Knowledge-based Energy Function Research Articles

Fast and accurate Ab Initio Protein structure prediction using deep learning potentials.

Despite the immense progress recently witnessed in protein structure prediction, the modeling accuracy for proteins that lack sequence and/or structure homologs remains to be improved. We developed an open-source program, DeepFold, which integrates spatial restraints predicted by multi-task deep residual neural-networks along with a knowledge-based energy function to guide its gradient-descent folding simulations. The results on large-scale benchmark tests showed that DeepFold creates full-length models with accuracy significantly beyond classical folding approaches and other leading deep learning methods. Of particular interest is the modeling performance on the most difficult targets with very few homologous sequences, where DeepFold achieved an average TM-score that was 40.3% higher than trRosetta and 44.9% higher than DMPfold. Furthermore, the folding simulations for DeepFold were 262 times faster than traditional fragment assembly simulations. These results demonstrate the power of accurately predicted deep learning potentials to improve both the accuracy and speed of ab initio protein structure prediction.

Accurate flexible refinement for atomic-level protein structure using cryo-EM density maps and deep learning.

With the rapid progress of deep learning in cryo-electron microscopy and protein structure prediction, improving the accuracy of the protein structure model by using a density map and predicted contact/distance map through deep learning has become an urgent need for robust methods. Thus, designing an effective protein structure optimization strategy based on the density map and predicted contact/distance map is critical to improving the accuracy of structure refinement. In this article, a protein structure optimization method based on the density map and predicted contact/distance map by deep-learning technology was proposed in accordance with the result of matching between the density map and the initial model. Physics- and knowledge-based energy functions, integrated with Cryo-EM density map data and deep-learning data, were used to optimize the protein structure in the simulation. The dynamic confidence score was introduced to the iterative process for choosing whether it is a density map or a contact/distance map to dominate the movement in the simulation to improve the accuracy of refinement. The protocol was tested on a large set of 224 non-homologous membrane proteins and generated 214 structural models with correct folds, where 4.5% of structural models were generated from structural models with incorrect folds. Compared with other state-of-the-art methods, the major advantage of the proposed methods lies in the skills for using density map and contact/distance map in the simulation, as well as the new energy function in the re-assembly simulations. Overall, the results demonstrated that this strategy is a valuable approach and ready to use for atomic-level structure refinement using cryo-EM density map and predicted contact/distance map.

Pairing a high-resolution statistical potential with a nucleobase-centric sampling algorithm for improving RNA model refinement

Refining modelled structures to approach experimental accuracy is one of the most challenging problems in molecular biology. Despite many years’ efforts, the progress in protein or RNA structure refinement has been slow because the global minimum given by the energy scores is not at the experimentally determined “native” structure. Here, we propose a fully knowledge-based energy function that captures the full orientation dependence of base–base, base–oxygen and oxygen–oxygen interactions with the RNA backbone modelled by rotameric states and internal energies. A total of 4000 quantum-mechanical calculations were performed to reweight base–base statistical potentials for minimizing possible effects of indirect interactions. The resulting BRiQ knowledge-based potential, equipped with a nucleobase-centric sampling algorithm, provides a robust improvement in refining near-native RNA models generated by a wide variety of modelling techniques.

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.

Incorporating a multiobjective knowledge-based energy function into differential evolution for protein structure prediction

Despite the rapid development of computer techniques and the unremitting efforts of researchers, the protein structure prediction (PSP) problem remains challenging in computational biology and bioinformatics. In this study, we model the PSP problem as a multiobjective optimization problem and propose a free modeling approach called MODE-K to solve this problem. Our efforts center on two aspects. First, we use a knowledge-based energy function called RWplus as the evaluation criterion. This function is decomposed into two terms: a distance-dependent energy term and an orientation-dependent energy term. Second, we employ a multiobjective differential evolution coupled with an external archive to perform conformation space searching. After conformation space searching, a cluster method is introduced to select the final predicted structure from a set of decoy structures. We use eighteen test proteins to verify the performance of the proposed approach. The experimental results demonstrate the effectiveness of the proposed approach and indicate that incorporating knowledge-based energy functions into multiobjective approaches to solve the PSP problem is promising.

