AbDesign: an algorithm for combinatorial backbone design guided by natural conformations and sequences

Abstract

Computational design of protein function has made substantial progress, generating new enzymes, binders, inhibitors, and nanomaterials not previously seen in nature. However, the ability to design new protein backbones for function – essential to exert control over all polypeptide degrees of freedom – remains a critical challenge. Most previous attempts to design new backbones computed the mainchain from scratch. Here, instead, we describe a combinatorial backbone and sequence optimization algorithm called AbDesign, which leverages the large number of sequences and experimentally determined molecular structures of antibodies to construct new antibody models, dock them against target surfaces and optimize their sequence and backbone conformation for high stability and binding affinity. We used the algorithm to produce antibody designs that target the same molecular surfaces as nine natural, high-affinity antibodies; in six the backbone conformation at the core of the antibody binding surface is similar to the natural antibody targets, and in several cases sequence and sidechain conformations recapitulate those seen in the natural antibodies. In the case of an anti-lysozyme antibody, designed antibody CDRs at the periphery of the interface, such as L1 and H2, show a greater backbone conformation diversity than the CDRs at the core of the interface, and increase the binding surface area compared to the natural antibody, which could enhance affinity and specificity.

Introduction

Molecular recognition underlies many central biological processes. The ability to design novel protein interactions is a stringent test of our understanding of the physicochemical principles that govern molecular recognition and holds promise for creating specific and sensitive molecules for use as therapeutics, diagnostics, and research probes. Recent strategies in protein-binder design used naturally occurring proteins as scaffolds on which binding surfaces were designed^1–4. These strategies relied either on a small number of protein scaffolds ^2,3 or several hundred different scaffolds^4–7 to achieve the structural characteristics required for binding. In all cases the designed scaffolds were treated as rigid structures with minimal perturbation of their backbone degrees of freedom. These strategies resulted in the experimentally validated design of homooligomers^8–12, inhibitors ^4,6, and a protein purification reagent⁵. Several generalizations have been made about successfully designed binding surfaces: 1. they comprise surfaces rich in secondary structure (α-helices and β-sheets); 2. Interactions with the ligand are largely mediated by hydrophobic amino acid sidechains; and 3. The buried surface area upon binding is at or smaller than the average for naturally occurring protein-protein interactions (1600 Ų)¹³. The design of large and polar surfaces, essential to make computational binder design general, remains an unmet challenge^14–17.

We reasoned that a key to solving the challenge of designing large and polar binding surfaces lies with the design of the protein backbone, since the backbone provides many additional conformation degrees of freedom that have so far been untapped by binder-design strategies. Designing backbones for function, however, is an unsolved problem due to uncertainty in assessing the contributions to free energy from polar groups and due to the large conformation space open to the protein backbone¹⁸. As a step to address the challenge of designing backbones in binders we suggest an algorithm that uses conformation and sequence information from naturally occurring proteins belonging to the same fold family in order to constrain backbone design and amino acid sequence choices, thereby limiting modeling uncertainty while exposing a large space of conformations to computational design. We test this approach by computing antibody models that target pre-chosen protein epitopes and assess sequence and backbone conformation recovery compared to natural antibodies in complex with the same epitopes.

Antibody structure, function, and engineering

The key challenge in the design of backbones for function is that the designed surface needs both to bind its target and be conformationally stable; the design of antibodies for function therefore brings into focus the need to develop methods that simultaneously optimize both binding and stability, challenges which have hitherto been approached by computational design separately ^7,19,20. Natural antibodies are built of sequence blocks that alternate conserved with highly variable segments^21–23. The molecular structures of antibodies show that the conserved segments belong to a structurally homologous and rigid structure known as the framework, which confers stability to the antibody, whereas the variable segments cluster at the ligand-binding surface, and are therefore termed the complementarity-determining regions (CDRs). Despite their tremendous binding-surface diversity, all CDRs except H3 fall into a handful of discrete conformations termed ‘canonical conformations’ ^22,24–26. For instance, in hundreds of antibody molecular structures only seven conformation variants are observed for L2 ²⁴. Each canonical conformation is characterized by key conserved residue identities, which are important for maintaining the backbone conformation ^{21,22,24,25,27}. Some other fold families, such as ankyrin-repeat proteins and the Rossman fold, which similar to antibodies are associated with many molecular functions, are likewise modular, with a clear separation between a structurally conserved region and a variable region, where function is typically encoded²⁸. The ability to design diverse backbones within fold families could therefore have many applications.

A key attraction for protein engineering lies in antibodies’ modular architecture, suggesting that a large combinatorial complexity of well-folded backbones could be tapped. As early as the 1980s, observations on the structural modularity of antibodies made by Lesk and Chothia ²⁹ proposed that synthetic antibodies could be constructed by combining fragments of naturally occurring antibodies. From this insight, Winter and co-workers devised a method for antibody humanization, in which CDRs from a mouse antibody were grafted onto a human antibody framework to generate a humanized functional antibody^30,31, opening the way to safe therapeutic antibody engineering. These early advances raised excitement that the complete design of antibodies from first principles is achievable³², but until recently, computational tools for protein design had not matured sufficiently to realize this objective.

An important advantage of computational design over conventional protein-engineering methods has been its ability to generate binders of specific sites of interest on target molecules with atomic accuracy. Site-specific targeting has been essential to the design of broad-specificity influenza inhibitors, a pH-sensitive binder, and an enzyme inhibitor ^4–6. In contrast to this ability to target specific molecular surfaces, conventional antibody-engineering methods, such as animal immunization and repertoire selection³³, are capable of isolating binders to target molecules, but there is no general method to target binders to specific epitopes^34,35, hampering efforts to generate specific binders, inhibitors, and allosteric effectors^36–38. To be sure, in certain systems selection methods were developed to isolate antibodies that bind specific epitopes on target molecules^39–43; yet these capabilities are challenging and rely on specific properties of the target molecule, such as naturally high antigenic variability outside the target site⁴⁴.

Computational antibody design may in future complement existing antibody-engineering techniques, and open new avenues for generating antibodies that target specific sites and even rare conformations on target receptors and enzymes.

Recent work on computational antibody design aimed to increase binding affinity^45–47, identify favorable positions for experimental random mutagenesis⁴⁸, modify binding specificity⁴⁹ and increase thermo-resistance⁵⁰. An antibody design strategy was suggested by Pantazes et al. ^51–53 that capitalizes on observations that antibody CDRs exhibit canonical conformations. In this method a representative set of antibody CDRs is designed from canonical conformations, and then docked and designed to bind the target epitope. The resulting output from this procedure is a CDR library that can be grafted on a selected antibody framework. The AbDesign algorithm reported below differs in three important respects from this strategy: first, rather than segmenting the CDRs individually AbDesign segments the antibody backbone using junctions of high structure conservation, generating structurally compatible framework-CDR interactions; second, AbDesign derives sequence information from natural antibodies to constrain sequence optimization to amino acid identities that are important for the stability of the modeled conformation; and third, AbDesign conducts combinatorial backbone design, sampling backbones from all the natural antibodies in the structure database, including highly homologous ones, to improve binding affinity and antibody stability. The procedure is general and can be adapted, in principle, to any modular protein fold family.

