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 β sheets. The method can be used generally to integrate different sources of information for forcefield improvement.     

Native fold and docking pose discrimination by the same residue‐based scoring function

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH‐SixthSense, a single residue‐based statistical potential that can be successfully employed in both contexts. BACH‐SixthSense shares the same approach as BACH, a knowledge‐based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain‐sidechain contacts are crucial novel features of BACH‐SixthSense. The performance of BACH‐SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state‐of‐the‐art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH‐SixthSense in recognizing near‐native docking poses within CAPRI decoy sets is good as well. Proteins 2015; 83:621–630. © 2015 Wiley Periodicals, Inc.     

Template‐free protein structure prediction and quality assessment with an all‐atom free‐energy model

Biophysical forcefields have contributed less than originally anticipated to recent progress in protein structure prediction. Here, we have investigated the selectivity of a recently developed all‐atom free‐energy forcefield for protein structure prediction and quality assessment (QA). Using a heuristic method, but excluding homology, we generated decoy‐sets for all targets of the CASP7 protein structure prediction assessment with <150 amino acids. The decoys in each set were then ranked by energy in short relaxation simulations and the best low‐energy cluster was submitted as a prediction. For four of nine template‐free targets, this approach generated high‐ranking predictions within the top 10 models submitted in CASP7 for the respective targets. For these targets, our de‐novo predictions had an average GDT_S score of 42.81, significantly above the average of all groups. The refinement protocol has difficulty for oligomeric targets and when no near‐native decoys are generated in the decoy library. For targets with high‐quality decoy sets the refinement approach was highly selective. Motivated by this observation, we rescored all server submissions up to 200 amino acids using a similar refinement protocol, but using no clustering, in a QA exercise. We found an excellent correlation between the best server models and those with the lowest energy in the forcefield. The free‐energy refinement protocol may thus be an efficient tool for relative QA and protein structure prediction. Proteins 2009. © 2009 Wiley‐Liss, Inc.     

TOUCHSTONEX: protein structure prediction with sparse NMR data

TOUCHSTONEX, a new method for folding proteins that uses a small number of long-range contact restraints derived from NMR experimental NOE (nuclear Overhauser enhancement) data, is described. The method employs a new lattice-based, reduced model of proteins that explicitly represents C(alpha), C(beta), and the sidechain centers of mass. The force field consists of knowledge-based terms to produce protein-like behavior, including various short-range interactions, hydrogen bonding, and one-body, pairwise, and multibody long-range interactions. Contact restraints were incorporated into the force field as an NOE-specific pairwise potential. We evaluated the algorithm using a set of 125 proteins of various secondary structure types and lengths up to 174 residues. Using N/8 simulated, long-range sidechain contact restraints, where N is the number of residues, 108 proteins were folded to a C(alpha)-root-mean-square deviation (RMSD) from native below 6.5 A. The average RMSD of the lowest RMSD structures for all 125 proteins (folded and unfolded) was 4.4 A. The algorithm was also applied to limited experimental NOE data generated for three proteins. Using very few experimental sidechain contact restraints, and a small number of sidechain-main chain and main chain-main chain contact restraints, we folded all three proteins to low-to-medium resolution structures. The algorithm can be applied to the NMR structure determination process or other experimental methods that can provide tertiary restraint information, especially in the early stage of structure determination, when only limited data are available.     

Toward a “Structural BLAST”: Using structural relationships to infer function

We outline a set of strategies to infer protein function from structure. The overall approach depends on extensive use of homology modeling, the exploitation of a wide range of global and local geometric relationships between protein structures and the use of machine learning techniques. The combination of modeling with broad searches of protein structure space defines a “structural BLAST” approach to infer function with high genomic coverage. Applications are described to the prediction of protein–protein and protein–ligand interactions. In the context of protein–protein interactions, our structure‐based prediction algorithm, PrePPI, has comparable accuracy to high‐throughput experiments. An essential feature of PrePPI involves the use of Bayesian methods to combine structure‐derived information with non‐structural evidence (e.g. co‐expression) to assign a likelihood for each predicted interaction. This, combined with a structural BLAST approach significantly expands the range of applications of protein structure in the annotation of protein function, including systems level biological applications where it has previously played little role.     

