INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Biomolecular association is proposed to occur in two steps: 1) encounter, which involves diffusion-limited orientation of the two molecules driven by nonspecific, long-range, electrostatic forces followed by collision to form a hydrophobically associated encounter complex; and 2) docking with the formation of specific contacts and noncovalent bonds (Haselkorn et al., 1974; Ross and Subramanian, 1981; Schreiber and Fersht, 1996). Electrostatic interactions would therefore be expected to directly influence the initial association, through steering, and the strength of docked complex due to electrostatic interactions of salt bridges and hydrogen bonds. Ligand binding also often induces conformational changes in both receptor and ligand during the docking step (Musci et al., 1988; Nicholson et al., 1995; Wagner 1995; Sparrer et al., 1996; Kawaguchi et al., 1997; Walters et al., 1997; Lindner et al., 1999).

Antibody-antigen complexes have long served as models to study general principals of protein-protein interactions and molecular recognition, both experimentally (Kabat et al., 1977; Smith-Gill, 1991; Wilson and Stanfield, 1993; Tsumoto et al., 1994; Braden and Poljak, 1995; Dall'Acqua et al., 1998) and computationally (Novotny et al., 1989; Chong et al., 1999; Freire, 1999). High-affinity antibodies, very specific toward their antigens (Eaton et al., 1995), or proposed to have "lock and key" type of binding (Wedemayer et al., 1997), have higher electrostatic interactions with their antigens (Chong et al., 1999). In contrast, more cross-reactive antibodies are believed to be more flexible and involve less specific contacts. It is becoming increasingly evident that flexibility may also play a major role in specificity and dynamics of high-affinity antibodies (Mian et al., 1991; Foote and Milstein 1994; Ditzel et al., 1996; Sheriff et al., 1996; Diaw et al., 1997), even in cases where crystal structures of the complexed and uncomplexed antibodies did not indicate significant induced fit (Lindner et al., 1999). Nevertheless, the functional role and the structural basis of conformational change in antibody binding remains unpredictable for any given complex, and the structural and thermodynamic determinants of antibody specificity and affinity are not completely understood.

We have previously proposed that differences in fine specificity among three structurally and functionally related antibody-protein complexes reflect their relative flexibilities, which are modulated, at least in part, by intramolecular salt links and salt-link networks within the complementarity-determining regions (CDRs), and by the proportions of hydrophobic and electrostatic residues (S. Mohan and S. J. Smith-Gill, submitted). Monoclonal antibodies HyHEL8, HyHEL10 and HyHEL26 (HH8, HH10 and HH26, respectively), share more than 90% of sequence homology (Fig. 1, a and b), and are specific for similar epitopes on hen egg white lysozyme (HEL) (Newman et al., 1992; Y. Li, C. A. Lipschultz, and S. J. Smith-Gill, unpublished results) (Fig. 1 c), with similar affinity (Lavoie et al., 1992, 1999). The structural, functional, and physical properties of HH8, HH10, and HH26 correlate with their cross-reactivity properties, ranking HH8 at one extreme, HH26 at the other, and HH10 intermediate. Of particular interest to the present study are the varying number of intramolecular salt bridges at the binding sites, which rank HH8 < HH10 < HH26, and the differences in the proportion of hydrophobic residues, which rank HH8 > HH10 > HH26 (Smith-Gill et al., 1987; S. Mohan and S. J. Smith-Gill, submitted). Salt bridges and hydrogen bonds have important roles in protein structure and function (Perutz, 1970; Barlow and Thornton, 1983; Musafia et al., 1995; Xu et al., 1997a,b), and have been linked to protein stability (Kumar et al., 2000; Yip et al., 1998), and flexibility (Sinha et al., 2001a,b). Modification of intramolecular salt bridges in HH10 alters its cross-reactivity (Lavoie et al., 1992, 1999). Therefore, we hypothesize that, among the three antibodies, HH26 has the most rigid binding site, whereas HH8 has the most flexible binding site.

View larger version (58K): [in this window] [in a new window]   FIGURE 1   Illustration of HH antibodies structural associations with HEL. Sequence alignment of (a) light-chains, and (b) heavy-chains of HH8, HH10, and HH26 antibodies. Colored areas represent the complementarity determining regions (CDRs). Red depicts conserved residues and blue depicts substitutions. Conserved and substituted residues are only shown for CDRs. There are no insertions and deletions, and CDRs are of identical lengths (Padlan et al., 1989). The substitutions occur in CDRs and the frame work regions of the antibodies. Light chains of these antibodies are encoded from the same Vk germ line gene, while their heavy chains belong to the same family (Lavoie et al., 1992). Two charged residues, which might be playing important roles in the electrostatically driven binding, are somatically mutated to hydrophobic residues in HH8. The residue Lys-49L, in CDR 2 of the light chain and residue Asp-101H, in CDR 3 of the heavy chain, present in HH10 and HH26, have been mutated to threonines in HH8. These residue differences have been shown to play a role in determining the binding mechanisms of these antibodies, possibly through long range effects (Lavoie et al., 1992). Similarly, the positions of two tyrosines, Tyr-53H and Tyr-58H, in CDR 2 of the heavy chain in HH10 and HH26, are occupied by phenylalanines in HH8. (c) HH10-HEL (PDB ID:3hfm) is shown. Heavy chain, light chain, and HEL are shown by purple, yellow, and red, respectively. Contact epitope and paratope residues (Lavoie et al., 1999) are illustrated in green. Epitope and paratope residues are also shown by their side chains. The names and positions of epitope residues are shown. Insight II (ACCELRYS) was used to generate the picture.

