antigen complexes

ProO.Biophys.molec.Biol.,Vol. 58, pp. 203-224, 1992. Printed in Great Britain. All rightsreserved.

0079--6107/92 $15.00 © 1992Pergamon Press Ltd

ELECTROSTATIC FIELDS IN ANTIBODIES ANTIBODY/ANTIGEN COMPLEXES

AND

JIRI NOVOTNY* a n d K I M SHARP t

*Department of Macromolecular Modelling, Bristol-Myers Squibb Research Institute, Princeton, NJ 08343-4000, U.S.A. ?Department of Biochemistry and Biophysics, University of Pennsylvania School of Medicine, Philadelphia, PA 19104-6059, U.S.A.

CONTENTS I. INTRODUCTION

203

II. ANTIBODIESAS PARADIGMSOF BIOLOGICALSPECIFICITY

204

III. ATTRIBUTIONOF FREE ENERGY OF BINDINGIN MACROMOLECULARCOMPLEXES

205

IV. CALCULATIONOF ELECTROSTATICFIELDS AROUND ANTIBODY/ANTIGENCOMPLEXES

207

V. ANTIBODYELECTROSTATICFIELDS

208

VI. BINDINGENERGY CONTRIBUTIONFROMSURFACECHARGE DESOLVATION

221 222

VII. CONCLUSIONS

222 222

ACKNOWLEDGEMENTS REFERENCES

I. I N T R O D U C T I O N Central to molecular biology is the question of specific molecular interactions. Plant and animal organisms have evolved complex macromolecular assemblies such as photosynthetic centers, chromatin, chloroplasts, centriole, Golgi apparati, ribosomes, ribonucleoprotein particles, microvilli, low density lipoprotein particles, myosin/actin filaments, microtubules, viruses, to name but a few. This self-organization of living matter, unparalleled in the rest of the physical world, is mediated by weak noncovalent forces that add to create specific affinities among particular pairs of nucleic acid, protein, sugar and lipid molecules. DNA-repressor (see Harrison, 1991; for review), enzyme-inhibitor (see Bode and Huber, 1991; for review) and antigen-antibody complexes (see below) are the most thoroughly studied binary macromolecular complexes for which three-dimensional structures exist with sufficient atomic detail. This review concentrates on electrostatic phenomena in antibody-antigen interactions. Using the linearized Poisson-Boltzmann equation as implemented in the program DELPHI (Gilson et al., 1988; Sharp et al., 1990c), we calculated electrostatic potentials generated by antibody molecules and their specific complexes under physiological conditions, i.e. dissolved in physiological salt solutions. Having studied equienergetic contours of these fields, and difference fields graphically showing desolvation effects that accompany antigen-antibody complex formation, we then tried to formulate a set of rules generalizing electrostatic aspects of antigen-antibody interactions and, indeed, of complex protein polyelectrolytes in general. Based on this and our other work (Sharp and Novotny, 1992), we believe that, because of the energetic cost of desolvation, electrostatic interactions among proteins essentially always oppose complex formation; and that charge complementarity on the two molecular contact surfaces, although important and necessary, primarily defines specificity without favorably contributing to the stability of the complex. Electrostatic phenomena summarized in this review also highlight the importance of macromolecular shape as a determinant of binding specificity and energetics, and help to explain the 203

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biophysical origin of the propensity of concave parts of protein surface towards providing binding sites to ligands of various compositions and sizes (Nicholls et al., 1991). II. ANTIBODIES

AS PARADIGMS

OF BIOLOGICAL

SPECIFICITY

Structure of immunoglobulin molecules has evolved to fit its dual function, namely, to recognize specifically foreign antigens in the blood stream, to neutralize them, and to mediate destruction of the antigen-antibody complex by the complement system. The threedimensional structure of antibody molecules is modular, with multiple domains (about 110 amino acids long and folded into an anti-parallel fl-sheet bilayer) connected into two types of polypeptide chains ("light", mol. wt. 25,000 and "heavy", mol. wt. 50,000; see, e.g. Davies et al., 1990; Alzari et al., 1988, for reference). Homologous domains from the light and heavy chains associate via their fl-sheet surfaces to form dimeric structures, so that the complete molecule is a tetramer with the general formula H 2 L 2 . The two N-terminal domains of each chain contain hypervariable polypeptide segments whose length and amino acid sequence varies from one molecule to another (Wu and Kabat, 1970). It is this variability that allows for construction of antigen-combining sites fitting a great many antigenic structures with diverse chemical compositions and molecular shapes. Each antibody molecule carries two identical antigen-combining sites. In the process of antigen destruction, after multiple antibodies became attached to a macromolecular antigen, the Clq component of complement binds to the part of antibody molecule distal from the antigen binding site (the CH3-CH a domain dimer of the Fc fragment*) and initiates the complement cascade. The antigen-combining site, which is the primary focus of the review, is carried in the dimeric module composed of VL and VH domains (the Fv fragment, Fig. 1). The module represents a stable, independent protein folding unit as demonstrated by proteolysis (Hochman et al., 1973) and construction of chimeric, single chain Fv fragments genetically engineered and expressed in bacteria (Huston et al., 1988; Bird et al., 1988; Skerra and Pl/ickthun, 1988). Each of the light and heavy chain variable domains contains three hypervariable regions (Wu and Kabat, 1970) corresponding to loops connecting two flstrands of an anti-parallel fl-hairpin. All the six loops from the two domains come to close proximity in the immunoglobulin fold, forming a contiguous surface of the antigencombining site. Thus, the loops are often termed complementarity-determining regions or CDRs (Fig. 1). The advent ofmonoclonal antibody production, by K6hler and Milstein (1975), had been the essential technological breakthrough allowing preparation of large quantities of homogenous antibodies from a single committed B cell clone. Molecules produced by these cells have identical amino acid sequences, as opposed to the polyclonal specific antibody mixture isolated from blood, which contains molecules of different primary structures, sharing the same antigenic specificity but differing in atomic details of their antigencombining site architecture. X-ray crystallographic strucures of immunoglobulin Fab fragments, either free or complexed with small ligands such as phosphoryl choline, were available since 1973 (see, e.g. Davies et al., 1990; Alzari et al., 1988; Huber et al., 1976, for reviews). The first threedimensional structure of an Fab fragment complexed with a protein antigen (lysozyme) became available only a decade later, however (Amit et al., 1986). Since that time, X-ray crystallographic structures of several new protein antigen-antibody complexes have been solved, and have been deposited with the Brookhaven Protein Data Bank (Bernstein et al., 1977). An impressive collection of 11 independent antibody Fab fragments available from the Protein Data Bank, either free or complexed with their specific antigens, forms the basis of this review (Table 1). *Abbreviations used for description of immunoglobulin domains and corresponding proteolytic fragments are as follows: V, variable; C, constant; L, light chain; H, heavy chain; Fv, a noncovalent dimer of the VL and VH domains; Fab, antigen-binding proteolytic fragment, i.e. a 50,000 mol. wt. fragment consisting of VL, CL, VH and CH1 domains forming VL/VH and CL/CH 1 domain pairs; Fc, crystallizable fragment, a homodimer of the two C-proximal H chain domains, i.e. CH2 and CH3.