All-Atom Knowledge-Based Potential for RNA Structure Discrimination Based on the Distance-Scaled Finite Ideal-Gas Reference State.

Noncoding RNAs are increasingly found to play a wide variety of roles in living organisms. Yet, their functional mechanisms are poorly understood because their structures are difficult to determine experimentally. As a result, developing more effective computational techniques to predict RNA structures becomes increasingly an urgent task. One key challenge in RNA structure prediction is the lack of an accurate free energy function to guide RNA folding and discriminate native and near-native structures from decoy conformations. In this study, we developed an all-atom distance-dependent knowledge-based energy function for RNA that is based on a reference state (distance-scaled finite ideal-gas reference state, DFIRE) proven successful for protein structure discrimination. Using four separate benchmarks including RNA puzzles, we found that this DFIRE-based RNA statistical energy function is able to discriminate native and near-native structures against decoys with performance comparable with or better than several existing scoring functions compared. The energy function is expected to be useful for improving the detection of RNA near-native structures.

A comprehensive computational study of amino acid interactions in membrane proteins

Transmembrane proteins play a fundamental role in a wide series of biological processes but, despite their importance, they are less studied than globular proteins, essentially because their embedding in lipid membranes hampers their experimental characterization. In this paper, we improved our understanding of their structural stability through the development of new knowledge-based energy functions describing amino acid pair interactions that prevail in the transmembrane and extramembrane regions of membrane proteins. The comparison of these potentials and those derived from globular proteins yields an objective view of the relative strength of amino acid interactions in the different protein environments, and their role in protein stabilization. Separate potentials were also derived from α-helical and β-barrel transmembrane regions to investigate possible dissimilarities. We found that, in extramembrane regions, hydrophobic residues are less frequent but interactions between aromatic and aliphatic amino acids as well as aromatic-sulfur interactions contribute more to stability. In transmembrane regions, polar residues are less abundant but interactions between residues of equal or opposite charges or non-charged polar residues as well as anion-π interactions appear stronger. This shows indirectly the preference of the water and lipid molecules to interact with polar and hydrophobic residues, respectively. We applied these new energy functions to predict whether a residue is located in the trans- or extramembrane region, and obtained an AUC score of 83% in cross validation, which demonstrates their accuracy. As their application is, moreover, extremely fast, they are optimal instruments for membrane protein design and large-scale investigations of membrane protein stability.

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.

Modeling transcriptional activation changes to Gal4 variants via structure-based computational mutagenesis.

As a DNA binding transcriptional activator, Gal4 promotes the expression of genes responsible for galactose metabolism. The Gal4 protein from Saccharomyces cerevisiae (baker’s yeast) has become a model for studying eukaryotic transcriptional activation in general because its regulatory properties mirror those of several eukaryotic organisms, including mammals. Given the availability of a crystallographic structure for Gal4, here we implement an in silico mutagenesis technique that makes use of a four-body knowledge-based energy function, in order to empirically quantify the structural impacts associated with single residue substitutions on the Gal4 protein. These results were used to examine the structure-function relationship in Gal4 based on a recently published experimental mutagenesis study, whereby functional changes to a uniformly distributed set of 1,068 single residue Gal4 variants were obtained by measuring their transcriptional activation levels relative to wild-type. A significant correlation was observed between computed (scalar) structural effect data and measured activity values for this collection of single residue Gal4 variants. Additionally, attribute vectors quantifying position-specific environmental impacts were generated for each of the Gal4 variants via computational mutagenesis, and we implemented supervised classification and regression statistical machine learning algorithms to train predictive models of variant Gal4 activity based on these structural changes. All models performed well under cross-validation testing, with balanced accuracy reaching 91% among the classification models, and with the actual and predicted activity values displaying a correlation as high as r = 0.80 for the regression models. Reliable predictions of transcriptional activation levels for Gal4 variants that have yet to be studied can be instantly generated by submitting their respective structure-based feature vectors to the trained models for testing. Such a computational pre-screening of Gal4 variants may potentially reduce costs associated with running large-scale mutagenesis experiments.

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.