Material and Methods

Source code and structure models availability

The methods have been implemented within the Rosetta macromolecular modeling software suite ⁵⁴ and are available through the Rosetta Commons agreement. All of the methods have been implemented through RosettaScripts⁵⁵, and all scripts are available as Supplemental Data. Top-ranked structure models targeting each of the epitopes studied in this paper are provided in the supplement. These models were automatically generated, filtered, and ranked using the methods presented below; we note that designs chosen for experimental testing are typically selected from a larger pool, visually inspected for flaws and manually corrected prior to testing.

Binding mode criteria

Following guidelines by the Critical Assessment of PRediction of Interactions (CAPRI) we use the interface-root mean square deviation (I_RMS) with a cutoff of 4 Å to define which designs fail to recapitulate the natural binding mode⁵⁶. This measure computes the Cα rmsd on all ligand residues with atoms within 10 Å of the antibody in a structure in which the natural and designed antibody structure are aligned.

Energy and structure filters

Shape complementarity (Sc) was computed using the algorithm described in ref. 57 implemented in Rosetta⁵⁴. Sc ranges from 0 (no shape complementarity) to 1 (perfect shape complementarity). Antibody designs with Sc values less than 0.6 were rejected. Protein packing quality at the antibody core and antibody-ligand interface were calculated using “RosettaHoles” (Packstat)⁶⁰ implemented in Rosetta⁵⁴. Antibody designs with Packstat values less than 0.57 were rejected.

The binding energy is defined as the difference between the total system energy in the bound and unbound states. In each state, interface residues are allowed to repack. For numerical stability, binding-energy calculations were repeated three times, and the average was taken.

Antibody stability is defined as the Rosetta all-atom system energy of the antibody monomer when the ligand is eliminated from the system.

All-atom energies were calculated using the default Rosetta energy (score12), which is dominated by contributions from van der Waals packing, solvation, and hydrogen bonding.

Docking of the antibody scaffolds to the target epitope

Each initial antibody scaffold was aligned to the natural antibody framework in the experimentally determined molecular structure using a customized PyMol script⁵⁸, and the ligand coordinates were combined with the designed antibody model to produce a single coordinate file. The resulting binding mode was perturbed with RosettaDock⁵⁹ using low-resolution docking (centroid mode).

Boltzmann conformational probabilities of interface side chains

Boltzmann conformational probabilities were calculated as described in ref. 61. For each partner in the complex and for each residue that contributes more than 1 R.e.u to the predicted binding energy we iterate, in the unbound state, over all the backbone-dependent rotamers in the Dunbrack library defined within the Rosetta software. For each rotamer, all residues within a 6Å shell are repacked and minimized. The energy E of each such state is then evaluated using the Rosetta all-atom energy function (score12) ⁶². The probability of the conformation of residue i, p_i, is then computed assuming a Boltzmann distribution:

$$P_i=\frac{e^{\frac{-E_i}{K_{B}T}}}{{\displaystyle \sum _s{e}^{\frac{-Es}{K_{B}T}}}}$$ (1)

Where s is the rotameric state, K_B is the Boltzmann constant, and T is the absolute temperature. K_BT was set to 0.8 R.e.u. E_i is the energy of the unbound state.

Backbone segment clustering and sequence profiles

The antibody structures in our database were aligned separately to the variable heavy and variable light domains of antibody 4m5.3, (PDB entry 1X9Q)⁴⁶. We then extracted the coordinates of the CDRs according to VL, L3, VH, and H3 definitions (Table 3) and clustered them according to length. For L3 and H3 we preformed additional conformational clustering using BCL::cluster⁶³. This additional clustering was needed due to the higher conformational diversity of L3 and H3 compared to the other

Table 3.

Comparison of CDR definitions segments²²,²⁴,⁶⁴,⁶⁵. Backbone conformations were clustered with a 2.0 Å C_α RMSD radius.

CDR		Chothia	CDR definitions used for sequence constraints b	Segment definitions used for PSSMs and backbone modeling
VLa	L1	L24-L34	L23-L35	L23-L88
	L2	L50-L56	L46-L55
L3		L89-L97	L88-L98	L88-98
VHa	H1	H26-H32	H26-H37	H25-H92
	H2	H50-H58	H45-H58
H3		H95-H102	H93-H103	H93-H103

^aIncluding CDRs 1 and 2 and intervening framework positions.

^bSee Results, section a.

The resulting clusters were visually inspected for common sequence motifs, and clusters that contained several different sequence motifs were manually split; conversely, conformation clusters that shared sequence motifs were merged. Clustering results in 207 H3 bins, and the top 50 clusters (by size) were used to generate the conformation representatives (algorithm, section d).

For each backbone conformation cluster we generated a Position Specific Scoring Matrix (PSSM) of unique sequences that belong to this cluster using the PSI-BLAST suite⁶⁶ with default parameters. In the case of singleton backbone conformations (in H3) the BLOSUM62 scoring matrix is used to provide a statistical model for tolerance to amino acid substitutions.

Code-integrity tests

The integrity of the Rosetta source code is maintained through a set of integration tests. Antibody conformation sampling and sequence design are tested with three tests: the splice_out integration test ensures that the algorithm can properly extract backbone segments from the source antibody and create a new torsion database; the splice_in integration test checks that the algorithm can read the torsion database and impose a new backbone conformation onto the template antibody; and the splice_seq_constraints integration test checks that the algorithm can add sequence constraints to an antibody structure.

Algorithm performance

Following precomputation of sequence and backbone-torsion databases a typical design trajectory takes approximately 7 hours on a standard CPU. The protocol is divided into two parts. First, the complex formed between the designed antibody scaffold (algorithm, section d) and the target molecule is subjected to docking, design, and minimization (algorithm, section e); this step takes only 3 minutes; the vast majority of time is spent in the downstream refinement steps (algorithm, section f). To make efficient use of computational resources AbDesign applies energy and structure filtering before going into refinement; on average, only 4% of all trajectories pass this filtering. Depending on the availability of computational resources and the magnitude of the design problem, filters at this step can be adjusted.

Checkpointing

We use checkpointing to ensure that if a design trajectory is prematurely terminated due to computer resource outage it can be resumed from the last backup point. A PDB-formatted file containing the coordinate information of the complex is saved to disk along with the details on the design stage, complex stability, and binding energies, whenever a sampled backbone improves the objective function (algorithm, section g). When AbDesign is initiated it automatically checks for the existence of checkpointing files; if those are found, AbDesign will continue from the last checkpoint. Restarting simulations from the backup point takes less than 30 seconds.

Results

AbDesign: an algorithm for combinatorial backbone-sequence optimization in protein-fold families

Using Figure 1 as a visual guide we present a step-by-step description of the AbDesign process. The core algorithmic elements were written in C++ within the Rosetta software suite of macromolecular modeling⁵⁴, and the design protocols were written using RosettaScripts⁵⁵ enabling users to modify parameters to best suit their design goal, control the execution flow and even to extend the algorithm to protein families other than antibodies. RosettaScripts used in this paper are available in the supplement. AbDesign addresses four related challenges: 1. Leveraging knowledge from conformation and sequence databases to constrain design choices; 2. Encoding residue correlations between the variable segments, which largely lack stabilizing secondary-structure elements, and the framework, which forms a tightly packed and stable structural foundation; 3. Efficient sampling of the large backbone and sequence combinatorial space encoded in a fold family; and 4. Designing conformations and sequences that optimize both protein stability and target-molecule binding. In the following sections we describe the different elements of the algorithm in detail and how they relate to these design challenges.

Figure 1. Overview of the design protocol workflow.