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205

TABLE 1. X-RAY CRYSTALLOGRAPHICSTRUCTURESOF ANTIBODYFv FRAGMENTSUSED IN ELECTROSTATICFIELD CALCULATIONS

Antibody

Antigen

Mouse hybridoma D1.3 Mouse hybridoma R19.9 Mouse hybridoma HyHEL-5 Mouse hybridoma HyHEL-10 Mouse myeloma J539 Human cryoglobulin KOL Mouse myeloma McPC 603 Human myeloma NEW Mouse hybridoma 36-71 Mouse hybridoma 4-4-20 Mouse hybridoma 26-10

Hen lysozyme Phenyl arsonate Hen lysozyme Hen lysozyme Galactan Unknown Phosphoryl choline Menadione Phenyl arsonate Fluorescein Digoxin

Atomic Coordinates available for: Fab-antigen complex 1 Fab fragment 2 Fab-antigen complex 3 Fab-antigen complex4 Fab fragment 5 Fab fragment 6 Fab-antigen complex 7 Fab fragment s Fab fragment, antigen modelled 9 Fab-antigenl° Fab-antigen complex ~

i AMIT,P. M., MARIUZZA,R. A., PHILLIPS,S. E. V. and POLJAK,R. (1986) Science 233, 555-580; BHAT,T. N., BENTLEY, G. A., FISCHMANN,T. O., BOULOT,G. and POLJAK, R. J. (1990) Nature 347, 483-485; FISCHMANN,T. O., BENTLEY,G. A., BHAT,T. N., BOULOT,G., MARIUZZA,R. A., PHILLIPS,S. E. V., TELLO,D. and POLJAK,R. J. (1991) J. biol. Chem. 266, 12915-12920.

2 LASCOMBE,M. B., ALZARI,P. M., BOULOT,G., SALUDJIAN,P., TOUGARD,P., BEREK,C., HABA,S., ROSEN,E. M., NISONOFF,A. and POLJAK, R. (1989) Proc. natn. Acad. Sci. U.S.A. 86, 607-611. 3 SHERIFF,S., SILVERTON,E. W., PADLAN,E. A., COHEN,G. H., SMITH-GILL,S. J., FINZEL,B. C. and DAVIES,D. R. (1987) Proc. natn. Acad. Sci. U.S.A. 84, 8075-8079. 4 PADLAN,E. A., SILVERTON,E. W., SHERIFF,S., COHEN,G. H., SMITH-GILL,S. J. and DAVIES,n. R. (1989) Proc. natn. Acad. Sci. U.S.A. 86, 5938-5942. 5 SUH, S. W., BHAT,T. N., NAVIA,i . A., COHEN,G. H., RAO,D. N., RUDIKOFF,S. and DAVIES,D. R. (1986) Proteins 1, 74-86. 6 MARQUART,M., DEISENHOFER,J., PALM, W. and HUBER,R. (1980) J. molec. Biol. 141, 369-391. 7 SATOW,Y., COHEN, G. H., PADLAN, E. A. and DAVIES,D. R. (1986) J. molec. Biol. 190, 593-604. 8 SAUL,F. A., AMZEL,L. M. and POLJAK,R. J. (1978) J. biol. Chem. 253, 585-597. 9 STRONG, R. K., CAMPBELL,R., ROSE, D. R., PETSKO,G. A., SHARON,J. and MARGOLIES,M. N. (1991) Biochemistry 30, 3739-3748; STRONG,R. K., PETSKO,G. A., SHARON,J. and MARGOLIES,i . N. (1991)Biochemistry 30, 3749-3757; ROSE,D. R., STRONG,R. K., MARGOLIES,i . N., GEFTER,M. L. and PETSKO,G. A. (1990) Proc. natn. Acad. Sci. U.S.A. 87, 338 342. 1o HERRON,J. N., HE, X. M., MASON,M. L., VOSS,E. W. and EDMUNDSON,A. B. (1989) Proteins 5, 271-280. t t JEFFREY,P. D., STRONG,R. K., CAMPBELL,R. L., PETSKO,G. A., MARGOLIES,M. N., HABER,E. and SHERIFF,S. (1992) Nature, manuscript submitted. III. ATTRIBUTION OF FREE ENERGY OF BINDING MACROMOLECULAR COMPLEXES C o n c e p t s such as b i n d i n g specificity o r c o m p l e x stability have t h e r m o d y n a m i c s of b i m o l e c u l a r reactions. F o r e x a m p l e , in the r e a c t i o n

