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BIOLOGICAL SCIENCES / BIOPHYSICS
Molecular evolution of affinity and flexibility in the immune system

Ian F. Thorpe and Charles L. Brooks, III^*

Center for Theoretical Biological Physics and Department of Molecular Biology, The Scripps Research Institute, 10550 North Torrey Pines Road, La Jolla, CA 92037

Edited by Peter G. Wolynes, University of California at San Diego, La Jolla, CA, and approved April 11, 2007 (received for review November 13, 2006)

	Abstract

Top Abstract Results and Discussion Concluding Remarks Methods Acknowledgements References

 
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 | antibody | ligand association | binding | entropy

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.

View larger version (54K): [in this window] [in a new window]   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.

	Results and Discussion

Top Abstract Results and Discussion Concluding Remarks Methods Acknowledgements References

 
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.

View larger version (42K): [in this window] [in a new window]   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.

View this table: [in this window] [in a new window]   Table 1. C mean squared fluctuations for network residues

View larger version (55K): [in this window] [in a new window]   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.

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.

View larger version (13K): [in this window] [in a new window]   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

Top Abstract Results and Discussion Concluding Remarks Methods Acknowledgements References

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

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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 H). Moreover, the difference of these energy terms (H) 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).

	Acknowledgements

Top Abstract Results and Discussion Concluding Remarks Methods Acknowledgements References

 
We thank Professor Floyd E. Romesberg, Dr. Joerg Zimmermann, and Erin Oakman for stimulating discussions and Professor Romesberg for sharing his unpublished observations with us. I.F.T. thanks Jessica M. J. Swanson for technical assistance. I.F.T. was supported by La Jolla Interfaces in Science. This work was supported by National Institutes of Health Grant GM37554.

	Footnotes

 

Abbreviations: FLU, fluorescein; GL, germ line; IM, intermediate; AM, affinity mature; HB, hydrogen bond; Ab-L, antibody–ligand; MD, molecular dynamics; QH, quasiharmonic.

*To whom correspondence should be addressed. E-mail: brooks{at}scripps.edu

Author contributions: I.F.T. and C.L.B. designed research; I.F.T. performed research; I.F.T. and C.L.B. analyzed data; and I.F.T. and C.L.B. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/cgi/content/full/0610064104/DC1.

© 2007 by The National Academy of Sciences of the USA

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Top Abstract Results and Discussion Concluding Remarks Methods Acknowledgements References

 

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This Article Abstract Figures Only Full Text (PDF) Supporting Information Alert me when this article is cited Alert me if a correction is posted Citation Map Services Email this article to a colleague Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed Alert me to new issues of the journal Add to My File Cabinet Download to citation manager Request Copyright Permission Citing Articles Citing Articles via CrossRef Citing Articles via ISI Web of Science (1) Citing Articles via Google Scholar Google Scholar Articles by Thorpe, I. F. Articles by Brooks, C. L. Search for Related Content PubMed PubMed Citation Articles by Thorpe, I. F. Articles by Brooks, C. L., III Pubmed/NCBI databases Substance via MeSH Medline Plus Health Information Immune System and Disorders Social Bookmarking                What's this?