Molecular evolution of affinity and flexibility in the immune system

Abstract

The immune system responds to the introduction of foreign antigens by rapidly evolving antibodies with increasing affinity for the antigen (i.e., maturation). To investigate the factors that control this process at the molecular level, we have assessed the changes in flexibility that accompany ligand binding at four stages of maturation in the 4-4-20 antibody. Our studies, based on molecular dynamics, indicate that increased affinity for the target ligand is associated with a decreased entropic cost to binding. The entropy of binding is unfavorable, opposing favorable enthalpic contributions that arise during complex formation. Computed binding free energies for the various antibody–ligand complexes qualitatively reproduce the trends observed in the experimentally derived values, although the absolute magnitude of free-energy differences is overestimated. Our results support the existence of a correlation between high-affinity interactions and decreased protein flexibility in this series of antibody molecules. This observation is likely to be a general feature of molecular association processes and key to the molecular evolution of antibody responses.

Molecular recognition plays a central role in many biological processes, including the regulation of development, cell signaling, and neutralization of foreign molecules by the immune system. Consequently, there is significant interest in elucidating the mechanisms involved in recognition processes from both experimental (1, 2) and theoretical (3, 4) perspectives; this subject is discussed in a number of reviews (5–7). Secreted antibodies (Abs) play a central role in the immune response and bind to their target antigens with both high affinity and specificity. These molecules serve as excellent models with which to examine the mechanisms of molecular recognition. The Ab 4-4-20 is particularly useful in this regard, as it binds to the chromophore fluorescein (FLU) with high affinity (8). Interaction of 4-4-20 with FLU has greatly facilitated structural, kinetic and, thermodynamic characterization of this Ab (9–12). Romesberg and colleagues (13–15) have characterized evolution of the immunological response for the well studied 4-4-20. They have deduced a sequence of mutations that engender increased affinity for the target ligand during the maturation process; evidence has been presented that the flexibility of the binding pocket decreases in concert with gains in affinity.

As maturation proceeds, affinity for FLU increases going from the germ line (GL) Ab through two intermediates (IMs) (IM1 and IM2, respectively) until finally the highest affinity mature (AM) 4-4-20 Ab is attained. As determined by surface plasmon resonance, the dissociation constant of AM for FLU is 220 nM (14). IM2 has a dissociation constant of 400 nM and differs from AM in that residue 46 in the light chain is leucine (L^L46) rather than the valine (V^L46) present in the crystal structure. V^L46 does not interact with the ligand directly (see Fig. 1). However, it interacts with arginine residue R^L34, which forms a hydrogen bond (HB) directly to the ligand (14). IM1 has a dissociation constant of 2640 nM and a further modification relative to IM2 in which R^L34 is replaced by a histidine. Thus, going from AM to IM2 to IM1 involves in each case one amino acid substitution. GL has a dissociation constant of 35 μM (15) and 10 amino acid substitutions distributed throughout the heavy chain compared with IM1 (Fig. 1). Throughout this work the Kabat numbering system is used (16); conversion to crystallographic numbering for the full amino acid sequence of each Ab is provided in supporting information (SI) Table 3.

Fig. 1.

Ab structure and simulation preparation. Lower left displays the 1FLR crystal structure of the mature 4-4-20 antigen binding fragment (Fab). The Fab was truncated along the dashed line to generate the MD simulation system at the apex of the illustration. Solvent sphere around the binding pocket and mutated residues are displayed in ball-and-stick representation. Heavy and light chains are displayed in red and blue, respectively; restrained regions are shown in orange. Lower right shows interactions between light-chain residues 46 and 34 and FLU.

In this study, we use simulation methods to investigate the proposed link between increased affinity and decreased flexibility in these antibody–ligand (Ab-L) complexes. Higher-affinity interactions between the bound molecules are observed to be associated with a reduced entropic cost to binding. Rigidification upon binding has been noted in prior studies of 4-4-20 (17, 18). Our current work extends the scope of previous investigations by demonstrating the conversion from an induced-fit model of binding to a lock-and-key model as maturation proceeds. Our observations support proposals previously put forward by Romesberg and colleagues regarding the correlation between high-affinity interactions and reduced flexibility of the binding pocket in the 4-4-20 Ab (Floyd Romesberg, personal communication). The simulations were also used to compare binding free energies for the various Ab-L complexes, which qualitatively reproduce the experimentally determined trends. We discuss the significance of our findings with respect to general features of molecular evolution in proteins.

