Benchmarking a computational design method for the incorporation of metal ion‐binding sites at symmetric protein interfaces

The design of novel metal‐ion binding sites along symmetric axes in protein oligomers could provide new avenues for metalloenzyme design, construction of protein‐based nanomaterials and novel ion transport systems. Here, we describe a computational design method, symmetric protein recursive ion‐cofactor sampling (SyPRIS), for locating constellations of backbone positions within oligomeric protein structures that are capable of supporting desired symmetrically coordinated metal ion(s) chelated by sidechains (chelant model). Using SyPRIS on a curated benchmark set of protein structures with symmetric metal binding sites, we found high recovery of native metal coordinating rotamers: in 65 of the 67 (97.0%) cases, native rotamers featured in the best scoring model while in the remaining cases native rotamers were found within the top three scoring models. In a second test, chelant models were crossmatched against protein structures with identical cyclic symmetry. In addition to recovering all native placements, 10.4% (8939/86013) of the non‐native placements, had acceptable geometric compatibility scores. Discrimination between native and non‐native metal site placements was further enhanced upon constrained energy minimization using the Rosetta energy function. Upon sequence design of the surrounding first‐shell residues, we found further stabilization of native placements and a small but significant (1.7%) number of non‐native placement‐based sites with favorable Rosetta energies, indicating their designability in existing protein interfaces. The generality of the SyPRIS approach allows design of novel symmetric metal sites including with non‐natural amino acid sidechains, and should enable the predictive incorporation of a variety of metal‐containing cofactors at symmetric protein interfaces.     

A simple reference state makes a significant improvement in near-native selections from structurally refined docking decoys

Near-native selections from docking decoys have proved challenging especially when unbound proteins are used in the molecular docking. One reason is that significant atomic clashes in docking decoys lead to poor predictions of binding affinities of near native decoys. Atomic clashes can be removed by structural refinement through energy minimization. Such an energy minimization, however, will lead to an unrealistic bias toward docked structures with large interfaces. Here, we extend an empirical energy function developed for protein design to protein-protein docking selection by introducing a simple reference state that removes the unrealistic dependence of binding affinity of docking decoys on the buried solvent accessible surface area of interface. The energy function called EMPIRE (EMpirical Protein-InteRaction Energy), when coupled with a refinement strategy, is found to provide a significantly improved success rate in near native selections when applied to RosettaDock and refined ZDOCK docking decoys. Our work underlines the importance of removing nonspecific interactions from specific ones in near native selections from docking decoys.     

Systematic optimization model and algorithm for binding sequence selection in computational enzyme design

A systematic optimization model for binding sequence selection in computational enzyme design was developed based on the transition state theory of enzyme catalysis and graph‐theoretical modeling. The saddle point on the free energy surface of the reaction system was represented by catalytic geometrical constraints, and the binding energy between the active site and transition state was minimized to reduce the activation energy barrier. The resulting hyperscale combinatorial optimization problem was tackled using a novel heuristic global optimization algorithm, which was inspired and tested by the protein core sequence selection problem. The sequence recapitulation tests on native active sites for two enzyme catalyzed hydrolytic reactions were applied to evaluate the predictive power of the design methodology. The results of the calculation show that most of the native binding sites can be successfully identified if the catalytic geometrical constraints and the structural motifs of the substrate are taken into account. Reliably predicting active site sequences may have significant implications for the creation of novel enzymes that are capable of catalyzing targeted chemical reactions.     

On the Importance of the Distance Measures Used to Train and Test Knowledge-Based Potentials for Proteins

Knowledge-based potentials are energy functions derived from the analysis of databases of protein structures and sequences. They can be divided into two classes. Potentials from the first class are based on a direct conversion of the distributions of some geometric properties observed in native protein structures into energy values, while potentials from the second class are trained to mimic quantitatively the geometric differences between incorrectly folded models and native structures. In this paper, we focus on the relationship between energy and geometry when training the second class of knowledge-based potentials. We assume that the difference in energy between a decoy structure and the corresponding native structure is linearly related to the distance between the two structures. We trained two distance-based knowledge-based potentials accordingly, one based on all inter-residue distances (PPD), while the other had the set of all distances filtered to reflect consistency in an ensemble of decoys (PPE). We tested four types of metric to characterize the distance between the decoy and the native structure, two based on extrinsic geometry (RMSD and GTD-TS*), and two based on intrinsic geometry (Q* and MT). The corresponding eight potentials were tested on a large collection of decoy sets. We found that it is usually better to train a potential using an intrinsic distance measure. We also found that PPE outperforms PPD, emphasizing the benefits of capturing consistent information in an ensemble. The relevance of these results for the design of knowledge-based potentials is discussed.     

