PROTEINS: Structure, Function, and Genetics 30:249–263 (1998) Structural Modeling of the Complex Between an Acetylcholine Receptor-Mimicking Antibody and Its Snake Toxin Antigen Catherine Tenette-Souaille and Jeremy C. Smith* Section de Biophysique des Protéines et des Membranes, DBCM, CEA-Saclay, Gif-sur-Yvette, France ABSTRACT The antibody Ma2-3 neutralizes the functional, acetylcholine receptor binding activity of its antigen, neurotoxin a, and exhibits several other properties in common with the receptor itself. We present here the results of calculations examining the threedimensional structure of the toxin a:Ma2-3 complex. The antigen structure, determined by nuclear magnetic resonance spectroscopy,1 was docked to models of the variable fragment of the antibody combining site2 by using a method based on surface complementarity and maximization of buried surface area3,4 while taking into account the possibility of conformational change on complexation. Extensive experimental information on the location of the functional epitope was incorporated into the analysis and used to screen candidate geometries of the complex resulting from the modeling. Eight plausible structures that are in accord with the experimental data were derived. Common structural features of the models are discussed, and residues of the antibody-combining site that are expected to play important roles in complexation are identified. In particular, three epitope residues that, according to mutagenesis experiments, make particularly strong contributions to the binding, interact excentrically and do not make contact with the central loops of the combining site, L3 and H3. Proteins 30:249–263, 1998. r 1998 Wiley-Liss, Inc. Key words: antibody-antigen complex; snake toxin; protein docking INTRODUCTION The structural characterization of protein-protein complexes in general, and antibody-antigen complexes in particular, presents a major challenge to structural biology. Although hundreds of antibodies have been sequenced,5 only approximately 60 antibodies and 10 antibodies complexed with protein antigens have been determined crystallographically, and the rate that X-ray structures are being solved lags behind that of sequence generation.6 Among the reasons for this lag are the time-consuming nature of the crystallographic process and the fact that the r 1998 WILEY-LISS, INC. obtention of crystals suitable for structural analysis is sometimes not possible. Consequently, there is a need to develop noncrystallographic methods capable of providing information on the three-dimensional (3-D) structures of antibodies, antigens, and their complexes. Among the methods that can be applied are molecular modeling and simulation. Computational methods exist for calculating structures of antibody combining sites, given the primary sequence, and for determining the structures of protein-protein complexes, given the structures of the isolated proteins. Some of the methods for combining site modeling use energy calculations and involve techniques such as uniform search in internal coordinate space,7,8 random generation of backbone conformations,9 Monte Carlo simulation,10 and high-temperature molecular dynamics.11 These methods have provided useful models in several cases. A procedure combining energy calculations with screening of the database of existing structures also has been developed and has given satisfactory results for the structure prediction of two antilysozyme antibodies.12 Several methods for the calculation of protein-protein complex geometries, starting from the structures of the isolated molecules have been developed13,14 and have succeeded in some cases. Notable among the successes are those of six groups that accepted a recent challenge to determine the b-lactamase inhibitory protein:TEM-1 b-lactamase association and correctly predicted the general mode of association.15 Ideally, a combination of the above methods would enable the structure of any antibody: protein antigen complex to be derived, given the primary sequence of the antibody and the 3-D structure of the antigen. However, no single method of antibody structure or protein-protein complex structure calculation has proved to be completely reliable. The combining site generation methods have modeled the shorter complementarity determining region (CDR) loops more accurately than the longer ones, with typical RMS deviations from crystal structures of approxi- *Correspondence to: Jeremy C. Smith, Section de Biophysique des Protéines et des Membranes, DBCM, CEA-Saclay, 91191 Gif-sur-Yvette, France. Received 10 January 1997; Accepted 2 July 1997 250 C. TENETTE-SOUAILLE AND J.C. SMITH mately 1 Å for the shorter loops but sometimes greater than 2 Å for the longer ones. Similarly, protein-protein docking predictions are still fraught with difficulties, as evidenced by the failure of three different methods to identify uniquely the pancreatic trypsin inhibitor:trypsin complex.4,16,17 The chances of successful structure prediction can be enhanced by incorporating information from experiments that identify residues important for the binding interaction and thus can be used to screen candidate structures obtained from the modeling procedures. This approach is used in this study, in