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

Amino acid variation analysis of surface spike glycoprotein at 614 in SARS-CoV-2 strains

As severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) continues to disperse globally with worrisome speed, identifying amino acid variations in the virus could help to understand the characteristics of it. Here, we studied 489 SARS-CoV-2 genomes obtained from 32 countries from the Nextstrain database and performed phylogenetic tree analysis by clade, country, and genotype of the surface spike glycoprotein (S protein) at site 614. We found that virus strains from mainland China were mostly distributed in Clade B and Clade undefined in the phylogenetic tree, with very few found in Clade A. In contrast, Clades A2 (one case) and A2a (112 cases) predominantly contained strains from European regions. Moreover, Clades A2 and A2a differed significantly from those of mainland China in age of infected population (P = 0.0071, mean age 40.24 to 46.66), although such differences did not exist between the US and mainland China. Further analysis demonstrated that the variation of the S protein at site 614 (QHD43416.1: p.614D>G) was a characteristic of stains in Clades A2 and A2a. Importantly, this variation was predicted to have neutral or benign effects on the function of the S protein. In addition, global quality estimates and 3D protein structures tended to be different between the two S proteins. In summary, we identified different genomic epidemiology among SARS-CoV-2 strains in different clades, especially in an amino acid variation of the S protein at 614, revealing potential viral genome divergence in SARS-CoV-2 strains.

KORP: knowledge-based 6D potential for fast protein and loop modeling

Motivation

Knowledge-based statistical potentials constitute a simpler and easier alternative to physics-based potentials in many applications, including folding, docking and protein modeling. Here, to improve the effectiveness of the current approximations, we attempt to capture the six-dimensional nature of residue–residue interactions from known protein structures using a simple backbone-based representation.

Results

We have developed KORP, a knowledge-based pairwise potential for proteins that depends on the relative position and orientation between residues. Using a minimalist representation of only three backbone atoms per residue, KORP utilizes a six-dimensional joint probability distribution to outperform state-of-the-art statistical potentials for native structure recognition and best model selection in recent critical assessment of protein structure prediction and loop-modeling benchmarks. Compared with the existing methods, our side-chain independent potential has a lower complexity and better efficiency. The superior accuracy and robustness of KORP represent a promising advance for protein modeling and refinement applications that require a fast but highly discriminative energy function.

Availability and implementation

http://chaconlab.org/modeling/korp.

Supplementary information

Supplementary data are available at Bioinformatics online.

Application of information theory to a three-body coarse-grained representation of proteins in the PDB: insights into the structural and evolutionary roles of residues in protein structure

Knowledge-based methods for analyzing protein structures, such as statistical potentials, primarily consider the distances between pairs of bodies (atoms or groups of atoms). Considerations of several bodies simultaneously are generally used to characterize bonded structural elements or those in close contact with each other, but historically do not consider atoms that are not in direct contact with each other. In this report, we introduce an information-theoretic method for detecting and quantifying distance-dependent through-space multibody relationships between the sidechains of three residues. The technique introduced is capable of producing convergent and consistent results when applied to a sufficiently large database of randomly chosen, experimentally solved protein structures. The results of our study can be shown to reproduce established physico-chemical properties of residues as well as more recently discovered properties and interactions. These results offer insight into the numerous roles that residues play in protein structure, as well as relationships between residue function, protein structure, and evolution. The techniques and insights presented in this work should be useful in the future development of novel knowledge-based tools for the evaluation of protein structure.