A knowledge-based potential function predicts the specificity and relative binding energy of RNA-binding proteins

RNA-protein interactions are fundamental to gene expression. Thus, the molecular basis for the sequence dependence of protein-RNA recognition has been extensively studied experimentally. However, there have been very few computational studies of this problem, and no sustained attempt has been made towards using computational methods to predict or alter the sequence-specificity of these proteins. In the present study, we provide a distance-dependent statistical potential function derived from our previous work on protein-DNA interactions. This potential function discriminates native structures from decoys, successfully predicts the native sequences recognized by sequence-specific RNA-binding proteins, and recapitulates experimentally determined relative changes in binding energy due to mutations of individual amino acids at protein-RNA interfaces. Thus, this work demonstrates that statistical models allow the quantitative analysis of protein-RNA recognition based on their structure and can be applied to modeling protein-RNA interfaces for prediction and design purposes.     

Free energies for coarse-grained proteins by integrating multibody statistical contact potentials with entropies from elastic network models

We propose a novel method of calculation of free energy for coarse grained models of proteins by combining our newly developed multibody potentials with entropies computed from elastic network models of proteins. Multi-body potentials have been of much interest recently because they take into account three dimensional interactions related to residue packing and capture the cooperativity of these interactions in protein structures. Combining four-body non-sequential, four-body sequential and pairwise short range potentials with optimized weights for each term, our coarse-grained potential improved recognition of native structure among misfolded decoys, outperforming all other contact potentials for CASP8 decoy sets and performance comparable to the fully atomic empirical DFIRE potentials. By combing statistical contact potentials with entropies from elastic network models of the same structures we can compute free energy changes and improve coarse-grained modeling of protein structure and dynamics. The consideration of protein flexibility and dynamics should improve protein structure prediction and refinement of computational models. This work is the first to combine coarse-grained multibody potentials with an entropic model that takes into account contributions of the entire structure, investigating native-like decoy selection.     

Using the Unfolded State as the Reference State Improves the Performance of Statistical Potentials

Distance-dependent statistical potentials are an important class of energy functions extensively used in modeling protein structures and energetics. These potentials are obtained by statistically analyzing the proximity of atoms in all combinatorial amino-acid pairs in proteins with known structures. In model evaluation, the statistical potential is usually subtracted by the value of a reference state for better selectivity. An ideal reference state should include the general chemical properties of polypeptide chains so that only the unique factors stabilizing the native structures are retained after calibrating on reference state. However, reference states available as of this writing rarely model specific chemical constraints of peptide bonds and therefore poorly reflect the behavior of polypeptide chains. In this work, we proposed a statistical potential based on unfolded state ensemble (SPOUSE), where the reference state is summarized from the unfolded state ensembles of proteins produced according to the statistical coil model. Due to its better representation of the features of polypeptides, SPOUSE outperforms three of the most widely used distance-dependent potentials not only in native conformation identification, but also in the selection of close-to-native models and correlation coefficients between energy and model error. Furthermore, SPOUSE shows promising possibility of further improvement by integration with the orientation-dependent side-chain potentials.     

A "solvated rotamer" approach to modeling water-mediated hydrogen bonds at protein-protein interfaces

Water-mediated hydrogen bonds play critical roles at protein-protein and protein-nucleic acid interfaces, and the interactions formed by discrete water molecules cannot be captured using continuum solvent models. We describe a simple model for the energetics of water-mediated hydrogen bonds, and show that, together with knowledge of the positions of buried water molecules observed in X-ray crystal structures, the model improves the prediction of free-energy changes upon mutation at protein-protein interfaces, and the recovery of native amino acid sequences in protein interface design calculations. We then describe a "solvated rotamer" approach to efficiently predict the positions of water molecules, at protein-protein interfaces and in monomeric proteins, that is compatible with widely used rotamer-based side-chain packing and protein design algorithms. Finally, we examine the extent to which the predicted water molecules can be used to improve prediction of amino acid identities and protein-protein interface stability, and discuss avenues for overcoming current limitations of the approach.     

