Knowledge-based potentials in protein design

Knowledge-based potentials are statistical parameters derived from databases of known protein properties that empirically capture aspects of the physical chemistry of protein structure and function. These potentials play a key role in protein design by improving the accuracy of physics-based models of interatomic interactions and enhancing the computational efficiency of the design process by limiting the complexity of searching sequence space. Recently, knowledge-based potentials (in isolation or in combination with physics-based potentials) have been applied to the modification of existing protein function, the redesign of natural protein folds and the complete design of a non-natural protein fold. In addition, knowledge-based potentials appear to be providing important information about the global topology of amino acid interactions in natural proteins. A detailed study of the methods and products of these protein design efforts promises to greatly expand our understanding of proteins and the evolutionary process that created them.     

Stochastic modeling of noninteracting probes in the protein structure space for construction of knowledge-based potentials for atom-atom interactions

Knowledge-based potentials are extensively used to represent atomic interactions in modeling the protein structure. We consider a number of problems in constructing efficient knowledge-based potentials for biopolymer modeling. We show that some limitations can be overcome by normalizing estimated interactions through the distribution of distances between noninteracting random probes in protein structure space. We demonstrate that knowledge-based potentials thus constructed can be efficiently applied for analysis of the hydration state of proteins atoms. With this approach, one can predict the locations of structural water molecules in a protein globule. We have also succeeded in recognizing the correctly folded protein structure among many misfolded decoys in cases when the interaction with water solvent is dominant for structure formation.     

Application of noninteracting probes in the protein structure space for the construction of statistical potentials for atom-atom interactions

Some effects hindering the construction of knowledge-based potentials of atom-atom interactions in problems of biopolymer modeling have been considered. It was shown that some limitations are overcome by considering the distribution of distances between noninteracting probes in the protein structure space. It was shown that knowledge-based potentials thus constructed can be effectively used to analyze the hydration of protein atoms. Using this approach, it is possible to predict the structure water location in a protein globule and recognize the correctly folded protein structure among decoys.     

Statistical mechanics-based method to extract atomic distance-dependent potentials from protein structures

In this study, we have developed a statistical mechanics-based iterative method to extract statistical atomic interaction potentials from known, nonredundant protein structures. Our method circumvents the long-standing reference state problem in deriving traditional knowledge-based scoring functions, by using rapid iterations through a physical, global convergence function. The rapid convergence of this physics-based method, unlike other parameter optimization methods, warrants the feasibility of deriving distance-dependent, all-atom statistical potentials to keep the scoring accuracy. The derived potentials, referred to as ITScore/Pro, have been validated using three diverse benchmarks: the high-resolution decoy set, the AMBER benchmark decoy set, and the CASP8 decoy set. Significant improvement in performance has been achieved. Finally, comparisons between the potentials of our model and potentials of a knowledge-based scoring function with a randomized reference state have revealed the reason for the better performance of our scoring function, which could provide useful insight into the development of other physical scoring functions. The potentials developed in this study are generally applicable for structural selection in protein structure prediction.     

Evaluating mixture models for building RNA knowledge-based potentials

Ribonucleic acid (RNA) molecules play important roles in a variety of biological processes. To properly function, RNA molecules usually have to fold to specific structures, and therefore understanding RNA structure is vital in comprehending how RNA functions. One approach to understanding and predicting biomolecular structure is to use knowledge-based potentials built from experimentally determined structures. These types of potentials have been shown to be effective for predicting both protein and RNA structures, but their utility is limited by their significantly rugged nature. This ruggedness (and hence the potential's usefulness) depends heavily on the choice of bin width to sort structural information (e.g. distances) but the appropriate bin width is not known a priori. To circumvent the binning problem, we compared knowledge-based potentials built from inter-atomic distances in RNA structures using different mixture models (Kernel Density Estimation, Expectation Minimization and Dirichlet Process). We show that the smooth knowledge-based potential built from Dirichlet process is successful in selecting native-like RNA models from different sets of structural decoys with comparable efficacy to a potential developed by spline-fitting - a commonly taken approach - to binned distance histograms. The less rugged nature of our potential suggests its applicability in diverse types of structural modeling.     

