Minimalist representations and the importance of nearest neighbor effects in protein folding simulations

Ensemble-based molecular docking and spectrofluorometric analysis of interaction between cytotoxin and tumor necrosis factor receptor 1

Cytotoxin (CTX) is a three-finger toxin presents predominantly in cobra venom. The functional site of the toxin is located at its three hydrophobic loop tips. Its actual mechanism of cytotoxicity remains inconclusive as few conflicting hypotheses have been proposed in addition to direct cytolytic effects. The present work investigated the interaction between CTX and death receptor families via ensemble-based molecular docking and fluorescence titration analysis. Multiple sequence alignments of different CTX isoforms obtained a conserved CTX sequence. The three-dimensional structure of the conserved CTX was later determined using homology modelling, and its quality was validated. Ensemble-based molecular docking of CTX was performed with different death receptors, such as Fas-ligand and tumor necrosis factor receptor families. Our results showed that tumor necrosis factor receptor 1 (TNFR1) was the best receptor interacting with CTX attributed to the interaction of all three functional loops and evinced with low HADDOCK, Z-score and RMSD value. The interaction between CTX and TNFR1 was also supported by a concentration-dependent reduction of fluorescence intensity with increasing binding affinity. The possible intermolecular interactions between CTX and TNFR1 were Van der Waals forces and hydrogen bonding. Our findings suggest a possibility that CTX triggers apoptosis cell death through non-covalent interactions with TNFR1.Communicated by Ramaswamy H. Sarma.

Dydrogesterone and levonorgestrel at environmentally relevant concentrations have antagonist effects with rhythmic oscillation in brain and eyes of zebrafish

Synthetic progestins levonorgestrel (LNG) and dydrogesterone (DDG) are frequency detected in surface water. Combined effects of LNG and DDG on gonad differentiation are similar to LNG single exposure in juvenile zebrafish. However, LNG and DDG mixtures have stronger effects on spermatogenesis in testes of adult zebrafish, which show variable at different life stage. Effects of LNG and DDG mixtures on eyes and brain remain unknown. Here we investigated effects of LNG, DDG and their mixtures on eyes and brain. Zebrafish were exposed to LNG, DDG and their mixtures from 2 hpf to 144 dpf. Rhythm and vision related biological processes were enriched in eyes and brain in LNG and DDG treatments, which indicated rhythmic oscillation in eyes and brain. The qPCR data revealed that both LNG and DDG decreased transcription of arntl2 and clocka, while increased transcription of per1a, per1b, rpe65a and tefa in eyes and brain. However, DDG and LNG mixtures had slight effect on transcription of genes related to rhythm and vision. In addition, LNG and DDG reduced the thickness of inner nuclear layer in the eyes. Bliss independent model revealed that LNG and DDG had antagonist effects on transcription and histology in eyes and brain. Moreover, LNG and DDG formed the same hydrogen bonds with green-sensitive opsin-4 and rhodopsin kinase GRK7a. Taken together, LNG and DDG competed with each other for the same binding residues resulting in antagonist effect in their mixtures treatments, and have significant ecological implications to assess combined effects of progestins mixtures on fish in different organs.

Gene-specific features enhance interpretation of mutational impact on acid α-glucosidase enzyme activity

We present a computational model for predicting mutational impact on enzymatic activity of human acid α-glucosidase (GAA), an enzyme associated with Pompe disease. Using a model that combines features specific to GAA with other general evolutionary and physiochemical features, we made blind predictions of enzymatic activity relative to wildtype human GAA for >300 GAA mutants, as part of the Critical Assessment of Genome Interpretation 5 GAA challenge. We found that gene-specific features can improve the performance of existing impact prediction tools that mostly rely on general features for pathogenicity prediction. Majority of the poorly predicted mutants that lower wildtype GAA enzyme activity occurred on the surface of the GAA protein. We also found that gene-specific features were uncorrelated with existing methods and provided orthogonal information for interpreting the origin of pathogenicity, particular in variants that are poorly predicted by existing general methods. Specific variants in GAA, when investigated in the context of its protein structure, suggested gene-specific information like the disruption of local backbone torsional geometry and disruption of particular sidechain-sidechain hydrogen bonds as some potential sources for pathogenicity.

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.

RaptorX-Angle: real-value prediction of protein backbone dihedral angles through a hybrid method of clustering and deep learning

Background

Protein dihedral angles provide a detailed description of protein local conformation. Predicted dihedral angles can be used to narrow down the conformational space of the whole polypeptide chain significantly, thus aiding protein tertiary structure prediction. However, direct angle prediction from sequence alone is challenging.