Results and Discussion

A Molecular Description of Maturation.

The amino acid changes associated with each stage of maturation are depicted in Fig. 2. The effects of these changes on Ab flexibility can be understood most clearly by treating them as perturbations that progressively reduce the affinity of each Ab in the sequence AM → IM2 → IM1 → GL. Compared with AM, V^L46 is substituted by L^L46 in IM2. Although not interacting with FLU directly, L^L46 engenders a steric clash with R^L34. This steric clash perturbs the structure of the combining site, disrupting the HB between R^L34 and FLU that was described in the Introduction. Going from IM2 to IM1, R^L34 is replaced by H^L34, a less proficient HB donor. The mutations that differentiate IM1 from GL include residues involved in a network of HB and van der Waals contacts. This group of residues stretches from the periphery of the variable domain to the interior of the combining site (Fig. 2). In cases where the network encompasses mutation sites, the amino acid changes that occur generally induce the burial of more interfacial surface area in IM1 compared with GL. This more expansive surface facilitates van der Waals interactions and allows for enhanced packing of the residue interfaces in IM1 relative to GL. The network also includes nonmutated residues that directly interact with FLU through van der Waals contacts.

Fig. 2.

Interactions modified as a result of mutations. (Top) Structural interactions that differentiate AM from IM2 and IM1. (Middle) The network of residues (van der Waals spheres) that mediate flexibility differences between these three Abs and GL. The residues are displayed as they occur in GL. Mutated residues are colored according to atomic number, and nonmutated residues are displayed in purple. (Bottom) Residues involved this network as they occur in AM. Interactions between residues are depicted as arrows. Residues restrained during each of the simulations are displayed in bold. Mutated residues are circled and displayed with the corresponding residue from GL in parentheses.

Coupling within this network of residues depends on a number of specific interactions. Residues G^H100f thru D^H101 form part of a β-strand that configures light-chain residues 46 and 34 to interact favorably with FLU (Fig. 2). The side chain of D^H101 also forms a HB directly to the side chain of R^L34 in AM. Heavy-chain residues 84–87 form part of a helix that interacts with heavy chain residue 38; helix propensities may play a role in governing the effects caused by these residues. In AM, R^H38 interacts with the helix through a HB to D^H86, concomitant with a HB to nearby Y^H90. Y^H90 also forms a HB to D^H86. These three heavy-chain residues form an integrated HB network. The entire network of residues is fairly rigid in both bound and unbound complexes of AF. As affinity decreases, these residues become progressively more flexible in the unbound state, which is demonstrated by the mean squared fluctuations of residues in this network (Table 1).

Table 1.

C_α mean squared fluctuations for network residues

Residue	Complex	Unbound
AM	0.15	0.15
IM2	0.20	0.24
IM1	0.18	0.26
GL	0.12	0.29

Average mean squared fluctuation (Ų) for C_α atoms located in residues displayed in Fig. 2 Bottom. The contribution of residues restrained or adjacent to restrained regions has been excluded from the average. Fluctuations are reduced in the bound state relative to that in the unbound state for IM 2, IM 1, and GL. This effect is most pronounced in GL.

Flexibility Changes Correlate with Maturation.

In Table 2 we present a comparison of binding free energies for the four Ab systems. The binding free energies of IM2, IM1, and GL are displayed relative to that of the highest-affinity AM molecule and exhibit good qualitative agreement with experimental results. The free energies are further decomposed into enthalpic and entropic contributions. The enthalpic portions of the binding free energies all favor binding. This effect is most pronounced for the AM and IM2 proteins. However, enthalpic contributions are insufficient to reproduce the experimentally measured trend in binding affinities. For example, the lowest-affinity GL has an even more favorable binding enthalpy than the higher-affinity IM1. Entropic contributions are large and disfavor binding, acting to oppose enthalpic contributions. This compensation between entropic and enthalpic contributions has also been noted in other studies (19–22). It is only after enthalpic and entropic contributions are combined that the experimentally determined trend is recovered, highlighting the important role that entropic changes play in binding.