which we examine the structure of the complex of the monoclonal IgG2a-k antibody, Ma2-3 with its antigen, neurotoxin a from Naja nigricollis (Kd 5 1.9 3 1029 M18 ). Toxin a binds to the nicotinic acetylcholine receptor (AChR), blocking transmission at the neuromuscular junction. Site-directed mutagenesis experiments have defined residues important in binding to AChR.19 The epitope of Ma2-3 on toxin a has also been delineated by using nuclear magnetic resonance (NMR) spectroscopy,20 chemical modification,18 and site-directed mutagenesis.21 The functional site and epitope largely overlap. In accord with this result, it was found that Ma2-3 is a neutralizing antibody, preventing binding of toxin a to AChR.21 Ma2-3 also recognizes and neutralizes all the native short toxins tested.18 These results raise the question of to what extent, if at all, Ma2-3 might mimic the AChR cholinergic binding site. This possibility was discussed in recent work that showed that 1) like AChR, Ma2-3 elicits anti-AChR antibodies, which in turn elicit antitoxin antibodies; 2) the region 106-122 of the a-chain of AChR shares 66% primary structure identity with CDR regions of Ma2-3; and 3) 8 of the 10 epitope residues of the homologous erabutoxin a also belong to the 10residue epitope recognized by AChR.21 The following data were incorporated in the present docking analysis: 1) the solution structure of the antigen, toxin a determined by NMR spectroscopy,1 2) the results of extensive modeling of the combiningsite of Ma2-3,2 and 3) the results of three sets of experiments, performed to map the Ma2-3 epitope: chemical modification of Lys and Trp residues,18 the determination, using NMR, of the H-D exchange rates of labile amide hydrogens in toxin a, free and bound to the antibody,20 and binding experiments on site-directed mutants of the homologous erabutoxin a from Laticauda semifasciata.21 In what follows, the NMR results on the structure of isolated toxin a and the modeled structures of Ma2-3 are used as input for an algorithm that generates protein-protein complexes based on surface complementarity and the hydrophobic effect.3,4 The complexes generated are screened for consistency with the experimental functional epitope mapping data. Eight complexes that satisfy the modeling and experimental criteria are found. The eight com- plexes have structural features in common. In particular, the models suggest that the main interactions that determine the binding affinity are made away from the central loops, H3 and L3. METHODS Common properties of antibody-antigen association have been described.22,23 Immune recognition is based largely on structural complementarity of the proteins, but conformational changes may take place on association.24–26 Therefore, the approach used here is based largely on structural complementarity but makes some allowance for conformational change. Input Structural Data Antigen NMR work resulted in eight plausible structures of toxin a.1 The average of these structures was used as a starting point for this study. This structure was refined by performing minimizations of the potential energy of the hydrated toxin, using the program CHARMM.27 The hydrating water molecules were generated by solvating the toxin in a large water box and removing water molecules lying either closer than 2.6 Å to any heavy atom or farther than 6.0 Å from all atoms of the protein. In two initial minimizations the water molecules were free to move whereas the toxin heavy atoms were harmonically restrained to their initial positions with a force constant of 50, then 25 kcal · mol21 · Å22. In the third minimization, the toxin backbone atoms were restrained by a harmonic potential of force constant 5 kcal · mol21 · Å22, whereas the water molecules and toxin sidechain atoms were free to move. The eight NMR toxin structures and the energy-minimized average structure are shown in Figure 1. The polypeptide chain of the toxin is organized into three adjacent loops forming a large b-sheet that emerges from a globular core containing four disulphide bonds. The toxin can be described as having two opposite faces. The face closest to the C-terminal loop is slightly convex. The backbone variation among the eight structures is very low, whereas side-chain orientations are different in all structures for residues 29–34, corresponding to the tip of loop 2. Antibody In previous work, described in detail in Ref. 2, structural modeling was performed on the isolated Ma2-3 variable fragment. Three different tried and tested methods of combining site generation— uniform conformational sampling,7 high-temperature molecular dynamics,11 and a combined algorithm12—were used with relaxed acceptance criteria to generate a large number of geometries. These structures were clustered into 13 classes, from which four thermally interconvertible conformations were selected as being most likely to be populated in solution. In this study, to increase the likelihood of STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX 251 TABLE I. List of the Epitope Residues Identified by Site-Directed Mutagenesis on Toxin a Gln7 Arg33 Fig. 1. Superposition of the eight NMR structures (fine lines) of toxin a (PDB code 1NEA1) and the average structure (bold line). Loops 1, 2, and 