Simplified protein models: predicting folding pathways and structure using amino acid sequences

We demonstrate the ability of simultaneously determining a protein's folding pathway and structure using a properly formulated model without prior knowledge of the native structure. Our model employs a natural coordinate system for describing proteins and a search strategy inspired by the observation that real proteins fold in a sequential fashion by incrementally stabilizing nativelike substructures or "foldons." Comparable folding pathways and structures are obtained for the twelve proteins recently studied using atomistic molecular dynamics simulations [K. Lindorff-Larsen, S. Piana, R. O. Dror, D. E. Shaw, Science 334, 517 (2011)], with our calculations running several orders of magnitude faster. We find that nativelike propensities in the unfolded state do not necessarily determine the order of structure formation, a departure from a major conclusion of the molecular dynamics study. Instead, our results support a more expansive view wherein intrinsic local structural propensities may be enhanced or overridden in the folding process by environmental context. The success of our search strategy validates it as an expedient mechanism for folding both in silico and in vivo.

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.

InterEvScore: a novel coarse-grained interface scoring function using a multi-body statistical potential coupled to evolution

MOTIVATION

Structural prediction of protein interactions currently remains a challenging but fundamental goal. In particular, progress in scoring functions is critical for the efficient discrimination of near-native interfaces among large sets of decoys. Many functions have been developed using knowledge-based potentials, but few make use of multi-body interactions or evolutionary information, although multi-residue interactions are crucial for protein-protein binding and protein interfaces undergo significant selection pressure to maintain their interactions.

RESULTS

This article presents InterEvScore, a novel scoring function using a coarse-grained statistical potential including two- and three-body interactions, which provides each residue with the opportunity to contribute in its most favorable local structural environment. Combination of this potential with evolutionary information considerably improves scoring results on the 54 test cases from the widely used protein docking benchmark for which evolutionary information can be collected. We analyze how our way to include evolutionary information gradually increases the discriminative power of InterEvScore. Comparison with several previously published scoring functions (ZDOCK, ZRANK and SPIDER) shows the significant progress brought by InterEvScore.

AVAILABILITY

http://biodev.cea.fr/interevol/interevscore

CONTACT

guerois@cea.fr

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

On docking, scoring and assessing protein-DNA complexes in a rigid-body framework

We consider the identification of interacting protein-nucleic acid partners using the rigid body docking method FTdock, which is systematic and exhaustive in the exploration of docking conformations. The accuracy of rigid body docking methods is tested using known protein-DNA complexes for which the docked and undocked structures are both available. Additional tests with large decoy sets probe the efficacy of two published statistically derived scoring functions that contain a huge number of parameters. In contrast, we demonstrate that state-of-the-art machine learning techniques can enormously reduce the number of parameters required, thereby identifying the relevant docking features using a miniscule fraction of the number of parameters in the prior works. The present machine learning study considers a 300 dimensional vector (dependent on only 15 parameters), termed the Chemical Context Profile (CCP), where each dimension reflects a specific type of protein amino acid-nucleic acid base interaction. The CCP is designed to capture the chemical complementarities of the interface and is well suited for machine learning techniques. Our objective function is the Chemical Context Discrepancy (CCD), which is defined as the angle between the native system's CCP vector and the decoy's vector and which serves as a substitute for the more commonly used root mean squared deviation (RMSD). We demonstrate that the CCP provides a useful scoring function when certain dimensions are properly weighted. Finally, we explore how the amino acids on a protein's surface can help guide DNA binding, first through long-range interactions, followed by direct contacts, according to specific preferences for either the major or minor grooves of the DNA.

Generation of atomic four-body statistical potentials derived from the delaunay tessellation of protein structures

Delaunay tessellation of the atomic coordinates for a crystallographic protein structure yields an aggregate of non-overlapping and space-filling irregular tetrahedral simplices. The vertices of each simplex objectively identify a quadruplet of nearest neighbor atoms in the protein. Here we apply Delaunay tessellation to 1417 high-resolution structures of single chains that share low sequence identity, for the purpose of determining the relative frequencies of occurrence for all possible nearest neighbor atomic quadruplet types. Alternative distributions are explored by varying two fundamental parameters: atomic alphabet selection and cutoff length for admissible simplex edges. The distributions are then converted to four-body potential functions by implementing the inverted Boltzmann principle, which requires calculating the distribution of the reference state. Two alternative definitions for the reference state are presented, which introduces a third parameter, and we derive and compare an array of such potential functions. These knowledge-based statistical potentials based on higher-order interactions complement and generalize the more commonly encountered atom-pair potentials, for which a number of approaches are described in the literature.