Briefly, structures of naturally occurring antibodies are extracted from the Protein Data Bank (PDB)⁹² and aligned to a template antibody structure. Backbone segment conformations and sequences are extracted into two correlated databases: a Position-Specific Site Matrix (PSSM, step 1) database (step 1) and a backbone-torsion database (step 2), where PSSMs and their respective torsion databases are linked. From the torsion database a set of antibody conformations representing all combinations of canonical conformations is generated (step 3), docked against the target surface (step 4) and designed for optimal binding affinity, subject to sequence constraints derived from the PSSMs (step 5). Antibodies passing structure and energy filters are then subjected to a backbone and sequence refinement protocol (step 7): for each backbone segment (VL, VH, L3, H3) alternative conformations are sampled from the pre-computed torsion database and designed in the context of the modeled antibody-bound structure. The backbone conformation with the highest computed stability and affinity for the ligand is selected using fuzzy-logic design, and serves as input in the optimization of the next backbone segment. Finally, designs are filtered using energy and structural criteria derived from natural antibodies (step 8).

a. Sequence constraints from natural antibodies guide amino acid design choices

The stability of a protein conformation relative to unfolded and misfolded states relies on both positive and negative design elements; whereas positive design elements address the target conformation and are amenable to modeling, negative design with respect to the vast conformation space open to a loop is impractical for modeling^18,67. A key advantage of computational design of proteins belonging to a diverse fold family, such as antibodies, is that we can extract statistics regarding amino acid choices on a per-position basis that encode at least some of these elements, and use these statistics to guide the design process (Figure 1, step 1). Moreover, by correlating natural backbone conformations and sequences we can classify sets of natural protein-segment sequences that fold into particular conformation classes (such as antibody canonical conformations), and maintain for each of these classes its own unique sequence profile.

For each segment cluster we generate a Position Specific Scoring Matrix (PSSM) using the PSI-BLAST software package⁶⁸. The sequence constraints encoded in the PSSMs are stringent in the antibody framework and relaxed at the CDRs, giving sequence optimization room to explore different residue combinations for interacting with ligand, while maintaining the antibody’s structural integrity. The PSSM is used during all design calculations in two ways. First, design sequence choices are restricted only to identities above a conservation threshold according to the PSSM. The cutoffs are determined separately for the binding site (PSSM score >=0 for all antibody residues with C_β’s within a 10 Å distance cut-off of the ligand), CDRs (>=1, Table 3, methods), and framework positions (>=2). Effectively, positions that are important for binding are allowed more room to vary from the family consensus than positions in the antibody framework. Second, the all-atom energy function is modified to include a term that biases the sequence towards the more likely identities according to the PSSM. The bias towards the sequence consensus is weighted 50% more strongly away from the binding site.

b. A pre-computed database of backbone conformations for each antibody segment

Backbone-conformation sampling is computationally demanding^69–72 and despite some success ⁷³ backbone design for function has led to conformations that deviated from the original computed models^19,74. By designing proteins in a conformationally highly diverse family, such as antibodies, we can make use of hundreds of naturally occurring conformation variants for each backbone segment, where the conformations are likely to be stable within the host protein fold. In a precomputation step we extract the conformations of natural antibodies (Figure 1 step 2) and store them in a database for use during design. 788 variable light κ chains and 785 variable heavy-chain structures are superimposed on a template antibody (throughout this manuscript, we use as template antibody 4m5.3, Protein Data Bank (PDB) entry 1X9Q, a high-expression, high-affinity anti-fluorescein antibody⁷⁵, although the choice of template is arbitrary). λ variable light chains were not included in the current database because of the relatively small number of available structures in the PDB (1300 variable κ chains versus 265 variable λ chains ⁷⁶), although AbDesign can address λ chains without changes to the algorithm.

Next we identify positions on the protein backbone, which are structurally highly conserved in all antibody molecules; due to the high homology such positions can serve as effective junctions or stems for recombining backbones from antibodies. Past structural analysis suggested to use stems corresponding to each individual CDR, for instance at the start and end of CDR1 (L24 -- L34, H26 -- H32, Chothia numbering²⁵), CDR2 (L50 -- L56, H52 -- H56), and CDR3(L89 -- L97, H95 -- H102)^{21,22,25–27,30,47,77–81}. Our preliminary in silico experiments using such stem choices, however, resulted in structurally unrealistic designed antibodies with poor packing between the CDR and the framework sidechains. Instead we use the disulfide-linked cysteines in each of the variable domains as stems for a segment comprising CDR1 and CDR2 and the framework region, and the second disulfide-linked cysteine and a conserved position at the end of CDR3 (position numbers 100 in the variable κ domain 103 in the variable heavy domain^25,26, Figure 2) as the stems for the CDR3 segments; these stems are very well aligned in all antibodies of known structure (Figure 2). Genomic recombination of the V and (D)J genes typically occurs three amino acid positions C-terminally to the second cysteine in each variable domain; we find, however, that the genomic-recombination sites are structurally poorly aligned in a set of diverse antibodies compared to the disulfide-linked cysteines, which therefore provide more favorable junctions for joining conformation fragments.

Figure 2. Natural V (D) J gene segmentation versus conformation segmentation used in AbDesign represented on the 4m5.3 (PDB entry 1X9Q) antibody.

AbDesign segments the antibody structure at the disulfide-linked cysteines and in a structurally conserved position at the end of CDR3 (stem positions are underlined). Natural antibody recombination follows a similar, but not precisely the same, segmentation (bars above sequence and the V, D, and J labels). Sequence and structure are color-coded by conformation segments (red: CDRs L1&L2 and framework, green: L3, blue: H1&H2, yellow: H3). Gray segments are only subjected to sequence, rather than backbone optimization.

By using segment boundaries that are close to the VDJ genomic segmentation we directly embody conformation and sequence correlations between the CDRs and the framework that were refined by natural selection, encoding both local and global sequence-structure relationships. As a concrete example for the importance of the correlations between conformations and sequences, the H3 backbone cluster H3.15.8 (Table S1) is in an extended conformation, while the conformation from the cluster H3.16.5 is kinked ⁸²; the two clusters’ sequence profiles are correspondingly characterized by different amino acid conservation patterns (Figure 3), which are encoded in the respective PSSMs used during design.

Figure 3. Sequence and conformation coupling during design.

During design of a new backbone the PSSMs used to constrain sequence choices are altered. In this example, the H3 backbone segment from antibody 5G9 (PDB entry: 1AHW) is modeled in the context of the 4m5.3 antibody (PDB entry: 1X9Q). Web-logos for the two conformation segments are shown on the right, revealing different amino acid conservation patterns, which are important for the structural integrity of the modeled segment. For instance, the H3 backbone conformation from 1X9Q is in an extended conformation, whereas the imposed H3 backbone conformation is kinked ⁸², and characterized by a hydrogen bond between the conserved stem Trp (Trp103, Chothia numbering) Nε1 atom and a carbonyl oxygen (Met100, Chothia numbering). The conserved salt bridge between Arg94 and Asp101 is similarly frequently observed in kinked conformations. Surrounding residues in a 6 Å shell around the inserted backbone segment are also designed and repacked under sequence constraints to accommodate the new backbone conformation. In the example shown, residues Phe27 and Tyr32 from the heavy chain and residue Tyr32 from the light chain are repacked to avoid clashes with the designed H3 conformation.

