All-atom Energy Function Research Articles

A memetic algorithm enables efficient local and global all-atom protein-protein docking with backbone and side-chain flexibility

Protein complex formation is encoded by specific interactions at the atomic scale, but the computational cost of modeling proteins at this level often requires use of simplified energy models and limited conformational flexibility. In particular, use of all-atom energy functions and backbone and side-chain flexibility results in rugged energy landscapes that are difficult to explore. In this study, we develop a protein-protein docking algorithm, EvoDOCK, that combines the strength of a differential evolution algorithm for efficient exploration of the global search space with the benefits of a local optimization method to refine detailed atomic interactions. EvoDOCK enabled accurate and fast local and global protein-protein docking using an all-atom energy function with side-chain flexibility. Comparison with a standard method built on Monte Carlo optimization demonstrated improved accuracy and increases in computational speed of up to 35 times. The evolutionary algorithm also enabled efficient atomistic docking with backbone flexibility.

Correction to “The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design”

ADVERTISEMENT RETURN TO ISSUEPREVErratumNEXTORIGINAL ARTICLEThis notice is a correctionCorrection to “The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design”Rebecca F. AlfordRebecca F. AlfordMore by Rebecca F. Alfordhttps://orcid.org/0000-0003-0306-8476, Andrew Leaver-FayAndrew Leaver-FayMore by Andrew Leaver-Fay, Jeliazko R. JeliazkovJeliazko R. JeliazkovMore by Jeliazko R. Jeliazkov, Matthew J. O’MearaMatthew J. O’MearaMore by Matthew J. O’Meara, Frank P. DiMaioFrank P. DiMaioMore by Frank P. DiMaio, Hahnbeom ParkHahnbeom ParkMore by Hahnbeom Parkhttps://orcid.org/0000-0002-7129-1912, Maxim V. ShapovalovMaxim V. ShapovalovMore by Maxim V. Shapovalov, P. Douglas RenfrewP. Douglas RenfrewMore by P. Douglas Renfrew, Vikram K. MulliganVikram K. MulliganMore by Vikram K. Mulligan, Kalli KappelKalli KappelMore by Kalli Kappel, Jason W. LabonteJason W. LabonteMore by Jason W. Labonte, Michael S. PacellaMichael S. PacellaMore by Michael S. Pacellahttps://orcid.org/0000-0001-8919-147X, Richard BonneauRichard BonneauMore by Richard Bonneau, Philip BradleyPhilip BradleyMore by Philip Bradley, Roland L. Dunbrack Jr.Roland L. Dunbrack, Jr.More by Roland L. Dunbrack, Jr., Rhiju DasRhiju DasMore by Rhiju Das, David BakerDavid BakerMore by David Baker, Brian KuhlmanBrian KuhlmanMore by Brian Kuhlman, Tanja KortemmeTanja KortemmeMore by Tanja Kortemme, and Jeffrey J. Gray*Jeffrey J. GrayMore by Jeffrey J. Grayhttps://orcid.org/0000-0001-6380-2324Cite this: J. Chem. Theory Comput. 2022, 18, 7, 4594Publication Date (Web):June 6, 2022Publication History Published online6 June 2022Published inissue 12 July 2022https://doi.org/10.1021/acs.jctc.2c00500Copyright © 2022 American Chemical SocietyRIGHTS & PERMISSIONSArticle Views336Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (420 KB) Get e-Alerts Get e-Alerts

Inferring Protein Sequence-Function Relationships with Large-Scale Positive-Unlabeled Learning.

Machine learning can infer how protein sequence maps to function without requiring a detailed understanding of the underlying physical or biological mechanisms. It is challenging to apply existing supervised learning frameworks to large-scale experimental data generated by deep mutational scanning (DMS) and related methods. DMS data often contain high-dimensional and correlated sequence variables, experimental sampling error and bias, and the presence of missing data. Notably, most DMS data do not contain examples of negative sequences, making it challenging to directly estimate how sequence affects function. Here, we develop a positive-unlabeled (PU) learning framework to infer sequence-function relationships from large-scale DMS data. Our PU learning method displays excellent predictive performance across ten large-scale sequence-function datasets, representing proteins of different folds, functions, and library types. The estimated parameters pinpoint key residues that dictate protein structure and function. Finally, we apply our statistical sequence-function model to design highly stabilized enzymes.