Automated real-space refinement of protein structures using a realistic backbone move set

Crystals of many important biological macromolecules diffract to limited resolution, rendering accurate model building and refinement difficult and time-consuming. We present a torsional optimization protocol that is applicable to many such situations and combines Protein Data Bank-based torsional optimization with real-space refinement against the electron density derived from crystallography or cryo-electron microscopy. Our method converts moderate- to low-resolution structures at initial (e.g., backbone trace only) or late stages of refinement to structures with increased numbers of hydrogen bonds, improved crystallographic R-factors, and superior backbone geometry. This automated method is applicable to DNA-binding and membrane proteins of any size and will aid studies of structural biology by improving model quality and saving considerable effort. The method can be extended to improve NMR and other structures. Our backbone score and its sequence profile provide an additional standard tool for evaluating structural quality.

NCACO-score: an effective main-chain dependent scoring function for structure modeling

Background

Development of effective scoring functions is a critical component to the success of protein structure modeling. Previously, many efforts have been dedicated to the development of scoring functions. Despite these efforts, development of an effective scoring function that can achieve both good accuracy and fast speed still presents a grand challenge.

Results

Based on a coarse-grained representation of a protein structure by using only four main-chain atoms: N, Cα, C and O, we develop a knowledge-based scoring function, called NCACO-score, that integrates different structural information to rapidly model protein structure from sequence. In testing on the Decoys'R'Us sets, we found that NCACO-score can effectively recognize native conformers from their decoys. Furthermore, we demonstrate that NCACO-score can effectively guide fragment assembly for protein structure prediction, which has achieved a good performance in building the structure models for hard targets from CASP8 in terms of both accuracy and speed.

Conclusions

Although NCACO-score is developed based on a coarse-grained model, it is able to discriminate native conformers from decoy conformers with high accuracy. NCACO is a very effective scoring function for structure modeling.

A probabilistic and continuous model of protein conformational space for template-free modeling

One of the major challenges with protein template-free modeling is an efficient sampling algorithm that can explore a huge conformation space quickly. The popular fragment assembly method constructs a conformation by stringing together short fragments extracted from the Protein Data Base (PDB). The discrete nature of this method may limit generated conformations to a subspace in which the native fold does not belong. Another worry is that a protein with really new fold may contain some fragments not in the PDB. This article presents a probabilistic model of protein conformational space to overcome the above two limitations. This probabilistic model employs directional statistics to model the distribution of backbone angles and 2(nd)-order Conditional Random Fields (CRFs) to describe sequence-angle relationship. Using this probabilistic model, we can sample protein conformations in a continuous space, as opposed to the widely used fragment assembly and lattice model methods that work in a discrete space. We show that when coupled with a simple energy function, this probabilistic method compares favorably with the fragment assembly method in the blind CASP8 evaluation, especially on alpha or small beta proteins. To our knowledge, this is the first probabilistic method that can search conformations in a continuous space and achieves favorable performance. Our method also generated three-dimensional (3D) models better than template-based methods for a couple of CASP8 hard targets. The method described in this article can also be applied to protein loop modeling, model refinement, and even RNA tertiary structure prediction.

A novel side-chain orientation dependent potential derived from random-walk reference state for protein fold selection and structure prediction

BACKGROUND

An accurate potential function is essential to attack protein folding and structure prediction problems. The key to developing efficient knowledge-based potential functions is to design reference states that can appropriately counteract generic interactions. The reference states of many knowledge-based distance-dependent atomic potential functions were derived from non-interacting particles such as ideal gas, however, which ignored the inherent sequence connectivity and entropic elasticity of proteins.