Fully differentiable coarse-grained and all-atom knowledge-based potentials for RNA structure evaluation

RNA molecules play integral roles in gene regulation, and understanding their structures gives us important insights into their biological functions. Despite recent developments in template-based and parameterized energy functions, the structure of RNA--in particular the nonhelical regions--is still difficult to predict. Knowledge-based potentials have proven efficient in protein structure prediction. In this work, we describe two differentiable knowledge-based potentials derived from a curated data set of RNA structures, with all-atom or coarse-grained representation, respectively. We focus on one aspect of the prediction problem: the identification of native-like RNA conformations from a set of near-native models. Using a variety of near-native RNA models generated from three independent methods, we show that our potential is able to distinguish the native structure and identify native-like conformations, even at the coarse-grained level. The all-atom version of our knowledge-based potential performs better and appears to be more effective at discriminating near-native RNA conformations than one of the most highly regarded parameterized potential. The fully differentiable form of our potentials will additionally likely be useful for structure refinement and/or molecular dynamics simulations.     

Ligand-supported homology modelling of protein binding-sites using knowledge-based potentials

A new approach, MOBILE, is presented that models protein binding-sites including bound ligand molecules as restraints. Initially generated, homology models of the target protein are refined iteratively by including information about bioactive ligands as spatial restraints and optimising the mutual interactions between the ligands and the binding-sites. Thus optimised models can be used for structure-based drug design and virtual screening. In a first step, ligands are docked into an averaged ensemble of crude homology models of the target protein. In the next step, improved homology models are generated, considering explicitly the previously placed ligands by defining restraints between protein and ligand atoms. These restraints are expressed in terms of knowledge-based distance-dependent pair potentials, which were compiled from crystallographically determined protein-ligand complexes. Subsequently, the most favourable models are selected by ranking the interactions between the ligands and the generated pockets using these potentials. Final models are obtained by selecting the best-ranked side-chain conformers from various models, followed by an energy optimisation of the entire complex using a common force-field. Application of the knowledge-based pair potentials proved efficient to restrain the homology modelling process and to score and optimise the modelled protein-ligand complexes. For a test set of 46 protein-ligand complexes, taken from the Protein Data Bank (PDB), the success rate of producing near-native binding-site geometries (rmsd<2.0A) with MODELLER is 70% when the ligand restrains the homology modelling process in its native orientation. Scoring these complexes with the knowledge-based potentials, in 66% of the cases a pose with rmsd <2.0A is found on rank 1. Finally, MOBILE has been applied to two case studies modelling factor Xa based on trypsin and aldose reductase based on aldehyde reductase.     

Protein modeling with reduced representation: statistical potentials and protein folding mechanism

A high resolution reduced model of proteins is used in Monte Carlo dynamics studies of the folding mechanism of a small globular protein, the B1 immunoglobulin-binding domain of streptococcal protein G. It is shown that in order to reproduce the physics of the folding transition, the united atom based model requires a set of knowledge-based potentials mimicking the short-range conformational propensities and protein-like chain stiffness, a model of directional and cooperative hydrogen bonds, and properly designed knowledge-based potentials of the long-range interactions between the side groups. The folding of the model protein is cooperative and very fast. In a single trajectory, a number of folding/unfolding cycles were observed. Typically, the folding process is initiated by assembly of a native-like structure of the C-terminal hairpin. In the next stage the rest of the four-ribbon beta-sheet folds. The slowest step of this pathway is the assembly of the central helix on the scaffold of the beta-sheet.     

Analysis of knowledge-based protein-ligand potentials using a self-consistent method

We propose a self-consistent approach to analyze knowledge-based atom-atom potentials used to calculate protein-ligand binding energies. Ligands complexed to actual protein structures were first built using the SMoG growth procedure (DeWitte & Shakhnovich, 1996) with a chosen input potential. These model protein-ligand complexes were used to construct databases from which knowledge-based protein-ligand potentials were derived. We then tested several different modifications to such potentials and evaluated their performance on their ability to reconstruct the input potential using the statistical information available from a database composed of model complexes. Our data indicate that the most significant improvement resulted from properly accounting for the following key issues when estimating the reference state: (1) the presence of significant nonenergetic effects that influence the contact frequencies and (2) the presence of correlations in contact patterns due to chemical structure. The most successful procedure was applied to derive an atom-atom potential for real protein-ligand complexes. Despite the simplicity of the model (pairwise contact potential with a single interaction distance), the derived binding free energies showed a statistically significant correlation (approximately 0.65) with experimental binding scores for a diverse set of complexes.     