Table 2.

Thermodynamic parameters characterizing Ab-L binding

Parameter	Residue
	AM	IM 2	IM 1	GL
ΔΔGexp	—	0.36	1.46	3.00
ΔΔGcalc	—	4.47	15.32	41.43
ΔH	−23.19	−23.08	−10.49	−14.29
−ΤΔS	22.97	27.55	25.81	55.72
−ΤΔSPint	9.32	15.45	13.14	42.55
−ΤΔSLint	3.05	2.48	2.51	2.82
−ΤΔSLtrans/rot	10.6	9.62	10.16	10.35

Experimentally determined (exp) and computed (calc) ΔΔG values are given with respect to AM. Protein and ligand contributions are subscripted P and L, respectively. Internal and external (translation/rotation) contributions are denoted by the appropriate superscripts. T = 298 K; unless otherwise noted all values are in kcal/mol (1 kcal = 4.184 kJ). Note the large entropic change for GL.

Entropic changes within the Ab are directly related to the decrease in fluctuations that occurs upon ligand binding (SI Text) and are the primary determinants for the binding affinity trends. This observation contrasts with assumptions that protein degrees of freedom are not significantly altered during ligand binding (23). Contributions from the ligand degrees of freedom are comparatively much less significant. In Fig. 3 the mean squared fluctuations of heavy atoms around the binding site in AF and GL have been projected onto the protein backbone to demonstrate the effects of maturation. One can observe that the binding cleft undergoes a structural rearrangement as a result of binding, becoming more compact as it envelopes the bound ligand. This structural rearrangement is more pronounced for GL. With respect to flexibility, two observations are noteworthy. First, GL exhibits more flexibility than AF at each stage of binding, displaying the overall rigidification that occurs with maturation. Second, there is a greater loss of flexibility upon binding for GL. The increased flexibility in the unbound state of GL is caused primarily by a mobile loop that directly interacts with the bound ligand. Although AF also becomes more rigid upon binding, the associated flexibility changes are much less prominent for this protein.

Fig. 3.

Mean squared fluctuations of heavy atoms around the binding cleft projected unto the protein backbone. Bound conformations (Upper) and unbound conformations (Lower) are displayed with AF (Left) and GL (Right). The color scale is proportional to the magnitude of the fluctuations observed and ranges from dark blue for more rigid regions to red for regions that are most flexible. With the color scale used, there is much less difference between the light blue and green regions than between green and yellow: the yellow and red regions exhibit significantly larger fluctuations than the remainder of the Abs. Note that the binding pocket becomes more “open” without the presence of the ligand; this conformational rearrangement is more prominent for GL. Also observe that GL exhibits more flexibility than AF at each stage of binding. GL exhibits a greater loss of flexibility on binding, caused primarily by the loop region at the lower left of the binding cleft, which interacts directly with the bound ligand. Whereas there are isolated regions that actually gain flexibility during binding, there is a net decrease in flexibility for the bound state when the entire binding cleft is considered.

Increased protein rigidity upon binding has also been observed in earlier studies of 4-4-20 by Lim and colleagues (17, 18) and in other Ab systems (2). Indeed, the positive correlation between protein rigidity and binding affinity is likely to be a general feature of molecular association processes (24). The magnitude of entropy lost during binding increases as affinity is decreased (i.e., from AM → IM2 → IM1 → GL, respectively). This trend is determined primarily by fluctuations of the unbound proteins. As binding affinity decreases the Abs become more flexible in the unbound state, leading to larger entropic losses when the ligand is bound. The loss of entropy we observe upon binding is most pronounced for the lowest-affinity GL variant. In addition, the more favorable binding enthalpy in GL relative to IM1 indicates that the driving force for selection of IM1 in preference to GL during the course of maturation is not enthalpic in nature. These observations reveal that the mutations that convert GL to IM1 mediate their effects by reducing the entropic cost of binding rather than by facilitating favorable enthalpic interactions. The association free-energy difference that drives the conversion of IM2 to AM is also dominated by its entropic component. Modulating entropic properties may be a general feature of affinity-enhancing mutations that do not interact directly with the ligand. A similar result for residues distal to the binding interface has been observed in the context of DNA–protein interactions (25).