Diverse effects of distance cutoff and residue interval on the performance of distance-dependent atom-pair potential in protein structure prediction

BackgroundAs one of the most successful knowledge-based energy functions, the distance-dependent atom-pair potential is widely used in all aspects of protein structure prediction, including conformational search, model refinement, and model assessment. During the last two decades, great efforts have been made to improve the reference state of the potential, while other factors that also strongly affect the performance of the potential have been relatively less investigated.ResultsBased on different distance cutoffs (from 5 to 22 Å) and residue intervals (from 0 to 15) as well as six different reference states, we constructed a series of distance-dependent atom-pair potentials and tested them on several groups of structural decoy sets collected from diverse sources. A comprehensive investigation has been performed to clarify the effects of distance cutoff and residue interval on the potential’s performance. Our results provide a new perspective as well as a practical guidance for optimizing distance-dependent statistical potentials.ConclusionsThe optimal distance cutoff and residue interval are highly related with the reference state that the potential is based on, the measurements of the potential’s performance, and the decoy sets that the potential is applied to. The performance of distance-dependent statistical potential can be significantly improved when the best statistical parameters for the specific application environment are adopted.

Next Generation Evolutionary Sampling and Energy Function Guided ab initio Protein Structure Prediction

The conformation of a protein is vital to understand its function. Homology and ab initio modeling are the two major strategies to solve the protein structure prediction from sequence. The homology methods are not applicable in the absence of homologous sequences. This makes the ab initio modeling unavoidable. The development of ab initio method hinges on the effective conformational space sampling and the accurate energy function to guide the search process. In addition, recent studies demonstrates that it is possible to sample and predict good quality protein structure without using native fragments from known protein structures. Towards this goal, we developed an ab initio method that applies a memory assisted Evolutionary Algorithm (EA) to sample the energy hyper-surface of the protein folding process, looking for the global minimum or the native fold of the protein. Sampling of the energy hyper-surface of the protein is achieved by novel mutation and crossover operations based on angular rotation and translation capabilities. Furthermore, the crossover operations in current generation are enhanced by the use of the best parent selected from previous generation. In addition, we developed and employed a knowledge-based novel energy function, called 3DIGARS, which can differentiate the native structure that corresponds to the most thermodynamically stable state, compared to the possible decoy structures most effectively. The 3DIGARS energy function is an optimized combination of crucial properties such as hydrophobic versus hydrophilic properties, sequence-specific predicted accessibility and ubiquitous phi-psi angular characterization. The samples obtained from the sampling of the energy hyper-surface are scored using 3DIGARS and passed through the EA operators for natural selection and processing. The merits of the proposed approach has been rigorously examined and found to be effective.

STRUM: structure-based prediction of protein stability changes upon single-point mutation

Mutations in human genome are mainly through single nucleotide polymorphism, some of which can affect stability and function of proteins, causing human diseases. Several methods have been proposed to predict the effect of mutations on protein stability; but most require features from experimental structure. Given the fast progress in protein structure prediction, this work explores the possibility to improve the mutation-induced stability change prediction using low-resolution structure modeling. We developed a new method (STRUM) for predicting stability change caused by single-point mutations. Starting from wild-type sequences, 3D models are constructed by the iterative threading assembly refinement (I-TASSER) simulations, where physics- and knowledge-based energy functions are derived on the I-TASSER models and used to train STRUM models through gradient boosting regression. STRUM was assessed by 5-fold cross validation on 3421 experimentally determined mutations from 150 proteins. The Pearson correlation coefficient (PCC) between predicted and measured changes of Gibbs free-energy gap, ΔΔG, upon mutation reaches 0.79 with a root-mean-square error 1.2 kcal/mol in the mutation-based cross-validations. The PCC reduces if separating training and test mutations from non-homologous proteins, which reflects inherent correlations in the current mutation sample. Nevertheless, the results significantly outperform other state-of-the-art methods, including those built on experimental protein structures. Detailed analyses show that the most sensitive features in STRUM are the physics-based energy terms on I-TASSER models and the conservation scores from multiple-threading template alignments. However, the ΔΔG prediction accuracy has only a marginal dependence on the accuracy of protein structure models as long as the global fold is correct. These data demonstrate the feasibility to use low-resolution structure modeling for high-accuracy stability change prediction upon point mutations. http://zhanglab.ccmb.med.umich.edu/STRUM/ CONTACT: qiang@suda.edu.cn and zhng@umich.edu Supplementary data are available at Bioinformatics online.