METHODOLOGY

We developed a new pair-wise distance-dependent, atomic statistical potential function (RW), using an ideal random-walk chain as reference state, which was optimized on CASP models and then benchmarked on nine structural decoy sets. Second, we incorporated a new side-chain orientation-dependent energy term into RW (RWplus) and found that the side-chain packing orientation specificity can further improve the decoy recognition ability of the statistical potential.

SIGNIFICANCE

RW and RWplus demonstrate a significantly better ability than the best performing pair-wise distance-dependent atomic potential functions in both native and near-native model selections. It has higher energy-RMSD and energy-TM-score correlations compared with other potentials of the same type in real-life structure assembly decoys. When benchmarked with a comprehensive list of publicly available potentials, RW and RWplus shows comparable performance to the state-of-the-art scoring functions, including those combining terms from multiple resources. These data demonstrate the usefulness of random-walk chain as reference states which correctly account for sequence connectivity and entropic elasticity of proteins. It shows potential usefulness in structure recognition and protein folding simulations. The RW and RWplus potentials, as well as the newly generated I-TASSER decoys, are freely available in http://zhanglab.ccmb.med.umich.edu/RW.

Fragment-free approach to protein folding using conditional neural fields

Motivation: One of the major bottlenecks with ab initio protein folding is an effective conformation sampling algorithm that can generate native-like conformations quickly. The popular fragment assembly method generates conformations by restricting the local conformations of a protein to short structural fragments in the PDB. This method may limit conformations to a subspace to which the native fold does not belong because (i) a protein with really new fold may contain some structural fragments not in the PDB and (ii) the discrete nature of fragments may prevent them from building a native-like fold. Previously we have developed a conditional random fields (CRF) method for fragment-free protein folding that can sample conformations in a continuous space and demonstrated that this CRF method compares favorably to the popular fragment assembly method. However, the CRF method is still limited by its capability of generating conformations compatible with a sequence.

Results: We present a new fragment-free approach to protein folding using a recently invented probabilistic graphical model conditional neural fields (CNF). This new CNF method is much more powerful than CRF in modeling the sophisticated protein sequence-structure relationship and thus, enables us to generate native-like conformations more easily. We show that when coupled with a simple energy function and replica exchange Monte Carlo simulation, our CNF method can generate decoys much better than CRF on a variety of test proteins including the CASP8 free-modeling targets. In particular, our CNF method can predict a correct fold for T0496_D1, one of the two CASP8 targets with truly new fold. Our predicted model for T0496 is significantly better than all the CASP8 models.

Contact:jinboxu@gmail.com

Backbone statistical potential from local sequence-structure interactions in protein loops

Native proteins have been optimized by evolution simultaneously for structure and sequence. Structural databases reflect this interdependency. In this paper, we present a new statistical potential for a reduced backbone representation that has both structure and sequence characteristics as variables. We use information from structural data available in the Protein Coil Library, selected on the basis of resolution and refinement factor. In these structures, the nonlocal interactions are randomly distributed and, thus, average out in statistics, so structural propensities due to local backbone-based interactions can be studied separately. We collect data in the form of local sequence-specific phi-psi backbone dihedral pairs. From these data, we construct dihedral probability density functions (DPDFs) that quantify any adjacent phi-psi pair distribution in the context of all possible combinations of local residue types. We use a probabilistic analysis to deduce how the correlations encoded in the various DPDFs as well as in residue frequencies propagate along the sequence and can be cumulated in a statistical potential capable of efficiently scoring a loop by its backbone conformation and sequence only. Our potential is able to identify with high accuracy the native structure of a loop with a given sequence among possible alternative conformations from sets of well-constructed decoys. Conversely, the potential can also be used for sequence prediction problems and is shown to score the native sequence of a given loop structure among the most fit of the possible sequence combinations. Applications for both structure prediction and sequence design are discussed.