A lipophilicity-based energy function for membrane-protein modelling and design.

Membrane-protein design is an exciting and increasingly successful research area which has led to landmarks including the design of stable and accurate membrane-integral proteins based on coiled-coil motifs. Design of topologically more complex proteins, such as most receptors, channels, and transporters, however, demands an energy function that balances contributions from intra-protein contacts and protein-membrane interactions. Recent advances in water-soluble all-atom energy functions have increased the accuracy in structure-prediction benchmarks. The plasma membrane, however, imposes different physical constraints on protein solvation. To understand these constraints, we recently developed a high-throughput experimental screen, called dsTβL, and inferred apparent insertion energies for each amino acid at dozens of positions across the bacterial plasma membrane. Here, we express these profiles as lipophilicity energy terms in Rosetta and demonstrate that the new energy function outperforms previous ones in modelling and design benchmarks. Rosetta ab initio simulations starting from an extended chain recapitulate two-thirds of the experimentally determined structures of membrane-spanning homo-oligomers with <2.5Å root-mean-square deviation within the top-predicted five models (available online: http://tmhop.weizmann.ac.il). Furthermore, in two sequence-design benchmarks, the energy function improves discrimination of stabilizing point mutations and recapitulates natural membrane-protein sequences of known structure, thereby recommending this new energy function for membrane-protein modelling and design.

Positive multistate protein design.

Structure-based computational protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. The usual approach considers a single rigid backbone as a target, which ignores backbone flexibility. Multistate design (MSD) allows instead to consider several backbone states simultaneously, defining challenging computational problems. We introduce efficient reductions of positive MSD problems to Cost Function Networks with two different fitness definitions and implement them in the Pompd (Positive Multistate Protein design) software. Pompd is able to identify guaranteed optimal sequences of positive multistate full protein redesign problems and exhaustively enumerate suboptimal sequences close to the MSD optimum. Applied to nuclear magnetic resonance and back-rubbed X-ray structures, we observe that the average energy fitness provides the best sequence recovery. Our method outperforms state-of-the-art guaranteed computational design approaches by orders of magnitudes and can solve MSD problems with sizes previously unreachable with guaranteed algorithms. https://forgemia.inra.fr/thomas.schiex/pompd as documented Open Source. Supplementary data are available at Bioinformatics online.

Localizing Frustration in Proteins Using All-Atom Energy Functions.

The problems of protein folding and protein design are two sides of the same coin. Protein folding involves exploring a protein's configuration space given a fixed sequence, whereas protein design involves searching in sequence space given a particular target structure. For a protein to fold quickly and reliably, its energy landscape must be biased toward the folded ensemble throughout its configuration space and must lack deep kinetic traps that would otherwise frustrate folding. Evolution has "designed" the sequences of many naturally occurring proteins, through an eons-long process of random mutation and selection, to yield landscapes with a minimal degree of frustration. The task facing humans hoping to design protein sequences that fold into particular structures is to use the available approximate energy functions to sculpt funneled landscapes that work in the laboratory. In this work, we demonstrate how to calculate several localized frustration measures using an all-atom energy function. Specifically, we employ the Rosetta energy function, which has been used successfully to design proteins and which has a natural pairwise decomposition that is suitably solvent-averaged. We calculate these newly developed frustration measures for both a mutated WW domain, FiP35, and a three-helix bundle that was designed completely by humans, Alpha3D. The structure of FiP35 exhibits less localized frustration than that of Alpha3D. A mutation toward the consensus sequence for WW domains in FiP35, which has been shown unexpectedly in experiment to disrupt folding, induces localized frustration by disrupting the hydrophobic core. By performing a limited redesign on the sequence of Alpha3D, we show that some, but not all, mutations that lower the energy also result in decreased frustration. The results suggest that, in addition to being useful for detecting residual frustration in protein structures, optimizing the localized frustration measures presented here may be a useful and automatic means of balancing positive and negative design in protein design tasks.