Different combinations of atomic interactions predict protein‐small molecule and protein‐DNA/RNA affinities with similar accuracy

Interactions between proteins and other molecules play essential roles in all biological processes. Although it is widely held that a protein's ligand specificity is determined primarily by its three‐dimensional structure, the general principles by which structure determines ligand binding remain poorly understood. Here we use statistical analyses of a large number of protein?ligand complexes with associated binding‐affinity measurements to quantitatively characterize how combinations of atomic interactions contribute to ligand affinity. We find that there are significant differences in how atomic interactions determine ligand affinity for proteins that bind small chemical ligands, those that bind DNA/RNA and those that interact with other proteins. Although protein‐small molecule and protein‐DNA/RNA binding affinities can be accurately predicted from structural data, models predicting one type of interaction perform poorly on the others. Additionally, the particular combinations of atomic interactions required to predict binding affinity differed between small‐molecule and DNA/RNA data sets, consistent with the conclusion that the structural bases determining ligand affinity differ among interaction types. In contrast to what we observed for small‐molecule and DNA/RNA interactions, no statistical models were capable of predicting protein?protein affinity with >60% correlation. We demonstrate the potential usefulness of protein‐DNA/RNA binding prediction as a possible tool for high‐throughput virtual screening to guide laboratory investigations, suggesting that quantitative characterization of diverse molecular interactions may have practical applications as well as fundamentally advancing our understanding of how molecular structure translates into function. Proteins 2015; 83:2100–2114. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc.     

VoroMQA: Assessment of protein structure quality using interatomic contact areas

In the absence of experimentally determined protein structure many biological questions can be addressed using computational structural models. However, the utility of protein structural models depends on their quality. Therefore, the estimation of the quality of predicted structures is an important problem. One of the approaches to this problem is the use of knowledge‐based statistical potentials. Such methods typically rely on the statistics of distances and angles of residue‐residue or atom‐atom interactions collected from experimentally determined structures. Here, we present VoroMQA (Voronoi tessellation‐based Model Quality Assessment), a new method for the estimation of protein structure quality. Our method combines the idea of statistical potentials with the use of interatomic contact areas instead of distances. Contact areas, derived using Voronoi tessellation of protein structure, are used to describe and seamlessly integrate both explicit interactions between protein atoms and implicit interactions of protein atoms with solvent. VoroMQA produces scores at atomic, residue, and global levels, all in the fixed range from 0 to 1. The method was tested on the CASP data and compared to several other single‐model quality assessment methods. VoroMQA showed strong performance in the recognition of the native structure and in the structural model selection tests, thus demonstrating the efficacy of interatomic contact areas in estimating protein structure quality. The software implementation of VoroMQA is freely available as a standalone application and as a web server at http://bioinformatics.lt/software/voromqa . Proteins 2017; 85:1131–1145. © 2017 Wiley Periodicals, Inc.     

Optimized distance‐dependent atom‐pair‐based potential DOOP for protein structure prediction

The DOcking decoy‐based Optimized Potential (DOOP) energy function for protein structure prediction is based on empirical distance‐dependent atom‐pair interactions. To optimize the atom‐pair interactions, native protein structures are decomposed into polypeptide chain segments that correspond to structural motives involving complete secondary structure elements. They constitute near native ligand–receptor systems (or just pairs). Thus, a total of 8609 ligand–receptor systems were prepared from 954 selected proteins. For each of these hypothetical ligand–receptor systems, 1000 evenly sampled docking decoys with 0–10 Å interface root‐mean‐square‐deviation (iRMSD) were generated with a method used before for protein–protein docking. A neural network‐based optimization method was applied to derive the optimized energy parameters using these decoys so that the energy function mimics the funnel‐like energy landscape for the interaction between these hypothetical ligand–receptor systems. Thus, our method hierarchically models the overall funnel‐like energy landscape of native protein structures. The resulting energy function was tested on several commonly used decoy sets for native protein structure recognition and compared with other statistical potentials. In combination with a torsion potential term which describes the local conformational preference, the atom‐pair‐based potential outperforms other reported statistical energy functions in correct ranking of native protein structures for a variety of decoy sets. This is especially the case for the most challenging ROSETTA decoy set, although it does not take into account side chain orientation‐dependence explicitly. The DOOP energy function for protein structure prediction, the underlying database of protein structures with hypothetical ligand–receptor systems and their decoys are freely available at http://agknapp.chemie.fu‐berlin.de/doop/ . Proteins 2015; 83:881–890. © 2015 Wiley Periodicals, Inc.     