Match_Motif: A rapid computational tool to assist in protein–protein interaction design

In order to generate protein assemblies with a desired function, the rational design of protein–protein binding interfaces is of significant interest. Approaches based on random mutagenesis or directed evolution may involve complex experimental selection procedures. Also, molecular modeling approaches to design entirely new proteins and interactions with partner molecules can involve large computational efforts and screening steps. In order to simplify at least the initial effort for designing a putative binding interface between two proteins the Match_Motif approach has been developed. It employs the large collection of known protein–protein complex structures to suggest interface modifications that may lead to improved binding for a desired input interaction geometry. The approach extracts interaction motifs based on the backbone structure of short (four residues) segments and the relative arrangement with respect to short segments on the partner protein. The interaction geometry is used to search through a database of such motifs in known stable bound complexes. All matches are rapidly identified (within a few seconds) and collected and can be used to guide changes in the interface that may lead to improved binding. In the output, an alternative interface structure is also proposed based on the frequency of occurrence of side chains at a given interface position in all matches and based on sterical considerations. Applications of the procedure to known complex structures and alternative arrangements are presented and discussed. The program, data files, and example applications can be downloaded from https://www.groups.ph.tum.de/t38/downloads/.     

Tertiary motifs as building blocks for the design of protein‐binding peptides

Despite advances in protein engineering, the de novo design of small proteins or peptides that bind to a desired target remains a difficult task. Most computational methods search for binder structures in a library of candidate scaffolds, which can lead to designs with poor target complementarity and low success rates. Instead of choosing from pre‐defined scaffolds, we propose that custom peptide structures can be constructed to complement a target surface. Our method mines tertiary motifs (TERMs) from known structures to identify surface‐complementing fragments or “seeds.” We combine seeds that satisfy geometric overlap criteria to generate peptide backbones and score the backbones to identify the most likely binding structures. We found that TERM‐based seeds can describe known binding structures with high resolution: the vast majority of peptide binders from 486 peptide‐protein complexes can be covered by seeds generated from single‐chain structures. Furthermore, we demonstrate that known peptide structures can be reconstructed with high accuracy from peptide‐covering seeds. As a proof of concept, we used our method to design 100 peptide binders of TRAF6, seven of which were predicted by Rosetta to form higher‐quality interfaces than a native binder. The designed peptides interact with distinct sites on TRAF6, including the native peptide‐binding site. These results demonstrate that known peptide‐binding structures can be constructed from TERMs in single‐chain structures and suggest that TERM information can be applied to efficiently design novel target‐complementing binders.     

Comparing folding codes for proteins and polymers

Proteins fold to unique compact native structures. Perhaps other polymers could be designed to fold in similar ways. The chemical nature of the monomer “alphabet” determines the “energy matrix” of monomer interactions—which defines the folding code, the relationship between sequence and structure. We study two properties of energy matrices using two-dimensional lattice models: uniqueness, the number of sequences that fold to only one structure, and encodability, the number of folds that are unique lowest-energy structures of certain monomer sequences. For the simplest model folding code, involving binary sequences of H (hydrophobic) and P (polar) monomers, only a small fraction of sequences fold uniquely, and not all structures can be encoded. Adding strong repulsive interactions results in a folding code with more sequences folding uniquely and more designable folds. Some theories suggest that the quality of a folding code depends only on the number of letters in the monomer alphabet, but we find that the energy matrix itself can be at least as important as the size of the alphabet. Certain multi-letter codes, including some with 20 letters, may be less physical or protein-like than codes with smaller numbers of letters because they neglect correlations among inter-residue interactions, treat only maximally compact conformations, or add arbitrary energies to the energy matrix.     

Assessing the energy landscape of CAPRI targets by FunHunt

RosettaDock has repeatedly created high-resolution structures of protein complexes in the CAPRI experiment, thanks to the explicit modeling of conformational changes of the monomers at the side chain level. These models can be selected based on their energy. During the search for the lowest-energy model, RosettaDock samples a deep funnel around the native orientation, but additional funnels may appear in the energy landscape, especially in cases where backbone conformational changes occur upon binding. We have previously developed FunHunt, a Support Vector Machine-based classifier that distinguishes the energy funnels around the native orientation from other funnels in the energy landscape. Here we assess the ability of FunHunt to help in model selection in the CAPRI experiment. For all of 12 recent CAPRI targets, FunHunt clearly identifies a near-native funnel in comparison to the funnel around the lowest energy model identified by the RosettaDock global search protocol. FunHunt is also able to choose a near-native orientation among models submitted by predictor groups, demonstrating its general applicability for model selection. This suggests that FunHunt will be a valuable tool in coming CAPRI rounds for the selection of models, and for the definition of regions that need further refinement with restricted backbone flexibility.     