RefineD: improved protein structure refinement using machine learning based restrained relaxation.

Protein structure refinement aims to bring moderately accurate template-based protein models closer to the native state through conformational sampling. However, guiding the sampling towards the native state by effectively using restraints remains a major issue in structure refinement. Here, we develop a machine learning based restrained relaxation protocol that uses deep discriminative learning based binary classifiers to predict multi-resolution probabilistic restraints from the starting structure and subsequently converts these restraints to be integrated into Rosetta all-atom energy function as additional scoring terms during structure refinement. We use four restraint resolutions as adopted in GDT-HA (0.5, 1, 2 and 4 Å), centered on the Cα atom of each residue that are predicted by ensemble of four deep discriminative classifiers trained using combinations of sequence and structure-derived features as well as several energy terms from Rosetta centroid scoring function. The proposed method, refineD, has been found to produce consistent and substantial structural refinement through the use of cumulative and non-cumulative restraints on 150 benchmarking targets. refineD outperforms unrestrained relaxation strategy or relaxation that is restrained to starting structures using the FastRelax application of Rosetta or atomic-level energy minimization based ModRefiner method as well as molecular dynamics (MD) simulation based FG-MD protocol. Furthermore, by adjusting restraint resolutions, the method addresses the tradeoff that exists between degree and consistency of refinement. These results demonstrate a promising new avenue for improving accuracy of template-based protein models by effectively guiding conformational sampling during structure refinement through the use of machine learning based restraints. http://watson.cse.eng.auburn.edu/refineD/. Supplementary data are available at Bioinformatics online.

Bayesian inference of protein conformational ensembles from limited structural data.

Many proteins consist of folded domains connected by regions with higher flexibility. The details of the resulting conformational ensemble play a central role in controlling interactions between domains and with binding partners. Small-Angle Scattering (SAS) is well-suited to study the conformational states adopted by proteins in solution. However, analysis is complicated by the limited information content in SAS data and care must be taken to avoid constructing overly complex ensemble models and fitting to noise in the experimental data. To address these challenges, we developed a method based on Bayesian statistics that infers conformational ensembles from a structural library generated by all-atom Monte Carlo simulations. The first stage of the method involves a fast model selection based on variational Bayesian inference that maximizes the model evidence of the selected ensemble. This is followed by a complete Bayesian inference of population weights in the selected ensemble. Experiments with simulated ensembles demonstrate that model evidence is capable of identifying the correct ensemble and that correct number of ensemble members can be recovered up to high level of noise. Using experimental data, we demonstrate how the method can be extended to include data from Nuclear Magnetic Resonance (NMR) and structural energies of conformers extracted from the all-atom energy functions. We show that the data from SAXS, NMR chemical shifts and energies calculated from conformers can work synergistically to improve the definition of the conformational ensemble.

A structural homology approach for computational protein design with flexible backbone.

Structure-based Computational Protein design (CPD) plays a critical role in advancing the field of protein engineering. Using an all-atom energy function, CPD tries to identify amino acid sequences that fold into a target structure and ultimately perform a desired function. Energy functions remain however imperfect and injecting relevant information from known structures in the design process should lead to improved designs. We introduce Shades, a data-driven CPD method that exploits local structural environments in known protein structures together with energy to guide sequence design, while sampling side-chain and backbone conformations to accommodate mutations. Shades (Structural Homology Algorithm for protein DESign), is based on customized libraries of non-contiguous in-contact amino acid residue motifs. We have tested Shades on a public benchmark of 40 proteins selected from different protein families. When excluding homologous proteins, Shades achieved a protein sequence recovery of 30% and a protein sequence similarity of 46% on average, compared with the PFAM protein family of the target protein. When homologous structures were added, the wild-type sequence recovery rate achieved 93%. Shades source code is available at https://bitbucket.org/satsumaimo/shades as a patch for Rosetta 3.8 with a curated protein structure database and ITEM library creation software. Supplementary data are available at Bioinformatics online.