For each segment (VL, L3, VH, and H3) of each of the natural antibodies in our database we extract the backbone dihedral angles (Φ, Ψ, and Ω) from the source antibody and replace the segment in the template with the source segment’s dihedral angles (Figure 1, step 2), introducing a main-chain cut site in a randomly chosen position in the inserted segment. Where the inserted segment is longer than the template antibody segment, residues are added to the model using idealized bond lengths and angles. We then refine the main chain using cyclic-coordinate descent (CCD) ⁷¹, small, and shear moves, as implemented in the CCD mover in Rosetta⁸³. During refinement the standard Rosetta all-atom energy function (score12)⁶² is modified by the addition of an energy term that favors closing the main-chain gap, and harmonic restraints that bias the Cα positions and the backbone-dihedral angles of each modeled amino acid to the values observed in the source antibody to minimize deviation from the source conformation. CCD alternates backbone moves with combinatorial amino acid sidechain packing. During packing steps we also allow combinatorial stochastic sequence optimization in the entire modeled segment and in a 6 Å shell surrounding the segment subject to amino acid constraints derived from the antibody PSSM. At the end of CCD we compute the root mean square deviation (RMSD) of the modeled segment from the source segment and if it exceeds 1 Å or if the main-chain gap score is greater than 0.5 we repeat the procedure. Segments that fail to meet the criteria above after 10 trials are discarded from further consideration. Although CCD was originally conceived as a method for loop closure⁷¹, here we find that, guided by coordinate and dihedral constraints from naturally occurring segments, CCD effectively refines segments up to 74 amino acids long to the RMSD and main-chain gap criteria above within, on average, 1.2 attempts. Given the above selection criteria, the natural backbone conformations are fitted onto the template scaffold in the majority of antibody entries in our database, ranging from 74% of the VH segments to 96% of L3 segments. Each trajectory takes on average 4.6 hours on an Intel Xeon 2.4GHz CPU. Backbone dihedral angles of successfully fitted segments are recorded in a backbone torsion database for subsequent use during design (Table S4).

c. Design subject to sequence constraints derived from natural antibodies

In sections (a) and (b), above, we pre-computed correlated PSSM and backbone-conformation databases. During design we load the pre-computed PSSM matrices associated with the current conformation (4 PSSM segments, one for each backbone segment), and combine them to generate a single PSSM matrix for the entire antibody. Whenever a different backbone conformation is sampled AbDesign replaces the relevant PSSM matrix associated with the swapped segment, automatically synchronizing the sequence constraints with the backbone conformation.

For efficiency, at different phases of design different sets of residues are subjected to combinatorial sequence optimization. For instance, several initial design phases only optimize the ligand-binding surface, whereas at the final stages of design there are several steps of sequence optimization over all antibody positions. Sequence constraints (section a) considerably reduce the combinatorial design problem: in a representative case, the latter step of full design over a 230 amino acid antibody variable fragment has a total of ~10¹¹⁷ different possible sequence combinations, equivalent to full combinatorial design of only 93 positions; increasing the PSSM cutoffs would further reduce this combinatorial space.

d. A representative set of antibody conformations

Combining the four antibody segments (VL, L3, VH, and H3) using all backbone conformations extracted in section (b) above would result in a prohibitively large library of antibody scaffolds for design. Observations made by Chothia and others^22,24, however, highlighted that each antibody backbone segment other than H3 falls into a handful of canonical conformations. We start the design process by generating a library of representative antibody backbones that spans the space of these canonical conformations plus a set of 50 H3 backbone conformations (Figure 1, step 3). We extract the conformation mean from each cluster and reduce the number of representative structures further by eliminating similar conformations by visual inspection. This procedure results in 5 (VL) x 2 (L3) x 9 (VH) x 50 (H3) = 4500 non-redundant conformation representatives (Table S2), exceeding the number of solved antibody structures (Methods). All sequence and conformation information from the template antibody is eliminated in constructing the conformation representatives, except for the relative orientation of the disulfide-bonded cysteines in the variable light and variable heavy domains. In other protein fold families, where canonical conformations have not been characterized, automated clustering of backbone conformations can be employed to generate the reduced set of conformation representatives²⁴.

e. Low-resolution docking and sequence design

Each of the 4,500 representative conformations generated in step d is aligned using PyMol⁸⁴ to the natural antibody to obtain conformations where the representative antibodies are bound to the target molecule in approximately the same orientation as the natural antibody. In each design trajectory, this conformation is perturbed using low-resolution (centroid) RosettaDock (Figure 1, step 5)⁸⁵ to randomize the initial binding orientation within the vicinity of the naturally observed binding mode, and the target protein-ligand surface is repacked to eliminate memory of the bound sidechain conformations. This procedure is in keeping with previous studies of binder and enzyme design ^7,20,86, where the target site for binding was constrained to the one observed in the natural complex to avoid sampling the impractically large space of orientation and sequence open to design of function. In the context of antibody design sequence-structure space is still larger than in previous studies due to the additional backbone-conformation degrees of freedom. Indeed, where intense experimental effort was invested many different antibodies and epitopes were discovered that target a single molecule⁸⁷, suggesting that without restricting to the natural target epitope a potentially large number of different binding modes and sequences might result. In cases where the target epitope or binding mode are not defined apriori docking software, such as PatchDock⁸⁸ or RosettaDock⁸⁵, can be used to generate the initial bound conformations, as was done in binder design applications^4–6; the AbDesign methodology can therefore be extended, in principle, to binder design in the absence of a known antibody-bound complex.

Following docking the antibody is designed subject to the PSSM constraints above and ligand sidechains within 10Å of the antibody are repacked (Figure 1, step 6). We then minimize the sidechains on the ligand and antibody and assess the complex using energy and structure filters.

f. Combinatorial rigid body, conformation, and sequence sampling

In step e we optimized the sequence of the representative antibodies; in this step we also sample the antibody backbone degrees of freedom from the torsion databases computed above (step b). For each of the four antibody segments we randomly sample 50 different backbone conformations from the relevant torsion database (Figure 1, step 7). The optimization objective function used to select the best conformation of the 50 randomly chosen conformations is specified in step g below. To improve the chances of acceptance, each sampled backbone is within a predefined sequence-length change with respect to the input conformation, ranging from ±2 for segment types VL, VH, and L3, and ±4 for H3. In this step AbDesign rigorously samples natural backbone conformations that are similar to the initial conformational representative antibody. Some of the sampled backbones vary by sub-angstrom RMSD values, thereby fine-tuning the backbone conformation.

AbDesign in effect samples combinations of naturally observed backbone conformations from a pre-computed menu of conformations, accessing an unprecedented combinatorial space of backbones for design, and addressing an important shortcoming of current design of function strategies, which have relied on a limited number of backbones (typically under 3,000)^7,89,90. In a protein superfamily comprising m protein structures each segmented into n structural fragments, a total diversity on the order of mⁿ backbones could, in principle, be accessed through AbDesign; applied to the antibodies in our set, m=700 molecular structures and n=4 segments (VL, L3, VH, and H3), leading to a total space of 10¹¹ different backbones. To be sure, not all resulting backbones are physically realistic, and the stability optimization of section g below tests that combinations of backbone fragments that destabilize the protein are not selected.