Orientation-dependent backbone-only residue pair scoring functions for fixed backbone protein design

Background

Empirical scoring functions have proven useful in protein structure modeling. Most such scoring functions depend on protein side chain conformations. However, backbone-only scoring functions do not require computationally intensive structure optimization and so are well suited to protein design, which requires fast score evaluation. Furthermore, scoring functions that account for the distinctive relative position and orientation preferences of residue pairs are expected to be more accurate than those that depend only on the separation distance.

Results

Residue pair scoring functions for fixed backbone protein design were derived using only backbone geometry. Unlike previous studies that used spherical harmonics to fit 2D angular distributions, Gaussian Mixture Models were used to fit the full 3D (position only) and 6D (position and orientation) distributions of residue pairs. The performance of the 1D (residue separation only), 3D, and 6D scoring functions were compared by their ability to identify correct threading solutions for a non-redundant benchmark set of protein backbone structures. The threading accuracy was found to steadily increase with increasing dimension, with the 6D scoring function achieving the highest accuracy. Furthermore, the 3D and 6D scoring functions were shown to outperform side chain-dependent empirical potentials from three other studies. Next, two computational methods that take advantage of the speed and pairwise form of these new backbone-only scoring functions were investigated. The first is a procedure that exploits available sequence data by averaging scores over threading solutions for homologs. This was evaluated by applying it to the challenging problem of identifying interacting transmembrane alpha-helices and found to further improve prediction accuracy. The second is a protein design method for determining the optimal sequence for a backbone structure by applying Belief Propagation optimization using the 6D scoring functions. The sensitivity of this method to backbone structure perturbations was compared with that of fixed-backbone all-atom modeling by determining the similarities between optimal sequences for two different backbone structures within the same protein family. The results showed that the design method using 6D scoring functions was more robust to small variations in backbone structure than the all-atom design method.

Conclusions

Backbone-only residue pair scoring functions that account for all six relative degrees of freedom are the most accurate and including the scores of homologs further improves the accuracy in threading applications. The 6D scoring function outperformed several side chain-dependent potentials while avoiding time-consuming and error prone side chain structure prediction. These scoring functions are particularly useful as an initial filter in protein design problems before applying all-atom modeling.

Elucidation of amyloid beta-protein oligomerization mechanisms: discrete molecular dynamics study

Oligomers of amyloid beta-protein (Abeta) play a central role in the pathology of Alzheimer's disease. Of the two predominant Abeta alloforms, Abeta(1-40) and Abeta(1-42), Abeta(1-42) is more strongly implicated in the disease. We elucidated the structural characteristics of oligomers of Abeta(1-40) and Abeta(1-42) and their Arctic mutants, [E22G]Abeta(1-40) and [E22G]Abeta(1-42). We simulated oligomer formation using discrete molecular dynamics (DMD) with a four-bead protein model, backbone hydrogen bonding, and residue-specific interactions due to effective hydropathy and charge. For all four peptides under study, we derived the characteristic oligomer size distributions that were in agreement with prior experimental findings. Unlike Abeta(1-40), Abeta(1-42) had a high propensity to form paranuclei (pentameric or hexameric) structures that could self-associate into higher-order oligomers. Neither of the Arctic mutants formed higher-order oligomers, but [E22G]Abeta(1-40) formed paranuclei with a similar propensity to that of Abeta(1-42). Whereas the best agreement with the experimental data was obtained when the charged residues were modeled as solely hydrophilic, further assembly from spherical oligomers into elongated protofibrils was induced by nonzero electrostatic interactions among the charged residues. Structural analysis revealed that the C-terminal region played a dominant role in Abeta(1-42) oligomer formation whereas Abeta(1-40) oligomerization was primarily driven by intermolecular interactions among the central hydrophobic regions. The N-terminal region A2-F4 played a prominent role in Abeta(1-40) oligomerization but did not contribute to the oligomerization of Abeta(1-42) or the Arctic mutants. The oligomer structure of both Arctic peptides resembled Abeta(1-42) more than Abeta(1-40), consistent with their potentially more toxic nature.