Surface plasmon resonance (SPR) analysis shows that the association kinetics of HH-HEL binding of these three complexes are best described by a two-step model (Lipschultz et al., 2000), which we interpret as an encounter followed by a docking or annealing, which may involve conformational rearrangements. The data also suggest that the energy barriers to docking are lowest in the HH8-HEL complex, highest in the HH26-HEL complex, and intermediate in HH10-HEL, especially in complexes with HEL containing epitope mutations (Li et al., 2001; S. Mohan and S. J. Smith-Gill, unpublished). Furthermore, among the three complexes, HH8-HEL derives the greatest proportion and amount of its free energy change from the docking step, HH26-HEL the least, and HH10-HEL an intermediate amount (Lipschultz et al., 2000; Li et al., 2001). Complex stability, as measured by net dissociation rates, is more sensitive to antigenic mutation in HH26 and HH10 complexes than in HH8 (Lavoie et al., 1999; Li et al., 2001). In addition, the three complexes differ in degree of sensitivity of their initial association rates to mutation, with HH8 being the least sensitive and HH26 the most (Lavoie et al., 1999; Li et al., 2001; S. Mohan and S. J. Smith-Gill, unpublished).

Here we utilize a combination of computational and experimental methods to examine in greater detail the structural and thermodynamic properties of these three complexes, specifically testing the hypothesis that the number and strength of electrostatic interactions influence association at both intermolecular and intramolecular levels. The former contributes directly to intermolecular complementarity and free energy of binding (Sheinerman et al., 2000; Kangas and Tidor, 2001), and the latter contributes indirectly to specificity and affinity by modulation of protein flexibility, or flexibility-rigidity compensations in general. Here we show that, overall, the electrostatic component dominates in HH26-HEL binding, and hydrophobicity dominates in HH8-HEL binding. We show that the number of short-range electrostatic interactions, the electrostatic strengths, and the networking pattern of binding-site salt bridges, and the overall electrostatic contributions toward binding correspond to the association properties of these antibodies. This indicates that the electrostatic properties have striking functional significance in governing the flexibility and rigidity with which protein-protein binds. We also show that electrostatic interactions can have a differential impact on the encounter and docking steps of association. These results provide an insight into the structural and thermodynamic manifestation of flexibility and rigidity.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Antibody-antigen complexes

The coordinates for the HH10-HEL and HH10Fv-HEL complexes, and unbound HEL, were obtained from the protein data bank (PDB) (Bernstein et al., 1977) (PDB ID: HH10-HEL, 3hfm; HH10Fv-HEL, 1c08; HEL, 1bwh). HH10-HEL, HH10Fv-HEL, and unbound HEL were crystal structures at 3.0-, 2.3-, and 1.8-Å resolutions, respectively. HH8-HEL and HH26-HEL were theoretical structures, generated in this lab (S. Mohan and S. J. Smith-Gill, submitted) using "Model Homologue" module of LOOK software (Molecular Application Group) package. The module uses the algorithm "segmod" (Levitt, 1992), which homology models the target protein, using template structure, by optimizing the packing interactions between the side chains. HH10-HEL was used as a template to model HH8-HEL and HH26-HEL (S. Mohan and S. J. Smith-Gill, submitted).

Hydrogen bonds, salt bridges and buried surface area

The presence of a hydrogen bond is inferred when two nonhydrogen atoms with opposite partial charges are within a distance of 3.5 Å. Geometrical goodness of H-bonds was assessed by computing the two angles: _D between vectors BD-D and D-A, where BD is covalently bonded to D; and _A between D-A and A-BA, where BA is covalently bonded to A. Hydrogen-bonds with both the angles in the range of 90-150^o were considered to be of good geometry, and are listed here. Salt bridges are inferred upon meeting the two criteria: the centroids of the oppositely charged side-chain functional groups of charged residues (Asp, Glu, Lys, Arg, and His) are within 4.0 Å; and Aspartate or glutamate side-chain carbonyl oxygen atom is within 4.0 Å distance from nitrogen atom of arginine, lysine or histidine side chains. When, for the same pair of residues, there are more than one pair of nitrogen-oxygen atoms present within 4.0 Å, the salt bridge has been counted only once. If a salt bridge involves a CDR or an epitope residue, it is considered to be a binding-site salt bridge.

Solvent-accessible surface area is calculated with a probe radius of 1.4 Å, using the algorithm of Lee and Richards (1971). The surface area buried upon the complex formation is the difference in solvent-accessible surface area between free and bound states:

Hydrophobicity

Electrostatic contributions of salt bridges

We have computed the electrostatic strength of salt bridges using a continuum electrostatic approach to solve the linearized Poisson-Boltzmann equation, using the DELPHI computer program developed by Honig and co-workers (Gilson et al., 1985; Gilson and Honig, 1987). The method has been widely used (Hendsch and Tidor, 1994; Xu et al., 1997a; Lounnas and Wade, 1997; Sinha et al., 2001a) and experimentally supported (Waldburger et al., 1995, 1996). The electrostatic contribution of a salt bridge to the free energy of folding is calculated as described by Hendsch and Tidor (1994). The electrostatic strength of a salt bridge is measured relative to computer mutation of salt-bridging side chains to their hydrophobic isosters. A hydrophobic isoster is the salt-bridging side chain with its partial atomic charges set to zero (Hendsch and Tidor, 1994). Side chain alone in solution was used for the unfolded state, which was therefore used as a reference state. The electrostatic contributions of salt bridges are calculated for folded state, as compared to the unfolded state. The electrostatic strength of a salt bridge can be divided into three component terms: G_desol, the sum of the charge desolvation penalties paid by the salt-bridging side chains, when they are brought from the dielectric of 80.0 (in water) to the dielectric of 4.0 (in the protein interior); G_bridge, the favorable energy change due to electrostatic interaction between opposite charges of salt-bridging side chains; and G_protein, electrostatic interactions of salt-bridging side chains with the charges in the rest of the protein. The total electrostatic energy upon the salt-bridge formation would be

(1)

The DELPHI software package calculates the electrostatic potential in and around macromolecules, using the iterative finite difference solution to the Poisson-Boltzmann equation. The desolvation penalty, bridge term, and protein term were calculated as described by Hendsch and Tidor (1994). The desolvation penalty of a salt-bridging side chain upon protein folding was computed by setting the partial charges of all atoms, except ones in the salt-bridging side chain, to 0. The reaction field energy was calculated for each salt-bridging side chain, with its respective partial charges on. The charge desolvation was computed similarly in the unfolded state. Thus, in the unfolded model, the salt-bridging side chains are present in solvent, and are infinitely separated from each other. The coordinates for salt-bridging side chains are taken from x-ray structure, and, for unfolded-state calculation, these were placed at exactly the same position on the finite-difference grid as they occupy in the folded state. For each of the salt-bridging side chains, the reaction field energy in the unfolded state was subtracted from the reaction field energy in the folded state to give the charge desolvation penalty. The sum of the charge desolvation penalties of both side chains is the charge desolvation penalty of the salt bridge, G_desol.