Beyond Thermodynamic Constraints: Evolutionary Sampling Generates Realistic Protein Sequence Variation.

Biological evolution generates a surprising amount of site-specific variability in protein sequences. Yet, attempts at modeling this process have been only moderately successful, and current models based on protein structural metrics explain, at best, 60% of the observed variation. Surprisingly, simple measures of protein structure, such as solvent accessibility, are often better predictors of site-specific variability than more complex models employing all-atom energy functions and detailed structural modeling. We suggest here that these more complex models perform poorly because they lack consideration of the evolutionary process, which is, in part, captured by the simpler metrics. We compare protein sequences that are computationally designed to sequences that are computationally evolved using the same protein-design energy function and to homologous natural sequences. We find that, by a wide variety of metrics, evolved sequences are much more similar to natural sequences than are designed sequences. In particular, designed sequences are too conserved on the protein surface relative to natural sequences, whereas evolved sequences are not. Our results suggest that evolutionary simulation produces a realistic sampling of sequence space. By contrast, protein design-at least as currently implemented-does not. Existing energy functions seem to be sufficiently accurate to correctly describe the key thermodynamic constraints acting on protein sequences, but they need to be paired with realistic sampling schemes to generate realistic sequence alignments.

The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design.

Over the past decade, the Rosetta biomolecular modeling suite has informed diverse biological questions and engineering challenges ranging from interpretation of low-resolution structural data to design of nanomaterials, protein therapeutics, and vaccines. Central to Rosetta's success is the energy function: a model parametrized from small-molecule and X-ray crystal structure data used to approximate the energy associated with each biomolecule conformation. This paper describes the mathematical models and physical concepts that underlie the latest Rosetta energy function, called the Rosetta Energy Function 2015 (REF15). Applying these concepts, we explain how to use Rosetta energies to identify and analyze the features of biomolecular models. Finally, we discuss the latest advances in the energy function that extend its capabilities from soluble proteins to also include membrane proteins, peptides containing noncanonical amino acids, small molecules, carbohydrates, nucleic acids, and other macromolecules.

The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design

The Rosetta All-Atom Energy Function for Macromolecular Modeling and Design

Structure Prediction of RNA Loops with a Probabilistic Approach.

The knowledge of the tertiary structure of RNA loops is important for understanding their functions. In this work we develop an efficient approach named RNApps, specifically designed for predicting the tertiary structure of RNA loops, including hairpin loops, internal loops, and multi-way junction loops. It includes a probabilistic coarse-grained RNA model, an all-atom statistical energy function, a sequential Monte Carlo growth algorithm, and a simulated annealing procedure. The approach is tested with a dataset including nine RNA loops, a 23S ribosomal RNA, and a large dataset containing 876 RNAs. The performance is evaluated and compared with a homology modeling based predictor and an ab initio predictor. It is found that RNApps has comparable performance with the former one and outdoes the latter in terms of structure predictions. The approach holds great promise for accurate and efficient RNA tertiary structure prediction.