Results

In this article, we present a novel method (named RaptorX-Angle) to predict real-valued angles by combining clustering and deep learning. Tested on a subset of PDB25 and the targets in the latest two Critical Assessment of protein Structure Prediction (CASP), our method outperforms the existing state-of-art method SPIDER2 in terms of Pearson Correlation Coefficient (PCC) and Mean Absolute Error (MAE). Our result also shows approximately linear relationship between the real prediction errors and our estimated bounds. That is, the real prediction error can be well approximated by our estimated bounds.

Conclusions

Our study provides an alternative and more accurate prediction of dihedral angles, which may facilitate protein structure prediction and functional study.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2065-x) contains supplementary material, which is available to authorized users.

A novel approach using C. elegans DNA damage-induced apoptosis to characterize the dynamics of uptake transporters for therapeutic drug discoveries

Organic cation transporter (OCT) function is critical for cellular homeostasis. C. elegans lacking OCT-1 displays a shortened lifespan and increased susceptibility to oxidative stress. We show that these phenotypes can be rescued by downregulating the OCT-1 paralogue, OCT-2. Herein, we delineate a biochemical pathway in C. elegans where uptake of genotoxic chemotherapeutics such as doxorubicin and cisplatin, and subsequent DNA damage-induced apoptosis of germ cells, are dependent exclusively upon OCT-2. We characterized OCT-2 as the main uptake transporter for doxorubicin, as well as a number of other therapeutic agents and chemical compounds, some identified through ligand-protein docking analyses. We provide insights into the conserved features of the structure and function and gene regulation of oct-1 and oct-2 in distinct tissues of C. elegans. Importantly, our innovative approach of exploiting C. elegans uptake transporters in combination with defective DNA repair pathways will have broad applications in medicinal chemistry.

Structure of a novel 13 nm dodecahedral nanocage assembled from a redesigned bacterial microcompartment shell protein

We report the crystal structure of a novel 60-subunit dodecahedral cage that results from self-assembly of a re-engineered version of a natural protein (PduA) from the Pdu microcompartment shell. Biophysical data illustrate the dependence of assembly on solution conditions, opening up new applications in microcompartment studies and nanotechnology.

Mitogen Activated Protein Kinase (MPK) Interacts With Auxin Influx Carrier (OsAux/LAX1) Involved in Auxin Signaling in Plant

Background

Mitogen activated protein kinases (MPKs) are serine/threonine protein kinases that contain characteristic T-x-Y motif in the activation loop region. MPKs are important signaling molecules involved in diverse signaling cascades that regulate plant growth, development and stress responses by conducting phosphorylation events in their target proteins. MPKs phosphorylate their target proteins at either S-P/T-P (Serine/Proline/Threonine) amino acid. To understand, if MPKs are involved in the auxin signaling cascade, we identified probable target proteins of MPKs involved in auxin signaling or transport processes.

Results

A genome-wide search of the rice genome database led us to identification of the OsAux/LAX1 gene as a potential downstream target protein of MPKs. In-silico analysis predicted that MPKs interact with OsAux/LAX1 proteins which were validated by a yeast two-hybrid assay that showed OsMPK3, OsMPK4 and OsMPK6 are physically interact with OsAux/LAX1 protein.

Conclusion

The yeast two-hybrid interaction showed that MPKs are directly involved in auxin signaling events in plants. This is the first study to report direct involvement of MPKs in the auxin signaling pathway.

MHJ_0461 is a multifunctional leucine aminopeptidase on the surface of Mycoplasma hyopneumoniae

Aminopeptidases are part of the arsenal of virulence factors produced by bacterial pathogens that inactivate host immune peptides. Mycoplasma hyopneumoniae is a genome-reduced pathogen of swine that lacks the genetic repertoire to synthesize amino acids and relies on the host for availability of amino acids for growth. M. hyopneumoniae recruits plasmin(ogen) onto its cell surface via the P97 and P102 adhesins and the glutamyl aminopeptidase MHJ_0125. Plasmin plays an important role in regulating the inflammatory response in the lungs of pigs infected with M. hyopneumoniae. We show that recombinant MHJ_0461 (rMHJ_0461) functions as a leucine aminopeptidase (LAP) with broad substrate specificity for leucine, alanine, phenylalanine, methionine and arginine and that MHJ_0461 resides on the surface of M. hyopneumoniae. rMHJ_0461 also binds heparin, plasminogen and foreign DNA. Plasminogen bound to rMHJ_0461 was readily converted to plasmin in the presence of tPA. Computational modelling identified putative DNA and heparin-binding motifs on solvent-exposed sites around a large pore on the LAP hexamer. We conclude that MHJ_0461 is a LAP that moonlights as a multifunctional adhesin on the cell surface of M. hyopneumoniae.