IN their origin in

ANTIGEN + ANTIBODY~COMPLEX, m o l a r c o n c e n t r a t i o n s of the a b o v e three m o l e c u l a r species is m e a s u r e d at e q u i l i b r i u m , a n d the strength (specificity) of the c o m p l e x is e s t i m a t e d from its relative c o n c e n t r a t i o n , i.e. the r a t i o KAS = [ C o m p l e x ] / [ A n t i b o d y ] [ A n t i g e n ] . T h e e x p e r i m e n t a l l y m e a s u r e d / ( A S relates to the G i b b s free energy of c o m p l e x f o r m a t i o n , AG, as AG = - R T l o g KAS (R, the gas c o n s t a n t , is the p r o d u c t of the B o l t z m a n n c o n s t a n t , k, a n d the A v o g a d r o c o n s t a n t , L : R = 8 . 3 1 4 kJ t o o l - 1 K - 1; TiN t e m p e r a t u r e in kelvin). C h a n g e s in G i b b s free energy, a t h e r m o d y n a m i c q u a n t i t y , can in principle be o b t a i n e d from a t o m i c structures of all the molecules involved in the r e a c t i o n , p r o v i d e d all the physical forces r e s p o n s i b l e for the c o m p l e x f o r m a t i o n are a c c u r a t e l y k n o w n ( N o v o t n y et al., 1989; W i l l i a m s et al., 1991; N i c h o l l s et al., 1991; W i l s o n et al., 1991; H o r t o n a n d Lewis, 1992). T h e r e is no d o u b t t h a t electrostatic i n t e r a c t i o n s between the a n t i b o d y a n d the a n t i g e n p l a y an i m p o r t a n t role in c o m p l e x f o r m a t i o n . Specificity of p r o t e i n - p r o t e i n i n t e r a c t i o n c o m e s from a large difference between b i n d i n g c o n s t a n t s c h a r a c t e r i z i n g b i n d i n g of specific a n d non-specific ligands. T h e r m o d y n a m i c a l l y , the higher b i n d i n g c o n s t a n t s for specific ligands arise from s t r o n g e r overall "forces" ( G i b b s free energy differences) b e t w e e n the a n t i b o d y a n d the antigen. M o s t of the forces r e s p o n s i b l e for b i n d i n g are distinctly s h o r t range: v a n d e r W a a l s - L o n d o n d i s p e r s i o n forces (Pauling, 1960), h y d r o p h o b i c force (i.e. difference in surface s o l v a t i o n , K a u z m a n n , 1959) a n d

206

J. NOVOTNYand K. SHARP

hydrogen bonds (Pauling, 1960) have vanishingly small values at distances greater than 2~, A, a "local" distance even on an atomic scale. While the first two types of forces can be said to be isotropic (spherically symmetrical), hydrogen bonds are strictly directional and require orientation of the participating groups. Electrostatic forces act at a distance but the high dielectric constant of water limits their reach effectively. Thus, the burial of charged atoms at a protein-protein interface distinctly increases their effective electrostatic field, but only at the expense of the energetically unfavourable desolvation of charged groups. A consequence of all this is that the two molecular surfaces, the antibody paratope (i.e. the binding site) and the antigenic epitope will enter into a stable complex only if they have complementary molecular shapes over a large area, and their surface charge distribution is such that interaction of opposite charges on the epitope and the paratope provide sufficient Coulombic attraction to stabilize the complex (Novotny et al., 1987). In virtually all the protein binding systems known to date binding sites are cavities or grooves. X-ray crystallography shows the antibody binding site to be a concave surface of the interface between the light and the heavy chain variable domains. In one case, a small hapten (phosphoryl choline) enters deeply into the interdomain pocket (Satow et al., 1986), in another case the principal antigen residue of a protein antigen (glutamine 121 of the hen eggwhite lysozyme) is buried in the interface while the rest of antigen-antibody contact area is rather fiat, if irregularly undulated (Amit et al., 1986). It is natural for the curvature of binding site cavities to match that of the antigens: binding sites that accommodate small ligands have high curvatures and appear as pockets; those directed towards large protein antigens have a low curvature, being more akin to valleys and grooves than to deep crevices. Why should the concave surface be favored as a specific combining site? Although no definitive answer is available at present, at last three good reasons can be cited. First, diffusion away from cavities is significantly slower than from flat surfaces, or through the solvent. Primitive "binding" properties of simple concave organic molecules such as crown ethers or cavitands demonstrate this very clearly (Cram, 1983), Second, electrostatic fields are enhanced or focused in cavities, even though solvent quenches the field at other, flat or convex parts of protein surface (Zauhar and Morgan, 1985; Klapper et al., 1986). Third, hydrophobicity of a surface is a function of its curvature relative to the size and curvature of a water molecule, and concave surfaces are more hydrophobic than flat or convex surfaces (Sharp et al., 1991b; Nicholls et al., 1991). A visual demonstration of the dielectric enhancement of electrostatic field at cavities is presented in Fig. 2. There, the negative field generated by a pair of carboxyl groups embedded in a low-dielectric (e = 2) protein (with no other charges present), is compared to that generated by the same groups in water (i.e. continuum of dielectric constant e = 80). The low dielectric of the protein not only allows the field to extend into a larger region of space, but also modifies the field according to the shape of the dielectric boundary. The field enhancement inside the binding site cavity is particularly clear. In addition to the effects that contribute to the formation of specific noncovalent macromolecular complexes (hydrophobicity, electrostatics and van der Waals-London forces) the Gibbs free energy changes AG accompanying complex formation also involve solute entropy changes (conformational, translational/rotational and vibrational) that oppose complex formation. For each of the above AG component terms, we can ask: how strong (and therefore important) is this effect compared to all the others? Does it contribute to specificity, or stability (or both), of the complex? Although much of this is still a matter of debate, the major issues may perhaps be summarized as follows. (1) The hydrophobic effect is the major stabilization factor of complex formation contributing, according to various estimates, between 25-72 cal (104-300 J) of Gibbs free energy stabilization per 1/~2 of protein-protein contact area (Chothia, 1974; Sharp et al., 1991b). (2) On complex formation, immobilization of a freely rotatable torsional degree of freedom (a side chain exposed to solvent) carries a free energy penalty of about 0.6 kcal (2.5 kJ, Novotny et al., 1989; Nicholls et al., 1991). (3) Van der Waals or dispersion/repulsion interactions probably constitute most of what

