Paweł Krupa

Lessons from application of the UNRES force field to predictions of structures of CASP10 targets

Significance With the example of the coarse-grained United Residue model of polypeptide chains, this paper demonstrates that the physics-based approach for protein-structure prediction can lead to exceptionally good results when correct domain packing is an issue, even for a highly homologous target. The reason for this is probably that emphasis is placed on energetically favorable residue–residue interactions, including those with residues in relatively flexible linker regions; these regions are usually very different in the target compared with those of proteins in the databases used for template-based modeling. The results suggest that a combination of bioinformatics and a physics-based approach could result in a major increase in the prediction capacity of existing approaches. The performance of the physics-based protocol, whose main component is the United Residue (UNRES) physics-based coarse-grained force field, developed in our laboratory for the prediction of protein structure from amino acid sequence, is illustrated. Candidate models are selected, based on probabilities of the conformational families determined by multiplexed replica-exchange simulations, from the 10th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP10). For target T0663, classified as a new fold, which consists of two domains homologous to those of known proteins, UNRES predicted the correct symmetry of packing, in which the domains are rotated with respect to each other by 180° in the experimental structure. By contrast, models obtained by knowledge-based methods, in which each domain is modeled very accurately but not rotated, resulted in incorrect packing. Two UNRES models of this target were featured by the assessors. Correct domain packing was also predicted by UNRES for the homologous target T0644, which has a similar structure to that of T0663, except that the two domains are not rotated. Predictions for two other targets, T0668 and T0684_D2, are among the best ones by global distance test score. These results suggest that our physics-based method has substantial predictive power. In particular, it has the ability to predict domain–domain orientations, which is a significant advance in the state of the art.

A unified coarse-grained model of biological macromolecules based on mean-field multipole–multipole interactions

AbstractA unified coarse-grained model of three major classes of biological molecules—proteins, nucleic acids, and polysaccharides—has been developed. It is based on the observations that the repeated units of biopolymers (peptide groups, nucleic acid bases, sugar rings) are highly polar and their charge distributions can be represented crudely as point multipoles. The model is an extension of the united residue (UNRES) coarse-grained model of proteins developed previously in our laboratory. The respective force fields are defined as the potentials of mean force of biomacromolecules immersed in water, where all degrees of freedom not considered in the model have been averaged out. Reducing the representation to one center per polar interaction site leads to the representation of average site–site interactions as mean-field dipole–dipole interactions. Further expansion of the potentials of mean force of biopolymer chains into Kubo’s cluster-cumulant series leads to the appearance of mean-field dipole–dipole interactions, averaged in the context of local interactions within a biopolymer unit. These mean-field interactions account for the formation of regular structures encountered in biomacromolecules, e.g., α-helices and β-sheets in proteins, double helices in nucleic acids, and helicoidally packed structures in polysaccharides, which enables us to use a greatly reduced number of interacting sites without sacrificing the ability to reproduce the correct architecture. This reduction results in an extension of the simulation timescale by more than four orders of magnitude compared to the all-atom representation. Examples of the performance of the model are presented. FigureComponents of the Unified Coarse Grained Model (UCGM) of biological macromolecules

Improvement of the Treatment of Loop Structures in the UNRES Force Field by Inclusion of Coupling between Backbone- and Side-Chain-Local Conformational States