3 are from left to right. The concave side of the protein side faces the viewer. The disulfide bridges are represented with a broken bold trace. The numbering scheme common to all short snake toxins is used in the present work. capturing the correct antibody conformation and to allow for possible conformational changes of the antibody on complexation, all 13 derived structural classes were used in the docking calculations with the antigen. Epitope mapping The Ma2-3 epitope on toxin a has been probed with three sets of experiments: (1) With the use of affinity chromatography and proton 2D-NMR spectroscopy, H-D exchange rates of the labile amide hydrogens of the toxin a were determined, unbound, and bound to the antibody.20 Eight amides had a protection factor larger than 10, a value considered significant compared with the errors incurred in the exchange measurements. These amides are in Gln6, Lys15, Lys26, Val28, Ile36, Ile37, and Arg38, suggesting that the Ma2-3 epitope is localized largely on loop 2 of toxin a. (2) Chemical modification of residues in toxin a and in the homologous erabutoxin a was performed.18 Erabutoxin a is another short curaremimetic toxin, with primary and tertiary structures very Lys27 Ile36 Trp29 Glu38 Asp31 Lys47 His32 Ile50 close to that of toxin a.1 Residue 18 is deleted in toxin a, but this deletion results in only minor structural differences, far from the functional epitope.28 The chemical modification experiments, performed on Lys residues 15, 27, 47, and 51 and Trp29, revealed that the sites by which the toxin binds to Ma2-3 contain at least the two terminal amino groups at position 27 and 47 and the indole group at position 29.18 (3) The epitope of erabutoxin a has been subjected to extensive mutational analysis, with a view to identifying the residues whose mutations affect the stability of the protein-antibody complex.21 This strategy has been used in a number of cases, and the results match structural analyses.29–32 More than 70% of the positions of erabutoxin a have been modified by site-directed mutagenesis and the affinity for Ma2-3 subsequently determined.19,21 As far as possible, the mutations were chosen to maximize the change in the chemical nature of the residues while minimizing the likelihood that structure would change significantly. Circular dichroism spectra of the mutants were identical to the native protein. Moreover, several of the mutants were subjected to X-ray crystallographic analysis, and no detectable structural change was observed. It was concluded that substantial differences in binding affinities were unlikely to be due to structural changes in the antigen.21 In Ref. 32 it was observed that residues whose mutations result in more than a tenfold affinity decrease in a protein-antibody complex belonged to the epitope identified by X-ray analysis. Mutations at 10 positions in the erabutoxin led to an Ma2-3 affinity constant ratio between the mutant and native species larger than 10 (see Table I). These positions are occupied by the same residues in toxin a, except at position 32 where a histidine is found. These residues form a contiguous surface on the concave face of the toxin, shown in Fig. 2. The three residues identified by chemical modification in Ref. 18 were included among the 10 identified by mutagenesis. The surface area covered by the identified epitope is approximately 700 Å2, a value comparable with other protein-protein complexes.22 The observed affinity constant decreases were higher than 500-fold in three cases: Gln7, Trp29, and Glu38, with two mutations of Glu38 leading to decreases of nearly four orders of magnitude, corresponding to decreases of nearly 5 kcal/mol in the 252 C. TENETTE-SOUAILLE AND J.C. SMITH A Fig. 2. Epitope of toxin a. A: Residues identified by chemical modification, NMR spectroscopy, and site-directed mutagenesis are numbered. B: Space-filling model of toxin a with, in green, functional epitope identified by site-directed mutagenesis. B STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX Fig. 3. 253 Definition of the six coordinates defining the relative positions of the two proteins. dissociation free energy. These three residues are spatially close to each other, forming a compact cluster. Presumably, Gln-7, Trp-29, and Glu-38 form an ‘‘energy core’’ for interaction of Ma2-3 with the toxin. This is in accord with several experimental and theoretical studies on protein-protein interactions that suggest in many cases of protein-protein recognition a limited number of core residues, three or four, contribute the major part of the affinity.30,33–38 Docking Procedure The algorithm used to dock the proteins was that of Refs. 3 and 4. It is based on low-resolution shape complementarity and buried surface area considerations. Both molecules are considered as rigid bodies, and each amino acid is represented as a sphere, placed at the side-chain centroid. The relative position of the two molecules is described by six degrees of freedom: five angles and one distance (see Fig. 3). For each geometry generated, an energy, EB, is calculated by using the equation EB 5 E* 2 gB*. E* represents molecular overlap. 