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207

is termed shape complementarity in binding, in that they would penalize intermolecular contacts that provide either overlap of atoms, or cavities, either directly or through induced strain. Well packed contact regions, though, are probably not much more favorable than the molecule/solvent contacts in the unbound complex. Surface tension data from organic liquid/water systems show that the work of adhesion between hydrocarbon and water interfaces is the same as that between two hydrocarbon interfaces (Nicholls et al., 1991; Adamson, 1990). Furthermore, dispersion forces are relatively small in magnitude. (4) Electrostatic effects accompanying complex formation involve: (i) creation of new clusters of charged atoms in the low dielectric constant (5=2) environment at the protein/protein interface of the complex; these charges can stabilize the complex through Coulombic attraction, the net effect being proportional to the atomic charges. (ii) Desolvation of charged groups; this is proportional to the square of the atomic charge, and so the desolvation process is always unfavorable, and often stronger, than the net Coulombic attraction (see below). The precise matching of charged groups with charged groups of opposite sign is an example of chemical complementarity between antibody and antigen, which in addition to the shape complementarity described above determines the specificity of the complex, i.e. a selection of a pair of complementary contact surfaces. Complex specificity imposed by this charge distribution can, however, only be achieved by paying a price in free energy of desolvation that decreases complex stability. How this energetic balance is achieved is one of the main themes of this review. IV. C A L C U L A T I O N OF ELECTROSTATIC FIELDS A R O U N D A N T I B O D Y / A N T I G E N COMPLEXES Electrostatic fields are calculated with the DelPhi program which is based on the finite difference solution to the Poisson-Boltzmann (PB) equation (Gilson et al., 1988; JeanCharles et al., 1990; Sharp and Honig, 1990b): V" e(r)Vqb(r)- ~K2 sinh(~b(r)) + 4~p(r) = 0 where e(r), ~b(r) and p(r) are the dielectric constant, electrostatic potential and molecular charge distributions as functions of the position r, and r is the Debye-Hfickel parameter, proportional to the square root of the ionic strength. To solve the Poisson-Boltzmann equation, the molecule and a region of surrounding solvent is mapped onto a cubic lattice. The grid scale is chosen to leave a 10 A border in between the protein surface and the edge of the rectangular grid, giving a lattice spacing between 1.13 points/A-1.24 points/A for the various complexes. X-ray crystallographic coordinates of antigen/antibody complexes were obtained from the Brookhaven Protein Data Bank, or directly from the authors. Hydrogen atoms were added to the crystallographic structures using the BUILDER routine of the molecular mechanics program INSIGHT/DISCOVER (Biosym Technologies Inc., San Diego, CA). Partial atomic charges were then assigned using the AMBER potential function (Weiner et al., 1986). The structure and polarity of the molecule is thus accounted for explicitly. Solvent and ionic strength effects are modelled with a continuum treatment. The boundary between the molecule and solvent is defined by the molecular or solvent excluded surface (Lee and Richards, 1971; Connolly, 1983), using a 1.4 A solvent probe. Values for the charge, dielectric constant and Debye-Hiickel parameter are then assigned to each of the lattice points. Lattice points outside the surface, in solvent, are assigned a dielectric constant of 80, and the Debye-H~ckel parameter for the appropriate ionic strength. Points inside the molecule are assigned a dielectric constant of 2 (Gilson and Honig, 1986; Sharp and Honig, 1990b; Harvey, 1989) and a Debye-Hiickel parameter of 0, thereby excluding solvent ions. In addition ions are excluded from a 2 A layer beyond the molecular surface, this value being the mean effective radius of NaCl ions in solution (Bockris and Reddy, 1970; Conway, 1981). In addition values for the potential on the boundary points of the lattice are estimated using the Debye-Hiickel potential approximation (Gilson et al., 1988). Solutions to the potential at all the interior lattice points are obtained using the finite

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J. NOVOTNY and K. SHARP

difference approximation to the Poisson-Boltzmann equation (FDPB) combined with overrelaxation (David and M c C a m m o n , 1989; Nicholls and Honig, 1991). F o r the antigen/antibody studies described here, the linear form of the Poisson-Boltzmann equation is used, which is sufficiently accurate for low or moderately charged molecules at physiological ionic strength (0.15 M) (Sharp and Honig, 1990). We used the commercially available version of D E L P H I program interfaced with the I N S I G H T molecular graphics, (Biosym Technologies Inc., San Diego, CA) running on a Silicon Graphics IRIS 4D/240GTX workstation. A single potential calculation require about 2 min of single processor time for a protein complex consisting of ~ 5300 atoms, including hydrogens, such as, e.g. an antibody Fv fragment complexed with lysozyme. V. A N T I B O D Y E L E C T R O S T A T I C F I E L D S To facilitate comparison of the different structures, all the coordinates were transformed into a c o m m o n frame of reference defined by the Fv fragments: the center of gravity of a reference Fv structure (anti-phenyl arsonate hybridoma 36-71) was translated into the origin of the cartesian coordinate system and the vertical (y) coordinate axis was made coincident with the approximate dyad axis of the V H - V L domain dimer. All the other Fv fragments were transferred into the same reference frame by (i) identifying four short backbone segments belonging to the most conserved parts of the domains, and (ii) using a least-square procedure to equivalence, and superimpose, the corresponding segments in all the Fv structures investigated (Table 2). TABLE 2. SUPERPOSITION OF Fv FRAGMENTS INTO A COMMON COORDINATE SYSTEM BASED ON THE V L-V H DYAD

Axis Backbone Overlayed VH Fv Fragment 36-71"t" 26-10 McPC 603 4-4-20 R19.9 J539 KOL NEW D1.3 HyHEL-5 HyHEL-10

strand C (//3) (res. no.) Trp-Val-(Lys)-Arg-Gln 36-40 Trp-Val-Arg-Gln 35-38 Trp-Val-Arg-Gln 36-39 Trp-Val-Arg-Gln 36-39 Trp-Val-Lys-GIn 36-39 Trp-Val-Arg-Gln 36-39 Trp-Val-Arg-GIn 36-39 Trp-Val-Arg-Gln 36-39 Trp-Val-Arg-Gln 36-39 Trp-Val-Lys-Gln 36-39 Trp-Ile-Arg-Lys 36-39

VL strand F (//6) (res. no.) Tyr-Phe-Cys 94-96 Tyr-Tyr-Cys 93-95 Tyr-Tyr-Cys 96-98 Tyr-Tyr-Cys 96-98 Tyr-Phe-Cys 94-96 Tyr-Tyr-Cys 94-96 Tyr-Phe-Cys 94-96 Tyr-Tyr-Cys 93-95 Tyr-Tyr-Cys 93-95 Tyr-Tyr-Gln 94-96 Tyr-Tyr-Cys 93-95

strand C (//3) (res. no.)

strand F (//6) (res. no.)

r.m.s.* [~]

Trp-Tyr-Gln-Gln 35-38 Trp-Tyr-Leu-Gln 40-43 Trp-Tyr-Gln-Gln 41-44 Trp-Tyr-Leu-Gln 40-43 Trp-Tyr-Gln-Gln 35-38 Trp-Tyr-Gln-Gln 34-37 Trp-Tyr-Gln-Gln 36-39 Trp-Tyr-Gln-Gln 37-40 Trp-Tyr-Gln-Gln 33-38 Trp-Tyr-Gln-Gln 85-87 Trp-Tyr-Gln-Gln 35-38

Tyr-Phe-Cys 86-88 Tyr-Phe-Cys 91-93 Tyr-Tyr-Cys 92-94 Tyr-Phe-Cys 91-93 Tyr-Phe-Cys 86-88 Tyr-Tyr-Cys 85-87 Tyr-Tyr-Cys 87-89 Tyr-Tyr-Cys 81-83 Tyr-Tyr-Cys 86-88 Tyr-Tyr-Cys 34-37 Tyr-Phe-Cys 86-88