It is worth noting that the computed entropic changes are rather large, which is to be expected, as these entropy values do not include contributions from solvent–solvent interactions. Water molecules gain rotational and translational entropy as the protein and ligand associate, decreasing the entropy lost upon binding. However, the manner in which bulk solvent is disrupted by the individual Abs does not differ appreciably. This effect can be assessed by evaluating the solvent-exposed surface area for each. The results of performing such calculations suggest that the total solvent-exposed surface for the various Abs is quite similar. Thus, solvent–solvent interactions are not expected to differ significantly among them. In this case, cancellation of the solvent–solvent contribution allows relative entropy changes to be reliably evaluated. Such an approach has previously been demonstrated to reproduce trends with regard to entropic changes (21). Another possible source of differences between our computed results and the experimental binding free-energy values is the neglect of part of the Ab molecules. Although the experimental probes of rigidity that motivated our efforts are restricted to the binding pocket (15), binding may involve processes that occur on larger length scales. For example, regions remote from the binding pocket may become more rigid to compensate for the increased flexibility of the binding cleft in the unbound proteins. A recent study by Piekarska et al. (26) has demonstrated the potential for such a phenomenon. This situation may be particularly relevant to GL, which undergoes more significant structural rearrangement upon binding (Fig. 3). This phenomenon would account for the markedly larger entropy change observed for GL. Such processes cannot be probed with the methods we have used, which are geared toward identifying localized phenomena at relatively short (i.e., molecular simulation) time scales. Neither can they be explored by the spectroscopic methods that motivate this work. It will be interesting to see whether other studies of this system can shed light on this question. Despite these caveats, we have confidence that the simulation results described in this study provide a good description of the qualitative nature of molecular interactions in the vicinity of the binding site and that our general observations are robust. In support of this assertion, it can be observed that the relative free-energy magnitudes demonstrated in Table 2 are well reproduced, generating the ratios of free-energy differences that are quite consistent across all four proteins. For example, the ratio of the free-energy difference between AM and IM2 relative to that between AM and IM1 is very similar when either the experimental or computed values are considered. This finding indicates that the qualitative trends of relative binding free energies can be reliably evaluated by these approaches.

Evolution of the Association Free-Energy Landscape.

Flexibility plays an important role in biological systems. Many molecular recognition processes depend on the participants' capacity to reorganize themselves to engender increased complementarity to their binding partner (27). Such abilities may be important for modulating the specificity of molecular recognition events (28). For example, this capacity could allow a specific cell surface receptor to recognize a variety of related ligands. A similar mechanism may allow the immunological repertoire of naïve Abs to recognize a more diverse assortment of antigens (29). However, our observations suggest that the immune system can use reduced flexibility as one mechanism by which to generate high-affinity binding as maturation proceeds. We can relate our observations to two paradigms for Ab binding: the induced-fit and lock-and-key models (30). In a prototypical induced-fit process, a flexible Ab conforms to complement the shape of a particular ligand upon binding. This process enables a single Ab to recognize multiple antigens. In the lock-and-key model the Ab provides a well defined binding pocket (lock) that is specific for one ligand (key), sacrificing broad specificity in favor of high affinity.

The induced-fit hypothesis is supported in all except AM, as the unbound Abs exhibit more flexibility than the bound species. For example, the flexibility observed in unbound GL is significantly abrogated in the bound complex. In the process, FLU fluctuations become restricted in a manner comparable to those observed for the highest-affinity AM (see previous section), suggesting that GL exhibits a high degree of complementarity to the ligand when bound. Such observations are best supported by an induced-fit model of binding.