2 gB* represents the hydrophobic free energy due to burial of the surface area B*. B* is estimated with an analytical approximation.39 The constant, g is taken equal to 50 cal/mol · Å2.4 This initial positioning algorithm is low resolution in that the residues are treated as spheres. Consequently, although the backbone geometry is expected to significantly influence the results of these calculations, side-chain conformation is expected to be less important. The backbone tracing of the antigen shows little variation among the eight NMR-derived geometries (see Fig. 1). Therefore, to reduce the combinatorial computational load, only the minimized average NMR structure of the antigen was used in all calculations. However, the 13 modeled antibody structures do manifest backbone conformational variations.2 Each of these structures was considered a priori to be equally likely to exist in the complex, and all were included in the docking. The same docking protocol was followed by using each of the 13 isolated Ma2-3 models. The toxin a was roughly positioned above the combining site of each Ma2-3 model, and geometries of the complex were produced in two ways: by uniform sampling (with a grid size of 10°) and by using Monte Carlo calculations, as described in Ref 4. First screening and clustering More than 3 3 106 solutions were obtained. These were subjected to two screening and clustering procedures. In the first, orientations yielding values of B* 254 C. TENETTE-SOUAILLE AND J.C. SMITH greater than 1200 Å2 were sorted according to EB and clustered: solutions were considered to belong to the same cluster if their latitude and longitude values were within 5° of the average orientation of the cluster and their spin angles x differed by less than 10°. The geometry with minimum energy EB within each cluster was retained for subsequent analysis. In the majority of crystallographic antibodyprotein antigen complexes five of the six CDR loops make contact with the antigen. Therefore, solutions were retained for which all 10 experimentally identified toxin epitope residues make contact with the antibody, and at least five of the six hypervariable loops make contact with the toxin. To determine the contacts, the surface accessibilities of each of the 10 residues defining the functional epitope and all residues from the combining site were calculated. A relaxed criterion was used because the side-chain positions had not been optimized: residues were considered as participating in the interface if their accessible surface area in the isolated protein was reduced by at least 20% in the complex. For each retained model, the surface area buried at the toxin a-Ma2-3 interface was recalculated, at atomic detail, with the Lee and Richards algorithm40 using a probe radius of 1.4 Å. Second clustering and screening The retained solutions were clustered further to group together models with similar toxin orientations but different antibody structures. Solutions with latitudes and longitudes within 10° were clustered together. Two quantities were calculated and used to choose a representative structure from each cluster. One of these was the energy EB. The other is a low-resolution, short-range scoring function for electrostatic complementarity, Eel, calculated by representing the residues with the same, simplified model that was used during the docking procedure,41 i.e., as spheres of radii ri centered at a distance Ri from their corresponding Ca atoms. Eel is the sum over the interface of terms Ei,j, between residues i and j, given by: 5 0 Ei j 5 I(i, j ) di, j if di, j $ (ri 1 Ri ) 1 (rj 1 Rj ) 1 d if di, j , (ri 1 Ri ) 1 (rj 1 Rj ) 1 d where di,j is the distance between the Ca atoms. The interaction matrix, I(i,j) is given in Table II. To soften the positional dependence of the function, the distance allowance was increased by d 5 1.0 Å. Twenty structural families were obtained at this stage. The energies EB and Eel were calculated for each model. Thirteen of the 20 families contained more than one model. In 11 of these the same model possessed the minimum value of both energies, and this model was selected for further refinement. For each of the other two groups, the complex was TABLE II. Matrix Used for the Electrostatic Interaction Calculations Positive Negative Polar Apolar Positive* Negative† Polar‡ Apolar§ 110 210 110 210 210 210 0 0 0 0 *Lys, Arg. †Asp, Glu. ‡Asn, Gln, Ser, Thr, Tyr, His. §Ala, Cys, Ile, Val, Phe, Gly, Leu, Pro, Trp, Met. TABLE III. Results of the Docking Calculations Between Toxin a and the 13 Antibody Fv Models Antibody 1 2 3 4 5 6 7 8 9 10 11 12 13 Total B* .1200 Å2 Clustering* Filtering† 2974 3079 3005 3620 3324 3361 3582 3423 2969 3558 2751 3114 2892 41,585 127 117 129 136 132 117 119 129 125 115 119 134 114 1613 6 4 9 0 5 1 1 0 1 8 4 5 7 51 *Number of clusters. †Number of solutions in which at least 5 Ma2–3 CDRs and the 10 functional epitope residues participate in the interface. retained that possessed the largest energy gap with the second-lowest energy complex for that criterion for which it had the lowest energy. CDR loops L1 and H2 were in poor, unusual conformations in certain of the models of the isolated antibody generated in the previous work.2 Models of the complexes in which these loops remained solvent exposed, and thus probably flexible, were retained. Two of the 20 models, in