Changing the current segment’s backbone conformation to any other conformation in the torsion database simply consists of imposing the backbone dihedral angles specified in the pre-computed database and can be done in well under a second on a standard CPU, opening the way to efficient sampling of backbone conformation space. At each backbone-sampling step we use combinatorial sidechain packing to design the sequence subject to the PSSM constraints above, and repack ligand residues within 10Å of the antibody. We then simultaneously minimize the sidechains on the ligand-binding surface and antibody and rigid-body orientation of the antibody relative to the ligand and the antibody heavy chain relative to the light chain. We repeat this design-minimization cycle three times starting with a soft-repulsive potential and ending with the standard all-atom energy function (score12). We then use the rotamer trials-minimization procedure, whereby single sidechains are selected at random, packed, and minimized to improve sidechain packing in the antibody core and in the antibody-ligand interface.

g. Optimization of ligand binding and protein stability

A key challenge in protein design of function is that the protein needs to be both stable in its designed conformation and bind its target molecule¹⁸. AbDesign implements a novel multiconstrained optimization scheme, fuzzy-logic design⁹¹, to select the designed backbone segments that best optimize ligand-binding energy and antibody stability. As explained in the previous step, for each of the four backbone segments (VL, L3, VH, and H3) we randomly sample 50 backbone conformations derived from that segment’s torsion database (section f), compute the binding energy (E_B) and stability (E_S) of the redesigned antibody, and transform each according to the following sigmoid function:

$$f(E)=\frac{1}{1+e^{(E-o)s}}$$ (2)

Where E is either the binding energy (E_B) or the energy of the unbound antibody (E_S), o is the sigmoid midpoint, where f(E) assumes a value of ½ and s is the steepness of the sigmoid around the midpoint. The sigmoid approaches values of 1 at low energies and 0 at high values. Before sampling conformations for each of the segments, parameter o in Eq. 1 is automatically reset to the energy value of the currently designed antibody, so both sigmoids are close to their midpoints at the start of refinement of each segment. The optimization objective function is the product of the two sigmoids: $o=f(E_S)\hspace{0.17em}\text{x}\hspace{0.17em}f(E_B),$ resulting in values approaching 1 when both E_S and E_B are low and values approaching 0 if either one of the energy criteria is high. The effect of optimizing this objective function is to find a backbone conformation that is both sufficiently stable and high affinity. For instance, a backbone conformation that improves binding energy by 10 Rosetta energy units (R.e.u.) has a transformed sigmoid value of 0.99, and improved stability by 10 R.e.u. (transformed value of 0.97), the product (E_S x E_B) equals 0.963, would be preferred to a backbone conformation that improves the binding energy by 1 R.e.u (transformed value of 0.61) and the stability by 30 R.e.u (transformed value 0.999, product equals 0.6) (Figure 4A). By optimizing this function during combinatorial backbone design binding energy and antibody stability improve by on average 100R.e.u. and 5R.e.u., respectively, relative to the starting designed scaffold antibody (Figure 4 B&C); thus, combinatorial backbone sampling and fuzzy-logic design can considerably improve two of the most important parameters for design of function.

Figure 4. Fuzzy-logic design is used to optimize binding affinity and antibody stability.

A. Plot of the fuzzy-logic objective function, which is the product of the stability and binding sigmoids (Eq. 1). A transformed value of a -10 R.e.u change in binding and stability is preferredto a -30 R.e.u change in stabilty and a -1 R.e.u change in binding. The product of the two transformations gauges the effect the incorporated segment has on the antibody’s stability and binding affinity for the target relative to the baseline score (the interim best scoring antibody structure so far). B & C. Comparison between the stability and binding energy of a set of designed antibodies before and after refinement (algorithm, section f). The X-axis is the calculated energy (R.e.u) of the antibody-target complex after sequence optimization (algorithm, section e) and before refinement. Y-axis is the designed antibody energy (R.e.u) after the backbone refinement phase (algorithm, section f).

h. Structure and energy filters derived from natural antibodies

At the end of the design simulation we filter antibody structure models using four parameters: predicted binding energy, buried surface area, packing quality between the antibody’s variable light and heavy domains and the bound ligand⁶⁰, and shape complementary⁵⁷ between the antibody and bound ligand (Figure 1, step 8). Cutoffs for each of these parameters are derived from a set of 303 natural antibody-protein complexes (Table S3) extracted from the PDB⁹² using the Structural Antibody Database (SabDab) ⁷⁶(Figure 5).

Figure 5. Energy and structure criteria used to filter designed antibody structures.

In the final step of AbDesign we filter the designed antibodies according to four parameters: predicted binding energy, buried surface area, shape complementarity between antibody structure and ligand, and packing quality between the variable light and heavy domains and the ligand. Cutoffs (green dashed lines) were derived from a set of 303 natural protein-binding antibodies (Table S3). Antibody designs (purple) that passed all filters are compared to the natural protein-binding antibodies (gold).

Structural characteristics of designed antibodies

To test AbDesign’s performance and highlight areas for future improvement, we selected a set of nine high-affinity (K_d < 20 nM), medium-to-high crystallographic resolution (<=2.5 Å), protein-binding antibodies from SAbDab ⁷⁶ (Table 1) as targets for design. For each natural antibody-protein complex we retain only the natural binding orientation, and eliminate all antibody sequence and backbone information; sidechains on the target molecule binding site are allowed to repack and minimize, in keeping with previous design of function studies^7,20. The natural antibody set comprises human antibodies Fab40,D5 neutralizing mAb, and BO2C11 (PDB entries: 3K2U⁹³ 2CMR⁹⁴, 1IQD⁹⁵ respectively), murine antibodies E8, D1.3 mAb,F10.6.6, JEL42, and 5E1 Fab (PDB entries: 1WEJ⁹⁶, 1VFB⁹⁷, 1P2C⁹⁸, 2JEL⁹⁹, 3MXW¹⁰⁰), and the humanized murine antibody D3H44 (PDB entry: 1JPS¹⁰¹). The ligand targets comprise convex (2JEL, 1IQD), flat (1P2C), and concave (3MXW) surfaces, containing helical (2CMR), sheet (1JPS), and loop (1P2C, 3K2U) secondary-structural elements. The conformation propensities in our dataset mirror those of protein-binding κ antibodies in the PDB (Table S2): eight antibodies in the set use the H1.14_H2.15 backbone conformation in the VH backbone segment; D1.3 mAb uses the H1.14_H2.14 conformation. Antibodies E8, D1.3 mAb, 5E1, D5, D3H44, Fab40 and F10.6.6 use the L1.11_L2.8 backbone conformation in the VL backbone segment, antibody JEL42 uses the L1.16_L2.8 backbone conformation and antibody BO2C11 uses the L1.12_L2.8 backbone conformation. For the L3 backbone segment all antibodies in the set use the L3.10.1 conformation, which dominates natural κ light chains . The H3 lengths in the set range from 7 (F10.6.6, Kabat and Chothia length^25,102) to 10 (Fab40 and D5) .

Table 1.

Structure and sequence comparison of top ranked designs and natural antibody targets

PDB entry	CDR Cα RMSD (Å)a						Overall sequence identity (%)	Interface sequence identityb(%)	CDR sequence identity(%)c		Core sequence identity (%)d	Source PDB namese				Sequence identity of design to segments’ germline (%)
	L1	L2	L3	H1	H2	H3			VH	VL		VL	L3	VH	H3	VL	VH
1JPS	0.52	0.18	0.4	0.67	0.36	0.35	63	36	75	63	67	1FVC	1XGQ	3MXW	3HR5	76	56
1WEJ	0.35	0.21	0.39	0.8	0.59	2.37	64	37	61	43	82	2WUB	1RIV	2WUC	3HR5	69	64
2CMR	0.26	0.31	0.42	2.04	0.36	0.73	64	26	61	68	75	3CXD	3IFL	3GI8	2DBL	58	70
3MXW	0.33	0.19	0.45	0.65	0.36	0.91	58	53	42	54	60	1T3F	1NBY	2I5Y	1ZTX	73	55
1VFB	0.4	0.19	0.42	0.32	0.39	0.84	63	27	60	56	80	2VDL	4LVE	3FO0	3HR5	58	62
2JEL	0.47	0.16	0.55	0.53	1.67	-	68	13	71	80	77	2IQ9	1CIC	1I8K	2HKF	66	84
3K2U	0.36	0.22	0.29	0.57	0.54	-	70	40	62	86	77	1U8M	1K4D	2CGR	1UWE	70	69
1P2C	0.29	0.27	0.24	1.02	1.9	-	52	34	52	59	64	1NGW	2F5A	3FO0	1FGN	68	72
1IQD	1.85	1.3	2.18	1.26	1.58	2.2	62	26	66	60	71	2NY7	1IGJ	1UJ3	1FL5	62	60

^aDashes signify mismatch between the lengths of the designed and the natural antibody CDRs.

^bOver all antibody residues within a 10 Å distance of the ligand.

^cOver CDR residues, excluding interface residues.

^dAll buried non-CDR residues.

^eSource PDBs from which the designed segments were derived.

We filter resulting designs using metrics developed to assess structure models, including binding energy, antibody stability, shape complementarity, packing statistics, and buried surface area. To rank the final design models we use only computed binding energy, and contrast the highest-affinity design with the target natural antibody, bound to the same epitope, according to the following structure and energy criteria: sequence identity, Cα RMSD, interface shape complementarity (Sc)⁵⁷, packing statistics⁶⁰, buried surface area, binding energy (Figure 5), and backbone-conformation clustering. The distributions of natural and filtered designs along the four parameters are similar, except in shape complementarity, which tends to be lower in designed complexes than in the natural ones. This is a general trend for designed complexes, which reflects the challenge of achieving the subtle steric complementarities seen in natural binders. Even though the design trajectories start from a binding orientation similar to the experimental bound complex, during design some antibodies migrate and bind at other sites. For the purposes of recapitulation analysis we eliminate designed antibodies with interface RMSD values⁵⁶ greater than 4 Å.

Subject to the above selection criteria, six out of the nine natural antibodies in our study set select H3 and L3 CDRs of the same length as the natural antibody targets; of those six, five select fragments belonging to the same conformation clusters as those of the target natural antibody and four are at the top 10% ranking in terms of computed binding energy (Table 1). Bound conformations with large buried surface area (>1800 Ų) are designed successfully more consistently than those with smaller buried surface area, suggesting that AbDesign is biased towards large interfaces; with larger binding surfaces computed binding energy rises and the number of conformations and sequences that are compatible with forming favorable inter-chain contacts drops, thereby increasing the probability of recovering the natural conformation.

To focus on the atomic details of designed antibodies we consider antibodies that target the same surface as the humanized anti-tissue factor antibody D3H44 (PDB entry 1JPS) and the anti-transmembrane glycoprotein D5 neutralizing mAb (PDB entry 2CMR). In preliminary simulations we noticed that the tissue-factor targeting designs used backbone conformations for H3 that were derived from naturally occurring anti-tissue factor antibodies; to eliminate bias, we removed anti tissue-factor entries from the backbone conformation dataset, and repeated the analysis. All backbone conformation segments comprising the designed antibodies belong to the same backbone conformation clusters as the experimentally determined structure of 1JPS (L1.11_L2.8, L3.10.1, H1.14_H2.15, H3.16.5) and 2CMR (H1.14_H2.15, H3.18.7, L1.11_L2.8, L3.10.1). The designs’ backbone conformations show a high level of agreement with the natural antibodies (Cα RMSD between design and natural antibody: 1.23 Å and 1.15 Å, for 1JPS and 2CMR, respectively; Figure 6). Previous studies noted that successfully de novo designed binding surfaces tended to be apolar and use regions high in secondary-structure content¹⁶, raising the question whether the all-atom energy function correctly balances contributions from hydrogen bonding, solvation, and electrostatics that are crucial for designing polar surfaces ¹⁸. It is therefore encouraging that in some cases designed antibodies capture the extensive hydrogen bonding across the interface as seen for example in the highest predicted binding energy designed anti-tissue factor antibody (Figure 7). Designed long-range interactions within the core of the variable domain, between the framework and the hypervariable CDRs, show the same characteristic hydrogen bonding, van der Waals, and aromatic stacking interactions observed in the natural antibodies from which the segment was extracted (Figure 8). The results demonstrate that when confined to choosing from naturally existing backbones and subject to sequence constraints the all-atom energy function is capable of correctly designing and ranking polar binding surfaces and the protein core, which provides structural stability to these surfaces.

Figure 6. Antibody designs have similar backbone conformations to natural antibodies that target the same surface.

Comparison between the backbone conformation of designed (magenta) and natural (orange) antibodies targeting to the same surface. (A). The anti-transmembrane glycoprotein (D5 neutralizing mAb, PDB entry 2CMR). C_α RMSD between the design and natural antibody is 1.1Å, and ligand interface RMSD is 2.7 Å. (B). The anti-tissue factor protein (D3H44, PDB entry 1JPS). C_α RMSD between design and natural antibody is 1.05 Å and ligand interface RMSD is 2Å.

Figure 7. Designed antibody-backbone atoms form polar contacts with the ligand and supporting polar interactions within the antibody.

The best predicted binding affinity design (magenta) of an anti tissue-factor antibody is shown with the target ligand (blue). Two polar contacts (dashed orange lines) are formed between the L3 Ser94 amide nitrogen and the carbonyl group of Thr167 from tissue factor and between Tyr92 carbonyl and the amide nitrogen of Lys169 from tissue factor. The hydroxyl group of Tyr 96 forms an additional hydrogen bond with the ε-amino group of Lys169. In addition the conserved Glu90 forms multiple hydrogen bonds with the backbone atoms of the L3 loop that stabilize the conformation.

Figure 8. Designed backbone fragments conserve the stabilizing interactions observed in the natural source antibody.

The natural VL segment from PDB entry 3IDI (orange) encodes long-range stabilizing interactions between CDR L1 and the framework, for instance, using hydrogen bonds (dashed green lines), hydrophobic, and aromatic-stacking interactions. Though the VL segment used in the design targeting tissue factor (target PDB entry: 1JPS, left) has a different sequence than that of the source fragment (right), the same types of stabilizing interactions are made in the designed fragment.

Although segments from the nine natural antibodies were included in the conformation databases used during design the natural backbone conformations were not selected by AbDesign in the majority of final high-scoring models; in addition, the sequence identities between the designed segments and the natural antibodies, as well as between the germline genes that gave rise to the designed and natural segments are low(Table 2); in fact all but one of the five designed antibodies’ segments that use similar backbone conformations as the target antibodies, originate from germline genes different from those of the nine natural antibodies (Table 2); furthermore, the amino acid sequence identities between the germline genes that gave rise to the backbone conformations used in designed antibodies and the germline progenitor genes of the natural antibodies are lower than 80%, except for two segments in the target antibody D1.3 (PDB entry: 1VFB), which share 90% sequence identity with the natural antibody’s V_H germline gene and 83% sequence identity with the natural J_k gene (Table 2). The sequence identities between the segments comprising the designed and the target antibody segments are below 75% (expect for the VH segment of the target antibody D1.3, PDB entry: 1VFB). By contrast, natural antibody segments derived from the same germline typically show sequence identities higher than 80%¹⁰³. The designed segments are quite far from the germline compared to naturally occurring segments, ranging from 50%-80% in designs, compared to 80%-100% in natural antibodies, suggesting that design could sample parts of sequence space that are inaccessible to natural antibody diversification processes. The ability to design antibody variants using backbone-conformation segments from germline genes other than those used in natural binders suggests that the conformation data encoded in the PDB are redundant, which may be important for fine tuning the backbone to the target site.