Atomic-Accuracy Prediction of Protein Loop Structures through an RNA-Inspired Ansatz

Consistently predicting biopolymer structure at atomic resolution from sequence alone remains a difficult problem, even for small sub-segments of large proteins. Such loop prediction challenges, which arise frequently in comparative modeling and protein design, can become intractable as loop lengths exceed 10 residues and if surrounding side-chain conformations are erased. Current approaches, such as the protein local optimization protocol or kinematic inversion closure (KIC) Monte Carlo, involve stages that coarse-grain proteins, simplifying modeling but precluding a systematic search of all-atom configurations. This article introduces an alternative modeling strategy based on a ‘stepwise ansatz’, recently developed for RNA modeling, which posits that any realistic all-atom molecular conformation can be built up by residue-by-residue stepwise enumeration. When harnessed to a dynamic-programming-like recursion in the Rosetta framework, the resulting stepwise assembly (SWA) protocol enables enumerative sampling of a 12 residue loop at a significant but achievable cost of thousands of CPU-hours. In a previously established benchmark, SWA recovers crystallographic conformations with sub-Angstrom accuracy for 19 of 20 loops, compared to 14 of 20 by KIC modeling with a comparable expenditure of computational power. Furthermore, SWA gives high accuracy results on an additional set of 15 loops highlighted in the biological literature for their irregularity or unusual length. Successes include cis-Pro touch turns, loops that pass through tunnels of other side-chains, and loops of lengths up to 24 residues. Remaining problem cases are traced to inaccuracies in the Rosetta all-atom energy function. In five additional blind tests, SWA achieves sub-Angstrom accuracy models, including the first such success in a protein/RNA binding interface, the YbxF/kink-turn interaction in the fourth ‘RNA-puzzle’ competition. These results establish all-atom enumeration as an unusually systematic approach to ab initio protein structure modeling that can leverage high performance computing and physically realistic energy functions to more consistently achieve atomic accuracy.

High-Resolution Comparative Modeling with RosettaCM

We describe an improved method for comparative modeling, RosettaCM, which optimizes a physically realistic all-atom energy function over the conformational space defined by homologous structures. Given a set of sequence alignments, RosettaCM assembles topologies by recombining aligned segments in Cartesian space and building unaligned regions de novo in torsion space. The junctions between segments are regularized using a loop closure method combining fragment superposition with gradient-based minimization. The energies of the resulting models are optimized by all-atom refinement, and the most representative low-energy model is selected. The CASP10 experiment suggests that RosettaCM yields models with more accurate side-chain and backbone conformations than other methods when the sequence identity to the templates is greater than ∼15%.

Efficient Sampling in Fragment-Based Protein Structure Prediction Using an Estimation of Distribution Algorithm

Fragment assembly is a powerful method of protein structure prediction that builds protein models from a pool of candidate fragments taken from known structures. Stochastic sampling is subsequently used to refine the models. The structures are first represented as coarse-grained models and then as all-atom models for computational efficiency. Many models have to be generated independently due to the stochastic nature of the sampling methods used to search for the global minimum in a complex energy landscape. In this paper we present , a fragment-based approach which shares information between the generated models and steers the search towards native-like regions. A distribution over fragments is estimated from a pool of low energy all-atom models. This iteratively-refined distribution is used to guide the selection of fragments during the building of models for subsequent rounds of structure prediction. The use of an estimation of distribution algorithm enabled to reach lower energy levels and to generate a higher percentage of near-native models. uses an all-atom energy function and produces models with atomic resolution. We observed an improvement in energy-driven blind selection of models on a benchmark of in comparison with the AbInitioRelax protocol.

Loop prediction for a GPCR homology model: Algorithms and results

We present loop structure prediction results of the intracellular and extracellular loops of four G-protein-coupled receptors (GPCRs): bovine rhodopsin (bRh), the turkey β1-adrenergic (β1Ar), the human β2-adrenergic (β2Ar) and the human A2a adenosine receptor (A2Ar) in perturbed environments. We used the protein local optimization program, which builds thousands of loop candidates by sampling rotamer states of the loops' constituent amino acids. The candidate loops are discriminated between with our physics-based, all-atom energy function, which is based on the OPLS force field with implicit solvent and several correction terms. For relevant cases, explicit membrane molecules are included to simulate the effect of the membrane on loop structure. We also discuss a new sampling algorithm that divides phase space into different regions, allowing more thorough sampling of long loops that greatly improves results. In the first half of the paper, loop prediction is done with the GPCRs' transmembrane domains fixed in their crystallographic positions, while the loops are built one-by-one. Side chains near the loops are also in non-native conformations. The second half describes a full homology model of β2Ar using β1Ar as a template. No information about the crystal structure of β2Ar was used to build this homology model. We are able to capture the architecture of short loops and the very long second extracellular loop, which is key for ligand binding. We believe this the first successful example of an RMSD validated, physics-based loop prediction in the context of a GPCR homology model.