0.0 1.4 0.5 0.6 0.7 0.6 0.5 0.6 0.6 0.5 0.4

* The root-mean-square differencebetween pairs of backbone atoms N, Cot,C and O on the residues specified. t The Fv fragment from the mouse anti-phenylarsonate hybridoma 36-71 has been used as the master structure on which all the other Fv fragmentswere superimposedby the least-squaresprocedure. In the 36-71 strand C, there is an insertion of one residue (Lys),with respect to all the other X-ray crystallographicstructures used. This residue was excluded from superpositions; that is, the pairs of dipeptides (e.g. Trp-Val and Arg-GIn)were matched in the two structures superimposed. The conserved features of antibody binding sites have previously been described (Novotny and Haber, 1985; Chothia et al., 1985). The V L - V H interface forms a close-packed, twisted //-barrel characterized by cross-sectional dimensions 1.04 × 0.66 nm (10.4 × 6.6 A) and a

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top-to-bottom twist angle of 212 ° (cf. Fig. 3). The geometry of the interface is preserved via invariance of some 12 side chains, both inside the domains and on their surface. Buried polar residues form a conserved hydrogen-bonded network that has a similar topological connectivity in the two domain types. Two hydrogen bonds contributed by invariant Gin side chains extend across the interface and anchor the//-sheets in their relative orientation. Invariant aromatic residues close-pack at the bottom of the binding site//-barrel with their ring planes oriented perpendicularly in the characteristic herringbone packing mode. About 18 nm 2 of protein surface is buried between the domains and some 30--40% of this contact surface is contributed by the hypervariable regions. The//-sheets that form the interface have edge strands that are strongly coiled by//-bulges. As a result, the edge strands fold back over their own//-sheet at two diagonally opposite corners. In the VL-VH dimer, residues from these edge strands form the central part of the interface and give what we call a three-layer packing: i.e. there is a third layer composed of side chains inserted between the two backbone side chain layers that are usually in contact. This three-layer packing is different from the common (aligned or orthogonal) fl-sheet packing recognized in other//-sheeted proteins (Chothia et al., 1977; Chothia and Janin, 1982). The conserved backbone segments chosen for mutual superposition of our Fv fragments were those whose side chains were parts of the invariant structural motifs: Gin L38 and H39 (intra- and interdomain hydrogen bonding) and Tyr, Phe, Trp residues of the interdomain herringbone aromatic cluster (cf. e.g. Novotny and Haber, 1985; Table 2). Figure 3 depicts five of the eleven superimposed Fv structures, namely those carrying small-molecular weight haptens (36-71 with phenyl arsonate, 26-10 with digoxin, McPC 603 with phosphoryl choline and 4-4-20 with fluorescein) in their binding sites. There is a striking coincidence of the hapten locations and orientations in the binding sites. All the molecules are oriented with their longest axis of inertia essentially coincident with the VH-VL dyad axis, and at approximately the same depth with respect to the VH and VL //-sheeted framework. This fact is remarkable considering the wide variability of shapes and chemical characteristics of the binding sites with different antigenic specificities. The binding site for the haptens coincides with the junction between the D and J gene segments coding approximately for the H3 hypervariable loop and the last//-strand of the VH domain, and appears to be a hot spot of variability. A wide assortment of chemical (electrostatic) complements to various haptens seems to be generated here, as well as a great variety of concave shapes snugly fitting many hapten shapes. With the Fv fragments commonly oriented, we proceeded to calculate the electrostatic potentials surrounding the antibodies and the antigen-antibody complexes. In what follows, most of our color plates represent stereo diagrams of isoenergetic contours (potential contours) centered on the individual molecules. It is convenient to display contours in units of kT/e (k, Boltzmann constant; T, temperature in kelvin; 1 k T = 0.6 kcal = 2.5 kJ at 25°C). The energetic content of thermal motion at room temperature being 1 kT, the 1 kT/e contour shows approximate boundaries of a field capable of exerting a drag on a unit charge strong enough to overcome the random Brownian movements in solution. In our color plates, the proteins are represented either by Ca backbone tracings, or by a mesh representation of the solvent-excluded surfaces which can also be obtained directly from the DELPHI program. What general features may one expect in the electrostatic potential fields of a set of homologous molecules? Firstly, the larger scale features will be dominated by the formally charged side chains (positive arginines and lysines, negative aspartates and glutamates) on the surface of the protein. Figure 4 shows that this is indeed the case. For clarity, 3 kT/e contours, delimiting areas of strong potential, not extending very far from the protein surface, are displayed, and can be seen as centered on all the formally charged side chains of the protein. Secondly, one may perhaps expect that the shape and distribution of the fields would be similar among homologous proteins. This, however, is clearly not the case, as the surfacelocated charged side chains vary in number and position between individual homologs. The same situation has previously been described for trypsins from various vertebrates (Soman et al., 1989). A more important question is, has the shape of the electrostatic field been