Table 2.

Structure and energy parameters of natural and designed antibody complexes

PDB entry	Natural antibody						Designed antibody
	Ligand	Kd(nM)b	Predicted binding energy (R.e.u)a	Buried surface area (Å)	Packing score a	Shape complementaritya	Predicted binding energy (R.e.u) a	buried surface area (Å)	Packing score a	Shape complementaritya	buried surface area (Å)	Ligand interface RMSD (Å)	Predicted binding energy rankc
1JPS	Tissue factor	0.1	-25	1950	0.66	0.70	-34.4	2171	0.62	0.59	2171	2.00	17 (5212)
1WEJ	Cytochrome C	15.8	-16	1220	0.70	0.75	-24.5	1535	0.67	0.62	1535	2.00	3 (93)
2CMR	Transmembrane glycoprotein	0.05	-22	2110	0.58	0.72	-26.3	2162	0.57	0.60	2162	1.40	11 (297)
3MXW	Sonic hedgehog protein	0.7	-21	1882	0.70	0.51	-32.2	2011	0.69	0.58	2011	2.72	24 (1274)
1VFB	Lysozyme	3.7	-22	1405	0.67	0.69	-24.3	1493	0.64	0.60	1493	3.20	24 (250)
2JEL	Phosphocarrier protein HPr	3.7	-17	1549	0.66	0.58	-20.4	1353	0.62	0.60	1353	2.70	9 (50)
3K2U	Hepatocyte growth factor activator	0.16	-29.2	1982	0.62	0.68	-26.6	1695	0.58	0.62	1695	3.20	51 (112)
1P2C	Lysozyme	0.098	-17	1467	0.68	0.67	-22.2	1566	0.68	0.60	1566	3.90	138 (659)
1IQD	Coagulation factor VIII	0.014	-32	2134	0.70	0.78	-24.7	1632	0.66	0.67	1632	2.80	762 (2802)

^aSee methods for details.

^bObtained from the “SabDab” database.

^cValues in parentheses signify how many designs with I_RMS<4 Å were computed (Table S6).

The ability to sample and design many realistic backbone conformations can be used to highlight where design may be useful to engineering, and areas for improvement in design methodology. For some targets AbDesign selects models with backbone conformations similar to the natural antibody, but ranks these models poorly in comparison to others. In the case of the anti-lysozyme antibody F10.6.6 (PDB entry 1P2C) the natural antibody buries a relatively small surface area and is in the 20th percentile of the overall predicted binding-energy ranking (Table 1). Most of the top-ranked designs that target the same lysozyme epitope bury larger surfaces (>1600 Ų) by using longer L1 and L3 segments (Figure 9a). These results highlight the modularity of the antibody scaffold, and a potentially useful strategy to refine existing antibodies by diversifying CDRs at the periphery of the binding site; such diversification could increase affinity and specificity for the target or increase antibody stability. Ideally, however, a design algorithm should be able to consistently predict conformations that are known to form high-affinity binding surfaces, and better methods for ranking the designed proteins should be developed to correctly identify experimentally verified binders. The anti-hepatocyte growth factor activator antibody (PDB entry 3K2U) has a binding surface area of 1980Ų, while the best-ranked similar-conformation design buries only 1700 Ų (Table 1). This difference in buried surface area is due to a change in the packing angle between the light and heavy variable domains of the natural and designed antibodies (Figure 9b); more extensive sampling of the orientation of the two antibody variable domains than done here may be necessary to address such inaccuracies. The design examples studied here and provided in the supplement can serve as a reference point for testing improvements in all-atom energy functions, backbone and rigid-body sampling strategies, and ranking of resulting designs.

Figure 9. AbDesign favors larger binding surfaces.

(A). Comparison between the top-ranked anti-lysozyme design (magenta) and the natural antibody, F10.6.6, PDB entry 1P2C (gold). The designed antibody uses a longer L1 (16 amino acid, compared to 11 in the natural antibody) and a longer L3 (11 amino acids compared to 10), increasing the buried surface area from 1470 Å2 to 1680 Å2. (B) Comparison between the anti-hepatocyte growth factor activator designed antibody (magenta) and the natural antibody, Fab40, PDB entry 3K2U (orange). Structures are oriented so CDRs are pointing towards the viewer. A 10o difference in the packing angle between the variable light and heavy domains creates a gap between the CDRs of the natural antibody’s variable light and heavy domains compared to the designed one (marked by red arrows). This opening in the light and heavy domain interface produces a larger binding surface in the natural antibody compared to the design.

AbDesign sequence recapitulation and interface side chain rigidity

We compute sequence recapitulation for designs of similar conformation and length as the natural targets, and find that they are in the range of past design recapitulation studies. The values are not directly comparable, however, since past design work dealt with either functional-site design^7,20,86 or the protein core¹⁰⁴, whereas AbDesign deals with both, and since here we constrain sequence and backbone-conformation choices using data from natural antibodies, whereas past design studies used all-atom energy functions and modeled backbones without additional restraints. Sequence within the antibody core is recapitulated to within roughly 60-80% identity, which is higher than a previous study attempting to recapitulate native identities in the protein core (51%¹⁰⁴), and the binding surface sequence identity is approximately 30%, similar to a previous protein-binding study (interface residue sequence identity between 10-40%) ⁷. In some cases residues at the interface and the antibody core encouragingly conserve side-chain conformations at atomic accuracy (Figure 10).

Figure 10. Designed antibodies recapitulate the identity and conformation of binding surface and core residues.

The anti-tissue factor design. Tissue factor is shown in surface representation colored by vacuum electrostatics using Pymol (69). Residues at the VL/VH interface are shown as sticks. The natural antibody D3H44 (PDB entry: 1JPS) is colored orange.

Amino acid conformational plasticity has the potential to reduce binding specificity and affinity^18,61 and design algorithms that rigidify sidechains at the binding surface were successful in generating the first designed protein inhibitors^4–7 and small-molecule binders⁹⁰. A computational metric to assess sidechain rigidity was suggested which computes the Boltzmann weight of the bound sidechain conformation in the ensemble of all sidechain conformations when the binder is dissociated from its target⁶¹. Designed binders using existing strategies⁶¹ typically show lower sidechain-conformation Boltzmann weights, and presumably lower rigidity, than natural binders. Previous design attempts, which incorporated sidechain rigidity into the design scheme, have either explicitly accounted for it during design^6,7 or have used this metric as an additional filter for evaluating designs posteriori⁹⁰. We hypothesized that the sequence-structure rules encoded in the backbone-conformation library and the related PSSMs implicitly constrain residues in the designed antibody binding surfaces to more rigid choices. A comparison of the sidechain conformational plasticity at the binding surfaces of 303 natural high-affinity antibodies (Table S3) with the designed antibodies encouragingly shows that designed aromatic residues at the binding surface that contribute more than 1 R.e.u to the predicted binding energy have conformation-probability densities somewhat higher than natural antibodies (Figure 11). The proportion of low-probability sidechain conformations (<5% probability), which are unlikely to be in their intended conformation in the unbound state, is less than 10%, and more than half of the designed interface residues have sidechain-conformation probabilities above 15%, a higher fraction than in the set of natural antibodies.

Figure 11. Designed sidechains are predicted to be rigid.

(A). The sidechain conformation probabilities in the unbound state were computed using the method in Ref. 61. AbDesign produces antibody complexes with a lower proportion of low-probability conformations (≤ 0.05 probability) compared to natural antibody complexes. The natural antibody complex set comprises 303 antibody-protein complexes (supplemental table S3) extracted from the SabDab database, and the designed antibody set includes all designs generated and filtered by the design protocol. (B). The designed antibody against the sonic hedgehog protein. The constrained tyrosine (colored green, with rotamer Boltzmann probability 90%) is stabilized by packing against surrounding backbone atoms and the side chain atoms of Tyr53 and a hydrogen bond with Asn31. (C). The anti-tissue factor protein designed antibody. Tyr137 on H1 (rotamer Boltzmann probability: 60%) is stabilized by packing against the backbone atoms of H1 and H3 and the side chain of Phe132.

The Boltzmann weight of the bound sidechain conformation is a computed metric based on sidechain-conformation libraries ^61,105 and so these results must be treated with caution in the absence of experimental structures of bound and unbound designs. Still, the high computed sidechain rigidity values suggest that by optimizing antibody stability and by biasing sequence optimization towards the antibody sequence consensus AbDesign may encode some elements that are necessary for lock-and-key molecular recognition^106–109. Two examples, the anti-tissue factor designed antibody and an anti-sonic hedgehog protein designed antibody, demonstrate how interface sidechain rigidity is encoded by contacts between the designed sidechains and neighboring sidechain and mainchain atoms (Figure 11).

Discussion

Despite breakthroughs in the design of new molecular function in regions high in secondary-structural elements^2,4–6,110, successful design of function in loop segments has been elusive ^{14,17,18,73,111}. AbDesign uses information encoded in large protein families, such as antibodies, to infer local and global sequence-structure relationships, within loops and between loops and spatially neighboring structural elements, and to define rules that guide the computational-design process. By sampling combinations of compatible backbone fragments, which have been refined by evolutionary selection, AbDesign accesses an unprecedentedly large space of feasible backbone conformations, enabling the design of fine shape and chemical complementarities needed for design of function ¹⁸. Although ultimate proof lies in experimental validation of designed antibodies, the design examples provided here offer promising signs that some of the current limitations in computational design may be addressed by this approach¹⁶: designed surfaces comprise more polar interaction networks, loops, and larger binding regions than in previous design studies. Additionally, designed sidechains are predicted to be more rigid than in natural antibodies, whereas previous studies noted lower sidechain conformation probabilities than natural sets ^7,61; higher rigidity could enhance affinity and specificity.

A key element of the AbDesign strategy is backbone segmentation along boundaries that are highly conserved in homologous structures (the disulfide-bonded cysteines and conserved positions at the end of CDR3). Existing strategies for CDR grafting, for instance in therapeutic antibody humanization, implant CDRs into the most homologous target framework, but these strategies often result in reduced binding affinity and specificity¹¹². Our in silico results suggest that despite high sequence conservation in the framework, the specific stabilizing contacts formed between the CDRs and their natural frameworks are important for the structural integrity of the antibody, as noted by previous analysis⁸¹. Our strategy of using large backbone segments that contain the inter-molecular contacts between the framework and CDRs 1 and 2 generate antibody models with well-packed cores and high fidelity of the designed backbone for the one observed in the source antibody, features that are likely essential for the structural integrity of the designed segment and for its desired activity. Two additional elements of the AbDesign strategy are: first, direct coupling between sequence and conformation constraints to ensure that the designed sequence is compatible with its backbone; and second, selecting from among a large combination of conformations the backbones and sequences that simultaneously optimize both antibody stability and ligand binding. The AbDesign algorithm is general and could, in principle, be applied to any protein family with a sufficiently heterogeneous set of experimentally determined three-dimensional structures. For example, enzymes belonging to Rossman fold and repeat proteins such as ankyrins share with antibodies the structural separation between a largely conserved scaffold that stabilizes the protein and a structurally diverse region (usually comprising loops, as in antibodies), where specific function is encoded²⁸; indeed, these fold families are unusually enriched for binding different molecules, suggesting that designing within these fold families could generate many desired molecular functions.

The design examples studied here show that AbDesign can in some cases retrieve backbone conformations and sequence elements observed in natural antibodies that target the same site. The design algorithm does not exclusively produce natural-like binders, however, and additional candidates, differing in backbone conformation, sequence, and binding mode, are suggested with equal and often improved computed affinity. These results might be due to inaccuracies in the forcefield or sampling method, or they could represent alternative solutions to binding the target epitope; indeed, different natural antibodies are known to bind the same epitope¹¹³. In particular, our results on the anti-lysozyme antibody suggest that AbDesign could propose antibodies that share large regions with natural antibodies, but that form additional interactions to those observed in the natural antibodies, highlighting the versatility of the antibody scaffold; these additional interactions could increase specificity and affinity. AbDesign may therefore be used to suggest variants of natural antibody binders for experimental selection of higher-affinity, higher-specificity, or higher-stability antibodies, and in the future may enable designing antibodies completely from scratch.

By sampling many different backbone combinations AbDesign allows us to highlight important areas for improvement in design methodology. It is encouraging that the AbDesign strategy is able to recapitulate sequence and structure features seen in naturally occurring polar and large binding surfaces, whereas previous design analyses noted biases towards hydrophobic and small surfaces¹⁶. A difference between previous design algorithms and the one reported here is that AbDesign restricts sampling to a choice between physically realistic backbone conformations and to the natural amino acid combinations that are compatible with these backbone conformations; the results suggest that when confined to such discrete choices – albeit to a very large space of such choices -- the all-atom energy function can reproduce polar surfaces seen in natural binders, and often ranks them highly. AbDesign is generally biased towards designs with large binding surfaces (> 1800 Ų, Table 1), reflecting the correlation between buried surface area and binding affinity in natural protein-protein interactions¹¹⁴. The antibodies with small binding surfaces selected in our study nevertheless have high experimentally determined affinity for their targets, such as in the case of the anti-cytochrome c, E8 antibody (PDB entry: 1WEJ) with buried surface area upon binding of 1200 Ų and KD of 16nM⁹⁶. Despite the natural antibody’s high affinity for its target, AbDesign prefers antibodies that bury 1500 Ų of surface area upon binding. These results highlight the importance of developing metrics to rank designs in addition to stability and binding energy. Indeed, previous design of function applications^4,5,110 and our study relied on structure selection criteria, such as the intermolecular shape compementarity⁵⁷ and packing defects⁶⁰. We expect that additional filters that address the geometry of hydrogen bonding and the ability of water molecules to be bound and stabilized at the binding interface may make important additional contributions to appropriate selection and ranking of design models. An advantage of design within a large family of proteins, such as antibodies, is the availability of a large set of experimentally determined structures of natural exemplars with which to test different metrics, and the current results can provide a useful reference point for testing improved metrics to accurately rank the propensity of design models to bind their intended targets. We also note that more extensive sampling of the rigid-body orientation between the antibody light and heavy domains than done here may improve the accuracy of the design calculations. The AbDesign method is the first, to our knowledge, to combine backbone, protein-core, and functional-site design, and could be used to test and refine molecular forcefields^115,116.