Principles for computational design of binding antibodies.

Natural proteins must both fold into a stable conformation and exert their molecular function. To date, computational design has successfully produced stable and atomically accurate proteins by using so-called "ideal" folds rich in regular secondary structures and almost devoid of loops and destabilizing elements, such as cavities. Molecular function, such as binding and catalysis, however, often demands nonideal features, including large and irregular loops and buried polar interaction networks, which have remained challenging for fold design. Through five design/experiment cycles, we learned principles for designing stable and functional antibody variable fragments (Fvs). Specifically, we (i) used sequence-design constraints derived from antibody multiple-sequence alignments, and (ii) during backbone design, maintained stabilizing interactions observed in natural antibodies between the framework and loops of complementarity-determining regions (CDRs) 1 and 2. Designed Fvs bound their ligands with midnanomolar affinities and were as stable as natural antibodies, despite having >30 mutations from mammalian antibody germlines. Furthermore, crystallographic analysis demonstrated atomic accuracy throughout the framework and in four of six CDRs in one design and atomic accuracy in the entire Fv in another. The principles we learned are general, and can be implemented to design other nonideal folds, generating stable, specific, and precise antibodies and enzymes.

Combined covalent-electrostatic model of hydrogen bonding improves structure prediction with Rosetta.

Interactions between polar atoms are challenging to model because at very short ranges they form hydrogen bonds (H-bonds) that are partially covalent in character and exhibit strong orientation preferences; at longer ranges the orientation preferences are lost, but significant electrostatic interactions between charged and partially charged atoms remain. To simultaneously model these two types of behavior, we refined an orientation dependent model of hydrogen bonds [Kortemme et al. J. Mol. Biol. 2003, 326, 1239] used by the molecular modeling program Rosetta and then combined it with a distance-dependent Coulomb model of electrostatics. The functional form of the H-bond potential is physically motivated and parameters are fit so that H-bond geometries that Rosetta generates closely resemble H-bond geometries in high-resolution crystal structures. The combined potentials improve performance in a variety of scientific benchmarks including decoy discrimination, side chain prediction, and native sequence recovery in protein design simulations and establishes a new standard energy function for Rosetta.

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

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 five cases interface sequence identity is above 30%, and in four of those the backbone conformation at the core of the antibody binding surface is within 1 Å root-mean square deviation from the natural antibodies. Designs recapitulate polar interaction networks observed in natural complexes, and amino acid sidechain rigidity at the designed binding surface, which is likely important for affinity and specificity, is high compared to previous design studies. In designed anti-lysozyme antibodies, complementarity-determining regions (CDRs) at the periphery of the interface, such as L1 and H2, show greater backbone conformation diversity than the CDRs at the core of the interface, and increase the binding surface area compared to the natural antibody, potentially enhancing affinity and specificity.

Relaxation of backbone bond geometry improves protein energy landscape modeling.

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine-grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse-grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large-scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non-native structures. We also find that incorporating bonded geometry flexibility improves low resolution X-ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.

Efficient sampling of protein conformational space using fast loop building and batch minimization on highly parallel computers.

All-atom sampling is a critical and compute-intensive end stage to protein structural modeling. Because of the vast size and extreme ruggedness of conformational space, even close to the native structure, the high-resolution sampling problem is almost as difficult as predicting the rough fold of a protein. Here, we present a combination of new algorithms that considerably speed up the exploration of very rugged conformational landscapes and are capable of finding heretofore hidden low-energy states. The algorithm is based on a hierarchical workflow and can be parallelized on supercomputers with up to 128,000 compute cores with near perfect efficiency. Such scaling behavior is notable, as with Moore's law continuing only in the number of cores per chip, parallelizability is a critical property of new algorithms. Using the enhanced sampling power, we have uncovered previously invisible deficiencies in the Rosetta force field and created an extensive decoy training set for optimizing and testing force fields.

Algorithm discovery by protein folding game players.