Three enhancements to the inference of statistical protein‐DNA potentials

The energetics of protein‐DNA interactions are often modeled using so‐called statistical potentials, that is, energy models derived from the atomic structures of protein‐DNA complexes. Many statistical protein‐DNA potentials based on differing theoretical assumptions have been investigated, but little attention has been paid to the types of data and the parameter estimation process used in deriving the statistical potentials. We describe three enhancements to statistical potential inference that significantly improve the accuracy of predicted protein‐DNA interactions: (i) incorporation of binding energy data of protein‐DNA complexes, in conjunction with their X‐ray crystal structures, (ii) use of spatially‐aware parameter fitting, and (iii) use of ensemble‐based parameter fitting. We apply these enhancements to three widely‐used statistical potentials and use the resulting enhanced potentials in a structure‐based prediction of the DNA binding sites of proteins. These enhancements are directly applicable to all statistical potentials used in protein‐DNA modeling, and we show that they can improve the accuracy of predicted DNA binding sites by up to 21%. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Analyses on hydrophobicity and attractiveness of all‐atom distance‐dependent potentials

Accurate model evaluation is a crucial step in protein structure prediction. For this purpose, statistical potentials, which evaluate a model structure based on the observed atomic distance frequencies in comparison with those in reference states, have been widely used. The reference state is a virtual state where all of the atomic interactions are turned off, and it provides a standard to measure the observed frequencies. In this study, we examined seven all‐atom distance‐dependent potentials with different reference states. As results, we observed that the variations of atom pair composition and those of distance distributions in the reference states produced systematic changes in the hydrophobic and attractive characteristics of the potentials. The performance evaluations with the CASP7 structures indicated that the preference of hydrophobic interactions improved the correlation between the energy and the GDT‐TS score, but decreased the Z‐score of the native structure. The attractiveness of potential improved both the correlation and Z‐score for template‐based modeling targets, but the benefit was smaller in free modeling targets. These results indicated that the performances of the potentials were more strongly influenced by their characteristics than by the accuracy of the definitions of the reference states.     

Can molecular dynamics simulations provide high‐resolution refinement of protein structure?

Recent advances in efficient and accurate treatment of solvent with the generalized Born approximation (GB) have made it possible to substantially refine the protein structures generated by various prediction tools through detailed molecular dynamics simulations. As demonstrated in a recent CASPR experiment, improvement can be quite reliably achieved when the initial models are sufficiently close to the native basin (e.g., 3-4 A C(alpha) RMSD). A key element to effective refinement is to incorporate reliable structural information into the simulation protocol. Without intimate knowledge of the target and prediction protocol used to generate the initial structural models, it can be assumed that the regular secondary structure elements (helices and strands) and overall fold topology are largely correct to start with, such that the protocol limits itself to the scope of refinement and focuses the sampling in vicinity of the initial structure. The secondary structures can be enforced by dihedral restraints and the topology through structural contacts, implemented as either multiple pair-wise C(alpha) distance restraints or a single sidechain distance matrix restraint. The restraints are weakly imposed with flat-bottom potentials to allow sufficient flexibility for structural rearrangement. Refinement is further facilitated by enhanced sampling of advanced techniques such as the replica exchange method (REX). In general, for single domain proteins of small to medium sizes, 3-5 nanoseconds of REX/GB refinement simulations appear to be sufficient for reasonable convergence. Clustering of the resulting structural ensembles can yield refined models over 1.0 A closer to the native structure in C(alpha) RMSD. Substantial improvement of sidechain contacts and rotamer states can also be achieved in most cases. Additional improvement is possible with longer sampling and knowledge of the robust structural features in the initial models for a given prediction protocol. Nevertheless, limitations still exist in sampling as well as force field accuracy, manifested as difficulty in refinement of long and flexible loops.     