However, the induced-fit and lock-and-key models are not mutually exclusive. The unbound Abs also become less flexible as more favorable binding free energies are generated during maturation. This result suggests that they adopt a more limited number of conformations preconfigured to exhibit favorable interactions with the ligand, consistent with the lock-and-key model. In this way the mutations that accompany maturation eliminate configurations with less favorable binding interactions. The mechanism by which proteins are able to modulate their function by altering the regions of configuration space that they access may be quite generic. For example, in our previous studies of catalysis in the dihydrofolate reductase enzyme, deleterious mutations were shown to increase the likelihood that unproductive regions of conformational space are explored by the protein (31). A similar observation was made in recent studies of lactose permease (28).

In such a model, conformations that are amenable to a protein's specific function may be predominantly occupied under optimal conditions. Suboptimal amino acid composition (i.e., deleterious mutations) allows additional areas of the protein free-energy surface to be accessed that are not compatible with its original functional properties. This situation increases the amount of conformational space that must be explored for a productive state to be achieved, hindering efficient performance of the molecule. Conversely, mutations that increase functional proficiency may generate these outcomes by limiting the accessible conformation space to regions that facilitate functional characteristics. We can relate these ideas to the concept of a funneled free-energy surface that has often been applied to protein folding (32, 33).

Just as one may use a funneled energy landscape to characterize the folding process, one can envision a “functional funnel,” wherein native protein interactions are geared toward producing distinct functional properties. By extension, one can also envision a funneled landscape for protein–ligand interactions (34). Although the broad significance of this concept has only recently become more widely acknowledged, this perspective should not be surprising as protein structure and function are intimately linked. In this context, our results demonstrate that the Ab-L association funnel becomes deeper with maturation because of more favorable enthalpic interactions. Concomitant loss of entropy leads to a narrowing of the energy landscape (Fig. 4). We note that similar observations have been recently reported by Chang et al. (35) for HIV protease. However, while those authors focused on ligand degrees of freedom, our present study emphasizes the effect of binding on protein fluctuations. Our observations illustrate how molecular evolution can improve binding by progressively limiting the conformation space accessible to Abs. We expect this finding to be a general feature of molecular recognition and other evolved functional properties of proteins.

Fig. 4.

Effect of maturation on binding free-energy landscape. The potential energy hypersurface of each protein is represented as a series of 1D basins (conformational substates). The wide basins in GL allow for the possibility of binding a diverse assortment of ligands. The increased depth of these basins with maturation indicates the enhanced enthalpic interactions that are engendered. These basins become narrower as a result of maturation and after ligand binding, leading to smaller amplitude fluctuations within each basin and decreased entropy.

Concluding Remarks

This study demonstrates that a link between flexibility and affinity exists for Ab-L interactions, with enhanced affinity associated with a decreased entropic cost to binding. This effect is caused primarily by loss of flexibility in the unbound states. We observe that the environment of the combining site becomes more flexible when the ligand is absent or when affinity decreases. The entropic changes that accompany binding disfavor complex formation, a phenomenon noted in several other studies (17, 18, 20–22, 35). We find that the induced-fit paradigm predominantly applies to less mature antibodies and is substituted by more of a lock-and-key description of binding as maturation proceeds. These observations are likely to be a general feature of Ab-L interactions and other molecular association processes (24).

Our findings indicate that affinity-enhancing mutations occurring outside of the binding pocket can act to reduce the entropic cost to binding, which has important ramifications for the study of molecular recognition. Efforts to modulate protein–ligand interactions usually have focused on direct participants to the binding interface. However, it may also be useful to target regions remote from the binding site. Rigidifying these regions may make association more favorable by reducing unfavorable entropy losses upon binding (25). The sequential stages of Ab maturation investigated in this study offer a unique window into the molecular evolution of high-affinity interactions.