Reduced C(beta) statistical potentials can outperform all-atom potentials in decoy identification

We developed a series of statistical potentials to recognize the native protein from decoys, particularly when using only a reduced representation in which each side chain is treated as a single C(beta) atom. Beginning with a highly successful all-atom statistical potential, the Discrete Optimized Protein Energy function (DOPE), we considered the implications of including additional information in the all-atom statistical potential and subsequently reducing to the C(beta) representation. One of the potentials includes interaction energies conditional on backbone geometries. A second potential separates sequence local from sequence nonlocal interactions and introduces a novel reference state for the sequence local interactions. The resultant potentials perform better than the original DOPE statistical potential in decoy identification. Moreover, even upon passing to a reduced C(beta) representation, these statistical potentials outscore the original (all-atom) DOPE potential in identifying native states for sets of decoys. Interestingly, the backbone-dependent statistical potential is shown to retain nearly all of the information content of the all-atom representation in the C(beta) representation. In addition, these new statistical potentials are combined with existing potentials to model hydrogen bonding, torsion energies, and solvation energies to produce even better performing potentials. The ability of the C(beta) statistical potentials to accurately represent protein interactions bodes well for computational efficiency in protein folding calculations using reduced backbone representations, while the extensions to DOPE illustrate general principles for improving knowledge-based potentials.     

Distance-scaled,finite ideal-gas reference state improves structure-derived potentials of mean force for structure selection and stability prediction

The distance-dependent structure-derived potentials developed so far all employed a reference state that can be characterized as a residue (atom)-averaged state. Here, we establish a new reference state called the distance-scaled, finite ideal-gas reference (DFIRE) state. The reference state is used to construct a residue-specific all-atom potential of mean force from a database of 1011 nonhomologous (less than 30% homology) protein structures with resolution less than 2 A. The new all-atom potential recognizes more native proteins from 32 multiple decoy sets, and raises an average Z-score by 1.4 units more than two previously developed, residue-specific, all-atom knowledge-based potentials. When only backbone and C(beta) atoms are used in scoring, the performance of the DFIRE-based potential, although is worse than that of the all-atom version, is comparable to those of the previously developed potentials on the all-atom level. In addition, the DFIRE-based all-atom potential provides the most accurate prediction of the stabilities of 895 mutants among three knowledge-based all-atom potentials. Comparison with several physical-based potentials is made.     

Influence of protein structure databases on the predictive power of statistical pair potentials

A long standing goal in protein structure studies is the development of reliable energy functions that can be used both to verify protein models derived from experimental constraints as well as for theoretical protein folding and inverse folding computer experiments. In that respect, knowledge-based statistical pair potentials have attracted considerable interests recently mainly because they include the essential features of protein structures as well as solvent effects at a low computing cost. However, the basis on which statistical potentials are derived have been questioned. In this paper, we investigate statistical pair potentials derived from protein three-dimensional structures, addressing in particular questions related to the form of these potentials, as well as to the content of the database from which they are derived. We have shown that statistical pair potentials depend on the size of the proteins included in the database, and that this dependence can be reduced by considering only pairs of residue close in space (i.e., with a cutoff of 8 Å). We have shown also that statistical potentials carry a memory of the quality of the database in terms of the amount and diversity of secondary structure it contains. We find, for example, that potentials derived from a database containing α-proteins will only perform best on α-proteins in fold recognition computer experiments. We believe that this is an overall weakness of these potentials, which must be kept in mind when constructing a database. Proteins 31:139–149, 1998. © 1998 Wiley-Liss, Inc.     

Fast optimization of statistical potentials for structurally constrained phylogenetic models

Background  

Statistical approaches for protein design are relevant in the field of molecular evolutionary studies. In recent years, new, so-called structurally constrained (SC) models of protein-coding sequence evolution have been proposed, which use statistical potentials to assess sequence-structure compatibility. In a previous work, we defined a statistical framework for optimizing knowledge-based potentials especially suited to SC models. Our method used the maximum likelihood principle and provided what we call the joint potentials. However, the method required numerical estimations by the use of computationally heavy Markov Chain Monte Carlo sampling algorithms.     

Novel knowledge-based potentials for ligand docking: variational approach to the old problem

The variational approach of evaluation for knowledge-based potentials is considered for the first time. In this approach, the problem to derive knowledge-based potentials is solved as the optimization task in the multiparametric model of atom types, reference states and interaction cutoff radii. Using analogy to liquid state theory we offered four new reference states and derived corresponding knowledge-based potentials. The cutoff radii and atom types are optimized to minimize averaged root-mean square deviations (RMSD) of the ligand docked positions regarding to the experimentally determined poses. The number of atom types is varied on the developed atom type tree with 6 root (C, N, O, S, P and the halogen type) and 49 apical atom types. We showed a pronounced effect of atom type choice on docking accuracy and proved that splitting of elements C, N and O of the periodic system up to the 18 optimal atom types essentially improves docking accuracy.     