OPUS-PSP: an orientation-dependent statistical all-atom potential derived from side-chain packing

Here we report an orientation-dependent statistical all-atom potential derived from side-chain packing, named OPUS-PSP. It features a basis set of 19 rigid-body blocks extracted from the chemical structures of all 20 amino acid residues. The potential is generated from the orientation-specific packing statistics of pairs of those blocks in a non-redundant structural database. The purpose of such an approach is to capture the essential elements of orientation dependence in molecular packing interactions. Tests of OPUS-PSP on commonly used decoy sets demonstrate that it significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and consistency in achieving high Z-scores across decoy sets. As OPUS-PSP excludes interactions among main-chain atoms, its success highlights the crucial importance of side-chain packing in forming native protein structures. Moreover, OPUS-PSP does not explicitly include solvation terms, and thus the potential should perform well when the solvation effect is difficult to determine, such as in membrane proteins. Overall, OPUS-PSP is a generally applicable potential for protein structure modeling, especially for handling side-chain conformations, one of the most difficult steps in high-accuracy protein structure prediction and refinement.     

A simple probabilistic model of multibody interactions in proteins

Protein structure prediction methods typically use statistical potentials, which rely on statistics derived from a database of know protein structures. In the vast majority of cases, these potentials involve pairwise distances or contacts between amino acids or atoms. Although some potentials beyond pairwise interactions have been described, the formulation of a general multibody potential is seen as intractable due to the perceived limited amount of data. In this article, we show that it is possible to formulate a probabilistic model of higher order interactions in proteins, without arbitrarily limiting the number of contacts. The success of this approach is based on replacing a naive table‐based approach with a simple hierarchical model involving suitable probability distributions and conditional independence assumptions. The model captures the joint probability distribution of an amino acid and its neighbors, local structure and solvent exposure. We show that this model can be used to approximate the conditional probability distribution of an amino acid sequence given a structure using a pseudo‐likelihood approach. We verify the model by decoy recognition and site‐specific amino acid predictions. Our coarse‐grained model is compared to state‐of‐art methods that use full atomic detail. This article illustrates how the use of simple probabilistic models can lead to new opportunities in the treatment of nonlocal interactions in knowledge‐based protein structure prediction and design. Proteins 2013; 81:1340–1350. © 2013 Wiley Periodicals, Inc.     

Effective knowledge‐based potentials

Empirical or knowledge‐based potentials have many applications in structural biology such as the prediction of protein structure, protein–protein, and protein–ligand interactions and in the evaluation of stability for mutant proteins, the assessment of errors in experimentally solved structures, and the design of new proteins. Here, we describe a simple procedure to derive and use pairwise distance‐dependent potentials that rely on the definition of effective atomic interactions, which attempt to capture interactions that are more likely to be physically relevant. Based on a difficult benchmark test composed of proteins with different secondary structure composition and representing many different folds, we show that the use of effective atomic interactions significantly improves the performance of potentials at discriminating between native and near‐native conformations. We also found that, in agreement with previous reports, the potentials derived from the observed effective atomic interactions in native protein structures contain a larger amount of mutual information. A detailed analysis of the effective energy functions shows that atom connectivity effects, which mostly arise when deriving the potential by the incorporation of those indirect atomic interactions occurring beyond the first atomic shell, are clearly filtered out. The shape of the energy functions for direct atomic interactions representing hydrogen bonding and disulfide and salt bridges formation is almost unaffected when effective interactions are taken into account. On the contrary, the shape of the energy functions for indirect atom interactions (i.e., those describing the interaction between two atoms bound to a direct interacting pair) is clearly different when effective interactions are considered. Effective energy functions for indirect interacting atom pairs are not influenced by the shape or the energy minimum observed for the corresponding direct interacting atom pair. Our results suggest that the dependency between the signals in different energy functions is a key aspect that need to be addressed when empirical energy functions are derived and used, and also highlight the importance of additivity assumptions in the use of potential energy functions.     