which loops in unusual conformations made significant contacts with the toxin, were rejected. Refinement of the atomic-detail models In the final stage of the calculations the interface side chains of the 18 remaining models were positioned by using energy minimization and molecular dynamics calculations with CHARMM, parameter set 22. In these calculations all residues farther than 11 Å from the interface were kept fixed. Side chains of all residues having at least one atom less than 9 Å from an atom of the other molecule were free to move. A soft harmonic constraint was applied to the main-chain atoms of these residues and to all atoms of residues between 9 and 11 Å from the interface. Three consecutive molecular dynamics calculations were performed for each of the 18 models. In the STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX Fig. 4. 255 Distribution of the angular parameter values of the 51 selected orientations. first, the toxin was translated 2 Å away from Ma2-3 along the axis between the molecular centers of mass. In the second and third, the toxin was translated back to its initial position in successive 1-Å steps. In each of the three runs 200 steps of steepest descent minimization was performed followed by heating to 400 K in 2 ps and finally running 5 ps further molecular dynamics without temperature control. Subsequently, the system was relaxed by cooling to approximately 0 K in 2 ps and energy minimized with the Adopted Basis Set Newton Raphson algorithm in CHARMM. Several properties of the resulting atomic detail models were examined. Among these were the antigen-antibody interaction energies, calculated as the sum of van der Waals and electrostatic energies of the CHARMM potential function. Another energy also was evaluated, DGAT, which estimates the solvation free energy of the complex, i.e., the free energy in transferring the complex from solution to the gas phase. DGAT was calculated by using the empirical relation of Eisenberg and McLachlan42: DGAT 5 oN k51DskAk where where Dsk is the solvation parameter and Ak the accessible surface area of atom k. The atomic solvation parameters used were those in Ref. 43. RESULTS AND DISCUSSION Generation and Preliminary Screening of Models In Table III are listed the numbers of complexes with B* greater than 1200 Å2 for each of the 13 antibody models, together with the numbers of complexes retained after the first clustering and screen- 256 C. TENETTE-SOUAILLE AND J.C. SMITH TABLE IV. Number of Residues of Each Antibody CDR* in Contact With a Toxin Residue. Models With 5 or 6 CDRs Contacting Are in Boldface Complex L1 L2 L3 H1 H2 H3 Total 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 3 6 3 4 4 2 1 1 0 4 3 2 0 0 0 0 0 0 7 0 0 0 0 4 7 5 1 4 1 7 6 5 5 0 3 6 1 2 2 3 5 1 1 1 3 4 3 1 0 0 1 3 0 1 1 3 1 1 0 2 1 1 3 1 2 1 2 2 2 3 3 2 0 6 7 3 1 0 0 1 6 4 8 0 1 1 0 8 2 0 8 3 2 2 2 8 5 7 6 5 4 4 6 6 6 4 7 6 20 20 15 13 13 17 15 16 19 22 21 15 15 14 14 18 15 15 *CDR limits are those used for the Fv modeling.2 ing procedure. This procedure resulted in the elimination of approximately 99% of the solutions with B* greater than 1200 Å2, leaving 51 models. Figure 4 shows the distributions of the relative orientations of the molecules in these 51 models. The f1, f2, u1, and u2 values are distributed relatively narrowly, whereas the spin angle x is dispersed, with only one region, [230°:60°], being relatively unpopulated. This reflects the fact that, although the proximity of the epitope to the combining site is known, the relative orientation is not. The second clustering, performed without differentiating between antibody models, led to 20 families containing between one and eight members. Representative structures were chosen from each family, as described in Methods, leaving 18 retained solutions. Analysis of the 18 Selected Complexes The 18 models were refined at atomic detail by using energy minimization and molecular dynamics calculation as described in Methods. The resulting structures were analyzed to characterize features in common. The paratope A list of intermolecular contacts made by each Ma2-3 CDR in each side-chain refined model is given in Table IV. Figure 5 shows the number of times each Ma2-3 residue contacts the antigen, summed over the 18 refined models. The total number of residues making contact in each model varies from 13 to 22, distributed over 4–6 CDRs. In 18 of the 20 models most of the contacts are found to involve only one or two CDRs, the exceptions being models 4 and 10. Loop H3 was contacting in all 18 models and H1 in all but one of them. The other loops, L1, L2, L3, and H2, are less frequently implicated, making contacts in 7, 5, 3, and 6 models, respectively. Figure 6 shows a view from above the Ma2-3 combining site. The accessible surface area of loop L3 is approximately 250 Å2, small compared with that in the only other crystallographic structure with an eight-residue L3 loop: HyHEL5 (430 Å2 ).44 The relatively low accessible surface area of this loop is consistent with it forming part of the paratope in only 3 of the 18 models of the complex. Those residues of any given CDR making contact with the antibody are mostly the same ones in each model. For the central loops, L3 and H3, these are the residues most