UniCon3D: de novo protein structure prediction using united-residue conformational search via stepwise, probabilistic sampling.

Motivation: Recent experimental studies have suggested that proteins fold via stepwise assembly of structural units named ‘foldons’ through the process of sequential stabilization. Alongside, latest developments on computational side based on probabilistic modeling have shown promising direction to perform de novo protein conformational sampling from continuous space. However, existing computational approaches for de novo protein structure prediction often randomly sample protein conformational space as opposed to experimentally suggested stepwise sampling.Results: Here, we develop a novel generative, probabilistic model that simultaneously captures local structural preferences of backbone and side chain conformational space of polypeptide chains in a united-residue representation and performs experimentally motivated conditional conformational sampling via stepwise synthesis and assembly of foldon units that minimizes a composite physics and knowledge-based energy function for de novo protein structure prediction. The proposed method, UniCon3D, has been found to (i) sample lower energy conformations with higher accuracy than traditional random sampling in a small benchmark of 6 proteins; (ii) perform comparably with the top five automated methods on 30 difficult target domains from the 11th Critical Assessment of Protein Structure Prediction (CASP) experiment and on 15 difficult target domains from the 10th CASP experiment; and (iii) outperform two state-of-the-art approaches and a baseline counterpart of UniCon3D that performs traditional random sampling for protein modeling aided by predicted residue-residue contacts on 45 targets from the 10th edition of CASP.Availability and Implementation: Source code, executable versions, manuals and example data of UniCon3D for Linux and OSX are freely available to non-commercial users at http://sysbio.rnet.missouri.edu/UniCon3D/.Contact: chengji@missouri.eduSupplementary information: Supplementary data are available at Bioinformatics online.

NMRe: a web server for NMR protein structure refinement with high-quality structure validation scores.

Protein structure refinement is a necessary step for the study of protein function. In particular, some nuclear magnetic resonance (NMR) structures are of lower quality than X-ray crystallographic structures. Here, we present NMRe, a web-based server for NMR structure refinement. The previously developed knowledge-based energy function STAP (Statistical Torsion Angle Potential) was used for NMRe refinement. With STAP, NMRe provides two refinement protocols using two types of distance restraints. If a user provides NOE (Nuclear Overhauser Effect) data, the refinement is performed with the NOE distance restraints as a conventional NMR structure refinement. Additionally, NMRe generates NOE-like distance restraints based on the inter-hydrogen distances derived from the input structure. The efficiency of NMRe refinement was validated on 20 NMR structures. Most of the quality assessment scores of the refined NMR structures were better than those of the original structures. The refinement results are provided as a three-dimensional structure view, a secondary structure scheme, and numerical and graphical structure validation scores. NMRe is available at http://psb.kobic.re.kr/nmre/.

BCL::MP-fold: Membrane protein structure prediction guided by EPR restraints.

For many membrane proteins, the determination of their topology remains a challenge for methods like X-ray crystallography and nuclear magnetic resonance (NMR) spectroscopy. Electron paramagnetic resonance (EPR) spectroscopy has evolved as an alternative technique to study structure and dynamics of membrane proteins. The present study demonstrates the feasibility of membrane protein topology determination using limited EPR distance and accessibility measurements. The BCL::MP-Fold (BioChemical Library membrane protein fold) algorithm assembles secondary structure elements (SSEs) in the membrane using a Monte Carlo Metropolis (MCM) approach. Sampled models are evaluated using knowledge-based potential functions and agreement with the EPR data and a knowledge-based energy function. Twenty-nine membrane proteins of up to 696 residues are used to test the algorithm. The RMSD100 value of the most accurate model is better than 8 Å for 27, better than 6 Å for 22, and better than 4 Å for 15 of the 29 proteins, demonstrating the algorithms' ability to sample the native topology. The average enrichment could be improved from 1.3 to 2.5, showing the improved discrimination power by using EPR data.