An atomic environment potential for use in protein structure prediction

We describe the derivation and testing of a knowledge-based atomic environment potential for the modeling of protein structural energetics. An analysis of the probabilities of atomic interactions in a dataset of high-resolution protein structures shows that the probabilities of non-bonded inter-atomic contacts are not statistically independent events, and that the multi-body contact frequencies are poorly predicted from pairwise contact potentials. A pseudo-energy function is defined that measures the preferences for protein atoms to be in a given microenvironment defined by the number of contacting atoms in the environment and its atomic composition. This functional form is tested for its ability to recognize native protein structures amongst an ensemble of decoy structures and a detailed relative performance comparison is made with a number of common functions used in protein structure prediction.     

The dependence of all-atom statistical potentials on structural training database

An accurate statistical energy function that is suitable for the prediction of protein structures of all classes should be independent of the structural database used for energy extraction. Here, two high-resolution, low-sequence-identity structural databases of 333 alpha-proteins and 271 beta-proteins were built for examining the database dependence of three all-atom statistical energy functions. They are RAPDF (residue-specific all-atom conditional probability discriminatory function), atomic KBP (atomic knowledge-based potential), and DFIRE (statistical potential based on distance-scaled finite ideal-gas reference state). These energy functions differ in the reference states used for energy derivation. The energy functions extracted from the different structural databases are used to select native structures from multiple decoys of 64 alpha-proteins and 28 beta-proteins. The performance in native structure selections indicates that the DFIRE-based energy function is mostly independent of the structural database whereas RAPDF and KBP have a significant dependence. The construction of two additional structural databases of alpha/beta and alpha + beta-proteins further confirmed the weak dependence of DFIRE on the structural databases of various structural classes. The possible source for the difference between the three all-atom statistical energy functions is that the physical reference state of ideal gas used in the DFIRE-based energy function is least dependent on the structural database.     

Tertiary structural constraints on protein evolutionary diversity: templates, key residues and structure prediction

The pattern of residue substitution in divergently evolving families of globular proteins is highly variable. At each position in a fold there are constraints on the identities of amino acids from both the three-dimensional structure and the function of the protein. To characterize and quantify the structural constraints, we have made a comparative analysis of families of homologous globular proteins. Residues are classified according to amino acid type, secondary structure, accessibility of the sidechain, and existence of hydrogen bonds from sidechain to other sidechains or peptide carbonyl or amide functions. There are distinct patterns of substitution especially where residues are both solvent inaccessible and hydrogen bonded through their sidechains. The patterns of residue substitution can be used to construct templates or to identify 'key' residues if one or more structures are known. Conversely, analysis of conversation and substitution across a large family of aligned sequences in terms of substitution profiles can allow prediction of tertiary environment or indicate a functional role. Similar analyses can be used to test the validity of putative structures if several homologous sequences are available.     

Protein modeling and structure prediction with a reduced representation

Protein modeling could be done on various levels of structural details, from simplified lattice or continuous representations, through high resolution reduced models, employing the united atom representation, to all-atom models of the molecular mechanics. Here I describe a new high resolution reduced model, its force field and applications in the structural proteomics. The model uses a lattice representation with 800 possible orientations of the virtual alpha carbon-alpha carbon bonds. The sampling scheme of the conformational space employs the Replica Exchange Monte Carlo method. Knowledge-based potentials of the force field include: generic protein-like conformational biases, statistical potentials for the short-range conformational propensities, a model of the main chain hydrogen bonds and context-dependent statistical potentials describing the side group interactions. The model is more accurate than the previously designed lattice models and in many applications it is complementary and competitive in respect to the all-atom techniques. The test applications include: the ab initio structure prediction, multitemplate comparative modeling and structure prediction based on sparse experimental data. Especially, the new approach to comparative modeling could be a valuable tool of the structural proteomics. It is shown that the new approach goes beyond the range of applicability of the traditional methods of the protein comparative modeling.