Splitting statistical potentials into meaningful scoring functions: Testing the prediction of near-native structures from decoy conformations

Background  

Recent advances on high-throughput technologies have produced a vast amount of protein sequences, while the number of high-resolution structures has seen a limited increase. This has impelled the production of many strategies to built protein structures from its sequence, generating a considerable amount of alternative models. The selection of the closest model to the native conformation has thus become crucial for structure prediction. Several methods have been developed to score protein models by energies, knowledge-based potentials and combination of both.     

Novel knowledge-based mean force potential at the profile level

Background  

The development and testing of functions for the modeling of protein energetics is an important part of current research aimed at understanding protein structure and function. Knowledge-based mean force potentials are derived from statistical analyses of interacting groups in experimentally determined protein structures. Current knowledge-based mean force potentials are developed at the atom or amino acid level. The evolutionary information contained in the profiles is not investigated. Based on these observations, a class of novel knowledge-based mean force potentials at the profile level has been presented, which uses the evolutionary information of profiles for developing more powerful statistical potentials.     

A pairwise residue contact area-based mean force potential for discrimination of native protein structure

Background  

Considering energy function to detect a correct protein fold from incorrect ones is very important for protein structure prediction and protein folding. Knowledge-based mean force potentials are certainly the most popular type of interaction function for protein threading. They are derived from statistical analyses of interacting groups in experimentally determined protein structures. These potentials are developed at the atom or the amino acid level. Based on orientation dependent contact area, a new type of knowledge-based mean force potential has been developed.     

Protein sequence randomization: efficient estimation of protein stability using knowledge-based potentials

Modifications of the amino acid sequence generally affect protein stability. Here, we use knowledge-based potentials to estimate the stability of protein structures under sequence variation. Calculations on a variety of protein scaffolds result in a clear distinction of known mutable regions from arbitrarily chosen control patches. For example, randomly changing the sequence of an antibody paratope yields a significantly lower number of destabilized mutants as compared to the randomization of comparable regions on the protein surface. The technique is computationally efficient and can be used to screen protein structures for regions that are amenable to molecular tinkering by preserving the stability of the mutated proteins.     

Determining Rieske cluster reduction potentials

The Rieske iron-sulfur proteins have reduction potentials ranging from -150 to +400 mV. This enormous range of potentials was first proposed to be due to differing solvent exposure or even protein structure. However, the increasing number of available crystal structures for Rieske iron-sulfur proteins has shown this not to be the case. Colbert and colleagues proposed in 2000 that differences in the electrostatic environment, and not structural differences, of a Rieske proteins are responsible for the wide range of reduction potentials observed. Using computational simulation methods and the newly determined structure of Pseudomonas sp. NCIB 9816-4 naphthalene dioxygenase Rieske ferredoxin (NDO-F9816-4), we have developed a model to predict the reduction potential of Rieske proteins given only their crystal structure. The reduction potential of NDO-F9816-4, determined using a highly oriented pyrolytic graphite electrode, was -150+/-2 mV versus the standard hydrogen electrode. The predicted reduction potentials correlate well with experimentally determined potentials. Given this model, the effect of protein mutations can be evaluated. Our results suggest that the reduction potential of new proteins can be estimated with good confidence from 3D structures of proteins. The structure of NDO-F9816-4 is the most basic Rieske ferredoxin structure determined to date. Thus, the contributions of additional structural motifs and their effects on reduction potential can be compared with respect to this base structure.     

Derivation of protein-specific pair potentials based on weak sequence fragment similarity

A method is presented for the derivation of knowledge-based pair potentials that corrects for the various compositions of different proteins. The resulting statistical pair potential is more specific than that derived from previous approaches as assessed by gapless threading results. Additionally, a methodology is presented that interpolates between statistical potentials when no homologous examples to the protein of interest are in the structural database used to derive the potential, to a Go-like potential (in which native interactions are favorable and all nonnative interactions are not) when homologous proteins are present. For cases in which no protein exceeds 30% sequence identity, pairs of weakly homologous interacting fragments are employed to enhance the specificity of the potential. In gapless threading, the mean z score increases from -10.4 for the best statistical pair potential to -12.8 when the local sequence similarity, fragment-based pair potentials are used. Examination of the ab initio structure prediction of four representative globular proteins consistently reveals a qualitative improvement in the yield of structures in the 4 to 6 A rmsd from native range when the fragment-based pair potential is used relative to that when the quasichemical pair potential is employed. This suggests that such protein-specific potentials provide a significant advantage relative to generic quasichemical potentials.