Efficient conformational space exploration in ab initio protein folding simulation.

Ab initio protein folding simulation largely depends on knowledge-based energy functions that are derived from known protein structures using statistical methods. These knowledge-based energy functions provide us with a good approximation of real protein energetics. However, these energy functions are not very informative for search algorithms and fail to distinguish the types of amino acid interactions that contribute largely to the energy function from those that do not. As a result, search algorithms frequently get trapped into the local minima. On the other hand, the hydrophobic–polar (HP) model considers hydrophobic interactions only. The simplified nature of HP energy function makes it limited only to a low-resolution model. In this paper, we present a strategy to derive a non-uniform scaled version of the real 20×20 pairwise energy function. The non-uniform scaling helps tackle the difficulty faced by a real energy function, whereas the integration of 20×20 pairwise information overcomes the limitations faced by the HP energy function. Here, we have applied a derived energy function with a genetic algorithm on discrete lattices. On a standard set of benchmark protein sequences, our approach significantly outperforms the state-of-the-art methods for similar models. Our approach has been able to explore regions of the conformational space which all the previous methods have failed to explore. Effectiveness of the derived energy function is presented by showing qualitative differences and similarities of the sampled structures to the native structures. Number of objective function evaluation in a single run of the algorithm is used as a comparison metric to demonstrate efficiency.

Predicting DNA-binding proteins and binding residues by complex structure prediction and application to human proteome.

As more and more protein sequences are uncovered from increasingly inexpensive sequencing techniques, an urgent task is to find their functions. This work presents a highly reliable computational technique for predicting DNA-binding function at the level of protein-DNA complex structures, rather than low-resolution two-state prediction of DNA-binding as most existing techniques do. The method first predicts protein-DNA complex structure by utilizing the template-based structure prediction technique HHblits, followed by binding affinity prediction based on a knowledge-based energy function (Distance-scaled finite ideal-gas reference state for protein-DNA interactions). A leave-one-out cross validation of the method based on 179 DNA-binding and 3797 non-binding protein domains achieves a Matthews correlation coefficient (MCC) of 0.77 with high precision (94%) and high sensitivity (65%). We further found 51% sensitivity for 82 newly determined structures of DNA-binding proteins and 56% sensitivity for the human proteome. In addition, the method provides a reasonably accurate prediction of DNA-binding residues in proteins based on predicted DNA-binding complex structures. Its application to human proteome leads to more than 300 novel DNA-binding proteins; some of these predicted structures were validated by known structures of homologous proteins in APO forms. The method [SPOT-Seq (DNA)] is available as an on-line server at http://sparks-lab.org.

BCL::Fold—Protein topology determination from limited NMR restraints

When experimental protein NMR data are too sparse to apply traditional structure determination techniques, de novo protein structure prediction methods can be leveraged. Here, we describe the incorporation of NMR restraints into the protein structure prediction algorithm BCL::Fold. The method assembles discreet secondary structure elements using a Monte Carlo sampling algorithm with a consensus knowledge-based energy function. New components were introduced into the energy function to accommodate chemical shift, nuclear Overhauser effect, and residual dipolar coupling data. In particular, since side chains are not explicitly modeled during the minimization process, a knowledge based potential was created to relate experimental side chain proton-proton distances to Cβ -Cβ distances. In a benchmark test of 67 proteins of known structure with the incorporation of sparse NMR restraints, the correct topology was sampled in 65 cases, with an average best model RMSD100 of 3.4 ± 1.3 Å versus 6.0 ± 2.0 Å produced with the de novo method. Additionally, the correct topology is present in the best scoring 1% of models in 61 cases. The benchmark set includes both soluble and membrane proteins with up to 565 residues, indicating the method is robust and applicable to large and membrane proteins that are less likely to produce rich NMR datasets.

Statistical torsion angle potential energy functions for protein structure modeling: A bicubic interpolation approach

A set of grid type knowledge-based energy functions is introduced for ϕ-χ₁ , ψ-χ₁ , ϕ-ψ, and χ₁ -χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X-ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement.