Physics-based Energy Function Research Articles

Computational Design of Peptides with Improved Recognition of the Focal Adhesion Kinase FAT Domain.

We describe a two-stage computational protein design (CPD) methodology for the design of peptides binding to the FAT domain of the protein focal adhesion kinase. The first stage involves high-throughput CPD calculations with the Proteus software. The energies of the folded state are described by a physics-based energy function and of the unfolded peptides by a knowledge-based model that reproduces aminoacid compositions consistent with a helicity scale. The obtained sequences are filtered in terms of the affinity and the stability of the complex. In the second stage, design sequences are further evaluated by all-atom molecular dynamics simulations and binding free energy calculations with a molecular mechanics/implicit solvent free energy function.

Computational optimization of the SARS-CoV-2 receptor-binding-motif affinity for human ACE2

The coronavirus severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is responsible for the coronavirus disease 2019 pandemic, and the closely related SARS-CoV coronavirus enter cells by binding at the human angiotensin converting enzyme 2 (hACE2). The stronger hACE2 affinity of SARS-CoV-2 has been connected with its higher infectivity. In this work, we study hACE2 complexes with the receptor-binding domains (RBDs) of the human SARS-CoV-2 and human SARS-CoV viruses, using all-atom molecular dynamics simulations and computational protein design with a physics-based energy function. The molecular dynamics simulations identify charge-modifying substitutions between the CoV-2 and CoV RBDs, which either increase or decrease the hACE2 affinity of the SARS-CoV-2 RBD. The combined effect of these mutations is small, and the relative affinity is mainly determined by substitutions at residues in contact with hACE2. Many of these findings are in line and interpret recent experiments. Our computational protein design calculations redesign positions 455, 493, 494, and 501 of the SARS-CoV-2 receptor binding motif, which contact hACE2 in the complex and are important for ACE2 recognition. Sampling is enhanced by an adaptive importance sampling Monte Carlo method. Sequences with increased affinity replace CoV-2 glutamine by a negative residue at position 493; serine by a nonpolar or aromatic residue or an asparagine at position 494; and asparagine by valine or threonine at position 501. Substitutions at positions 455 and 501 have a smaller effect on affinity. Substitutions suggested by our design are seen in viral sequences encountered in other species, including bat and pangolin. Our results might be used to identify potential virus strains with higher human infectivity and assist in the design of peptide-based or peptidomimetic compounds with the potential to inhibit SARS-CoV-2 binding at hACE2.

A physics-based energy function allows the computational redesign of a PDZ domain

Computational protein design (CPD) can address the inverse folding problem, exploring a large space of sequences and selecting ones predicted to fold. CPD was used previously to redesign several proteins, employing a knowledge-based energy function for both the folded and unfolded states. We show that a PDZ domain can be entirely redesigned using a “physics-based” energy for the folded state and a knowledge-based energy for the unfolded state. Thousands of sequences were generated by Monte Carlo simulation. Three were chosen for experimental testing, based on their low energies and several empirical criteria. All three could be overexpressed and had native-like circular dichroism spectra and 1D-NMR spectra typical of folded structures. Two had upshifted thermal denaturation curves when a peptide ligand was present, indicating binding and suggesting folding to a correct, PDZ structure. Evidently, the physical principles that govern folded proteins, with a dash of empirical post-filtering, can allow successful whole-protein redesign.

SSIPe: accurately estimating protein-protein binding affinity change upon mutations using evolutionary profiles in combination with an optimized physical energy function.

Most proteins perform their biological functions through interactions with other proteins in cells. Amino acid mutations, especially those occurring at protein interfaces, can change the stability of protein-protein interactions (PPIs) and impact their functions, which may cause various human diseases. Quantitative estimation of the binding affinity changes (ΔΔGbind) caused by mutations can provide critical information for protein function annotation and genetic disease diagnoses. We present SSIPe, which combines protein interface profiles, collected from structural and sequence homology searches, with a physics-based energy function for accurate ΔΔGbind estimation. To offset the statistical limits of the PPI structure and sequence databases, amino acid-specific pseudocounts were introduced to enhance the profile accuracy. SSIPe was evaluated on large-scale experimental data containing 2204 mutations from 177 proteins, where training and test datasets were stringently separated with the sequence identity between proteins from the two datasets below 30%. The Pearson correlation coefficient between estimated and experimental ΔΔGbind was 0.61 with a root-mean-square-error of 1.93 kcal/mol, which was significantly better than the other methods. Detailed data analyses revealed that the major advantage of SSIPe over other traditional approaches lies in the novel combination of the physical energy function with the new knowledge-based interface profile. SSIPe also considerably outperformed a former profile-based method (BindProfX) due to the newly introduced sequence profiles and optimized pseudocount technique that allows for consideration of amino acid-specific prior mutation probabilities. Web-server/standalone program, source code and datasets are freely available at https://zhanglab.ccmb.med.umich.edu/SSIPe and https://github.com/tommyhuangthu/SSIPe. Supplementary data are available at Bioinformatics online.

Adoption of an improved PSO to explore a compound multi-objective energy function in protein structure prediction

The protein structure prediction (PSP) problem, i.e., predicting the three-dimensional structure of a protein from its sequence, remains challenging in computational biology. The inaccuracy of existing protein energy functions and the huge conformation search space make the problem difficult to solve. In this study, the PSP problem is modeled as a multi-objective optimization problem. A physics-based energy function and a knowledge-based energy function are combined to construct the three-objective energy function. An improved multi-objective particle swarm optimization coupled with two archives is employed to execute the conformation space search. In addition, a mechanism based on Pareto non-dominated sorting is designed to properly address the slightly worse solutions. Finally, the experimental results demonstrate the effectiveness of the proposed approach. A new perspective for solving the PSP problem by means of multi-objective optimization is given in this paper.

Hybrid receptor structure/ligand-based docking and activity prediction in ICM: development and evaluation in D3R Grand Challenge 3.

In context of D3R Grand Challenge 3 we have investigated several ligand activity prediction protocols that combined elements of a physics-based energy function (ICM VLS score) and the knowledge-based Atomic Property Field 3D QSAR approach. Activity prediction models utilized poses produced by ICM-Dock with ligand bias and 4D receptor conformational ensembles (LigBEnD). Hybrid APF/P (APF/Physics) models were superior to pure physics- or knowledge-based models in our preliminary tests using rigorous three-fold clustered cross-validation and later proved successful in the blind prediction for D3R GC3 sets, consistently performing well across four different targets. The results demonstrate that knowledge-based and physics-based inputs into the machine-learning activity model can be non-redundant and synergistic.

All-atom four-body knowledge-based statistical potential to distinguish native tertiary RNA structures from nonnative folds

Scientific breakthroughs in recent decades have uncovered the capability of RNA molecules to fulfill a wide array of structural, functional, and regulatory roles in living cells, leading to a concomitantly significant increase in both the number and diversity of experimentally determined RNA three-dimensional (3D) structures. Atomic coordinates from a representative training set of solved RNA structures, displaying low sequence and structure similarity, facilitate derivation of knowledge-based energy functions. Here we develop an all-atom four-body statistical potential and evaluate its capacity to distinguish native RNA 3D structures from nonnative folds based on calculated free energy scores. Atomic four-body nearest-neighbors are objectively identified by their occurrence as tetrahedral vertices in the Delaunay tessellations of RNA structures, and rates of atomic quadruplet interactions expected by chance are obtained from a multinomial reference distribution. Our four-body energy function, referred to as RAMP (ribonucleic acids multibody potential), is subsequently derived by applying the inverted Boltzmann principle to the frequency data, yielding an energy score for each type of atomic quadruplet interaction. Several well-known benchmark datasets reveal that RAMP is comparable with, and often outperforms, existing knowledge- and physics-based energy functions. To the best of our knowledge, this is the first study detailing an RNA tertiary structure-based multibody statistical potential and its comparative evaluation.

Full Protein Sequence Redesign with an MMGBSA Energy Function.

Computational protein design aims to create proteins with novel properties. A key element is the energy or scoring function used to select the sequences and conformations. We study the performance of an "MMGBSA" energy function, which combines molecular mechanics terms, a generalized Born and surface area (GBSA) solvent model, with approximations that make the model pairwise additive. Our approach is implemented in the Proteus software. The use of a physics-based energy function ensures a certain model transferability and explanatory power. As a first test, we redesign the sequence of nine proteins, one position at a time, with the rest of the protein having its native sequence and crystallographic conformation. As a second test, all positions are designed together. The contributions of individual energy terms are evaluated, and various parametrizations are compared. We find that the GB term significantly improves the results compared to simple Coulomb electrostatics but is affected by pairwise decomposition errors when all positions are designed together. The SA term, with distinct energy coefficients for nonpolar and polar atoms, makes a decisive contribution to obtain realistic protein sequences and can partially compensate for the absence of a GB term. With the best GBSA protocol, we obtain nativelike protein cores and Superfamily recognition of almost all of our sequences.

Antibody structure determination using a combination of homology modeling, energy‐based refinement, and loop prediction

We present the blinded prediction results in the Second Antibody Modeling Assessment (AMA-II) using a fully automatic antibody structure prediction method implemented in the programs BioLuminate and Prime. We have developed a novel knowledge based approach to model the CDR loops, using a combination of sequence similarity, geometry matching, and the clustering of database structures. The homology models are further optimized with a physics-based energy function (VSGB2.0), which improves the model quality significantly. H3 loop modeling remains the most challenging task. Our ab initio loop prediction performs well for the H3 loop in the crystal structure context, and allows improved results when refining the H3 loops in the context of homology models. For the 10 human and mouse derived antibodies in this assessment, the average RMSDs for the homology model Fv and framework regions are 1.19 Å and 0.74 Å, respectively. The average RMSDs for five non-H3 CDR loops range from 0.61 Å to 1.05 Å, and the H3 loop average RMSD is 2.91 Å using our knowledge-based loop prediction approach. The ab initio H3 loop predictions yield an average RMSD of 1.28 Å when performed in the context of the crystal structure and 2.67 Å in the context of the homology modeled structure. Notably, our method for predicting the H3 loop in the crystal structure environment ranked first among the seven participating groups in AMA-II, and our method made the best prediction among all participants for seven of the ten targets.

Encounter complexes and dimensionality reduction in protein–protein association

An outstanding challenge has been to understand the mechanism whereby proteins associate. We report here the results of exhaustively sampling the conformational space in protein-protein association using a physics-based energy function. The agreement between experimental intermolecular paramagnetic relaxation enhancement (PRE) data and the PRE profiles calculated from the docked structures shows that the method captures both specific and non-specific encounter complexes. To explore the energy landscape in the vicinity of the native structure, the nonlinear manifold describing the relative orientation of two solid bodies is projected onto a Euclidean space in which the shape of low energy regions is studied by principal component analysis. Results show that the energy surface is canyon-like, with a smooth funnel within a two dimensional subspace capturing over 75% of the total motion. Thus, proteins tend to associate along preferred pathways, similar to sliding of a protein along DNA in the process of protein-DNA recognition. DOI: http://dx.doi.org/10.7554/eLife.01370.001.

GUIDING PROBABILISTIC SEARCH OF THE PROTEIN CONFORMATIONAL SPACE WITH STRUCTURAL PROFILES

The roughness of the protein energy surface poses a significant challenge to search algorithms that seek to obtain a structural characterization of the native state. Recent research seeks to bias search toward near-native conformations through one-dimensional structural profiles of the protein native state. Here we investigate the effectiveness of such profiles in a structure prediction setting for proteins of various sizes and folds. We pursue two directions. We first investigate the contribution of structural profiles in comparison to or in conjunction with physics-based energy functions in providing an effective energy bias. We conduct this investigation in the context of Metropolis Monte Carlo with fragment-based assembly. Second, we explore the effectiveness of structural profiles in providing projection coordinates through which to organize the conformational space. We do so in the context of a robotics-inspired search framework proposed in our lab that employs projections of the conformational space to guide search. Our findings indicate that structural profiles are most effective in obtaining physically realistic near-native conformations when employed in conjunction with physics-based energy functions. Our findings also show that these profiles are very effective when employed instead as projection coordinates to guide probabilistic search toward undersampled regions of the conformational space.

Combining Statistical Potentials with Dynamics-Based Entropies Improves Selection from Protein Decoys and Docking Poses

Protein structure prediction and protein-protein docking are important and widely used tools, but methods to confidently evaluate the quality of a predicted structure or binding pose have had limited success. Typically, either knowledge-based or physics-based energy functions are employed to evaluate a set of predicted structures (termed "decoys" in structure prediction and "poses" in docking), with the lowest energy structure being assumed to be the one closest to the native state. While successful for many cases, failures are still common. Thus, improvements to structure evaluation methods are essential for future improvements. In this work, we combine multibody statistical potentials with dynamics models, evaluating fluctuation-based entropies that include contributions from the entire structure. This leads to enhanced selection of native-like structures for CASP9 decoys, refined ClusPro docking poses, as well as large sets of docking poses from the Benchmark 3.0 and Dockground data sets. The data used include both bound and unbound docking, and positive results are found for each type. Not only does this method yield improved average results, but for high quality docking poses, we often pick the best pose.

How Fast-Folding Proteins Fold

An outstanding challenge in the field of molecular biology has been to understand the process by which proteins fold into their characteristic three-dimensional structures. Here, we report the results of atomic-level molecular dynamics simulations, over periods ranging between 100 μs and 1 ms, that reveal a set of common principles underlying the folding of 12 structurally diverse proteins. In simulations conducted with a single physics-based energy function, the proteins, representing all three major structural classes, spontaneously and repeatedly fold to their experimentally determined native structures. Early in the folding process, the protein backbone adopts a nativelike topology while certain secondary structure elements and a small number of nonlocal contacts form. In most cases, folding follows a single dominant route in which elements of the native structure appear in an order highly correlated with their propensity to form in the unfolded state.

Quality Assessment of Predicted Protein Structures by Using Molecular Dynamic Simulations

In silico protein structure prediction using efficient fully automated servers continues to remain a challenging problem. While many of these servers can generate near-native structures, the lack of reliable structure quality assessment methods makes the identification of these structures problematic. The most common way of discriminating between predicted structures of a given protein is to employ either knowledge or physics based energy functions. Our recently developed MUFOLD-MD server uses an alternative ranking method of the predicted protein structures by testing their relative stability against gradual heating during all atom molecular dynamics (MD) simulations.

Selection of Near-Native Protein Structures by Means of Molecular Dynamics Simulations

In spite of recent advances, the problem of protein structure prediction from the amino acid sequence remains a challenging one. In general, once a large set of model protein structures is predicted one needs to define selection criteria for identifying the structure that is the closest to the native one. The most common way of discriminating between predicted structures of a given protein is to employ either knowledge or physics based energy functions. Here we present an alternative ranking method of the predicted structures of a protein by testing their stability during gradual heating achieved by all atom molecular dynamics (MD) simulations. In general, the smaller the RMSD of the structure of a protein is (with respect to its native one) the more stable this structure is. Thus, one can rank the quality of these structures by comparing the relative stability of the predicted structures against gradual heating. We refer to this approach as the MD-Ranking (MDR) method. We have successfully tested the MDR method on several sets of proteins. We have also tested the MDR method in the 2008 Critical Assessment of Techniques for Protein Structure Prediction (CASP8) competition as part of our MUFOLD-MD server, which worked as follows: i) it generated 10,000 structures using the ab initio method of the Rosetta software, ii) from these, 64 structures with the lowest Rosetta energy were selected, and iii) re-ranked with the MDR method. The top 5 models, with the best MDR score, were submitted to the CASP8 organizers. Based on the official CAP8 results, MUFOLD-MD was ranked as number one server in the Free Modeling category. Work supported by a grant from NIH [R21/R33-GM078601]. Major computer time was provided by the University of Missouri Bioinformatics Consortium.

Simultaneously Targeting Multiple Drug-Resistant Variants with Optimally Small Drug Cocktails: Application and Analysis of Novel Methods

Target mutation is a key problem in drug design. High mutational variation of a drug target leads to resistance: drugs which may have originally functioned as inhibitors lose potency because structural changes in the target lead to losses in binding affinity. One way to approach this problem is through the use of drug cocktails. Using integer-programming and physics-based energy functions, we can select an optimally small cocktail from the combinatorial space of possible drugs built from molecular fragments. This computational framework has been presented in previous work by Radhakrishnan and Tidor (J. Chem. Inf. Model., 2008). Current investigations involve analyzing and improving the efficiency of this method and applying it to rapidly varying targets in the HIV-1 system.

Improved Energy Selection of Nativelike Protein Loops from Loop Decoys.

We demonstrate the performance of a new implicit solvent model on native protein loop prediction from a large set of loop decoys of 4- to 12-residue in length. The physics-based energy function combines a hydrophobic potential of mean force (HPMF) description with a Generalized Born model for polarization of protein charge by the high dielectric solvent, which we combine with AMBER force field for the protein chain. The novelty of our energy function is the stabilizing effect of hydrophobic exposure to aqueous solvent that defines the HPMF hydration physics, which in principle should be an important stabilizing factor for loop conformations of a protein that typically are more solvent exposed. While our results for short loop decoy sets are comparably good to existing energy functions, we find demonstrable superiority for loop lengths of 8-residue and greater, and the quality of our predictions is largely insensitive to the length of the target loop on a filtered set of decoys. Given that the current weakness in loop modeling is the ability to select the most nativelike loop conformers from loop ensembles, this energy function provides a means for greater prediction accuracy in structure prediction of homologous and distantly related proteins, thereby aiding large-scale genomics efforts in comparative modeling.

Can molecular dynamics simulations help in discriminating correct from erroneous protein 3D models?

BackgroundRecent approaches for predicting the three-dimensional (3D) structure of proteins such as de novo or fold recognition methods mostly rely on simplified energy potential functions and a reduced representation of the polypeptide chain. These simplifications facilitate the exploration of the protein conformational space but do not permit to capture entirely the subtle relationship that exists between the amino acid sequence and its native structure. It has been proposed that physics-based energy functions together with techniques for sampling the conformational space, e.g., Monte Carlo or molecular dynamics (MD) simulations, are better suited to the task of modelling proteins at higher resolutions than those of models obtained with the former type of methods. In this study we monitor different protein structural properties along MD trajectories to discriminate correct from erroneous models. These models are based on the sequence-structure alignments provided by our fold recognition method, FROST. We define correct models as being built from alignments of sequences with structures similar to their native structures and erroneous models from alignments of sequences with structures unrelated to their native structures.ResultsFor three test sequences whose native structures belong to the all-α, all-β and αβ classes we built a set of models intended to cover the whole spectrum: from a perfect model, i.e., the native structure, to a very poor model, i.e., a random alignment of the test sequence with a structure belonging to another structural class, including several intermediate models based on fold recognition alignments. We submitted these models to 11 ns of MD simulations at three different temperatures. We monitored along the corresponding trajectories the mean of the Root-Mean-Square deviations (RMSd) with respect to the initial conformation, the RMSd fluctuations, the number of conformation clusters, the evolution of secondary structures and the surface area of residues. None of these criteria alone is 100% efficient in discriminating correct from erroneous models. The mean RMSd, RMSd fluctuations, secondary structure and clustering of conformations show some false positives whereas the residue surface area criterion shows false negatives. However if we consider these criteria in combination it is straightforward to discriminate the two types of models.ConclusionThe ability of discriminating correct from erroneous models allows us to improve the specificity and sensitivity of our fold recognition method for a number of ambiguous cases.

A composite score for predicting errors in protein structure models

Reliable prediction of model accuracy is an important unsolved problem in protein structure modeling. To address this problem, we studied 24 individual assessment scores, including physics-based energy functions, statistical potentials, and machine learning-based scoring functions. Individual scores were also used to construct approximately 85,000 composite scoring functions using support vector machine (SVM) regression. The scores were tested for their abilities to identify the most native-like models from a set of 6000 comparative models of 20 representative protein structures. Each of the 20 targets was modeled using a template of <30% sequence identity, corresponding to challenging comparative modeling cases. The best SVM score outperformed all individual scores by decreasing the average RMSD difference between the model identified as the best of the set and the model with the lowest RMSD (DeltaRMSD) from 0.63 A to 0.45 A, while having a higher Pearson correlation coefficient to RMSD (r=0.87) than any other tested score. The most accurate score is based on a combination of the DOPE non-hydrogen atom statistical potential; surface, contact, and combined statistical potentials from MODPIPE; and two PSIPRED/DSSP scores. It was implemented in the SVMod program, which can now be applied to select the final model in various modeling problems, including fold assignment, target-template alignment, and loop modeling.

Comparison between Generalized-Born and Poisson–Boltzmann methods in physics-based scoring functions for protein structure prediction

Continuum solvent models such as Generalized-Born and Poisson-Boltzmann methods hold the promise to treat solvation effect efficiently and to enable rapid scoring of protein structures when they are combined with physics-based energy functions. Yet, direct comparison of these two approaches on large protein data set is lacking. Building on our previous work with a scoring function based on a Generalized-Born (GB) solvation model, and short molecular-dynamics simulations, we further extended the scoring function to compare with the MM-PBSA method to treat the solvent effect. We benchmarked this scoring function against seven publicly available decoy sets. We found that, somewhat surprisingly, the results of MM-PBSA approach are comparable to the previous GB-based scoring function. We also discussed the effect to the scoring function accuracy due to presence of large ligands and ions in some native structures of the decoy sets.