A simple physical model for the prediction and design of protein-DNA interactions

Protein-DNA interactions are crucial for many biological processes. Attempts to model these interactions have generally taken the form of amino acid-base recognition codes or purely sequence-based profile methods, which depend on the availability of extensive sequence and structural information for specific structural families, neglect side-chain conformational variability, and lack generality beyond the structural family used to train the model. Here, we take advantage of recent advances in rotamer-based protein design and the large number of structurally characterized protein-DNA complexes to develop and parameterize a simple physical model for protein-DNA interactions. The model shows considerable promise for redesigning amino acids at protein-DNA interfaces, as design calculations recover the amino acid residue identities and conformations at these interfaces with accuracies comparable to sequence recovery in globular proteins. The model shows promise also for predicting DNA-binding specificity for fixed protein sequences: native DNA sequences are selected correctly from pools of competing DNA substrates; however, incorporation of backbone movement will likely be required to improve performance in homology modeling applications. Interestingly, optimization of zinc finger protein amino acid sequences for high-affinity binding to specific DNA sequences results in proteins with little or no predicted specificity, suggesting that naturally occurring DNA-binding proteins are optimized for specificity rather than affinity. When combined with algorithms that optimize specificity directly, the simple computational model developed here should be useful for the engineering of proteins with novel DNA-binding specificities.     

An accurate, residue-level, pair potential of mean force for folding and binding based on the distance-scaled, ideal-gas reference state

Structure prediction on a genomic scale requires a simplified energy function that can efficiently sample the conformational space of polypeptide chains. A good energy function at minimum should discriminate native structures against decoys. Here, we show that a recently developed, residue-specific, all-atom knowledge-based potential (167 atomic types) based on distance-scaled, finite ideal-gas reference state (DFIRE-all-atom) can be substantially simplified to 20 residue types located at side-chain center of mass (DFIRE-SCM) without a significant change in its capability of structure discrimination. Using 96 standard multiple decoy sets, we show that there is only a small reduction (from 80% to 78%) in success rate of ranking native structures as the top 1. The success rate is higher than two previously developed, all-atom distance-dependent statistical pair potentials. Applied to structure selections of 21 docking decoys without modification, the DFIRE-SCM potential is 29% more successful in recognizing native complex structures than an all-atom statistical potential trained by a database of dimeric interfaces. The potential also achieves 92% accuracy in distinguishing true dimeric interfaces from artificial crystal interfaces. In addition, the DFIRE potential with the C(alpha) positions as the interaction centers recognizes 123 native structures out of a comprehensive 125-protein TOUCHSTONE decoy set in which each protein has 24,000 decoys with only C(alpha) positions. Furthermore, the performance by DFIRE-SCM on newly established 25 monomeric and 31 docking Rosetta-decoy sets is comparable to (or better than in the case of monomeric decoy sets) that of a recently developed, all-atom Rosetta energy function enhanced with an orientation-dependent hydrogen bonding potential.     

A physical reference state unifies the structure-derived potential of mean force for protein folding and binding

Extracting knowledge-based statistical potential from known structures of proteins is proved to be a simple, effective method to obtain an approximate free-energy function. However, the different compositions of amino acid residues at the core, the surface, and the binding interface of proteins prohibited the establishment of a unified statistical potential for folding and binding despite the fact that the physical basis of the interaction (water-mediated interaction between amino acids) is the same. Recently, a physical state of ideal gas, rather than a statistically averaged state, has been used as the reference state for extracting the net interaction energy between amino acid residues of monomeric proteins. Here, we find that this monomer-based potential is more accurate than an existing all-atom knowledge-based potential trained with interfacial structures of dimers in distinguishing native complex structures from docking decoys (100% success rate vs. 52% in 21 dimer/trimer decoy sets). It is also more accurate than a recently developed semiphysical empirical free-energy functional enhanced by an orientation-dependent hydrogen-bonding potential in distinguishing native state from Rosetta docking decoys (94% success rate vs. 74% in 31 antibody-antigen and other complexes based on Z score). In addition, the monomer potential achieved a 93% success rate in distinguishing true dimeric interfaces from artificial crystal interfaces. More importantly, without additional parameters, the potential provides an accurate prediction of binding free energy of protein-peptide and protein-protein complexes (a correlation coefficient of 0.87 and a root-mean-square deviation of 1.76 kcal/mol with 69 experimental data points). This work marks a significant step toward a unified knowledge-based potential that quantitatively captures the common physical principle underlying folding and binding. A Web server for academic users, established for the prediction of binding free energy and the energy evaluation of the protein-protein complexes, may be found at http://theory.med.buffalo.edu.     

A self-consistent knowledge-based approach to protein design

A simple and very efficient protein design strategy is proposed by developing some recently introduced theoretical tools which have been successfully applied to exactly solvable protein models. The design approach is implemented by using three amino acid classes and it is based on the minimization of an appropriate energy function. For a given native state the results of the design procedure are compared, through a statistical analysis, with the properties of an ensemble of sequences folding in the same conformation. If the success rate is computed on those sites designed with high confidence, it can be as high as 80%. The method is also able to identify key sites for the folding process: results for 2ci2 and barnase are in very good agreement with experimental results.     

Simulating protein evolution in sequence and structure space

Naturally occurring proteins comprise a special subset of all plausible sequences and structures selected through evolution. Simulating protein evolution with simplified and all-atom models has shed light on the evolutionary dynamics of protein populations, the nature of evolved sequences and structures, and the extent to which today's proteins are shaped by selection pressures on folding, structure and function. Extensive mapping of the native structure, stability and folding rate in sequence space using lattice proteins has revealed organizational principles of the sequence/structure map important for evolutionary dynamics. Evolutionary simulations with lattice proteins have highlighted the importance of fitness landscapes, evolutionary mechanisms, population dynamics and sequence space entropy in shaping the generic properties of proteins. Finally, evolutionary-like simulations with all-atom models, in particular computational protein design, have helped identify the dominant selection pressures on naturally occurring protein sequences and structures.     

Detecting the native ligand orientation by interfacial rigidity: SiteInterlock

Understanding the physical attributes of protein‐ligand interfaces, the source of most biological activity, is a fundamental problem in biophysics. Knowing the characteristic features of interfaces also enables the design of molecules with potent and selective interactions. Prediction of native protein‐ligand interactions has traditionally focused on the development of physics‐based potential energy functions, empirical scoring functions that are fit to binding data, and knowledge‐based potentials that assess the likelihood of pairwise interactions. Here we explore a new approach, testing the hypothesis that protein‐ligand binding results in computationally detectable rigidification of the protein‐ligand interface. Our SiteInterlock approach uses rigidity theory to efficiently measure the relative interfacial rigidity of a series of small‐molecule ligand orientations and conformations for a number of protein complexes. In the majority of cases, SiteInterlock detects a near‐native binding mode as being the most rigid, with particularly robust performance relative to other methods when the ligand‐free conformation of the protein is provided. The interfacial rigidification of both the protein and ligand prove to be important characteristics of the native binding mode. This measure of rigidity is also sensitive to the spatial coupling of interactions and bond‐rotational degrees of freedom in the interface. While the predictive performance of SiteInterlock is competitive with the best of the five other scoring functions tested, its measure of rigidity encompasses cooperative rather than just additive binding interactions, providing novel information for detecting native‐like complexes. SiteInterlock shows special strength in enhancing the prediction of native complexes by ruling out inaccurate poses. Proteins 2016; 84:1888–1901. © 2016 Wiley Periodicals, Inc.     

Detecting selection for negative design in proteins through an improved model of the misfolded state

Proteins that need to be structured in their native state must be stable both against the unfolded ensemble and against incorrectly folded (misfolded) conformations with low free energy. Positive design targets the first type of stability by strengthening native interactions. The second type of stability is achieved by destabilizing interactions that occur frequently in the misfolded ensemble, a strategy called negative design. Here, we investigate negative design adopting a statistical mechanical model of the misfolded ensemble, which improves the usual Gaussian approximation by taking into account the third moment of the energy distribution and contact correlations. Applying this model, we detect and quantify selection for negative design in most natural proteins, and we analytically design protein sequences that are stable both against unfolding and against misfolding. Proteins 2013; 81:1102–1112. © 2013 Wiley Periodicals, Inc.