Computational design of antibody affinity improvement beyond in vivo maturation

Computational design depends critically on two capabilities: accurate energetic evaluation and thorough conformational search. Previous work has addressed many problems related to the design of improved protein-protein binding affinity, such as the design of stable protein folds^2-4, binding pockets for peptides and small molecules^5-7, altered protein-protein specificity^8-12, and altered enzymatic activity^13-15. The design of improved antigen-binding affinity has met with limited success, however^16-19. Challenges for protein-protein affinity design include conformational change upon binding, interfacial trapped water molecules, polar and charged side chains, and the trade-off of protein-solvent with protein-protein interactions from the unbound to bound state. Fine free energy discrimination for redesign from nanomolar to picomolar affinities is a particular challenge.

A robust design strategy should both produce a considerable fraction of designs that are successful when tested experimentally, and yield substantial improvements across multiple systems. Though there are potentially many mutations that confer improved binding affinity for a particular interaction, calculations need only identify a subset to be successful. Our approach utilizes thorough optimization techniques that exhaustively rank-order the best solutions in a discretized search space. Although some of these solutions are expected to be improved designs, others will be unsuccessful but may be useful in learning about deficiencies in the energy functions, search procedures, or other methodology.

First we attempted to redesign the model antibody D1.3 for improved binding to its antigen, hen egg-white lysozyme. Single mutations at each of 60 complementarity determining region (CDR) positions to the 20 common side chains, excluding proline and cysteine, were designed using a physics-based energy function and a hierarchical search procedure. (Physics-based refers to an energy function constructed from and parameterized by theoretical and experimental models of the underlying physical interactions; by contrast, knowledge-based refers to potentials statistically derived from observational data, which often takes the form of structure databases.) A striking feature was that predictions for improved binding were dominated by mutations to large amino acids (Supplementary Fig. 1 online), many of which exhibited improved van der Waals packing interactions that outweighed disfavored net Poisson-Boltzmann continuum electrostatic solvation and interaction. Our confidence in these designs was low because many had unsatisfied hydrogen bonding, or a predicted packing improvement of a magnitude uncharacteristically large for a single amino-acid substitution. Nevertheless, 17 single mutations, most with calculated improved total binding free energy, were selected for experimental binding affinity measurement. Only three mutations improved affinity (Supplementary Table 1 online), with 2.4-fold improvement for the best single mutant (Supplementary Fig. 2 online). We found that the calculated electrostatic term of binding was a better predictor for improvement than the total calculated binding free energy, that improvements from mutations to larger amino acids were mostly not realized, and that avoiding potentially destabilizing mutations was important. This led to two questions: Could electrostatics-based predictions alone be used to design binding affinity improvements? Is there a physics-based explanation for the seemingly inaccurate calculated packing improvements?

In our second attempt, we used only the electrostatic term of the computed binding free energy to predict improvements in affinity, but kept the original design procedure and full energy function for side-chain conformational search. Since there were few computed opportunities for improving D1.3 based on electrostatics, new antibodies were chosen to explore both the new method and the possibility that D1.3 is anomalous.

Our second target for redesign was the antibody D44.1. It binds lysozyme, facilitating experiments, but its epitope is different from that of D1.3. In addition, D44.1 has low nanomolar affinity, maintaining the challenge of nanomolar-to-picomolar affinity maturation. Single mutations were designed at all D44.1 CDR positions, and then mutations were ranked by the electrostatic binding free energy term. In contrast to the D1.3 design, there were many computed opportunities for electrostatic improvement. We measured experimental binding affinity for the nine largest-magnitude predictions, choosing no more than two mutations per position. Six of the nine mutants bind tighter than wild type, and the best mutation, L92 Asn-to-Ala, exhibits 8-fold improvement (Table 1A, Fig. 1A). In addition, following the original design procedure, two mutations predicted to increase packing interactions were tested; as expected, neither mutation led to an improvement in affinity (Table 1A).

The successful D44.1 single mutations were combined and tested experimentally. The six favorable mutations span five positions, where L32 and L92 are the only positions in direct contact with each other in the wild-type crystal structure. Contrary to prediction, this double mutant is not as improved as the L92 single mutant alone. The mutations at the other three positions are additive with L92, yielding a quadruple mutant with 43-pM affinity, 100-fold improved over wild type (Table 1A, Fig. 1A). Figure 1B-D displays the designed interactions. Measurements of dissociation and association rate constants for D44.1 and the high-affinity quadruple mutant revealed that both kinetic steps were improved, including a 23-fold slower off-rate (Table 1B). Each ratio of k_off to k_on is in agreement with the independently measured K_d. Increasing ionic strength from 167 mM to 1.67 M screens the designed quadruple-mutant interaction by approximately 4-fold, in agreement with calculation (+0.9 kcal/mol), whereas the wild type is marginally improved at high salt, in contrast to calculation (+0.3 kcal/mol; Table 1B).