For electrostatic interactions between salt-bridging side chains, the linearized Poisson-Boltzmann equation was solved after setting all the partial charges of the molecule to 0, except those on one of the salt-bridging side chains. The potential at each partial charge position on the other side chain was determined to estimate the bridge term,

(2)

where  is the potential, and q is magnitude at i partial charge of the other side chain.

The contribution due to charge interactions between salt-bridging side chains and the rest of the protein is estimated by solving the Poisson-Boltzmann equation in the folded state, with atomic charges, except for those in salt-bridging side chains, set to 0. The protein term, G_Protein, is calculated as

(3)

where i ranges over all partial charges in whole protein, excluding charged atoms of salt-bridging side chains.

The strength of pentad and triad salt-bridge networks were computed considering each as a unit. The electrostatic strength of the salt-bridge network was computed similarly, by taking into account the charge desolvation penalty of all interacting side chains, all possible electrostatic interactions and the protein term. A salt-bridge network will have favorable and unfavorable interactions, between opposite and like charges, respectively.

The protein structure was mapped on 79 × 79 × 79 point 3-dimensional grid for iterative finite difference calculations. The grid spacing was kept 0.83 Å. Hydrogen atoms were added to the structures, and the protonation state of the charged residues were defined at pH 7.0, using the BIOPOLYMER module of INSIGHT II (ACCELRYS). PARSE3 set of atomic charges and radii (Sitkoff et al., 1994) were used, with a solvent probe radius of 1.4 Å. The dielectric constant of solute (protein) was kept at 4.0 and that of solvent was kept at 80.0. The ionic strength of 145 mM was used to simulate the physiological conditions. The output energy value in units kT, where k is the Boltzman constant and T is the absolute temperature, were multiplied with the conversion factor 0.592 to obtain the results in kilo-calories per mole at the room temperature, 25°C. For each calculation, the structures were first mapped on the grid where the molecule occupied 50% of the grid and Debye-Huckel boundary conditions were applied (Klapper et al., 1986). The resulting rough calculations were used as a boundary condition for focused calculation, where molecule extent was kept 95% on the grid. The results of focused calculations are shown here.

Electrostatic contribution to antibody antigen binding

The electrostatic contributions are calculated as the sum of charge desolvation penalties paid by antibody and antigen upon complex formation plus their electrostatic interactions. The electrostatic contributions were calculated for bound state, compared to the unbound. The reference state used here was unbound state. The continuum electrostatic approach was used to solve the linearized Poisson-Boltzmann equation, by means of the finite difference method, as described above, using DELPHI software.

Point mutation

Structures with alanine mutations were generated using the "Mutant Modeling" module of the software package LOOK3.0 (Molecular Applications Group, Palo Alto, CA). This module used an algorithm `cara' (Lee and Subbiah, 1991), which models the side-chain conformation of substituted residues and the residues with which it contacts. The method applies the simulated annealing algorithm to optimize side-chain Van der Waals interactions. The predictions using this method have been shown to be accurate, particularly for nonsurface residues (Lee and Subbiah, 1991). Lysine was substituted with alanine in the sequence. This sequence was used as a new sequence to generate a model, using the original structure as template. The new mutant was used for binding energy calculations.

Binding kinetics

HEL or single-site mutants were expressed and purified in Pichia pastoris (Li et al., 2000, 2001), and immobilized on a CM5 sensor chip. Recombinant Fab (Li et al., 2001) was used as analyte, and the binding was monitored by SPR, using a BIAcore1000 or BIAcore2000 instrument. The rate constants for encounter (k₊₁, k₁) and docking (k₊₂, k₂) were calculated by global analysis of the binding curves, using a two-step model and BIAeval3.02 software, as described and detailed elsewhere (Lipschultz et al., 2000; Li et al., 2001), and used to calculate affinities for encounter (Ka1 = k₊₁/k₁), docking (Ka2 = k₊₂/k₂) and the total binding (K = Ka1(1 + Ka2)). Gibbs free energy change for each equilibrium constant (encounter, G1; Docking, G2; Total, G) was calculated using the relationship: G = RT ln(Ka). G, the change in free energy due to a given mutant, was calculated as:

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

Hydrogen bonds at the antibody-antigen binding interface

S. Mohan and S. J. Smith-Gill (submitted) reported that, among the three antibodies, HH8Fv has the fewest and HH26Fv has the largest number of intermolecular hydrogen bonds and Van der Waals contacts in their respective complexes with HEL. Using different criteria (see Materials and Method) and the distance cut-offs (3.5 versus 3.0 Å) for H-Bond detection, we also find the same ranking among the three HH-HEL complexes for intra- and intermolecular hydrogen bonds (Table 1; Appendix). Among the three, only HH26-HEL complex contains an intermolecular main chain-main chain hydrogen bond, connecting Asp-92_L (The subscript represents chain ID throughout the text: H, heavy chain; L, light chain; Y, lysozyme.) to epitope residue Arg-21_Y (Fig. 2 f), implying close intermolecular associations. Epitope residue Arg-21_Y is a hot-spot of HH-HEL binding (Pons et al., 1999; Li et al., 2000, 2001), and, among the three antibodies, HH26 is most sensitive toward the mutations of this residue (Lavoie et al., 1999). Our results are consistent with previous reports that the interactions in antibody-antigen complexes are mainly via side chains, in contrast to interactions in proteinase-proteinase inhibitors, which are via main-chain atoms (Jackson, 1999). The ranking of the number of intra- and intermolecular hydrogen bonds (HH8 < HH10 < HH26) suggests that nonbonded interactions are least rigorous in HH8-HEL, most rigorous in HH26-HEL, and are intermediate in HH10-HEL.