New statistical potential for quality assessment of protein models and a survey of energy functions

Background

Scoring functions, such as molecular mechanic forcefields and statistical potentials are fundamentally important tools in protein structure modeling and quality assessment.

Results

The performances of a number of publicly available scoring functions are compared with a statistical rigor, with an emphasis on knowledge-based potentials. We explored the effect on accuracy of alternative choices for representing interaction center types and other features of scoring functions, such as using information on solvent accessibility, on torsion angles, accounting for secondary structure preferences and side chain orientation. Partially based on the observations made, we present a novel residue based statistical potential, which employs a shuffled reference state definition and takes into account the mutual orientation of residue side chains. Atom- and residue-level statistical potentials and Linux executables to calculate the energy of a given protein proposed in this work can be downloaded from http://www.fiserlab.org/potentials.

Conclusions

Among the most influential terms we observed a critical role of a proper reference state definition and the benefits of including information about the microenvironment of interaction centers. Molecular mechanical potentials were also tested and found to be over-sensitive to small local imperfections in a structure, requiring unfeasible long energy relaxation before energy scores started to correlate with model quality.

Template-based and free modeling by RAPTOR++ in CASP8

We developed and tested RAPTOR++ in CASP8 for protein structure prediction. RAPTOR++ contains four modules: threading, model quality assessment, multiple protein alignment, and template-free modeling. RAPTOR++ first threads a target protein to all the templates using three methods and then predicts the quality of the 3D model implied by each alignment using a model quality assessment method. Based upon the predicted quality, RAPTOR++ employs different strategies as follows. If multiple alignments have good quality, RAPTOR++ builds a multiple protein alignment between the target and top templates and then generates a 3D model using MODELLER. If all the alignments have very low quality, RAPTOR++ uses template-free modeling. Otherwise, RAPTOR++ submits a threading-generated 3D model with the best quality. RAPTOR++ was not ready for the first 1/3 targets and was under development during the whole CASP8 season. The template-based and template-free modeling modules in RAPTOR++ are not closely integrated. We are using our template-free modeling technique to refine template-based models.

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.

Explicit orientation dependence in empirical potentials and its significance to side-chain modeling

Protein structure modeling and prediction have important applications throughout the biological sciences, from the design of pharmaceuticals to the elucidation of enzyme mechanisms. At the core of most protein modeling is an energy function, the minimum of which represents the free energy "cost" for forming a correct protein structure. The most commonly used energy functions are knowledge-based statistical potential functions; that is, they are empirically derived from statistical analysis of a set of high-resolution protein structures. When that kind of potential function is constructed, the anisotropic orientation dependence between the interacting groups is a critical component for accurately representing key molecular interactions, such as those involved in protein side-chain packing. In the literature, however, many potential functions are limited in their ability to describe orientation dependence. In all-atom potentials, they typically ignore heterogeneous chemical-bond connectivity. In coarse-grained potentials, such as (semi)-residue-based potentials, the simplified representation of residues often reduces the sensitivity of the potential to side-chain orientation. Recently, in an effort to maximally capture the orientation dependence in side-chain interactions, a new type of all-atom statistical potential was developed: OPUS-PSP (potential derived from side-chain packing). The key feature of this potential is its explicit description of orientation dependence in molecular interactions, which is achieved with a basis set of 19 rigid-body blocks extracted from the chemical structures of 20 amino acid residues. This basis set is specifically designed to maximally capture the essential elements of orientation dependence in molecular packing interactions. The potential is constructed from the orientation-specific packing statistics of pairs of those blocks in a nonredundant structural database. On decoy set tests, OPUS-PSP significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and its consistency in achieving high Z scores across decoy sets. The application of OPUS-PSP to conformational modeling of side chains has led to another method, called OPUS-Rota. In terms of combined speed and accuracy, OPUS-Rota outperforms all of the other methods in modeling side-chain conformation. In this Account, we briefly outline the basic scheme of the OPUS-PSP potential and its application to side-chain modeling via OPUS-Rota. Future perspectives on the modeling of orientation dependence are also discussed. The computer programs for OPUS-PSP and OPUS-Rota can be downloaded at http://sigler.bioch.bcm.tmc.edu/MaLab . They are free for academic users.

Optimizing energy potential for protein fold recognition with parametric evaluation function

In this paper, a new optimization method is proposed to determine a simplified energy potential for protein fold recognition, which consists of the residue-residue contact, hydrophobicity, and pseudodihedral potentials. With a parametric evaluation function method, the Z-scores of all the proteins in a training set are optimized simultaneously to obtain the best parameter set of the potential. For this multi-objective and multi-constraint problem, the new optimization scheme is very effective. The derived potential is then tested on two high-quality decoy sets and compared with other classical fold recognition potentials. With the simplified energy potential, we achieve a high level of discrimination capability between correct and incorrect folds.

Mimicking the folding pathway to improve homology-free protein structure prediction

Since the demonstration that the sequence of a protein encodes its structure, the prediction of structure from sequence remains an outstanding problem that impacts numerous scientific disciplines, including many genome projects. By iteratively fixing secondary structure assignments of residues during Monte Carlo simulations of folding, our coarse-grained model without information concerning homology or explicit side chains can outperform current homology-based secondary structure prediction methods for many proteins. The computationally rapid algorithm using only single (phi,psi) dihedral angle moves also generates tertiary structures of accuracy comparable with existing all-atom methods for many small proteins, particularly those with low homology. Hence, given appropriate search strategies and scoring functions, reduced representations can be used for accurately predicting secondary structure and providing 3D structures, thereby increasing the size of proteins approachable by homology-free methods and the accuracy of template methods that depend on a high-quality input secondary structure.

A simple Calpha-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C(alpha)-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.

A Probabilistic Graphical Model for Ab Initio Folding

Despite significant progress in recent years, ab initio folding is still one of the most challenging problems in structural biology. This paper presents a probabilistic graphical model for ab initio folding, which employs Conditional Random Fields (CRFs) and directional statistics to model the relationship between the primary sequence of a protein and its three-dimensional structure. Different from the widely-used fragment assembly method and the lattice model for protein folding, our graphical model can explore protein conformations in a continuous space according to their probability. The probability of a protein conformation reflects its stability and is estimated from PSI-BLAST sequence profile and predicted secondary structure. Experimental results indicate that this new method compares favorably with the fragment assembly method and the lattice model.

How well can the accuracy of comparative protein structure models be predicted?

Comparative structure models are available for two orders of magnitude more protein sequences than are experimentally determined structures. These models, however, suffer from two limitations that experimentally determined structures do not: They frequently contain significant errors, and their accuracy cannot be readily assessed. We have addressed the latter limitation by developing a protocol optimized specifically for predicting the Calpha root-mean-squared deviation (RMSD) and native overlap (NO3.5A) errors of a model in the absence of its native structure. In contrast to most traditional assessment scores that merely predict one model is more accurate than others, this approach quantifies the error in an absolute sense, thus helping to determine whether or not the model is suitable for intended applications. The assessment relies on a model-specific scoring function constructed by a support vector machine. This regression optimizes the weights of up to nine features, including various sequence similarity measures and statistical potentials, extracted from a tailored training set of models unique to the model being assessed: If possible, we use similarly sized models with the same fold; otherwise, we use similarly sized models with the same secondary structure composition. This protocol predicts the RMSD and NO3.5A errors for a diverse set of 580,317 comparative models of 6174 sequences with correlation coefficients (r) of 0.84 and 0.86, respectively, to the actual errors. This scoring function achieves the best correlation compared to 13 other tested assessment criteria that achieved correlations ranging from 0.35 to 0.71.

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.