exposed to solvent.2 In loop L1, AsnL31 and its adjacent environment make contact, and in loop H1 the segment H31-H33 makes contact. In the models in which L2 and H2 make contact, almost all the residues participate approximately equivalently. Framework residues also make a number of contacts with the toxin, between 1 and 12 depending on the model. The framework residues most frequently implicated are TyrL49, the region between loops L1 and L2 around TyrL67, the N-terminal segment of the VH domain, and the region H26-H30, near loop H1. H26-H30 form the loop joining CDR H1 with the preceding b-strand: these residues belong to the hypervariable region H1 defined by Chothia and Lesk.45 All of the above framework regions are near the combining site and have been found to participate in antigen interactions in complexes with known structures. Antibody-combining sites are often rich in aromatic residues, particularly Tyr and Trp.23,46 In the Ma2-3 modeling there was a ring of Tyr residues of approximately 15 Å diameter at the top of the combining site, encircling H3. Two framework residues, TyrL49 and TyrL67, are part of this ring and make contact with the antigen in some of the models. The hypervariable loops contribute the other five Tyr residues of the ring: L50 (loop L2), L92 (loop L3), H32 and H33 (loop H1), and H52 (loop H2). One Trp (H50) is also nearby. These residues frequently make contacts with the antigen in the models. The epitope The experimental mapping of the epitope on the toxin has shown that at least 10 of its residues contribute significantly to the interaction with Ma2-3. Figure 7 shows the number of contacts made by each toxin residue, again summed over all 18 refined complexes. The 10 identified functional epitope residues are those most frequently implicated, together with Thr45. Six other residues make contact with the antibody in at least 9 of the 18 models. Six of the seven not previously identified residues are on the same face of the toxin as the identified functional epitope residues: Asn5, Gln10, and Lys15 in loop 1; STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX 257 Fig. 5. Number of contacts made by the Ma2-3 residues with toxin a in the 18 selected models. Limits of the CDRs are indicated by a bold trace. Tyr25 in loop 2; and Pro44 and Thr45 in loop 3 (see Fig. 3). The seventh, Gly49, is at the top of loop 3. Apart from Lys15 = Ala, mutations of these residues did produce affinity constant decreases relative to the native protein, although the changes observed (DKd , 6.0 nM) were not sufficiently large to warrant inclusion in the epitope based on the mutational data alone.21 Selection of Eight Final Models The docking energies, EB, and electrostatic energies, Eel, of the 18 complexes, calculated at low resolution, i.e., with the residues modeled as spheres, prior to the molecular dynamics side-chain positioning, are listed in Table V, together with their buried surface areas calculated at atomic detail. EB varies from 285 to 260 kcal · mol21, Eel from 2105 to 245 kcal · mol21 and the buried surface area from 1450 to 2350 Å2. EB and Eel were uncorrelated with the surface area (data not shown), and the minimum value of each property was found in different complexes. Atomic detail properties of the 18 side-chain optimized models are given in Table VI. The buried surface areas calculated at atomic detail are significantly smaller than those calculated at low resolution (listed in Table V), and the values calculated with the all-atom model are approximately 10% larger than with the heavy atom representation.22 For all but one model (complex 5), the heavy-atom buried surface areas are in the interval seen experimentally (1600 6 350 Å2 ). For this, and other reasons stated below, complex 5 was eliminated from the list of candidate models. The antibody-antigen interaction energies vary considerably among the complexes, from 2324.9 kcal · mol21 (complex 12) to 2119.2 kcal · mol21 (complex 5), but the solvation free energies less so, from 557.7 kcal · mol21 (complex 10) to 482.1 kcal · mol21 (complex 12). The buried surface area is roughly proportional to DGAT and roughly inversely proportional to Eint (data not shown). As a consequence of this and the fact that the interaction and solvation energies cannot simply be summed, the models cannot be ranked on a single energy scale. Discrimination between the models using the atomic detail criteria in Table VI is thus difficult. The energy minimization and molecular dynamics procedures were accompanied by small structural rearrangements. These, together with examination of the complexes at finer detail, led to the rejection of several complexes due to the absence of contacts by critical epitope residues. The contacts made by the functional epitope toxin residues in each of the 258 C. TENETTE-SOUAILLE AND J.C. SMITH Fig. 6. Space-filling representation of the Ma2-3 combining site (framework, light gray; L1, magenta; L2, cyan; L3, blue; H1, orange; H2, yellow; H3, red). TABLE V. Fv Model, Interaction Energy EB, Electrostatic Term Eel Calculated at Low Resolution, and Buried Surface Area Calculated With an All-Atom Representation, of the 18 Models of the Complex Obtained After Clustering and Screening EB Eel BSA* Complex Antibody (kcal · mol21) (kcal · mol21) (Å2) Fig. 7. Number of contacts made by the toxin residues with the antibody in the 18 selected models. Residues of the functional epitope are in bold. models are listed in Table VII. Table VII permits the elimination of five models: 3, 7, 5, 10, and 17, for which residues strongly implicated in the functional epitope do not interact with the antigen. In models 3 and 7, Glu38 does not interact with the antibody and in models 5 and 10 Gln7 does not interact. The experimental mutagenesis data indicate that the contribution of these residues to the binding to Ma2-3 is critical,21 and it is probable that they make direct contacts. Similarly, model 17 was rejected due to the absence of a contact between Ile50 and Ma2-3. For models 12 and 13, in which functional epitope residues Ile50 and Asp31 are listed in Table VII as not contacting the antibody, the cavities between these residues and the antibody were significantly smaller than a water molecule, and these models were thus retained. In complex 5 residue Lys47, at the periphery of the epitope, is unable to make contact with the antibody, providing yet another 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 1 1 2 2 3 3 3 5 5 7 10 10 10 12 12 13 13 271.8 268.7 264.3 265.3 261.5 274.7 273.0 261.8 267.1 264.8 264.8 277.4 270.6 267.4 282.7 274.3 273.1 269.9 278.6 260.6 266.0 268.9 281.7 247.6 262.4 257.1 2101.5 281.1 276.7 264.2 282.7 288.5 273.0 296.9 273.3 273.4 2031 2055 1921 1955 1493 2182 2177 1816 1886 1812 2259 2301 2297 2171 2167 2041 2250 2250 *BSA, buried surface area. reason to reject this model. Models 5 and 13–18 involve contacts with less than 5 CDRs and were eliminated on this basis. The eight remaining models are shown in Figure 8. In the functional epitope-mapping experiments STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX 259 TABLE VI. Properties of 18 Models of Ma2–3-toxin a Complex After MD Refinement Complex BSA* (Å2) Eint† (kcal · mol21) DGAT (kcal · mol21) Contact residues‡ Hydrogen bonds§ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1933 (1804) 1997 (1749) 1893 (1656) 1725 (1483) 1338 (1162) 1988 (1816) 2022 (1862) 1622 (1473) 1614 (1493) 1940 (1749) 2074 (1825) 2114 (1903) 2118 (1983) 2172 (1943) 1925 (1716) 1817 (1695) 2161 (1945) 2078 (1839) 2286.1 2251.1 2210.9 2195.4 2119.2 2226.2 2285.2 2194.6 2232.5 2256.0 2251.0 2324.9 2195.8 2271.1 2193.2 2205.3 2263.9 2182.1 2518.7 2501.9 2510.0 2527.0 2554.0 2519.3 2507.4 2540.9 2549.7 2557.7 2504.8 2482.1 2488.9 2503.8 2488.4 2502.9 2510.8 2511.3 18 1 26 22 1 23 17 1 19 18 1 19 9 1 14 22 1 24 25 1 24 14 1 20 16 1 21 15 1 25 21 1 26 21 1 24 20 1 22 24 1 26 20 1 23 20 1 19 23 1 23 19 1 23 16 14 10 13 4 12 15 12 14 13 10 18 7 12 10 6 11 12 *Surface area buried at the interface, calculated with an all-atom representation. The value in brackets was calculated with the heavy atoms only. †Interaction energy calculated as the sum of the intermolecular van der Waals and electrostatic terms. ‡Number of toxin and Ma2–3 residues that make a contact across the interface. Two residues are considered in contact if at least one pair of heavy atoms is at a distance less than the sum of their van der Waals radii plus 0.5 Å. §Number of interface hydrogen bonds, identified with QUANTA,48 with a maximal distance between the acceptor and the donor of 3.5 Å and a maximal angle X-A . . . D of 110°. TABLE VII. Description of the Contacts Made by the Functional Epitope Toxin Residues Complex Gln7 Lys27 Trp29 Asp31 His32 Arg33 Ile36 Glu38 Lys47 Ile50 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 h h v h — h h h h — h h h h v v h h h h h h v h h h h h h h v h h h h h h v h v v v h v h h v v v h h v h v h h v h h v h h h h h h — h h h h v v h v v h h h h h v v h v h v v v v h h h v h h h h h h h h h h h h h h v v v v v v v v v v v v v v v v v v h h — h h h — h h h h h h v v h v h h h h h — h h h h h h h h h h h h h v v v v v v v v v v v — v v v v — v h, hydrogen bond; v, van der Waals contact; —, no contact. Most satisfactory models are in boldface. See footnotes of Table VI. three residues were found to have an affinity constant decrease on mutation greater than 500: Gln7, Trp29, and Glu38. These large changes suggest that these three residues might form the energy core of the interaction with the paratope. Glu7 and Glu38 are indeed found to make hydrogen bonds with the antigen in all of the models, although their paratope partner residues vary according to the model. Trp29 hydrogen bonds in only two complexes. The energy core residues did not interact with the central CDR loops L3 and H3 in any of the models. The absence of an L3 interaction is probably related to the relatively low accessible surface area of this loop. H3 does make contact with the antigen in all models (see Table IV) but never with the energy core residues. This may be due to the fact that, in the isolated 260 C. TENETTE-SOUAILLE AND J.C. SMITH Fig. 8. Views of the eight final models for the complex. The color scheme for the space-filling representation of the antibody is given in Figure 6. The toxin backbone is represented as a green wire. The numbering of the complexes corresponds to Tables 4–7. Top panel: top left, complex 1; top right, complex 2; bottom left, complex 4; bottom