View larger version (55K): [in this window] [in a new window]   FIGURE 2   Salt bridges at the binding interface of HH8-HEL, HH10-HEL, and HH26-HEL complexes. (a) HH8-HEL: An intermolecular and two intramolecular salt bridges. (b) HH10-HEL: An intramolecular triad and an independent intramolecular salt-bridge. (c) Pentad present at the HH26-HEL binding interface. Intermolecular triad networked with intramolecular triad forms this pentad. The other two salt bridges present at the HH26-HEL interface (Table 2) are not shown in this picture. Salt bridges are shown as they map in the protein structure, whether networked or independent. Residues forming salt bridges are labeled: L, light chain; H, heavy chain; Y, HEL. Residue positions follow the chain names, which are followed by three-letter residue code. Distances between salt-bridge forming side-chains are shown in . (d, e, f) The complexity of salt-bridge interactions at the binding interfaces of (d) HH8-HEL, (e) HH10-HEL, and (f) HH26-HEL. Heavy chains are shown in purple, light-chains in yellow, and HEL in red. Salt-bridge-forming residues are shown in green and by their side chains. Residues forming an intermolecular (between light chain and HEL) main chain-main chain hydrogen bond, in the case of HH26-HEL, are shown in light blue and by their side chains. Picture is generated using Insight II package.

Intramolecular salt bridges

Computational and experimental analysis have shown that salt bridges can be stabilizing (Marqusee and Sauer, 1994; Xu et al., 1997a; Lounnas and Wade, 1997) or destabilizing (Hendsch and Tidor, 1994; Sun et al., 1991). Thermophilic proteins have stronger salt bridges than their mesophilic counterparts (Yip et al., 1998; Kumar et al., 2000), indicating the functional significance of strong salt bridges. Electrostatic strength of salt bridges have been linked to protein flexibility (Sinha et al., 2001a,b). The three HH-HEL complexes were computed for the number and electrostatic strength of salt bridges. The electrostatic strengths of salt bridges were computed using the continuum electrostatic method described by Hendsch and Tidor (1994). This method, widely used to quantitatively estimate electrostatic potentials, pH-dependent properties, and solvation free energies (Honig and Nicholls, 1995), models proteins in atomic details and treats solvent as a bulk. The three components of salt-bridge strength (Hendsch and Tidor, 1994) are salt-bridge interaction with solvent, electrostatic interaction between salt-bridging side chains, and salt-bridge interaction with the charges in the rest of the protein.

S. Mohan and S. J. Smith-Gill (submitted) reported that, among the three antibodies, the HH8-HEL complex had the fewest and HH26-HEL complex the largest number of intramolecular salt bridges in the Fv regions. They hypothesized that the differences in the number of intramolecular salt bridges account for differences in flexibilities and packing densities among the three Fvs. Using more stringent criteria for detecting salt bridges (see Materials and Methods) we also found that the HH8-HEL complex has fewer intramolecular salt bridges than either the HH10-HEL or HH26-HEL complexes (Table 2). In addition, the strengths of the intramolecular salt bridges at the binding site differ among the three complexes, being weakest in HH8-HEL and strongest in HH26-HEL (Table 3).

An intramolecular salt bridge, Lys-49_LAsp-101_H was identified in HH10-HEL and HH26-HEL complexes by Mohan and Smith-Gill. This interaction did not qualify as a salt bridge according to our criteria (see Materials and Methods). We have computed the electrostatic strengths of this ion pair to estimate the qualitative differences in these complexes. This ion pair is very strong, 14.956 kcal/mol, in HH26-HEL and only marginally stabilizing, 0.106 kcal/mol, in HH10-HEL. The very high stability of this ion-pair in HH26-HEL is mainly due to the very favorable protein term of HH26-HEL.

Salt-bridge networks and electrostatic forces at the antibody-antigen interface

The numbers, electrostatic strengths, arrangement complexities, and the degree of networking of salt bridges at the binding interface vary among the three complexes (Table 3, Fig. 3). HH8-HEL has one intermolecular salt bridge, and HH26-HEL has two, which are networked. The single intermolecular salt bridge, Asp-32_HLys-97_Y, in HH8-HEL is only marginally stabilizing with an electrostatic strength less than 2.0 kcal/mol (Table 3). In contrast, this salt bridge contributes nearly 8.0 kcal/mol in HH26-HEL complex (Table 3). The second intermolecular salt bridge in HH26-HEL also involves Lys-97_Y, and contributes over 11.0 kcal/mol. The electrostatic contribution correlates well with alanine scanning data, which show that Lys-97_Y is a hot-spot residue (contributing 4.0 kcal/mol or more to the binding energy) in the epitopes of HH10, HH26, and the related antibody HH63 (Pons et al., 1999; Li et al., 2000), but contributes only slightly over 1 kcal/mol in the HH8 complex (see next section).

View larger version (22K): [in this window] [in a new window]   FIGURE 3   Plot showing the electrostatic strengths of the salt bridges present at the HH8-HEL (blue), HH10-HEL (cyan), HH10Fv-HEL (yellow), and HH26-HEL (red) binding interfaces. Electrostatic strength of salt bridges (Gtot) is shown in kcal/mol. The numbers on the x axis represents the following salt bridges: 1, D32H-K97Y; 2, E99H-K97Y; 3, K64H-E88H; 4, R24L-D70L; 5, D99H-H34L; 6, D99H-K49L; 7, R97H-E99H; 8, R97H-D101H; 9, D48Y-R61Y; 10, R66H-D89H (first character is one-letter residue code, followed by residue position, which is followed by the chain identification). *, Intermolecular salt bridge.

HH10-HEL was reported to contain the Asp-32_HLys-97_Y intermolecular salt bridge (Padlan et al., 1989), based on the criterion that their oppositely charged atoms were present within a 3.4-Å distance. This interaction does not meet the two criteria of our method (see Materials and Methods) to qualify as a salt bridge in HH10-HEL complex. First, the O1 atom of aspartate was not within the 3.4-Å distance from N atom of lysine; the distance was found to be 3.6 Å. Second, although the distance was within 4 Å, a limit set in our method, the distance between the centroid of their opposite-charged groups were more than 4.0 Å. However, there is still an electrostatic interaction between these two residues, forming an ion pair, but its electrostatic strength is insignificant (0.07 kcal/mol).

