 9273(2) -2232(2) 8940(2) 44 N(5) 9723(2) -2805(2) 8013(1) 41 C(6) 10093(3) -2161(2) 7217(2) 41 C(7) 10599(2) -2688(2) 6194(2) 37 C(8) 10440(3) -2068(2) 5142(2) 45 C(9) 10808(3) -2560(2) 4145(2) 46 C(10) 11406(3) -3680(2) 4238(2) 42 C(ll) 11650(3) -4306(2) 5282(2) 43 C(12) 11222(3) -3811(2) 6259(2) 41 N(13) 11795(3) -4222(2) 3186(2) 56 0(14) 11243(3) -3821(2) 2224(2) 91 0(15) 12635(3) -5091(2) 3315(2) 89 Cl(16) 6160.7(8) -4462.3(5) 11566.2(5) 51

^Uav = where are the diagonal components of the tensor associated with a temperature factor of the form expC-Zn^EEUijaiajhihj ). Figure Al. ORTEP (100) drawing showing the atomic numbering scheme. Ellipsoids represent a 50% probability level Figure kl. Stereoview along the b axis depicting the molecular packing. The positive a axis lies along the horizon­ tal. The hydrogen atoms have been removed for clarity 110

Table A2. Bond distances (À) and angles (°)

N(l).-C(3) 1.312(3) C(9)-C(10) 1.377(3) N(2).-C(3) 1.313(3) C(ll)-C(10) 1.378(3) C(3)-N(4) 1.336(3) C(12)-C(ll) 1.373(3) N(4).-N(5) 1.372(3) C(7)-C(12) 1.389(3) N(5).-C(6) 1.266(3) C(10)-N(13) 1.458(3) C(6)-C(7) 1.463(3) 0(14)-N(13) 1.201(3) C(8)-C(7) 1.387(3) 0(15)-N(13) 1.214(3) C(8)-C(9) 1.370(3)

N(l)-C(3) -N(2) 121.4(2) C(8)-C(9)-C(10) 117.5(2) N(l)-C(3) -N(4) 118.2(2) C(9)-C(10)-C(ll) 122.8(2) N(2)-C(3) -N(4) 120.4(2) C(9)-C(10)-N(13) 118.4(2) C(3)-N(4) -N(5) 118.5(2) C(ll)-C(10)-N(13) 118.8(2) N(4)-N(5) -C(6) 115.5(2) C(12)-C(ll)-C(10) 118.7(2) N(5)-C(6) -C(7) 119.7(2) C(7)-C(12)-C(ll) 120.0(2) C(6)-C(7) -C(8) 119.9(2) C(10)-N(13)-0(14) 119.4(2) C(6)-C(7) -C(12) 120.7(2) 0(14)-N(13) 0(15) 122.2(2) C(8)-C(7) -C(12) 119.4(2) 0(15)-N(13)-C(10) 118.4(2) C(7)-C(8) -C(9) 121.4(2) Ill

Table A3. Hydrogen-bonding distances (À) and angles (°) with e.s.d.s in parentheses

Donor H Acceptor D-H H**'A D***A Angle

Intermolecular

N(l) H(18i) Cl(16) 0.91(3) 2.38(3) 3.240(2) 157(2)

N(4) H(2liii) Cl(16) 0.88(3) 2.39(3) 3.240(2) 162(2)

Intramolecualr

N(l) H(17) Cl(16) 0.84(2) 2.58(2) 3.340(2) 150(2)

N(2) H(20) Cl(16) 0.89(3) 2.47(3) 3.280(2) 152(3) 112

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ACKNOWLEDGEMENT

The support and encouragement of many people have helped to make this achievment possible. I wish to thank some of them here.

Of course, one of the biggest helpers of all was my (tor)mentor,

Dr. H. He exhibited a patience which sometimes verged on saintly (al­ though he is certainly not to be confused for a saint) as he tried to introduce a man who did not at first know the difference between a

Fourier and a foyer to the science of crystallography. I also thank him for the many conversations we shared on topics ranging from science to social isssues to sports. He is an intelligent and thorough scientist, and I feel that I learned a great deal from him.

I thank Dr. Metzler for serving as my co-major professor. Although he is not a crystallographer by training I know he shares a keen interest in the science and appreciates its value. He was nearly as excited as we were when we were finally able to outline the envelope of the dimer.

I also must thank my colleagues in chaos Yunge Cho and Kyung Hyun

Kim. From them I learned a little about another part of the world

(Korea), and I also had companions with which to share my joys and miseries. If it were not for Cho's discovery of the heavy atom deriv­ ative, Hgl^Z-, I would probably still be searching for one. I hope that

Kim has luck tracing the chain of adenylosuccinate synthetase. It is an interesting protein, and I feel that I am leaving it in capable hands.

Kim, send me a reprint after you have published the structure. 119

A post-doctor in the lab, M. N. Janakiraman, better known as Raman,

was also helpful. I enjoyed our many chats together, and I especially appreciate his patient explanations on several points which confused me.

He helped me to understand the rotation function, a subject in which I

was most thoroughly lost. Thank you Raman, you will make a fine

teacher. I also thank Raman for directing me toward Moon Gun Choi who

drew figures 1, 2 and 4 for me using his Macintosh personal computer.

I thank Dr. Fromm and the people in his group for allowing me to use

their equipment and for all of their help during the many protein puri­

fications I was involved in. Thanks to their help we will someday be

able to tell Dr. Fromm where lysine 140 is located in the protein

structure.

My families, both the Serra's and the Whitford's, were a source of

support for me. I realize that they did not really understand what I

was doing (sometimes I didn't understand what I was doing!), but I knew

that they were still proud of me. A man can't expect more than that,

and I consider myself lucky to have such fine parents and in-laws.

Lastly, I must thank the one who has given me the most support, my

wife, Tina. She is the balance in my life and the sunshine in my day

(It may sound corny, but it is true). She gave me encouragement when I

was depressed and shared my joys. I cannot begin to thank her enough

for her patience and understanding. I consider myself very lucky

indeed.