Two sets of calculations were made in an attempt to further improve the high-affinity D44.1 quadruple mutant. First, single mutations were designed based on the predicted structure of the quadruple mutant. These calculations reiterated many predictions seen in the original D44.1 design that had been lower-ranked and not tested experimentally, as well as predictions for mutating position L32, which neighbors the L92 Asn-to-Ala mutation and was found experimentally to not be additive. Second, double mutations were designed at all 93 pairs of contacting positions, and triple mutations were designed at positions H32, H98, and H100, based on cooperative packing at these positions. The double- and triple-mutant designs were filtered for favorable, cooperative predictions, requiring the double or triple mutation to exceed each single mutation and their energetic sum. Four single mutations, three double mutations, and one triple mutation were selected for experimental testing in the quadruple-mutant context (Supplementary Table 2 online). Only the H35+H99 double mutant was improved relative to the quadruple mutant, at 30-nM affinity, 140-fold improved over wild type (Table 1C, Figure 1A). Measurement of the individual H35 and H99 mutations revealed high cooperativity (Table 1C), consistent with the predicted salt-bridge and hydrogen-bond rearrangements (Fig. 1F-G). The diminished success rate of this subsequent design round may be due to smaller magnitude predictions, antibody destabilization, or design in a modeled rather than experimentally-determined structure.

Next, we applied our electrostatics-based methods to the anti-cancer therapeutic antibody cetuximab (Erbitux), which binds epidermal growth factor receptor (EGFR) to block ligand binding²⁰. Calculations revealed nine positions with opportunities for affinity-enhancing single mutations based on improved electrostatics. The five mutations of largest magnitude of predicted affinity improvement were selected for experimental testing in the single-chain antibody format, with one mutation per position, and no two positions in close proximity. The EGFR extracellular domain (EGFR-ECD) mutant used in the assays contains a point mutation that likely interferes with the H56 mutation. Three of the other four mutants bind EGFR tighter than does cetuximab; these three mutations were combined to produce a triple mutant with 10-fold overall improvement, from 490 pM to 52 pM (Table 1D, Fig. 2).

The transferability and utility of these electrostatics-based methods were further demonstrated by designs for which published data validates the predictions. One of our test cases was the antibody 4-4-20, which binds its small-molecule hapten, fluorescein, with 1.2 nM affinity, and was previously engineered using directed evolution to yield the antibody 4M5.3 with over 1,000-fold affinity improvement and 14 mutations²¹. Our designed single mutations in 4-4-20 revealed opportunities for improvement based on computed electrostatics at nine positions. Two of the predicted mutations, H31 Asp-to-His and H101 Ser-to-Ala, have already been shown to improve binding affinity as single mutations in 4M5.3²². Interestingly, the design missed the H102 Tyr-to-Ser mutation in 4M5.3 due to the rigid backbone constraint. Another test case was bevacizumab (Avastin), a therapeutic antibody that binds vascular endothelial growth factor (VEGF)²³, where we found five positions suitable for electrostatics-based improvement. The mutation H28 Thr-to-Asp and mutations at H31 and H101 are found in a published high-affinity variant of bevacizumab²⁴. Our other electrostatics-based predictions in both test systems remain to be tested.

The single mutations designed and experimentally validated in this work lead to enhanced binding affinity through one of two electrostatic mechanisms. In one mechanism, the removal of a poorly-satisfied polar group, a polar residue calculated to lose more free energy from desolvation than is recovered by interaction is mutated to a hydrophobic residue. These mutations account for the majority of improved energetics. In a second mechanism, the addition of a charged residue, net charge is changed to increase electrostatic interaction, often at the periphery of the antibody-antigen interface where desolvation is minimal. Unlike previous work using electrostatics to guide design^{25, 26}, these methods explicitly model the mutation, calculate a binding free energy relative to wild type, include positions that are partially or fully buried upon binding, and avoid opportunities where the mutation is predicted to destabilize the mutant protein.