The recently solved crystal structure of HH10Fv domain complexed with HEL, at 1.8-Å resolution (Kondoi et al., 1999) shows that the intermolecular salt bridge, Asp-32_H-Lys-97_Y, not present in HH10Fab-HEL, is present in HH10Fv-HEL (Table 2). In addition, HH10Fv-HEL buries a larger proportion of surface area and has more favorable interactions than the HH10Fab-HEL complex (Kondoi et al., 1999), and has minor conformational differences from HH10Fab-HEL at the binding interface (Kondoi et al., 1999). Analysis of intramolecular salt bridges shows that the HH10Fv-HEL complex also has fewer intramolecular salt bridges within the Fv than either of the three Fab-HEL complexes, and includes one between framework residues that is unique to that complex (Tables 2 and 3). Because the affinity of the HH10Fv-HEL complex is significantly lower than that of the HH10Fab-HEL complex (Kondoi et al., 1999), it may not be a representative of the molecular interactions of either HH10-Fab or HH10-Ig with HEL, even though the structure is of higher resolution. It has been suggested that the unfavorable effect of removing the constant region was compensated by favorable interactions between HH10 and HEL, in the case of HH10Fv-HEL complex (Kondoi et al., 1999). Nonetheless, the presence of the intermolecular salt bridge in the HH10Fv-HEL complex indicates an electrostatic interaction between these two residues. In addition, our Ala scanning data (next section) indicates that Lys-97_Y contributes 4.0 kcal/mol to binding, and HH10Fab-HEL double-mutant cycle analysis suggests a significant energetic interaction between Lys-97_Y and Asp-32_H (Pons et al., 1999).

In HH8-HEL, there are no salt-bridge networks, and the electrostatic strengths of the binding site salt bridges are very low (Table 3). In HH10-HEL, the two CDR inter-chain salt bridges are networked to form a triad, with relatively high electrostatic contributions. One of the salt bridges of the intramolecular triad is significantly stabilizing, and the other is marginally destabilizing. The total electrostatic strength of the triad is significantly high (Table 4).

Two intramolecular salt bridges in HH26-HEL form a triad, and are further networked with an intermolecular triad to form a pentad (Fig. 2 c). All salt bridges of this network are strongly stabilizing (7.78 kcal/mol or more), suggesting a functional/structural significance of the pentad. The total electrostatic strength of the pentad is very high (Table 4), as expected, because all four salt bridges within this network are strongly stabilizing (Table 3). Table 4 summarizes the components of the pentad electrostatic strength, and their electrostatic contributions. The pentad is considered as a unit, and its electrostatic strength is computed as described for salt bridges (see Materials and Methods). We have computed the bridge terms for all possible electrostatic interactions present in the pentad (Table 4). It is clear from Table 4 that destabilization due to unfavorable interactions between like charges is much smaller than the stabilization due to the favorable interactions between opposite charges. In the case of the triad, present in HH10-HEL, the destabilization due to unfavorable interaction is also high (Table 4). Electrostatic interaction of the pentad with the rest of the protein is also very favorable (Table 4). The strong electrostatic strength further corroborates the functional value of pentad, and the constituent salt bridges. It is possible that this pentad is acquired during the affinity maturation of the HH26 antibody, and is a major determinant of the high HH26-HEL binding specificity.

Only the HH26-HEL complex has an intramolecular salt bridge, Asp-48_Y-Arg-61_Y (also present in HH10Fv-HEL). This ion pair is also present in uncomplexed HEL. (Table 3, Fig. 3), in the epitope region of HEL, which is significantly stabilizing. In HH10Fv-HEL, the intermolecular salt bridge, Asp-32_H-Lys-97_Y is significantly stabilizing, but is not networked. One intramolecular salt bridge is stabilizing, but the other intramolecular salt bridge, Asp-48_Y-Arg-61_Y, present at the HEL binding site, is almost neutral.

The desolvation penalties, the bridge terms and the protein terms of the salt-bridge formation vary among the three complexes. Salt bridges in HH8-HEL pay lower desolvation penalties than salt bridges in HH10-HEL and HH26-HEL complexes. HH26-HEL salt bridges pay the highest desolvation penalties. Yet, this heavy penalty in HH26-HEL is compensated by very favorable bridge and protein terms. In HH10-HEL, on average, bridge and protein terms are more favorable than the HH8-HEL and less favorable than HH26-HEL. The bridge and protein terms in HH8-HEL salt bridges are only moderately favorable. The more a salt bridge is buried, the higher desolvation penalty it pays, but it will have stronger electrostatic interactions due to absence of solvent screening. The extent of the electrostatic protein environment will further determine the robustness of the charge-charge interactions between the salt-bridging side chains.

The higher number of salt bridges, the networking of very strong salt bridges, the preservation of the intramolecular salt bridge at the binding site of HEL, which is absent in HH8-HEL and HH10-HEL complexes, indicate an inherently electrostatic binding of HH26-HEL, which is likely to be a significant factor for high binding specificity of HH26 toward HEL. In contrast, weak electrostatic interactions may predispose HH8-HEL binding to be less specific. The weak electrostatic component of HH8-HEL binding implies an inherent flexible nature of the HH8-HEL binding site.