The UNited RESidue (UNRES) coarse-grained model of polypeptide chains, developed in our laboratory, enables us to carry out millisecond-scale molecular-dynamics simulations of large proteins effectively. It performs well in ab initio predictions of protein structure, as demonstrated in the last Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP10). However, the resolution of the simulated structure is too coarse, especially in loop regions, which results from insufficient specificity of the model of local interactions. To improve the representation of local interactions, in this work we introduced new side-chain-backbone correlation potentials, derived from a statistical analysis of loop regions of 4585 proteins. To obtain sufficient statistics, we reduced the set of amino-acid-residue types to five groups, derived in our earlier work on structurally optimized reduced alphabets, based on a statistical analysis of the properties of amino-acid structures. The new correlation potentials are expressed as one-dimensional Fourier series in the virtual-bond-dihedral angles involving side-chain centroids. The weight of these new terms was determined by a trial-and-error method, in which Multiplexed Replica Exchange Molecular Dynamics (MREMD) simulations were run on selected test proteins. The best average root-mean-square deviations (RMSDs) of the calculated structures from the experimental structures below the folding-transition temperatures were obtained with the weight of the new side-chain-backbone correlation potentials equal to 0.57. The resulting conformational ensembles were analyzed in detail by using the Weighted Histogram Analysis Method (WHAM) and Wards minimum-variance clustering. This analysis showed that the RMSDs from the experimental structures dropped by 0.5 Å on average, compared to simulations without the new terms, and the deviation of individual residues in the loop region of the computed structures from their counterparts in the experimental structures (after optimum superposition of the calculated and experimental structure) decreased by up to 8 Å. Consequently, the new terms improve the representation of local structure.

WeFold: A coopetition for protein structure prediction

The protein structure prediction problem continues to elude scientists. Despite the introduction of many methods, only modest gains were made over the last decade for certain classes of prediction targets. To address this challenge, a social‐media based worldwide collaborative effort, named WeFold, was undertaken by 13 labs. During the collaboration, the laboratories were simultaneously competing with each other. Here, we present the first attempt at “coopetition” in scientific research applied to the protein structure prediction and refinement problems. The coopetition was possible by allowing the participating labs to contribute different components of their protein structure prediction pipelines and create new hybrid pipelines that they tested during CASP10. This manuscript describes both successes and areas needing improvement as identified throughout the first WeFold experiment and discusses the efforts that are underway to advance this initiative. A footprint of all contributions and structures are publicly accessible at http://www.wefold.org. Proteins 2014; 82:1850–1868.

Physics-based potentials for the coupling between backbone- and side-chain-local conformational states in the united residue (UNRES) force field for protein simulations

The UNited RESidue (UNRES) model of polypeptide chains is a coarse-grained model in which each amino-acid residue is reduced to two interaction sites, namely, a united peptide group (p) located halfway between the two neighboring α-carbon atoms (Cαs), which serve only as geometrical points, and a united side chain (SC) attached to the respective Cα. Owing to this simplification, millisecond molecular dynamics simulations of large systems can be performed. While UNRES predicts overall folds well, it reproduces the details of local chain conformation with lower accuracy. Recently, we implemented new knowledge-based torsional potentials (Krupa et al. J. Chem. Theory Comput. 2013, 9, 4620–4632) that depend on the virtual-bond dihedral angles involving side chains: Cα···Cα···Cα···SC (τ(1)), SC···Cα···Cα···Cα (τ(2)), and SC···Cα···Cα···SC (τ(3)) in the UNRES force field. These potentials resulted in significant improvement of the simulated structures, especially in the loop regions. In this work, we introduce the physics-based counterparts of these potentials, which we derived from the all-atom energy surfaces of terminally blocked amino-acid residues by Boltzmann integration over the angles λ(1) and λ(2) for rotation about the Cα···Cα virtual-bond angles and over the side-chain angles χ. The energy surfaces were, in turn, calculated by using the semiempirical AM1 method of molecular quantum mechanics. Entropy contribution was evaluated with use of the harmonic approximation from Hessian matrices. One-dimensional Fourier series in the respective virtual-bond-dihedral angles were fitted to the calculated potentials, and these expressions have been implemented in the UNRES force field. Basic calibration of the UNRES force field with the new potentials was carried out with eight training proteins, by selecting the optimal weight of the new energy terms and reducing the weight of the regular torsional terms. The force field was subsequently benchmarked with a set of 22 proteins not used in the calibration. The new potentials result in a decrease of the root-mean-square deviation of the average conformation from the respective experimental structure by 0.86 Å on average; however, improvement of up to 5 Å was observed for some proteins.