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conserved in antibodies directed against the same hapten? This question cannot be answered with certainty for the lack of data. Three-dimensional structure of two mouse hybridomas directed against phenylarsonate, 36-71 and R19.9 are known, but only in the 36-71 molecule can we approximately locate the antigen. As discussed by Strong et al. (1991), attempts to locate the phenylarsonate binding site in R19.9 by direct homology with 36-71 runs into a problem of a serious steric clash between the H3 loop of the R19.9 structure and the antigen. At any rate, the electrostatic fields around the R19.9 and 36-71 binding sites are not very similar. Of the three antibodies directed against lysozyme, namely, D1.3, HyHEL-5 an HyHEL-10, each recognizes a different part of the lysozyme surface and the three lysozyme antigenic epitopes are essentially non-overlapping. The 36-71 Fv fragment is a good paradigm of a situation found more generally with antibodies directed towards small antigenic structures (haptens) (Fig. 5). Although the field contours directly at the binding site cavity are opposite in sign to the electric charge of the hapten, there seems to be no relation to fields found elsewhere on the surface. These are rather complex shapes seemingly distributed over the surface with no direct relationship to the binding function. There is one notable exception to this description: The 4-4-20 Fv fragment specific for fluorescein. The surface of this binding site is rather unusual (Fig. 6), with large overhangs mostly made of the side chains belonging to the H2 and H3 loops of the 4-4-20 antibody. It seems that, unless the 4-4-20 Fv fragment undergoes conformational changes upon hapten binding, a direct diffusion of the hapten into the binding site is possible only sideways, and not from the open space above the binding site. Positive fields around the 4-4-20 binding surface may promote lateral two-dimensional diffusion of the negatively charged ligand along the protein surface as seen in other proteins (e.g. in Cu, Zn superoxide dismutase, Sharp, 1987), and direct it into the combining site via this indirect, but unobstructed path leading into the binding site (Fig. 7). In the McPC 603 Fv fragment specific for the dipolar (zwitterionic) molecule phosphorylcholine (Fig. 8), the field dipole around the binding site cavity helps to orient the ligand correctly. That is, the bottom of the cavity, formed in part by the negatively charged Asp L97, actively attracts the positively charged trimethylammonium moiety of the hapten whereas the phosphate group of the hapten is close to the large positive field generated by the Arg H52 at the farther side of the binding cavity. The 26-10 Fvfra#ment is one of the binding sites directed towards neutral haptens. The antibody binds its hapten, the cardiac glycoside digoxin, in such a way that the steroid aglycon of digoxin, digoxigenin, fits snugly into a narrow groove on the surface of the antibody, with its lactone ring at the bottom of the cavity. The sugar tridigitoxose protrudes out into the solvent and is known to be irrelevant to binding (Mudgett-Hunter et al., 1985). The inside of the 26-10 binding cavity is devoid of any significant electrostatic field (Fig. 9). A different situation exists of the Fvfragment from mouse myeloma protein N E W known to have a low affinity for vitamin K (menadione). The NEW three-dimensional structure deposited with the Brookhaven Protein Data Bank is a free antibody, but a low resolution structure of the NEW-menadione complex was described by Amzel et al. (1974). The polypeptide chain segments found to contact the hapten are shown in Fig. 10. The segments delimit a region of a distinctive positive field. This field may enhance binding of dipolar menadione with aromatic keto groups harboring polarized oxygens with estimated partial atomic charges of .~0.5 electron units. In the Fvfragment .1539, known to bind galactan (Fig. 11 ), there is a weak negative field at the cavity on the J539 surface where the putative galactan binding site should be located. This field would probably provide a stabilizing interaction with the sugar antigen, since the latter has many hydroxyl groups with partial positive charges on the outwardly oriented hydrogens. Of the three antibodies against lysozyme, the HyHEL-5 (Fig. 12) and the HyHEL-IO antibody have conspicuous negative fields centered on their binding site cavities that well complement the overall positive fields surrounding the lysozyme antigen (Fig. 13). The size of the 1 kT/e potential contour is much larger than those found in antibodies directed against

Electrostatic fields in antibodies and antibody/antigen complexes

FIG. 1. A stereo ribbon diagram of the Fv fragment of the monoclonal 4-4-20 antibody specific for the hapten fluorescein. The VL domain, color-coded red, is on the left, the VH domain (magenta) is on the right. The hypervariable (complementarity-determining) loops are seen to surround the hapten on the top of the picture. The three loops from the VL domain are color-coded blue and are, clockwise from the front, the third, first and second hypervariable loop (L 1, L2 and L3 for short). Similarly, the VH loops are color-coded cyan and are, clockwise from the back of the picture, H3, H1 and H2. Note that the corresponding pairs of VL and VH loops (L1 and HI, L2 and H2; L3 and H3) are symmetryrelated by an approximate dyad.

FIG. 2. Comparison of 1 kT/e electrostatic potentials generated by a pair of glutamate residues H35 and HS0 of the HyHEL-5 Fv fragment, in the protein and in free solution. In this cross-section, the solvent-excluded surface of the HyHEL-5 Fv fragment is given in green; the 1 kT/e contour of the aqueous electrostatic potential is in red; and the 1 kT/e contour of the potential in the presence of the low-dielectric, uncharged, protein surrounding the two glutamate side chains is in magenta.

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FIG. 3. A stereo diagram of Fv fragments with bound small-molecular weight haptens: phenylarsonate (cyan), phosphoryl choline (red), digoxigenin (yellow) and fluorescein (magenta). VH domain is color-coded green, the VL domain blue.

FlG. 4. A stereo diagram of the solvent-excluded surface of the 4-4-20 Fv fragment (green) with positively and negatively charged side chains shown in cyan and magenta, respectively. + 3 , - 3 kT/e potential contours are shown in blue and red respectively. Potentials were calculated using only formally charged side chains.

Electrostatic fields in antibodies and antibody/antigen complexes

F,G. 5. Cross-section through the 36-71 Fv fragment showing the binding site cavity, and the phenylarsonate hapten in the binding site. + 1, - 1 kT/e potential contours are shown in blue and red respectively. Note the positive field emanating from the binding site cavity and completely engulfing the negatively charged hapten (in magenta).

FIG. 6. Binding site surface of the 4-4-20 antibody with fluorescein (magenta) bound to it.

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FIG. 7. Surface potentials around the 4-4-20 fluorescein binding site. + 1, - 1 kT/e potential contours are shown in blue and red respectively. The large positive field may direct the ligand, with net negative charge, into the binding site via lateral diffusion, avoiding the collisional approach by direct diffusion from "right" into the binding site.

FIG. 8. A cross-section through the McPC 603 Fv fragment (contours of the solvent excluded surface shown in green) with the antigen, phosphoryl choline, at the binding site (to the left). The space-filling representation of phosphorylcholine shows its phosphate moiety, in red and magenta, to be at the top of the binding site cavity, and the trimethylammonium group at the bottom (essentially only the methyl and methylene groups, color-coded green--c~rbun, and white---hydrogen, are visible). + 1 , - 1 kT/e potential contours are shown in blue and red respectively. The binding site cavity contains a negative potential and its walls are surrounded by a positive potential. This "dipolar" potential field both helps to orient the hapten in the binding site (attracting the trimethylammonium group to the bottom), and provides coulombic stabilization to the bound zwitterion.

Electrostatic fields in antibodies and antibody/antigen complexes

Fro. 9. Potentials around the binding site of the 26-10 antibody specific for the cardiac glycoside digoxin. The binding site cavity is neutral. + 1 , - 1 kT/e potential contours are shown in blue and red respectively.

FIG. 10. Potentials around the binding site cavity of the myeloma protein NEW. a-Carbon tracings of residues implicated in menadione binding are also shown, approximately delimiting the binding site surface. A distinct positive field at the site may have electrostatic attraction for the electrically neutral menadione carrying negatively polarized aromatic keto-groups. + 1 , - 1 kT/e potential contours are shown in blue and red respectively.

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FXG. 11. The putative binding site of the myeloma FV fragment J539 with specificity for galactan. The negative field at the binding site may provide a stabilizing interaction with the sugar antigen since the latter has many hydroxyl groups with partial positive charges on the outwardly oriented hydrogens.

FIG. 12. The Fv fragment of HyHEL-5, an anti-lysozyme hybridoma, shown with the lysozyme backbone of the antigen-antibody complex. A large negative field is found at the binding site. - 1 k T / e potential contours are shown in red.

Electrostatic fields in antibodies and antibody/antigen complexes

FI~. 13. The same HyHEL-51ysozyme complex as depicted in Fig. l l, showing the domination ofthe lysozyme positive potential. + 1 and - 1 kT/e potential contours are shown in blue and red, respectively.

FIG. 14. The potentials around the HyHEL-10 antibody against lysozyme. The four negatively charged aspartate side chains (Asp H 1, Asp H27, Asp H32 and Asp H 101) on the antibody, only one of which is in direct contact with the lysozyme antigen (Asp H32), are shown in space-filling representation. + 1 , - 1 kT/e potential contours are shown in blue and red respectively.

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FIG. 15. The complex of the D1.3 antibody with lysozyme. The antibody and antigen fields are not completely complementary, and some overlaps between contours of same sign, in particular positive/positive occur. + 1 , - 1 kT/e potential contours are shown in blue and red respectively.

FIG. 16. Contours of the difference potential showing changes in the induced surface charges accompanying surface desolvation when the HyHEL-5/lysozyme antibody/antigen complex is formed. The difference field has been calculated using only the side chain formal charges, i.e. Arg and Lys + 1, Glu and Asl~ - 1. The sign of the resulting fields depicts the large positive induced reaction field change arising from desolvation.of the predominantly negatively charged antibody surface (Fv fragment ~-carbon tracing shown in green) and the complementary negative reaction field change arising from desolvation of the predominantly positively charged lysozyme surface. The absolute value of the difference field magnitude is obtained by summing the potential field points enclosed in the positive and negative field envelopes, and is approximately zero. + 1,- 1 kT/e potential contours are shown in blue and red respectively.

Electrostatic fields in antibodies and antibody/antigen complexes

FIG. 17. Contours of difference potential showing changes in the induced surface charges upon desolvation accompanying the HyHEL-5/lysozyme complex formation. In contrast to the situation depicted in Fig. 16, the full set of AMBER partial charges has been used to calculate the field difference. Lysozyme (yellow) and HyHEL-5 Fv fragment (green) surfaces are shown together with the 1 kT/e contours of the negative (red) and positive (blue)difference potential contours. The contours are now clearly unbalanced, with the negative desolvation predominating. Consequently, the absolute value of the desolvation field (and the total desolvation energy as well) will not cancel out, as in Fig. 16.

FIG. 18. Comparison of the difference potential showing changes of induced surface charge due to the desolvation accompanying HyHEL-5/lysozyme complex formation. Magenta and cyan: - 1 , + 1 kT/e difference map contours respectively, obtained from formally charged side chains only. Red and blue (barely visible): - 1 , + 1 kT/e difference potentials from the complete AMBER partial charge set. Note that the negative potential region alone in the partial charge calculation extends over the same volume occupied by both the positive and negative potential regions arising from formal charges only.

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FIG. 19. Desolvation potentials in the McPC 603 Fv fragment complexed with phosphoryl choline. The hapten is shown is space-filling representation, the Fv fragment excluded volume surface is shown in green. Although the hapten is zwitterionic, the desolvation field is essentially completely negative and overwhelmingly contributed by the protein. The full AMBER partial charge set was used in the difference field calculations. Qualitatively similar pictures were obtained with the 36-71/phenyi arsonate and the 4-4-20/fluorescein complex. + 1 , - 1 kT/e potential contours are shown in blue and red respectively.

FIG. 20. Desolvation potentials in the 26-10 Fv fragment complexed with digoxigenin. As with the phosphoryl choline (Fig. 19), the bulk of the difference field is contributed by the protein. Although the total difference field is unbalanced, having a large negative contribution predominantly arising from desoivation of the solvent-exposed polypeptide backbone carbonyl oxygen, there is a visible contribution from a positively charged difference field closer to the hapten. + 1 - 1 kT/e potential contours are shown in blue and red respectively.

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small haptens. With fields of this size, protruding further into solvent, through-distance electrostatic effects such as, e.g. preorientation of the multipole ligand at its approach to the binding site, may become possible. Certainly, in the HyHEL-10 antibody, indirect effects of electrostatics on binding are well documented by the work of Lavoie et al. (1992). They demonstrated by site directed mutagenesis of negatively charged side chains close to, but not in direct contact with the lysozyme antigen, that their effect on binding is significant (several kcal of Gibbs free energy of binding). Figure 14, concentrating on the HyHEL-10 electrostatic field, presents a similar picture: a cluster of four negatively charged amino acids close to the binding site contributing strongly towards the size of the negative field seen at the binding site, yet being outside of a direct contact with the antigen. The electrostatic situation in another anti-lysozyme Fcfragment, DI.3, is depicted in Fig. 15. This figure illustrates well the point that, for large protein antigens, the surface distribution of the fields may not always be strictly complementary. Thus, one sees clear overlaps of positive lysozyme contours into the positive contours of the antibody. VI. BINDING ENERGY CONTRIBUTION FROM SURFACE CHARGE DESOLVATION The above discussion of field contours dealt with Coulombic or intermolecular charge-charge interactions mediated by fields created primarily by formal charges. In view of the importance of electrostatic desolvation, we have included a graphical account of these effects as well, and briefly discuss their importance. Electrostatic solvation of the charged atoms of a low dielectric polar molecule surrounded by a high dielectric aqueous environment can be described in terms of the reaction field that these charges induce in the solvent which acts back at the charges. This interaction is also referred to as a self energy term (Sharp and Honig, 1990). The solvent reaction field can be represented as a set of induced surface charges located at the dielectric boundary between the molecule and the solvent. In essence, the dipolar water molecules become attracted to, and oriented around, solute charged groups, so the dipoles interact favorably with the solute charge; thus, solvation always reduces the electrostatic potential energy. When proteinprotein complexes are formed, desolvation occurs on their contact surfaces, the induced surface charges are displaced, and the electrostatic energy of the system increases. Thus, desolvation always opposes complex formation and the absolute energetic cost of desolvation becomes a question of utmost importance. There is a direct way of displaying such desolvation effects using the DELPHI potential maps: The potential maps of the complex, the isolated antibody, and the free antigen, are calculated on identical lattices, and the latter two maps are subtracted from that of the complex. The difference maps can then be displayed and analyzed. Multiple positive and negative charges on the desolvated surfaces can result in overall cancellation, giving a small net desolvation energy. This is indicated in the difference maps by small, approximately equal-sized regions of positive and negative potentials located around the desolvated surfaces as, e.g. in the HyHel-5/lysozymedifference map calculated for the Asp, Glu, L-ys,Arg and His formal charges only (Fig. 16). When calculations are done with the complete set of partial atomic charges, however, we find the desolvation potential to be unbalanced and always negative (Figs 17-19). A more detailed analysis of this phenomenon shows that the negative bias results from a basic electrostatic assymmetry of protein backbone, and the way backbone atoms are exposed to solvent in folded proteins. Of the NH-C~t-CO atoms forming the peptide bond, the carbonyl oxygen is both the most highly charged (q = 0.55), and the most exposed to solvent. Consequently, most of the induced surface charge in proteins arises from the carbonyl oxygens (Sharp, 1991c), and even a neutral protein behaves as though its surface were somewhat negatively charged. Due in part to this peculiar solvation characteristic of the protein backbone, the net electrostatic binding energy ofcomplexation is usually unfavorable, even for protein antigens that display complementarity of formal charges in the contact region (Figs 17-19), or for haptens that are electrically neutral (Fig. 20).

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VII. CONCLUSIONS (1) The calculated field contours correspond closely to the distribution of formally charged side chains on the surface. (2) By and large, the sign of the field at the binding site is opposite to that of the hapten. For dipolar (zwitterionic) molecules, the field dipole helps in orienting the ligand. Binding sites to neutral molecules may have measureable fields (menadione, galactan), or may be neutral (digoxin). The fields do not extend very far (i.e. beyond ~ 4 A) into the solvent. Outside the binding site region the electrostatic potentials are complex and seemingly uncorrelated with the antigen binding. (3) Although there are local regions of electrostatic complementarity for large antigens, absolute complementarity is not a prerequisite for complex formation (e.g. D1.3/lysozyme). (4) There is no similarity between the binding site fields of R19.9 and 36-71 Fv fragments that bind the same charged ligand, phenylarsonate. Fields at the 4-4-20 binding site specific to fluorescein are such as to suggest lateral two-dimensional diffusion of the ligand along the protein surface into the site via the only unobstructed path. (5) With antibodies against lysozyme, the HyHEL-5 and HyHEL-10 antibodies have large negative fields complementing large positive fields of the antigen. In HyHEL-10, side chains that do not contact the antigen act through space to augment the field and increase the antibody affinity for the antigen. (6) Desolvation of antigen-antibody surfaces is an important component of the energetics of complex formation. The sign of the desolvation potential being the opposite to that of the solute potential, there is an overall approximate cancellation of desolvation when only formal side chain charges are considered. With complete partial charges however, the desolvation potential is unbalanced and desolvation generally opposes complex formation. The backbone carbonyl oxygen makes a large contribution to the desolvation due to its large solvent exposure and a significant partial charge. ACKNOWLEDGEMENTS We wish to thank our crystallographic colleagues for sharing with us atomic coordinates of the Fab/antigen complexes prior to their public release. In particular, Drs P. Alzari, R. Poljak and F. Saul (Pasteur Institute, Paris) allowed us to use the coordinates of the D1.3 complex; Drs G. Petsko (Bradeis University, Waltham), R. Strong (California Institute of Technology, Pasadena) and M. Margolies (Massachusetts General Hospital, Boston) provided us with the coordinates of the 36-71 complex; and Drs P. Jeffrey and S. Sheriff (Bristol-Myers Squibb Research Institute, Princeton) shared with us the coordinates of the 26-10 complex. REFERENCES AMZEL,L. M., POLJAK, R. J., SAUL, F., VARGA,J. M. and RICHARDS,F. F. (1974) The three-dimensional structure of a combining region ligand complex ofimmunoglobulin NEW at 3.5 A resolution. Proc. natn. Acad. Sci. U.S.A. 71, 1427-1430. ADAMSON, A. W. (1976) Physical Chemistry of Surfaces, John Wiley, New York. ALZARI, P. M., LASCOMBE,M. B. and POLJAK, R. J. 0988) A. Rev. lmmunol. 6, 555-580. AMIT, A. G., MARIUZZA, R. A., PHILLIPS, S. E. V. and POLJAK, R. (1986) Three-dimensional structure of an antibody-antigen complex at 2.8 A~ resolution. Science 233, 747-752. BERNSTEIN, F. C., KOETZLE,T. F., WILLIAMS,G. J. B., MEYER, E. F., BRICE, M. D., RODGERS,J. R., KENNARD, O., SHIMANOUCHI,T. and TASUMI,M. (1971) The protein data bank: a computer based archival file for macromolecular structures. J. molec. Biol. 112, 535-542. BHAT, T. N., BENTLEY,G. A., FISCHMANN,T. O., BOULOT, G. and POLJAK, R. J. (1990) Small rearrangements in structures of Fv and Fab fragments of antibody D1.3 on antigen binding. Nature 347, 483485. BIRD, R. E., HARDMAN, K. D., JACOBSON,J. W., JOHNSON, S., KAUFMAN,B. M., LEE, S. M., LEE, T., POPE, S. H., RIORDAN, G. S. and WHITLOW, M. (1988) Single-chain antigen binding proteins. Science 242, 423~426. BOCKRIS, J. O. and REDDY, A. K. N. (1970) Modern Electrochemistry, Plenum Press, New York. BODE, W. and HUaER, R. (1991) Ligand binding: proteinase protein inhibitor interactions. Current Opinion Struct. Biol. 1, 45-52. CHOTHIA, C. (1974) Hydrophobic bonding and accessible surface area. Nature 248, 338 339. CHOTHIA,C., LEVITT,M. and RICHARDSON,O. (1977) Structure of proteins: packing of ~t-helices and pleated sheets. Proc. natn. Acad. Sci. U.S.A. 74, 413~4134. CHOTHIA, C. and JAN1N,J. (1982) Orthogonal packing of fl-pleated sheets in proteins. Biochemistry 21, 3955-3965.

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