Electrostatic and hydrophobic components of binding

Conformationally flexible parts have relatively lower electrostatic interactions, and substantial hydrophobic interactions (Sinha et al., 2001a,b). We have examined the total electrostatic and hydrophobic contributions to the free energy of HH8, HH10, and HH26 binding to HEL (Table 5). Both antigen and antibody pay heavy charge desolvation penalties upon binding in all three complexes, but there are large differences among the three complexes in the electrostatic components of binding. HH10-HEL has significantly favorable electrostatic component in comparison to HH8-HEL, but it is less favorable in comparison to HH26-HEL. HH10-HEL and HH26-HEL are more similar to each other than to HH8-HEL. Their desolvation penalties are higher than that of HH8 by 4-5 kcal/mol, and they differ from each other by only 1 kcal/mol. HH10 and HH26 have 7.0 to 10.0 kcal/mol more favorable electrostatic interactions with HEL than HH8 with HEL, with a difference between them of 3.0 kcal/mol. Overall, the electrostatic contribution to the free energy of binding is lowest in HH8-HEL, intermediate in HH10-HEL, and highest in HH26-HEL. Among the three complexes, HH8-HEL has largest hydrophobic contributions. Compared to the differences in electrostatic contributions, the hydrophobic contributions are similar among all the complexes and their mutants. Significant differences are in electrostatic contributions. The finding is consistent with the earlier result that HH26 is more electrostatic in nature. We hypothesize that higher electrostatics make HH26 binding site more rigid and less cross-reactive.

Binding of HH8, HH10, and HH26 to Lys-97ala and Lys-96ala mutants of HEL

Previous alanine scanning mutagenesis showed that only three hot-spot epitope residues contribute more then 4 kcal/mol to the free energy of HH10-HEL complex formation (Pons et al., 1999). These three residues were reported to be Lys-97_Y, Lys-96_Y and Tyr-20_Y, where Lys-96_Y contributed the most, based on enzymatic activity assay (Pons et al., 1999). We modeled alanine mutants of the two charged epitope residues, Lys-96_Y and Lys-97_Y and calculated their electrostatic and hydrophobic components of binding. The impacts of these mutations on binding kinetics were also measured by SPR using site-directed mutants of HEL(K96A) and HEL(K97A). These two sequentially adjacent charged residues were particularly selected because, although adjacent residues on HEL, only Lys-97_Y forms an intermolecular salt-bridge, and because these two residues have been shown experimentally to be the hot-spots of binding (Pons et al., 1999). The analysis of the charged hot-spot mutants would allow straightforward estimation of the qualitative differences in the electrostatic properties of the three complexes.

SPR results confirm previous findings that Lys-97_Y is a hot spot residue in all three complexes, but showed that the energetic contribution of Lys-96_Y to binding is insignificant (Table 5). In fact, SPR studies show that, among all the epitope residues, Lys-97_Y contributes the largest amount to the free energy of binding in HH10-HEL and HH26-HEL complexes (S. J. Smith-Gill, C. A. Lipschultz, Y. Li, and S. Mohan, unpublished results). For HEL(K97A) complexes, G ranked HH8 < HH10 < HH26 (Table 5). For all three antibodies, the greatest impact of Lys-97_Y mutations on free energy change is at the encounter step of association (Fig. 4), which is consistent with the view that electrostatic forces play an important role in steering and orienting the molecules to form the encounter complex (Sines et al., 1990; Kozack et al., 1995; Antosiewicz and McCammon, 1995; Janin, 1997). The impact of HEL(K97A) mutation on free energy change of HH8 docking is insignificant (G2 < 0.5 kcal/mol). Experiments based on a lysozyme enzymatic activity assay (Pons et al., 1999) reported Lys-97_Y to contribute less then Lys-96_Y. The discrepancy may be due to the different buffer and pH conditions used, which may affect the protonation states of the charged groups. In an earlier study, it has been shown that the binding of HH10 to HEL with the mutants of charged epitope hot-spot residues is significantly pH dependent, where the shifts in pKas due to mutations would result in proton uptake or release (Sharp, 1998). Additionally, SPR results are directly calculated from binding data (at pH 7.4), whereas the results of Pons et al. (1999) are derived indirectly by estimating free lysozyme via enzymatic activity, at pH 6.0.

View larger version (28K): [in this window] [in a new window]   FIGURE 4   The binding kinetics of these mAbs conformed well to a two-step kinetic model describing an "induced fit" binding mode To obtain estimates of the rate constants, a data set containing association times (Ta) of at least two durations (Lipschultz et al., 2000) was analyzed globally to obtain estimates of rate constants. The parameters k+1, k1, k+2, k2, and Rmax were estimated with BIAeval 3.0.2 software (Biacore, Inc., Uppsala, Sweden), which uses the Marquat-Levenberg algorithm to simultaneously iteratively fit binding data of all curves within a given data set (global fit) to simultaneous rate equations, where B(0) = Rmax, [AB]*(0) = AB(0) = 0, and total RU = [AB]* + AB. Error terms were all less than 5% of the mean. Calculations were per formed carrying three significant figures. Equilibrium constants were calculated from the mean rate constants (Krauss et al., 1976; Barre et al., 1994; Lipschultz et al., 2000). (a) Free energy changes were calculated from the equilibrium constants (Lipschultz et al., 2000; Li et al., 2001) In all cases, total G calculated as above did not differ from G calculated directly from overall equilibrium constant KA. (b) The activation energies for the encounter and docking stages (G1Ï and G2Ï) were calculated from k+1 and k+2, respectively (S. Mohan et al., submitted), where, according to the transition state theory, where KÏ = kBTka/, ka is the forward rate constant, kB is Boltzmanns constant and  is Planck's constant.

Examination of the individual rate constants (Fig. 5, a-c) shows that the mechanisms underlying the encounter thermodynamic changes differ among the antibodies. For the HH8-HEL(K97A) complex, the association and dissociation rate constants of the encounter step (k₊₁ and k₁), are slowed and increased by 2-2.5 fold, respectively (Fig. 5 a), resulting in a net loss of ~1.0 kcal/mol from the encounter step (Fig. 4 a). The lower k₊₁ reflects a small increase of ~0.5 kcal/mol in activation energy for encounter (Fig. 4 b), whereas loss of ~1 kcal/mol from G1 and slightly higher k₁ suggests that encounter complex is also less stable than that of HEL complex. This is reflected in the higher T₅₀, which is a measure of the biological half-life of conversion of encounter complex to docked complex (Fig. 6, a and d). The apparently faster net off-rate (Fig. 5 d) reflects a higher proportion of complexes in the less stable encounter state (Fig. 6 d).