The modeled structures result from optimization with the full energy function, yet the van der Waals and nonpolar solvation energies are then discarded to predict improvement based on only the net electrostatic term. A potential problem is that different/wrong van der Waals parameters would produce altered equilibrium distances and hence altered electrostatic energies, particularly for short-range interactions. The specific mutations predicted and tested here may be less susceptible to this potential problem because they involve the calculation of solvation and medium-range electrostatic energies, which are not especially sensitive to precise atom locations. The energy for substitution of an unsatisfied polar group is dominated by its desolvation penalty, and the addition of a charged group at the interface periphery is not sensitive to precise side-chain placement. However, designs involving the introduction of a new short-range electrostatic contact, such as a new hydrogen bond, could be susceptible to this potential problem. Further work is necessary, but it could be that the energetic terms are actually appropriate for identifying low-energy structures for any sequence, but not for comparing energetics between sequences. Indeed, we think that the packing and nonpolar interactions are not balanced in some situations for accurate comparison of one amino acid to another, as described next.

We investigated the underlying physical model to address the seemingly inaccurate calculated packing interactions. The majority of problematic designs were at the binding site periphery, where mutation to a larger amino acid was predicted to be favorable due to increased intermolecular van der Waals interactions. In some cases, hydrogen-bonding groups were buried, but the unfavorable electrostatic term was outweighed by improved packing. In principle, a larger amino acid at the interface periphery will exhibit increased protein-protein interactions in the bound-state, counteracted by increased protein-water interactions in the unbound-state. However, these offseting energetics are calculated asymmetrically, with an atomistic Lennard-Jones potential for the protein-protein interactions, and a simple solvent-accessible surface area (SASA) nonpolar term for the protein-water interactions. The protein-water nonpolar interaction should be a function of the detailed geometry, including volume effects, as well as the particular protein atom types present. We implemented and parameterized an atomically-detailed nonpolar term based on work by Levy and co-workers (Supplementary Fig. 3 online)²⁷, and found that it reduced the magnitude of favorable prediction for many of the counterintuitive designs to larger side chains (Supplementary Fig. 4 online). In addition, unbound-state conformational search attenuated predictions for larger side chains by introducing an energetic cost to adopt the binding conformation (data not shown). Nevertheless, some incorrect predictions remain, and future work should address this issue.

This work presents a computational alternative to directed evolution for affinity maturation. Directed evolution is adept at accumulating successive, additive mutations, but (with the exception of large-scale shuffling) is less well suited for selecting variants whose encoding DNA is further from wild type. Experimental libraries generated using error-prone PCR generally do not cover all single amino-acid mutations, let alone all pairs or greater combinations of mutations, as 13 of the 19 possible single mutations require more than one base pair change, on average. Some classes of mutation require two base pair changes - for example, mutation to either negatively-charged residue from any codon of 10 of the 18 candidate side chains. Of the 12 single mutations found to improve D1.3, D44.1, or cetuximab, 10 required two base pair changes and would therefore have been substantially more difficult to identify by a method that relies on error-prone PCR. Also, the H35+H99 cooperative double mutation required concerted amino-acid mutation and three total base-pair changes. Computation has the capability to search a vastly larger space than accessible to either in vivo maturation or experimental selection techniques, potentially discovering larger and more beneficial evolutionary steps.

Our results present several design lessons. We find that computed electrostatics alone is a better predictor for improved binding than is computed total free energy. Electrostatics-based predictions yielded fewer false positives, more true positives, and a greater than 60% success rate for single mutations from wild type (Fig. 3). Predictions based on improved total free energy were dominated by mutations to larger amino acids that did not experimentally improve affinity; incorporation of improved nonpolar hydration models may improve accuracy of predicted packing changes^28-30. We find that designing single and double mutations allows for in-depth conformational search and avoids having any particular design flaw spoiling all results. In addition, avoiding destabilizing mutations based on calculated folding stability was important. Crystal structure resolution did not have a substantial effect, as the D44.1 and cetuximab structures are of 2.5- and 2.8-Å resolution, respectively, whereas the D1.3 structure is 1.8-Å resolution. Calculations in D1.3 showed few opportunities for electrostatics-based improvement, and accumulated evidence indicates that D1.3 is the anomaly, possibly because of the combination of the many large side chains and buried water molecules at the antibody-antigen interface.

Our results demonstrate novel capabilities for improving protein binding affinity using computational design. Maturation of the model system D44.1 by 140-fold to 30 pM, maturation of the therapeutic antibody cetuximab by 10-fold to 52 pM, and identification of known mutations in 4-4-20 and bevacizumab together indicate that our method is a noteworthy advance for antibody design and should be effective for other antibodies and protein interactions. Computational design holds the promise of far greater exploration of sequence space than possible experimentally, enabling rapid and inexpensive protein improvement.