Toward high‐resolution homology modeling of antibody Fv regions and application to antibody–antigen docking

High‐resolution homology models are useful in structure‐based protein engineering applications, especially when a crystallographic structure is unavailable. Here, we report the development and implementation of RosettaAntibody, a protocol for homology modeling of antibody variable regions. The protocol combines comparative modeling of canonical complementarity determining region (CDR) loop conformations and de novo loop modeling of CDR H3 conformation with simultaneous optimization of V_L‐V_H rigid‐body orientation and CDR backbone and side‐chain conformations. The protocol was tested on a benchmark of 54 antibody crystal structures. The median root mean square deviation (rmsd) of the antigen binding pocket comprised of all the CDR residues was 1.5 Å with 80% of the targets having an rmsd lower than 2.0 Å. The median backbone heavy atom global rmsd of the CDR H3 loop prediction was 1.6, 1.9, 2.4, 3.1, and 6.0 Å for very short (4–6 residues), short (7–9), medium (10–11), long (12–14) and very long (17–22) loops, respectively. When the set of ten top‐scoring antibody homology models are used in local ensemble docking to antigen, a moderate‐to‐high accuracy docking prediction was achieved in seven of fifteen targets. This success in computational docking with high‐resolution homology models is encouraging, but challenges still remain in modeling antibody structures for sequences with long H3 loops. This first large‐scale antibody–antigen docking study using homology models reveals the level of “functional accuracy” of these structural models toward protein engineering applications. Proteins 2009; 74:497–514. © 2008 Wiley‐Liss, Inc.     

Ab initio structure prediction of the antibody hypervariable H3 loop

Antibodies have the capability of binding a wide range of antigens due to the diversity of the six loops constituting the complementarity determining region (CDR). Among the six loops, the H3 loop is the most diverse in structure, length, and sequence identity. Prediction of the three‐dimensional structures of antibodies, especially the CDR loops, is an important step in the computational design and engineering of novel antibodies for improved affinity and specificity. Although it has been demonstrated that the conformation of the five non‐H3 loops can be accurately predicted by comparing their sequences against databases of canonical loop conformations, no such connection has been established for H3 loops. In this work, we present the results for ab initio structure prediction of the H3 loop using conformational sampling and energy calculations with the program Prime on a dataset of 53 loops ranging in length from 4 to 22 residues. When the prediction is performed in the crystal environment and including symmetry mates, the median backbone root mean square deviation (RMSD) is 0.5 Å to the crystal structure, with 91% of cases having an RMSD of less than 2.0 Å. When the prediction is performed in a noncrystallographic environment, where the scaffold is constructed by swapping the H3 loops between homologous antibodies, 70% of cases have an RMSD below 2.0 Å. These results show promise for ab initio loop predictions applied to modeling of antibodies. © 2012 Wiley Periodicals, Inc.     

The VSGB 2.0 model: a next generation energy model for high resolution protein structure modeling

A novel energy model (VSGB 2.0) for high resolution protein structure modeling is described, which features an optimized implicit solvent model as well as physics‐based corrections for hydrogen bonding, π–π interactions, self‐contact interactions, and hydrophobic interactions. Parameters of the VSGB 2.0 model were fit to a crystallographic database of 2239 single side chain and 100 11–13 residue loop predictions. Combined with an advanced method of sampling and a robust algorithm for protonation state assignment, the VSGB 2.0 model was validated by predicting 115 super long loops up to 20 residues. Despite the dramatically increasing difficulty in reconstructing longer loops, a high accuracy was achieved: all of the lowest energy conformations have global backbone RMSDs better than 2.0 Å from the native conformations. Average global backbone RMSDs of the predictions are 0.51, 0.63, 0.70, 0.62, 0.80, 1.41, and 1.59 Å for 14, 15, 16, 17, 18, 19, and 20 residue loop predictions, respectively. When these results are corrected for possible statistical bias as explained in the text, the average global backbone RMSDs are 0.61, 0.71, 0.86, 0.62, 1.06, 1.67, and 1.59 Å. Given the precision and robustness of the calculations, we believe that the VSGB 2.0 model is suitable to tackle “real” problems, such as biological function modeling and structure‐based drug discovery. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

The use of side-chain packing methods in modeling bacteriophage repressor and cro proteins.

In recent years, it has been repeatedly demonstrated that the coordinates of the main-chain atoms alone are sufficient to determine the side-chain conformations of buried residues of compact proteins. Given a perfect backbone, the side-chain packing method can predict the side-chain conformations to an accuracy as high as 1.2 Å RMS deviation (RMSD) with greater than 80% of the χ angles correct. However, similarly rigorous studies have not been conducted to determine how well these apply, if at all, to the more important problem of homology modeling per se. Specifically, if the available backbone is imperfect, as expected for practical application of homology modeling, can packing constraints alone achieve sufficiently accurate predictions to be useful? Here, by systematically applying such methods to the pairwise modeling of two repressor and two cro proteins from the closely related bacteriophages 434 and P22, we find that when the backbone RMSD is 0.8 Å, the prediction on buried side chain is accurate with an RMS error of 1.8 Å and approximately 70% of the χ angles correctly predicted. When the backbone RMSD is larger, in the range of 1.6–1.8 Å, the prediction quality is still significantly better than random, with RMS error at 2.2 Å on the buried side chains and 60% accuracy on χ angles. Together these results suggest the following rules-of-thumb for homology modeling of buried side chains. When the sequence identity between the modeled sequence and the template sequence is >50% (or, equivalently, the expected backbone RMSD is <1 Å), side-chain packing methods work well. When sequence identity is between 30–50%, reflecting a backbone RMS error of 1–2 Å, it is still valid to use side-chain packing methods to predict the buried residues, albeit with care. When sequence identity is below 30% (or backbone RMS error greater than 2 Å), the backbone constraint alone is unlikely to produce useful models. Other methods, such as those involving the use of database fragments to reconstruct a template backbone, may be necessary as a complementary guide for modeling.     

Antibody modeling assessment

A blinded study to assess the state of the art in three‐dimensional structure modeling of the variable region (Fv) of antibodies was conducted. Nine unpublished high‐resolution x‐ray Fab crystal structures covering a wide range of antigen‐binding site conformations were used as benchmark to compare Fv models generated by four structure prediction methodologies. The methodologies included two homology modeling strategies independently developed by CCG (Chemical Computer Group) and Accerlys Inc, and two fully automated antibody modeling servers: PIGS (Prediction of ImmunoGlobulin Structure), based on the canonical structure model, and Rosetta Antibody Modeling, based on homology modeling and Rosetta structure prediction methodology. The benchmark structure sequences were submitted to Accelrys and CCG and a set of models for each of the nine antibody structures were generated. PIGS and Rosetta models were obtained using the default parameters of the servers. In most cases, we found good agreement between the models and x‐ray structures. The average rmsd (root mean square deviation) values calculated over the backbone atoms between the models and structures were fairly consistent, around 1.2 Å. Average rmsd values of the framework and hypervariable loops with canonical structures (L1, L2, L3, H1, and H2) were close to 1.0 Å. H3 prediction yielded rmsd values around 3.0 Å for most of the models. Quality assessment of the models and the relative strengths and weaknesses of the methods are discussed. We hope this initiative will serve as a model of scientific partnership and look forward to future antibody modeling assessments. Proteins 2011; © 2011 Wiley‐Liss, Inc.     

Loop prediction for a GPCR homology model: Algorithms and results

We present loop structure prediction results of the intracellular and extracellular loops of four G‐protein‐coupled receptors (GPCRs): bovine rhodopsin (bRh), the turkey β1‐adrenergic (β1Ar), the human β2‐adrenergic (β2Ar) and the human A2a adenosine receptor (A2Ar) in perturbed environments. We used the protein local optimization program, which builds thousands of loop candidates by sampling rotamer states of the loops' constituent amino acids. The candidate loops are discriminated between with our physics‐based, all‐atom energy function, which is based on the OPLS force field with implicit solvent and several correction terms. For relevant cases, explicit membrane molecules are included to simulate the effect of the membrane on loop structure. We also discuss a new sampling algorithm that divides phase space into different regions, allowing more thorough sampling of long loops that greatly improves results. In the first half of the paper, loop prediction is done with the GPCRs' transmembrane domains fixed in their crystallographic positions, while the loops are built one‐by‐one. Side chains near the loops are also in non‐native conformations. The second half describes a full homology model of β2Ar using β1Ar as a template. No information about the crystal structure of β2Ar was used to build this homology model. We are able to capture the architecture of short loops and the very long second extracellular loop, which is key for ligand binding. We believe this the first successful example of an RMSD validated, physics‐based loop prediction in the context of a GPCR homology model. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

In silico predictions of 3D structures of linear and cyclic peptides with natural and non‐proteinogenic residues

We extended the use of Peplook, an in silico procedure for the prediction of three‐dimensional (3D) models of linear peptides to the prediction of 3D models of cyclic peptides and thanks to the ab initio calculation procedure, to the calculation of peptides with non‐proteinogenic amino acids. Indeed, such peptides cannot be predicted by homology or threading. We compare the calculated models with NMR and X‐ray models and for the cyclic peptides, with models predicted by other in silico procedures (Pep‐Fold and I‐Tasser). For cyclic peptides, on a set of 38 peptides, average root mean square deviation of backbone atoms (BB‐RMSD) was 3.8 and 4.1 Å for Peplook and Pep‐Fold, respectively. The best results are obtained with I‐Tasser (2.5 Å) although evaluations were biased by the fact that the resolved Protein Data Bank models could be used as template by the server. Peplook and Pep‐Fold give similar results, better for short (up to 20 residues) than for longer peptides. For peptides with non‐proteinogenic residues, performances of Peplook are sound with an average BB‐RMSD of 3.6 Å for ‘non‐natural peptides’ and 3.4 Å for peptides combining non‐proteinogenic residues and cyclic structure. These results open interesting possibilities for the design of peptidic drugs. Copyright © 2011 European Peptide Society and John Wiley & Sons, Ltd.     

The diversity of H3 loops determines the antigen‐binding tendencies of antibody CDR loops

Of the complementarity‐determining regions (CDRs) of antibodies, H3 loops, with varying amino acid sequences and loop lengths, adopt particularly diverse loop conformations. The diversity of H3 conformations produces an array of antigen recognition patterns involving all the CDRs, in which the residue positions actually in contact with the antigen vary considerably. Therefore, for a deeper understanding of antigen recognition, it is necessary to relate the sequence and structural properties of each residue position in each CDR loop to its ability to bind antigens. In this study, we proposed a new method for characterizing the structural features of the CDR loops and obtained the antigen‐binding ability of each residue position in each CDR loop. This analysis led to a simple set of rules for identifying probable antigen‐binding residues. We also found that the diversity of H3 loop lengths and conformations affects the antigen‐binding tendencies of all the CDR loops.     

Protein loop closure using orientational restraints from NMR data

Protein loops often play important roles in biological functions. Modeling loops accurately is crucial to determining the functional specificity of a protein. Despite the recent progress in loop prediction approaches, which led to a number of algorithms over the past decade, few rigorous algorithmic approaches exist to model protein loops using global orientational restraints, such as those obtained from residual dipolar coupling (RDC) data in solution nuclear magnetic resonance (NMR) spectroscopy. In this article, we present a novel, sparse data, RDC‐based algorithm, which exploits the mathematical interplay between RDC‐derived sphero‐conics and protein kinematics, and formulates the loop structure determination problem as a system of low‐degree polynomial equations that can be solved exactly, in closed‐form. The polynomial roots, which encode the candidate conformations, are searched systematically, using provable pruning strategies that triage the vast majority of conformations, to enumerate or prune all possible loop conformations consistent with the data; therefore, completeness is ensured. Results on experimental RDC datasets for four proteins, including human ubiquitin, FF2, DinI, and GB3, demonstrate that our algorithm can compute loops with higher accuracy, a three‐ to six‐fold improvement in backbone RMSD, versus those obtained by traditional structure determination protocols on the same data. Excellent results were also obtained on synthetic RDC datasets for protein loops of length 4, 8, and 12 used in previous studies. These results suggest that our algorithm can be successfully applied to determine protein loop conformations, and hence, will be useful in high‐resolution protein backbone structure determination, including loops, from sparse NMR data. Proteins 2012. © 2011 Wiley Periodicals, Inc.     

Predicting antibody hypervariable loop conformations. II: Minimization and molecular dynamics studies of MCPC603 from many randomly generated loop conformations

We describe a method for predicting the conformations of loops in proteins and its application to four of the complementarity determining regions [CDRs] in the crystallographically determined structure of MCPC603. The method is based on the generation of a large number of randomly generated conformations for the backbone of the loop being studied, followed by either minimization or molecular dynamics followed by minimization starting from these random structures. The details of the algorithm for the generation of the loops are presented in the first paper in this series (Shenkin et al. [submitted]). The results of minimization and molecular dynamics applied to these loops is presented here. For the two shortest CDRs studied (H1 and L2, which are five and seven amino acids long), minimizations and dynamics simulations which ignore interactions of the loop amino acids beyond the carbon beta replicate the conformation of the crystal structure closely. This suggests that these loops fold independently of sequence variation. For the third CDR (L3, which is nine amino acids), those portions of the CDR near its base which are hydrogen bonded to framework are well replicated by our procedures, but the top of the loop shows significant conformational variability. This variability persists when side chain interactions for the MCPC603 sequence are included. For a fourth CDR (H3, which is 11 amino acids long), new low-energy backbone conformations are found; however, only those which are close to the crystal are compatible with the sequence when side chain interactions are taken into account. Results from minimization and dynamics on single CDRs with all other CDRs removed are presented. These allow us to explore the extent to which individual CDR conformations are determined by interactions with framework only.     

Predicting antibody complementarity determining region structures without classification

Antibodies are used extensively in medical and biological research. Their complementarity determining regions (CDRs) define the majority of their antigen binding functionality. CDR structures have been intensively studied and classified (canonical structures). Here we show that CDR structure prediction is no different from the standard loop structure prediction problem and predict them without classification. FREAD, a successful database loop prediction technique, is able to produce accurate predictions for all CDR loops (0.81, 0.42, 0.96, 0.98, 0.88 and 2.25 ? RMSD for CDR-L1 to CDR-H3). In order to overcome the relatively poor predictions of CDR-H3, we developed two variants of FREAD, one focused on sequence similarity (FREAD-S) and another which includes contact information (ConFREAD). Both of the methods improve accuracy for CDR-H3 to 1.34 ? and 1.23 ? respectively. The FREAD variants are also tested on homology models and compared to RosettaAntibody (CDR-H3 prediction on models: 1.98 and 2.62 ? for ConFREAD and RosettaAntibody respectively). CDRs are known to change their structural conformations upon binding the antigen. Traditional CDR classifications are based on sequence similarity and do not account for such environment changes. Using a set of antigen-free and antigen-bound structures, we compared our FREAD variants. ConFREAD which includes contact information successfully discriminates the bound and unbound CDR structures and achieves an accuracy of 1.35 ? for bound structures of CDR-H3.     

High‐accuracy modeling of antibody structures by a search for minimum‐energy recombination of backbone fragments

Current methods for antibody structure prediction rely on sequence homology to known structures. Although this strategy often yields accurate predictions, models can be stereo‐chemically strained. Here, we present a fully automated algorithm, called AbPredict, that disregards sequence homology, and instead uses a Monte Carlo search for low‐energy conformations built from backbone segments and rigid‐body orientations that appear in antibody molecular structures. We find cases where AbPredict selects accurate loop templates with sequence identity as low as 10%, whereas the template of highest sequence identity diverges substantially from the query's conformation. Accordingly, in several cases reported in the recent Antibody Modeling Assessment benchmark, AbPredict models were more accurate than those from any participant, and the models' stereo‐chemical quality was consistently high. Furthermore, in two blind cases provided to us by crystallographers prior to structure determination, the method achieved <1.5 Ångstrom overall backbone accuracy. Accurate modeling of unstrained antibody structures will enable design and engineering of improved binders for biomedical research directly from sequence. Proteins 2016; 85:30–38. © 2016 Wiley Periodicals, Inc.     

Fast Protein Loop Sampling and Structure Prediction Using Distance-Guided Sequential Chain-Growth Monte Carlo Method

Loops in proteins are flexible regions connecting regular secondary structures. They are often involved in protein functions through interacting with other molecules. The irregularity and flexibility of loops make their structures difficult to determine experimentally and challenging to model computationally. Conformation sampling and energy evaluation are the two key components in loop modeling. We have developed a new method for loop conformation sampling and prediction based on a chain growth sequential Monte Carlo sampling strategy, called Distance-guided Sequential chain-Growth Monte Carlo (DiSGro). With an energy function designed specifically for loops, our method can efficiently generate high quality loop conformations with low energy that are enriched with near-native loop structures. The average minimum global backbone RMSD for 1,000 conformations of 12-residue loops is Å, with a lowest energy RMSD of Å, and an average ensemble RMSD of Å. A novel geometric criterion is applied to speed up calculations. The computational cost of generating 1,000 conformations for each of the x loops in a benchmark dataset is only about cpu minutes for 12-residue loops, compared to ca cpu minutes using the FALCm method. Test results on benchmark datasets show that DiSGro performs comparably or better than previous successful methods, while requiring far less computing time. DiSGro is especially effective in modeling longer loops (– residues).     

FREAD revisited: Accurate loop structure prediction using a database search algorithm

Loops are the most variable regions of protein structure and are, in general, the least accurately predicted. Their prediction has been approached in two ways, ab initio and database search. In recent years, it has been thought that ab initio methods are more powerful. In light of the continued rapid expansion in the number of known protein structures, we have re‐evaluated FREAD, a database search method and demonstrate that the power of database search methods may have been underestimated. We found that sequence similarity as quantified by environment specific substitution scores can be used to significantly improve prediction. In fact, FREAD performs appreciably better for an identifiable subset of loops (two thirds of shorter loops and half of the longer loops tested) than the ab initio methods of MODELLER, PLOP, and RAPPER. Within this subset, FREAD's predictive ability is length independent, in general, producing results within 2Å RMSD, compared to an average of over 10Å for loop length 20 for any of the other tested methods. We also benchmarked the prediction protocols on a set of 212 loops from the model structures in CASP 7 and 8. An extended version of FREAD is able to make predictions for 127 of these, it gives the best prediction of the methods tested in 61 of these cases. In examining FREAD's ability to predict in the model environment, we found that whole structure quality did not affect the quality of loop predictions. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Toward better refinement of comparative models: predicting loops in inexact environments

Achieving atomic-level accuracy in comparative protein models is limited by our ability to refine the initial, homolog-derived model closer to the native state. Despite considerable effort, progress in developing a generalized refinement method has been limited. In contrast, methods have been described that can accurately reconstruct loop conformations in native protein structures. We hypothesize that loop refinement in homology models is much more difficult than loop reconstruction in crystal structures, in part, because side-chain, backbone, and other structural inaccuracies surrounding the loop create a challenging sampling problem; the loop cannot be refined without simultaneously refining adjacent portions. In this work, we single out one sampling issue in an artificial but useful test set and examine how loop refinement accuracy is affected by errors in surrounding side-chains. In 80 high-resolution crystal structures, we first perturbed 6-12 residue loops away from the crystal conformation, and placed all protein side chains in non-native but low energy conformations. Even these relatively small perturbations in the surroundings made the loop prediction problem much more challenging. Using a previously published loop prediction method, median backbone (N-Calpha-C-O) RMSD's for groups of 6, 8, 10, and 12 residue loops are 0.3/0.6/0.4/0.6 A, respectively, on native structures and increase to 1.1/2.2/1.5/2.3 A on the perturbed cases. We then augmented our previous loop prediction method to simultaneously optimize the rotamer states of side chains surrounding the loop. Our results show that this augmented loop prediction method can recover the native state in many perturbed structures where the previous method failed; the median RMSD's for the 6, 8, 10, and 12 residue perturbed loops improve to 0.4/0.8/1.1/1.2 A. Finally, we highlight three comparative models from blind tests, in which our new method predicted loops closer to the native conformation than first modeled using the homolog template, a task generally understood to be difficult. Although many challenges remain in refining full comparative models to high accuracy, this work offers a methodical step toward that goal.     

A divide and conquer approach to fast loop modeling

We describe a fast ab initio method for modeling local segments in protein structures. The algorithm is based on a divide and conquer approach and uses a database of precalculated look-up tables, which represent a large set of possible conformations for loop segments of variable length. The target loop is recursively decomposed until the resulting conformations are small enough to be compiled analytically. The algorithm, which is not restricted to any specific loop length, generates a ranked set of loop conformations in 20-180 s on a desktop PC. The prediction quality is evaluated in terms of global RMSD. Depending on loop length the top prediction varies between 1.06 A RMSD for three-residue loops and 3.72 A RMSD for eight-residue loops. Due to its speed the method may also be useful to generate alternative starting conformations for complex simulations.     

Does conformational free energy distinguish loop conformations in proteins?

Limitations in protein homology modeling often arise from the inability to adequately model loops. In this paper we focus on the selection of loop conformations. We present a complete computational treatment that allows the screening of loop conformations to identify those that best fit a molecular model. The stability of a loop in a protein is evaluated via computations of conformational free energies in solution, i.e., the free energy difference between the reference structure and the modeled one. A thermodynamic cycle is used for calculation of the conformational free energy, in which the total free energy of the reference state (i.e., gas phase) is the CHARMm potential energy. The electrostatic contribution of the solvation free energy is obtained from solving the finite-difference Poisson-Boltzmann equation. The nonpolar contribution is based on a surface area-based expression. We applied this computational scheme to a simple but well-characterized system, the antibody hypervariable loop (complementarity-determining region, CDR). Instead of creating loop conformations, we generated a database of loops extracted from high-resolution crystal structures of proteins, which display geometrical similarities with antibody CDRs. We inserted loops from our database into a framework of an antibody; then we calculated the conformational free energies of each loop. Results show that we successfully identified loops with a "reference-like" CDR geometry, with the lowest conformational free energy in gas phase only. Surprisingly, the solvation energy term plays a confusing role, sometimes discriminating "reference-like" CDR geometry and many times allowing "non-reference-like" conformations to have the lowest conformational free energies (for short loops). Most "reference-like" loop conformations are separated from others by a gap in the gas phase conformational free energy scale. Naturally, loops from antibody molecules are found to be the best models for long CDRs (> or = 6 residues), mainly because of a better packing of backbone atoms into the framework of the antibody model.     

MoFvAb: Modeling the Fv region of antibodies

Knowledge of the 3-dimensional structure of the antigen-binding region of antibodies enables numerous useful applications regarding the design and development of antibody-based drugs. We present a knowledge-based antibody structure prediction methodology that incorporates concepts that have arisen from an applied antibody engineering environment. The protocol exploits the rich and continuously growing supply of experimentally derived antibody structures available to predict CDR loop conformations and the packing of heavy and light chain quickly and without user intervention. The homology models are refined by a novel antibody-specific approach to adapt and rearrange sidechains based on their chemical environment. The method achieves very competitive all-atom root mean square deviation values in the order of 1.5 Å on different evaluation datasets consisting of both known and previously unpublished antibody crystal structures.     

New computational method for prediction of interacting protein loop regions

Flexible loop regions of proteins play a crucial role in many biological functions such as protein–ligand recognition, enzymatic catalysis, and protein–protein association. To date, most computational methods that predict the conformational states of loops only focus on individual loop regions. However, loop regions are often spatially in close proximity to one another and their mutual interactions stabilize their conformations. We have developed a new method, titled CorLps, capable of simultaneously predicting such interacting loop regions. First, an ensemble of individual loop conformations is generated for each loop region. The members of the individual ensembles are combined and are accepted or rejected based on a steric clash filter. After a subsequent side‐chain optimization step, the resulting conformations of the interacting loops are ranked by the statistical scoring function DFIRE that originated from protein structure prediction. Our results show that predicting interacting loops with CorLps is superior to sequential prediction of the two interacting loop regions, and our method is comparable in accuracy to single loop predictions. Furthermore, improved predictive accuracy of the top‐ranked solution is achieved for 12‐residue length loop regions by diversifying the initial pool of individual loop conformations using a quality threshold clustering algorithm. Proteins 2010. © 2010 Wiley‐Liss, Inc.