Even with nonnative interactions, the updated folding transition states of the homologs Proteins G & L are extensive and similar

Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We characterize the TSEs for Protein G and NuG2b, a triple mutant of NuG2, using ψ analysis, a method for identifying contacts in the TSE. All three homologs are found to share a common and near-native TSE topology with interactions between all four strands. However, the helical content varies in the TSE, being largely absent in Proteins G & L but partially present in NuG2b. The variability likely arises from competing propensities for the formation of nonnative β turns in the naturally occurring proteins, as observed in our TerItFix folding algorithm. All-atom folding simulations of NuG2b recapitulate the observed TSEs with four strands for 5 of 27 transition paths [Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) Science 334(6055):517-520]. Our data support the view that homologous proteins have similar folding mechanisms, even when nonnative interactions are present in the transition state. These findings emphasize the ongoing challenge of accurately characterizing and predicting TSEs, even for relatively simple proteins.

Electronic polarization stabilizes tertiary structure prediction of HP-36

Molecular dynamic (MD) simulations with both implicit and explicit solvent models have been carried out to study the folding dynamics of HP-36 protein. Starting from the extended conformation, the secondary structure of all three helices in HP-36 was formed in about 50 ns and remained stable in the remaining simulation. However, the formation of the tertiary structure was difficult. Although some intermediates were close to the native structure, the overall conformation was not stable. Further analysis revealed that the large structure fluctuation of loop and hydrophobic core regions was devoted mostly to the instability of the structure during MD simulation. The backbone root-mean-square deviation (RMSD) of the loop and hydrophobic core regions showed strong correlation with the backbone RMSD of the whole protein. The free energy landscape indicated that the distribution of main chain torsions in loop and turn regions was far away from the native state. Starting from an intermediate structure extracted from the initial AMBER simulation, HP-36 was found to generally fold to the native state under the dynamically adjusted polarized protein-specific charge (DPPC) simulation, while the peptide did not fold into the native structure when AMBER force filed was used. The two best folded structures were extracted and taken into further simulations in water employing AMBER03 charge and DPPC for 25 ns. Result showed that introducing polarization effect into interacting potential could stabilize the near-native protein structure.

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.

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.

Potentials of mean force for protein structure prediction vindicated, formalized and generalized

Understanding protein structure is of crucial importance in science, medicine and biotechnology. For about two decades, knowledge-based potentials based on pairwise distances – so-called “potentials of mean force” (PMFs) – have been center stage in the prediction and design of protein structure and the simulation of protein folding. However, the validity, scope and limitations of these potentials are still vigorously debated and disputed, and the optimal choice of the reference state – a necessary component of these potentials – is an unsolved problem. PMFs are loosely justified by analogy to the reversible work theorem in statistical physics, or by a statistical argument based on a likelihood function. Both justifications are insightful but leave many questions unanswered. Here, we show for the first time that PMFs can be seen as approximations to quantities that do have a rigorous probabilistic justification: they naturally arise when probability distributions over different features of proteins need to be combined. We call these quantities “reference ratio distributions” deriving from the application of the “reference ratio method.” This new view is not only of theoretical relevance but leads to many insights that are of direct practical use: the reference state is uniquely defined and does not require external physical insights; the approach can be generalized beyond pairwise distances to arbitrary features of protein structure; and it becomes clear for which purposes the use of these quantities is justified. We illustrate these insights with two applications, involving the radius of gyration and hydrogen bonding. In the latter case, we also show how the reference ratio method can be iteratively applied to sculpt an energy funnel. Our results considerably increase the understanding and scope of energy functions derived from known biomolecular structures.

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.

Multiscale characterization of protein conformational ensembles

We propose a multiscale exploration method to characterize the conformational space populated by a protein at equilibrium. The method efficiently obtains a large set of equilibrium conformations in two stages: first exploring the entire space at a coarse-grained level of detail, then narrowing a refined exploration to selected low-energy regions. The coarse-grained exploration periodically adds all-atom detail to selected conformations to ensure that the search leads to regions which maintain low energies in all-atom detail. The second stage reconstructs selected low-energy coarse-grained conformations in all-atom detail. A low-dimensional energy landscape associated with all-atom conformations allows focusing the exploration to energy minima and their conformational ensembles. The lowest energy ensembles are enriched with additional all-atom conformations through further multiscale exploration. The lowest energy ensembles obtained from the application of the method to three different proteins correctly capture the known functional states of the considered systems.

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.

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.

Discriminative learning for protein conformation sampling

Protein structure prediction without using templates (i.e., ab initio folding) is one of the most challenging problems in structural biology. In particular, conformation sampling poses as a major bottleneck of ab initio folding. This article presents CRFSampler, an extensible protein conformation sampler, built on a probabilistic graphical model Conditional Random Fields (CRFs). Using a discriminative learning method, CRFSampler can automatically learn more than ten thousand parameters quantifying the relationship among primary sequence, secondary structure, and (pseudo) backbone angles. Using only compactness and self-avoiding constraints, CRFSampler can efficiently generate protein-like conformations from primary sequence and predicted secondary structure. CRFSampler is also very flexible in that a variety of model topologies and feature sets can be defined to model the sequence-structure relationship without worrying about parameter estimation. Our experimental results demonstrate that using a simple set of features, CRFSampler can generate decoys with much higher quality than the most recent HMM model.

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.

Fragment-HMM: a new approach to protein structure prediction

We designed a simple position-specific hidden Markov model to predict protein structure. Our new framework naturally repeats itself to converge to a final target, conglomerating fragment assembly, clustering, target selection, refinement, and consensus, all in one process. Our initial implementation of this theory converges to within 6 A of the native structures for 100% of decoys on all six standard benchmark proteins used in ROSETTA (discussed by Simons and colleagues in a recent paper), which achieved only 14%-94% for the same data. The qualities of the best decoys and the final decoys our theory converges to are also notably better.

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.

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.

OPUS-Ca: a knowledge-based potential function requiring only Calpha positions

In this paper, we report a knowledge-based potential function, named the OPUS-Ca potential, that requires only Calpha positions as input. The contributions from other atomic positions were established from pseudo-positions artificially built from a Calpha trace for auxiliary purposes. The potential function is formed based on seven major representative molecular interactions in proteins: distance-dependent pairwise energy with orientational preference, hydrogen bonding energy, short-range energy, packing energy, tri-peptide packing energy, three-body energy, and solvation energy. From the testing of decoy recognition on a number of commonly used decoy sets, it is shown that the new potential function outperforms all known Calpha-based potentials and most other coarse-grained ones that require more information than Calpha positions. We hope that this potential function adds a new tool for protein structural modeling.

Two-stage folding of HP-35 from ab initio simulations

Accurate ab initio simulation of protein folding is a critical step toward elucidation of protein-folding mechanisms. Here, we demonstrate highly accurate folding of the 35 residue villin headpiece subdomain (HP35) by all-atom molecular dynamics simulations using AMBER FF03 and the generalized-Born solvation model. In a set of 20 micros long simulations, the protein folded to the native state in multiple trajectories, with the lowest C(alpha) RMSD being 0.39 A for residues 2-34 (excluding residues 1 and 35). The native state had the highest population among all sampled conformations, and the center of most populated cluster had a C(alpha) RMSD of 1.63 A. Folding of this protein can be described as a two-stage process that followed a well-defined pathway. In the first stage, formation of helices II and III as a folding intermediate constituted the rate-limiting step and was initiated at a folding nucleus around residues Phe17 and Pro21. The folding intermediate further acted as a template that facilitated the folding and docking of helix I in the second stage. Detailed descriptions of the folding kinetics and the roles of key residues are presented.

Statistical potential for assessment and prediction of protein structures

Protein structures in the Protein Data Bank provide a wealth of data about the interactions that determine the native states of proteins. Using the probability theory, we derive an atomic distance-dependent statistical potential from a sample of native structures that does not depend on any adjustable parameters (Discrete Optimized Protein Energy, or DOPE). DOPE is based on an improved reference state that corresponds to noninteracting atoms in a homogeneous sphere with the radius dependent on a sample native structure; it thus accounts for the finite and spherical shape of the native structures. The DOPE potential was extracted from a nonredundant set of 1472 crystallographic structures. We tested DOPE and five other scoring functions by the detection of the native state among six multiple target decoy sets, the correlation between the score and model error, and the identification of the most accurate non-native structure in the decoy set. For all decoy sets, DOPE is the best performing function in terms of all criteria, except for a tie in one criterion for one decoy set. To facilitate its use in various applications, such as model assessment, loop modeling, and fitting into cryo-electron microscopy mass density maps combined with comparative protein structure modeling, DOPE was incorporated into the modeling package MODELLER-8.