Accurate protein structure modeling using sparse NMR data and homologous structure information

While information from homologous structures plays a central role in X-ray structure determination by molecular replacement, such information is rarely used in NMR structure determination because it can be incorrect, both locally and globally, when evolutionary relationships are inferred incorrectly or there has been considerable evolutionary structural divergence. Here we describe a method that allows robust modeling of protein structures of up to 225 residues by combining (1)H(N), (13)C, and (15)N backbone and (13)Cβ chemical shift data, distance restraints derived from homologous structures, and a physically realistic all-atom energy function. Accurate models are distinguished from inaccurate models generated using incorrect sequence alignments by requiring that (i) the all-atom energies of models generated using the restraints are lower than models generated in unrestrained calculations and (ii) the low-energy structures converge to within 2.0 Å backbone rmsd over 75% of the protein. Benchmark calculations on known structures and blind targets show that the method can accurately model protein structures, even with very remote homology information, to a backbone rmsd of 1.2-1.9 Å relative to the conventional determined NMR ensembles and of 0.9-1.6 Å relative to X-ray structures for well-defined regions of the protein structures. This approach facilitates the accurate modeling of protein structures using backbone chemical shift data without need for side-chain resonance assignments and extensive analysis of NOESY cross-peak assignments.

Modeling and design by hierarchical natural moves

We develop a unique algorithm implemented in the program MOSAICS (Methodologies for Optimization and Sampling in Computational Studies) that is capable of nanoscale modeling without compromising the resolution of interest. This is achieved by modeling with customizable hierarchical degrees of freedom, thereby circumventing major limitations of conventional molecular modeling. With the emergence of RNA-based nanotechnology, large RNAs in all-atom representation are used here to benchmark our algorithm. Our method locates all favorable structural states of a model RNA of significant complexity while improving sampling accuracy and increasing speed many fold over existing all-atom RNA modeling methods. We also modeled the effects of sequence mutations on the structural building blocks of tRNA-based nanotechnology. With its flexibility in choosing arbitrary degrees of freedom as well as in allowing different all-atom energy functions, MOSAICS is an ideal tool to model and design biomolecules of the nanoscale.

An enumerative stepwise ansatz enables atomic-accuracy RNA loop modeling

Atomic-accuracy structure prediction of macromolecules should be achievable by optimizing a physically realistic energy function but is presently precluded by incomplete sampling of a biopolymer's many degrees of freedom. We present herein a working hypothesis, called the "stepwise ansatz," for recursively constructing well-packed atomic-detail models in small steps, enumerating several million conformations for each monomer, and covering all build-up paths. By making use of high-performance computing and the Rosetta framework, we provide first tests of this hypothesis on a benchmark of 15 RNA loop-modeling problems drawn from riboswitches, ribozymes, and the ribosome, including 10 cases that are not solvable by current knowledge-based modeling approaches. For each loop problem, this deterministic stepwise assembly method either reaches atomic accuracy or exposes flaws in Rosetta's all-atom energy function, indicating the resolution of the conformational sampling bottleneck. As a further rigorous test, we have carried out a blind all-atom prediction for a noncanonical RNA motif, the C7.2 tetraloop/receptor, and validated this model through nucleotide-resolution chemical mapping experiments. Stepwise assembly is an enumerative, ab initio build-up method that systematically outperforms existing Monte Carlo and knowledge-based methods for 3D structure prediction.