View larger version (85K): [in this window] [in a new window]   FIGURE 5   (a-c) Rate constants for two-step association of (a) HH8, (b) HH10, and (c) HH26 complexes with HEL, HEL(K96A) and HEL(K97A), calculated as described in Fig. 4. Solid black, k+1; cross-hatched, k1; gray, k+2; diagonal, k2. k+1 is plotted on left axis; k1, k+2, k2 on the right axis. (d-f) Apparent association and dissociation rate constants of (d) HH8, (e) HH10, and (f) HH26 complexes with HEL, HEL(K96A), and HEL(K97A) were estimated from same data as (a-c) with BIAeval 3.0.2 software (Biacore Inc.), using Langmuir model. Solid black, kon (left axis); cross-hatch, koff (right axis). (g-i) Relative stability of the encounter complex are represented as 1/k1 (Solid black, left axis), and relative strengths of the close range steering effects (cross-hatch, right axis) as the product of the forward rate constants, k+1k+2 (Selzer and Schreiber, 2001).

View larger version (70K): [in this window] [in a new window]   FIGURE 6   (a-i) Representative sensograms of binding of the three Fabs to HEL and mutant antigens. The rate constants (k+1, k1, k+2, k2), calculated as described in the legend to Fig. 4 and shown in Fig. 5, were used to simulate the component curves for the encounter complex, [AB]*, and the docked complex, AB. In each panel , the original binding data; · · · ·, [AB]*; · · - · ·-, AB; and - - -, the fitted total binding. We define the point at which the [AB]* and AB curves cross as T50, where [AB]* = AB = 50% (RUtotal) (illustrated on time axis of panels a-c). Values for T50, determined from simulations at 10-nM concentrations and a series of increasing concentrations until T50 asymptotes at a minimum value (T50m), using the rate constants determined by global analysis (Figs. 4 and 5). T50m is a parameter that is unique and characteristic of each complex. When k+1 is rate limiting (i.e., k2 < k+2) T50m = t1/2 of k+2 (Lipschultz et al., 2000). All values are given in seconds. The values for T50m were calculated as T50mmut  T50mHEL for each respective antibody. The Fab concentrations in the binding curves depicted are: (a, d, g) HH8 21 nM on all three antigens; (b) HH10 21 nM on HEL; (c) HH26 21 nM on HEL; (e) HH10 640 nM on HEL(K97A); (f) HH26 146 nM on HEL(K97A); (h) HH10 100 nM on HEL(K96A); (i) HH26 210 nM on HEL(K96A). (j-l) simulations of (j) HH8, (k) HH10, and (l) HH26 binding to HEL (), HEL(K96A) (----), and HEL(K97A) (-..-). All antibodies are at a concentration of 10 nM. Insets show enlargements of HH10 and HH26 binding to HEL(K97A). Simulations are depicted to allow comparison of all complexes at the same concentration, which could not be reliably obtained experimentally because of the widely differing affinities.

In contrast to the HH8-HEL(K97A) complex, although the encounter association rate constants (k₊₁) of the HH10-HEL(K97A) and HH26-HEL(K97A) complexes are slowed by about the same order of magnitude as that of HH8-HEL(K97A) (~5× and 2.5×, respectively), the encounter dissociation constants (k₁) of both complexes are increased by about 20-fold (~25× and 18×, respectively) (Fig. 5, b and c). In both the HH10-HEL and HH26-HEL complexes, the loss of Lys-97 destabilizes the encounter complex (Fig. 5, b and c) and increases the activation energy required for encounter (Fig. 4 b). The loss of the electrostatic interaction with Lys-97_Y increases the encounter activation energy of HH10-HEL more than that of HH26-HEL complex, and increases the docking activation energy of HH26-HEL more than that of HH10-HEL complex (Fig. 4 b). The effects on the rate constants for the docking step are less dramatic, with 2-4-fold decrease in k₊₂ and a 2-4-fold increase in k₂ (Fig. 5, b and c). In both complexes, the large increase in k₂, coupled with smaller decrease in k₊₂, results in k₊₂ < k₁, and the rate-limiting step is shifted from the encounter to docking, consistent with the increase in the activation energy for docking in both complexes (Fig. 4 b). Thus, a smaller proportion of the complexes actually dock, and stabilities of the docked mutant complexes are lower than the stabilities of docked HEL complexes (Fig. 5, h and i and Fig. 6, e and f). The relative overall impact of the mutations on steering is related to the product k₁k₂, whereas the stability of encounter complex is proportional to 1/k₁ (Selzer and Schreiber, 2001). The mutation K97A affects the stability and the steering by about the same order of magnitude for each of the HH8-HEL and HH10-HEL complexes.

Because of the impact of slower docking and a faster dissociation of the encounter complexes, the impact of the mutations on the apparent association and dissociation rates are exaggerated (Fig. 5, d-f and Fig. 6, j-l). The apparent association appears to be much slower than it is because docking has become rate limiting. This can be seen in the association kinetics: an initial rapid association is followed by a slower prolonged association phase (Fig. 6, e and f), which results in a significantly slower net on rate using a 1-step Langmuir association model (Fig. 5, e and f). This is particularly true for the complexes of HH10 and HH26 with HEL(K97A). The encounter association rate constant k₊₁ in HH10-HEL(K97A) complex is ~5-fold lower (Fig. 5 b), but the apparent k_on is nearly 20-fold lower than the HH10-HEL complex (Figs. 5 e and 6 k). For the HH26-HEL(K97A) complex, the k₊₁ is ~3-fold lower (Fig. 5 c), whereas the apparent K_on is 60-fold lower than the HH26-HEL complex (Figs. 5 f and 6 l). For these complexes, the apparently large impact of the mutation on electrostatic steering is a combination of a decreased stability of the encounter complex and a slower conversion to the docked state. This can be clearly seen by comparing the simulated component curves of the respective HEL and HEL(K97A) complexes (Fig. 6, a-f). In the HH26-HEL(K97A) complex, docking is so severely affected that the majority of complexes never dock but rapidly dissociate. The HEL(K97A) mutation affects the transition states of the HH8 and HH10 encounter steps more than those of docking, but it affects the transition state of HH26 docking more than that of encounter.