Finally, we have shown how the funneled energy landscape emerges as a unifying concept that can be used to account for numerous protein properties. Although such ideas have to date been applied primarily to protein structural attributes (through folding), functional attributes of proteins are likewise determined by discrete topologies. Consequently, a unique folded state represents a free-energy minimum not only with respect to structure, but also with respect to functional properties. The impact of deleterious mutations in disrupting these properties is a well known phenomenon; such effects can be well described as perturbing the funneled free-energy surface that governs these functional features. This representation provides a simple and cohesive physical description that can be used to elucidate a broad range of protein characteristics as diverse as folding, enzyme catalysis, and ligand binding.

Methods

Molecular Simulations.

Classical molecular dynamics (MD) simulations of models for the four Ab (see Fig. 1) in both their bound and unbound states were carried out to asses the flexibility of these molecules. In each case a sphere of explicit water molecules was included to provide a realistic environment around the combining site. The simulations were then equilibrated for 200 ps while protein rmsd fluctuations were observed. No large-scale fluctuations of the rmsd were detected after this time period. MD trajectories were then propagated for 10 ns to adequately represent the equilibrium fluctuations of the Ab molecules. Simulation details are provided as SI Text. The MD trajectories were further used to derive thermodynamic quantities associated with binding as described below.

Enthalpies.

Upon completion of the MD simulations, explicit water molecules were removed and replaced with an implicit representation based on the generalized Born (GB) solvation model (36, 37). This particular GB implementation was previously developed in our group and has been shown to be quite accurate (38). Every configuration found in the trajectory for each Ab-L complex was used to evaluate the GB-solvated potential energy of the complex and its individual components by deleting the requisite molecules from the complex. This process is schematically depicted as:

where X denotes AM, IM2, IM1, or GL. Averaging these energy differences for each trajectory provides the solvated enthalpy change caused by binding (each ΔH). Moreover, the difference of these energy terms (ΔΔH) gives the difference in binding enthalpy between any two sets of Ab-L complexes.

Entropies.

Entropy estimates were derived based on the quasiharmonic (QH) model (39). The QH model was used because it directly uses the fluctuations that occur during the simulations to derive entropy measures (40, 41). This feature of the model enabled us to evaluate the proposals of Romesberg and colleagues (13–15) regarding the correlation between high affinity and reduced flexibility during binding in the 4-4-20 variants. Given that QH vibrational modes and frequencies are available, one can obtain an estimate for the entropy of the system by using standard procedures (42). The QH model is able to provide quite reasonable estimates for the internal entropy of molecular systems and does particularly well at evaluating entropy differences (as done in the present study) (19, 43, 44).

QH analysis operates under the assumption that a single minimum of the potential energy surface is populated. However, the dynamics of complex molecules such as proteins involves motion through a high-dimensional space containing a number of distinct basins, often referred to as conformational substates (45, 46). Transitions between these substates must be accounted for to deduce accurate entropy estimates (47). A brief discussion of this issue is presented in work by Ohkubo and Thorpe (48). We identified the substates occurring during the MD simulations and assessed the entropy of the protein within each by using QH analysis. In the context of the QH model, every substate provides an estimate of the vibrational density of states. These individual estimates were combined to evaluate the best estimate of the density of states for each system. This information was then used to determine the total entropy for a given trajectory (see SI Table 4 and SI Text).

Before QH analysis was carried out, snapshots from the MD trajectories were aligned to the average structure resulting from each substate to remove overall rotation and translation. We limited QH analysis of the proteins to those residues within 6 Å of the ligand in the Ab-L complex (identical residues were selected in the unbound Ab). This cut-off was chosen to more accurately assess the local environment of the binding pocket, in closer analogy to the experimental measurements of Zimmermann et al. (15). While changing the quantitative values obtained, the use of larger cutoffs did not adversely impact the qualitative nature of the trends reported in Table 2. For the complexes we performed QH analysis separately for the protein and ligand to assess the internal entropy of each molecule. Entropy values were combined with enthalpies to produce binding free energies using standard approaches (see SI Text).

Abbreviations

FLU

fluorescein

GL

germ line

IM

intermediate

AM

affinity mature

HB

hydrogen bond

Ab-L

antibody–ligand

MD

molecular dynamics

QH

quasiharmonic.