Foldit is a multiplayer online game in which players collaborate and compete to create accurate protein structure models. For specific hard problems, Foldit player solutions can in some cases outperform state-of-the-art computational methods. However, very little is known about how collaborative gameplay produces these results and whether Foldit player strategies can be formalized and structured so that they can be used by computers. To determine whether high performing player strategies could be collectively codified, we augmented the Foldit gameplay mechanics with tools for players to encode their folding strategies as "recipes" and to share their recipes with other players, who are able to further modify and redistribute them. Here we describe the rapid social evolution of player-developed folding algorithms that took place in the year following the introduction of these tools. Players developed over 5,400 different recipes, both by creating new algorithms and by modifying and recombining successful recipes developed by other players. The most successful recipes rapidly spread through the Foldit player population, and two of the recipes became particularly dominant. Examination of the algorithms encoded in these two recipes revealed a striking similarity to an unpublished algorithm developed by scientists over the same period. Benchmark calculations show that the new algorithm independently discovered by scientists and by Foldit players outperforms previously published methods. Thus, online scientific game frameworks have the potential not only to solve hard scientific problems, but also to discover and formalize effective new strategies and algorithms.

Modeling disordered regions in proteins using Rosetta.

Protein structure prediction methods such as Rosetta search for the lowest energy conformation of the polypeptide chain. However, the experimentally observed native state is at a minimum of the free energy, rather than the energy. The neglect of the missing configurational entropy contribution to the free energy can be partially justified by the assumption that the entropies of alternative folded states, while very much less than unfolded states, are not too different from one another, and hence can be to a first approximation neglected when searching for the lowest free energy state. The shortcomings of current structure prediction methods may be due in part to the breakdown of this assumption. Particularly problematic are proteins with significant disordered regions which do not populate single low energy conformations even in the native state. We describe two approaches within the Rosetta structure modeling methodology for treating such regions. The first does not require advance knowledge of the regions likely to be disordered; instead these are identified by minimizing a simple free energy function used previously to model protein folding landscapes and transition states. In this model, residues can be either completely ordered or completely disordered; they are considered disordered if the gain in entropy outweighs the loss of favorable energetic interactions with the rest of the protein chain. The second approach requires identification in advance of the disordered regions either from sequence alone using for example the DISOPRED server or from experimental data such as NMR chemical shifts. During Rosetta structure prediction calculations the disordered regions make only unfavorable repulsive contributions to the total energy. We find that the second approach has greater practical utility and illustrate this with examples from de novo structure prediction, NMR structure calculation, and comparative modeling.

Structure-guided forcefield optimization.

Accurate modeling of biomolecular systems requires accurate forcefields. Widely used molecular mechanics (MM) forcefields obtain parameters from experimental data and quantum chemistry calculations on small molecules but do not have a clear way to take advantage of the information in high-resolution macromolecular structures. In contrast, knowledge-based methods largely ignore the physical chemistry of interatomic interactions, and instead derive parameters almost exclusively from macromolecular structures. This can involve considerable double counting of the same physical interactions. Here, we describe a method for forcefield improvement that combines the strengths of the two approaches. We use this method to improve the Rosetta all-atom forcefield, in which the total energy is expressed as the sum of terms representing different physical interactions as in MM forcefields and the parameters are tuned to reproduce the properties of macromolecular structures. To resolve inaccuracies resulting from possible double counting of interactions, we compare distribution functions from low-energy modeled structures to those from crystal structures. The structural and physical bases of the deviations between the modeled and reference structures are identified and used to guide forcefield improvements. We describe improvements resolving double counting between backbone hydrogen bond interactions and Lennard-Jones interactions in helices; between sidechain-backbone hydrogen bonds and the backbone torsion potential; and between the sidechain torsion potential and Lennard-Jones interactions. Discrepancies between computed and observed distributions are also used to guide the incorporation of an explicit Cα-hydrogen bond in ß sheets. The method can be used generally to integrate different sources of information for forcefield improvement.