The decreases in the free energy attributable to the Lys-96_Y substitution (G_mut-wild) are less than half a kcal/mol, and insignificant compared to Lys-97_Y (Figs. 4 and 5 d-f). For the complexes with HEL(K96A), the differences of Lys-96_Y contributions in the three complexes can again be attributed to the electrostatic nature of binding in HH26-HEL, where lysine, being a charged epitope residue, has a more important role in HH26-HEL binding than in HH8-HEL and HH10-HEL (Table 5). Calculations show that the net effect of Lys-96_Y on these two complexes is destabilizing, as indicated by favorable G_{m(el+hydro)w(el+hydro)}, which is marginally negative in cases of HH8-HEL and HH10-HEL, showing that Lys-96_Y, by itself, does not contribute to the free energy of binding in these complexes. The computational data is supported by the experimental data (Table 5, Fig. 4). However, for both the HH10-HEL and HH26-HEL complexes, although the net G is insignificant, G1 is ~0.5 kcal/mol, and, in HH26-HEL G2, is nearly 1.0 kcal/mol (Fig. 4). The K97_Y mutation lowers the activation energy for HH26 docking by ~1 kcal/mol. The net impact of the mutation is unfavorable for both steps, but then stabilizing to the final complex in the case of HH26, as reflected by lower values of k₂, and a higher k₊₂ for HH26.

Lys-97_Y forms an intermolecular salt bridge in HH8-HEL and HH26-HEL complexes. In the complexes with HEL(K97A), G_{m(el+hydro)w(el+hydro)} is largest for HH26, and smallest for HH8. The decrease in the free energy of binding in all three cases is due to the significant loss in the electrostatic contribution (Table 5). The loss is largest in HH26-HEL(K97A) and smallest in HH8-HEL(K97A), as compared to their respective wild types. Higher sensitivity of HH26 binding to HEL(K97A), as compared to HH8 and HH10, corresponds to the observation that the intermolecular salt bridge, formed between Lys-97_Y and Asp-32_H, is very strong in HH26-HEL and is only marginally stabilizing in HH8-HEL. The stabilizing impact of this electrostatic interaction is primarily on the encounter complex, with a smaller impact on post-encounter docking step. In the case of the HH10-HEL complex, although the interaction between Asp-32_H and Lys-97_Y did not qualify as a salt bridge, discussed above, the contribution of Lys-97_Y toward the free energy of binding was higher than in HH8-HEL complex, apparently due to the higher electrostatic nature of binding in HH10-HEL as compared to HH8-HEL.

The large impact on the encounter step of the HH10 complex is in contrast with the effect of other Ala mutants, which generally have a larger impact on docking than on encounter of this antibody (Li et al., 2001; S. J. Smith-Gill, C. A. Lipschultz, and Y. Li, unpublished data). The Lys-97_Y mutation has a slightly greater effect on docking of HH26 than on HH10.

Considering that Lys-97_Y forms a stable intermolecular salt bridge, it is intuitive that Lys-97_Y will contribute more to the free energy of complex formation than Lys-96_Y. Furthermore, in all three complexes, the side chain of Lys-97_Y is buried to a larger extent than Lys-96_Y, upon complex formation (Table 6). HH26-HEL complex buries the largest surface area of Lys-97_Y-N atom among the three complexes (Table 6). The N atoms of Lys-96_Y are buried to similar extents in the three complexes. The more a side chain is buried in the protein interior the higher desolvation penalty it pays (Novotny and Sharp, 1992; Bruccoleri et al., 1997). However, in the protein interior, due to the absence of solvent screening, the charged side chain will have very favorable electrostatic interactions if the protein environment permits. Strong salt bridges are usually buried in the protein interior (Kumar and Nussinov, 1999). This further suggests that the free energy of binding in the three complexes derives larger amounts from Lys-97_Y than from Lys-96_Y.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS APPENDIX REFERENCES

The significance of this work is that the observed variations in the electrostatic properties of the three antibodies correlate with their binding properties. The high number of short-range electrostatic interactions, very strong salt bridges and a very strong salt-bridge pentad at the binding site, and the largest electrostatic contributions toward binding in HH26-HEL, limit flexibility, rendering the binding site geometry very rigid. Consequently, the epitope mutations are not accommodated due to very limited conformational flexibility, or geometrical adaptability. In contrast, the small number of electrostatic interactions, marginal strengths of binding-site salt bridges, and small electrostatic contributions toward binding in HH8-HEL, allow conformational flexibility with less specific geometrical constrains at the binding site. Thus this antibody accommodates epitope mutations and is cross-reactive. HH10-HEL has intermediate electrostatic properties, both in terms of number of short-range electrostatic interactions and electrostatic contributions. Therefore, its binding properties relating to conformational flexibility and specificity also fall among the three antibodies.

The differential impacts of charge mutations on the association steps of the complexes suggest mechanisms of associations in the three HH-HEL complexes. Three important conclusions can be drawn from the observations. First, the variations in electrostatic versus hydrophobic interactions correlate with, and can account for, many of the specificity and affinity differences among the antibodies. Second, electrostatic interactions play duo roles, directly, by affecting specificity and affinity through complementary polar and charged based intermolecular contacts at the binding interface, and indirectly, on structural effects, through stabilizing the partners and their complexes, and modulating flexibility properties of the antibodies. Third, electrostatic effects that could be interpreted as diffusional electrostatic steering effects on the initial association process are actually interactions that are taking place after collision, which alter the stabilities of the encounter complexes and the transition-state energies of both encounter and docking steps.

The networked salt bridges, especially Glu-99_H-Lys-97_Y, Arg-97_H-Glu-99_H, and Arg-97_H-Asp-101_H in HH26-HEL, stand as very strong, even when compared with the strengths of very stabilizing salt bridges reported in literature (Lounnas and Wade, 1997; Kumar and Nussinov, 1999). This agrees with the observation that networked salt bridges, ion pairs, and hydrogen bonds are usually stabilizing (Ku