right, complex 6. Bottom panel: Top left, complex 8; top right, complex 9; bottom left, complex 11; bottom right, complex 12. STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX antibody models, the most accessible segment of loop H3 (H101–H104) contains small residues with poor hydrogen-bonding capabilities, Gly-Ala-Thr-Ala. This is in contrast with other antibodies where large residues such as aromatics or charged residues are commonly found in this segment.46 One or two salt bridges are found in each of the models of the complex. The Ma2-3 CDR loops contain three positively charged residues: LysL24, ArgL54, and LysH59. All three are surface exposed in the models derived for the isolated antibody-combining site but are not near the top of the combining site. Residues located at these positions in the sequence rarely have been involved in direct interactions with antigens in known complexes.46 Although LysL24 does not interact with the antigen in any of the models, the possibility that the other two residues do interact cannot be completely excluded from the present modeling, because ArgL54 makes contact in three models and LysH59 in one. AspH31 is the only negatively charged residue mostly accessible to solvent in the models of isolated Ma2-3. This residue makes hydrogen bonds to the antigen in six of the eight models, and four of these are salt bridges (with either Lys15 or Lys47). The three other negatively charged residues, AspL32, AspL91, and AspH108, are mostly buried in the isolated antibody models (relative accessibility to solvent ,0.2) and form intraprotein hydrogen bonds. However, the models of the isolated antibody do not exclude the interaction of these residues with the antigen, and AspL32 and AspL91 are in positions in the sequence that interacts with antigen in some known complexes.46 AspL32 bonds to hydrogen in three of the eight models, AspH108 in one, and AspL91 in none. CONCLUSION Ma2-3 has so far resisted all attempts at crystallization, either with or without its antigen. However, this study illustrates how, in the absence of crystallographic data, the combination of molecular modeling with experiment can lead to progress in the understanding of the 3-D structural properties of an antibody-antigen complex. Eight models of the toxin a-Ma2-3 complex were selected from a starting set of 3 3 106 generated configurations, based on surface complementarity, buried surface area, and consistency with extensive epitope mapping data. The eight models show certain common characteristics. In particular, they possess the property that the three residues that, according to site-directed mutagenesis experiments, are most strongly implicated in the binding do not interact with the central loops H3 and L3. The problem of how to choose between generated models of a protein-protein complex is particularly 261 difficult. One is confronted with the fact that no particular energy or scoring scale has proved to be completely reliable. This difficulty will be lessened no doubt as computational power increases and our understanding of the basic chemical principles of molecular association improve, and the development of reliable methods for predicting the structure of antibody combining sites and their antigen complexes is clearly of fundamental as well as practical interest. In the meantime we have adopted an approach in which the model building is guided by energetic considerations, but relaxed acceptance criteria are used to take into account the uncertainties involved. This reduces the chance that the correct complex geometry will escape the screening. However, it requires the use of other assumptions to grade the quality of the models. These were based on experiment and assumed that those 10 residues identified as being part of the functional epitope are actually in contact with the antibody and that at least five of the six CDR loops of the antibody are in contact with the antigen. Although these assumptions hold in most cases, they are not 100% reliable. Consequently, to examine the reliability of the models proposed and to distinguish between them will require further experimentation. Crystallization attempts for the complex and the isolated antibody are being pursued. However, less direct experiments also can be performed, involving, for example, site-directed mutagenesis of the antibody. In particular, mutations of those regions of the CDRs that are predicted to be in contact with the antigen can be made and antigen-binding affinities assessed. Mutations of the ring of Tyr residues (into Phe and Ser, for example) would provide useful information. Among the charged residues, ArgL54 and AspH31 are the most solvent accessible and are the closest to the center of the combining site. Mutation of AsnL31 would allow the role of loop L1 to be examined and SerL52, AlaH54, and SerH55 would test loops L2 and H2. These experiments should permit the elimination of some of the models and are now in progress.47 ACKNOWLEDGMENTS We thank our colleagues at the Département d’Ingénierie des Protéines et des Membranes, CEASaclay, for having stimulated our interest in this project, for numerous discussions, and for performing complementary experimental work. 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