Alternate states of proteins revealed by detailed energy landscape mapping.

What conformations do protein molecules populate in solution? Crystallography provides a high-resolution description of protein structure in the crystal environment, while NMR describes structure in solution but using less data. NMR structures display more variability, but is this because crystal contacts are absent or because of fewer data constraints? Here we report unexpected insight into this issue obtained through analysis of detailed protein energy landscapes generated by large-scale, native-enhanced sampling of conformational space with Rosetta@home for 111 protein domains. In the absence of tightly associating binding partners or ligands, the lowest-energy Rosetta models were nearly all <2.5 Å C(α)RMSD from the experimental structure; this result demonstrates that structure prediction accuracy for globular proteins is limited mainly by the ability to sample close to the native structure. While the lowest-energy models are similar to deposited structures, they are not identical; the largest deviations are most often in regions involved in ligand, quaternary, or crystal contacts. For ligand binding proteins, the low energy models may resemble the apo structures, and for oligomeric proteins, the monomeric assembly intermediates. The deviations between the low energy models and crystal structures largely disappear when landscapes are computed in the context of the crystal lattice or multimer. The computed low-energy ensembles, with tight crystal-structure-like packing in the core, but more NMR-structure-like variability in loops, may in some cases resemble the native state ensembles of proteins better than individual crystal or NMR structures, and can suggest experimentally testable hypotheses relating alternative states and structural heterogeneity to function.

ROSETTA3: an object-oriented software suite for the simulation and design of macromolecules.

We have recently completed a full re-architecturing of the ROSETTA molecular modeling program, generalizing and expanding its existing functionality. The new architecture enables the rapid prototyping of novel protocols by providing easy-to-use interfaces to powerful tools for molecular modeling. The source code of this rearchitecturing has been released as ROSETTA3 and is freely available for academic use. At the time of its release, it contained 470,000 lines of code. Counting currently unpublished protocols at the time of this writing, the source includes 1,285,000 lines. Its rapid growth is a testament to its ease of use. This chapter describes the requirements for our new architecture, justifies the design decisions, sketches out central classes, and highlights a few of the common tasks that the new software can perform.

NMR structure determination for larger proteins using backbone-only data.

Conventional protein structure determination from nuclear magnetic resonance data relies heavily on side-chain proton-to-proton distances. The necessary side-chain resonance assignment, however, is labor intensive and prone to error. Here we show that structures can be accurately determined without nuclear magnetic resonance (NMR) information on the side chains for proteins up to 25 kilodaltons by incorporating backbone chemical shifts, residual dipolar couplings, and amide proton distances into the Rosetta protein structure modeling methodology. These data, which are too sparse for conventional methods, serve only to guide conformational search toward the lowest-energy conformations in the folding landscape; the details of the computed models are determined by the physical chemistry implicit in the Rosetta all-atom energy function. The new method is not hindered by the deuteration required to suppress nuclear relaxation processes for proteins greater than 15 kilodaltons and should enable routine NMR structure determination for larger proteins.

Prediction of structures of zinc-binding proteins through explicit modeling of metal coordination geometry.

Metal ions play an essential role in stabilizing protein structures and contributing to protein function. Ions such as zinc have well-defined coordination geometries, but it has not been easy to take advantage of this knowledge in protein structure prediction efforts. Here, we present a computational method to predict structures of zinc-binding proteins given knowledge of the positions of zinc-coordinating residues in the amino acid sequence. The method takes advantage of the "atom-tree" representation of molecular systems and modular architecture of the Rosetta3 software suite to incorporate explicit metal ion coordination geometry into previously developed de novo prediction and loop modeling protocols. Zinc cofactors are tethered to their interacting residues based on coordination geometries observed in natural zinc-binding proteins. The incorporation of explicit zinc atoms and their coordination geometry in both de novo structure prediction and loop modeling significantly improves sampling near the native conformation. The method can be readily extended to predict protein structures bound to other metal and/or small chemical cofactors with well-defined coordination or ligation geometry.

Structure prediction for CASP8 with all-atom refinement using Rosetta.

We describe predictions made using the Rosetta structure prediction methodology for the Eighth Critical Assessment of Techniques for Protein Structure Prediction. Aggressive sampling and all-atom refinement were carried out for nearly all targets. A combination of alignment methodologies was used to generate starting models from a range of templates, and the models were then subjected to Rosetta all atom refinement. For the 64 domains with readily identified templates, the best submitted model was better than the best alignment to the best template in the Protein Data Bank for 24 cases, and improved over the best starting model for 43 cases. For 13 targets where only very distant sequence relationships to proteins of known structure were detected, models were generated using the Rosetta de novo structure prediction methodology followed by all-atom refinement; in several cases the submitted models were better than those based on the available templates. Of the 12 refinement challenges, the best submitted model improved on the starting model in seven cases. These improvements over the starting template-based models and refinement tests demonstrate the power of Rosetta structure refinement in improving model accuracy.

Refinement of protein structures into low-resolution density maps using rosetta.

We describe a method based on Rosetta structure refinement for generating high-resolution, all-atom protein models from electron cryomicroscopy density maps. A local measure of the fit of a model to the density is used to directly guide structure refinement and to identify regions incompatible with the density that are then targeted for extensive rebuilding. Over a range of test cases using both simulated and experimentally generated data, the method consistently increases the accuracy of starting models generated either by comparative modeling or by hand-tracing the density. The method can achieve near-atomic resolution starting from density maps at 4-6 A resolution.

Structure prediction for CASP7 targets using extensive all-atom refinement with Rosetta@home.

We describe predictions made using the Rosetta structure prediction methodology for both template-based modeling and free modeling categories in the Seventh Critical Assessment of Techniques for Protein Structure Prediction. For the first time, aggressive sampling and all-atom refinement could be carried out for the majority of targets, an advance enabled by the Rosetta@home distributed computing network. Template-based modeling predictions using an iterative refinement algorithm improved over the best existing templates for the majority of proteins with less than 200 residues. Free modeling methods gave near-atomic accuracy predictions for several targets under 100 residues from all secondary structure classes. These results indicate that refinement with an all-atom energy function, although computationally expensive, is a powerful method for obtaining accurate structure predictions.

Absolute free-energy calculations of liquids using a harmonic reference state.

Absolute free-energy methods provide a potential solution to the overlap problem in free-energy calculations. In this paper, we report an extension of the previously published confinement method (J. Phys. Chem. B 2006, 110, 17212-20) to fluid simulations. Absolute free energies of liquid argon and liquid water are obtained accurately and compared with results from thermodynamic integration. The method works by transforming the liquid state into a harmonic, solid reference state. This is achieved using a special restraint potential that allows molecules to change their restraint position during the simulation, which circumvents the need for the molecules to sample the full extent of their translational freedom. The absolute free energy of the completely restrained reference state is obtained from a normal mode calculation. Because of the generic reference state used, the method is applicable to nonhomogeneous, diffusive systems and could provide an alternative method in situations in which solute annihilation fails due to the size of the solute. Potential applications include calculation of solvation energies of large molecules and free energies of peptide conformational changes in explicit solvent.

An efficient, path-independent method for free-energy calculations.

Classical free-energy methods depend on the definition of physical or nonphysical integration paths to calculate free-energy differences between states. This procedure can be problematic and computationally expensive when the states of interest do not overlap and are far apart in phase space. Here we introduce a novel method to calculate free-energy differences that is path-independent by transforming each end state into a reference state in which the vibrational entropy is the sole component of the total entropy, thus allowing direct computation of the relative free energy. We apply the method to calculate side-chain entropies of a beta-hairpin-forming peptide in a variety of backbone conformations, demonstrating its importance in determining structural propensities. We find that low-free-energy conformations achieve their stability through optimal trade off between enthalpic gains due to favorable interatomic interactions and entropic losses incurred by the same.