Molecular modeling of the binding modes of the iron‐sulfur protein to the Jac1 co‐chaperone from Saccharomyces cerevisiae by all‐atom and coarse‐grained approaches

The iron‐sulfur protein 1 (Isu1) and the J‐type co‐chaperone Jac1 from yeast are part of a huge ATP‐dependent system, and both interact with Hsp70 chaperones. Interaction of Isu1 and Jac1 is a part of the iron‐sulfur cluster biogenesis system in mitochondria. In this study, the structure and dynamics of the yeast Isu1–Jac1 complex has been modeled. First, the complete structure of Isu1 was obtained by homology modeling using the I‐TASSER server and YASARA software and thereafter tested for stability in the all‐atom force field AMBER. Then, the known experimental structure of Jac1 was adopted to obtain initial models of the Isu1–Jac1 complex by using the ZDOCK server for global and local docking and the AutoDock software for local docking. Three most probable models were subsequently subjected to the coarse‐grained molecular dynamics simulations with the UNRES force field to obtain the final structures of the complex. In the most probable model, Isu1 binds to the left face of the Γ‐shaped Jac1 molecule by the β‐sheet section of Isu1. Residues L105, L109, and Y163 of Jac1 have been assessed by mutation studies to be essential for binding (Ciesielski et al., J Mol Biol 2012; 417:1–12). These residues were also found, by UNRES/molecular dynamics simulations, to be involved in strong interactions between Isu1 and Jac1 in the complex. Moreover, N95, T98, P102, H112, V159, L167, and A170 of Jac1, not yet tested experimentally, were also found to be important in binding. Proteins 2015; 83:1414–1426.

Prediction of Protein Structure by Template-Based Modeling Combined with the UNRES Force Field.

A new approach to the prediction of protein structures that uses distance and backbone virtual-bond dihedral angle restraints derived from template-based models and simulations with the united residue (UNRES) force field is proposed. The approach combines the accuracy and reliability of template-based methods for the segments of the target sequence with high similarity to those having known structures with the ability of UNRES to pack the domains correctly. Multiplexed replica-exchange molecular dynamics with restraints derived from template-based models of a given target, in which each restraint is weighted according to the accuracy of the prediction of the corresponding section of the molecule, is used to search the conformational space, and the weighted histogram analysis method and cluster analysis are applied to determine the families of the most probable conformations, from which candidate predictions are selected. To test the capability of the method to recover template-based models from restraints, five single-domain proteins with structures that have been well-predicted by template-based methods were used; it was found that the resulting structures were of the same quality as the best of the original models. To assess whether the new approach can improve template-based predictions with incorrectly predicted domain packing, four such targets were selected from the CASP10 targets; for three of them the new approach resulted in significantly better predictions compared with the original template-based models. The new approach can be used to predict the structures of proteins for which good templates can be found for sections of the sequence or an overall good template can be found for the entire sequence but the prediction quality is remarkably weaker in putative domain-linker regions.

Maximum Likelihood Calibration of the UNRES Force Field for Simulation of Protein Structure and Dynamics

By using the maximum likelihood method for force-field calibration recently developed in our laboratory, which is aimed at achieving the agreement between the simulated conformational ensembles of selected training proteins and the corresponding ensembles determined experimentally at various temperatures, the physics-based coarse-grained UNRES force field for simulations of protein structure and dynamics was optimized with seven small training proteins exhibiting a variety of secondary and tertiary structures. Four runs of optimization, in which the number of optimized force-field parameters was gradually increased, were carried out, and the resulting force fields were subsequently tested with a set of 22 α-, 12 β-, and 12 α + β-proteins not used in optimization. The variant in which energy-term weights, local, and correlation potentials, side-chain radii, and anisotropies were optimized turned out to be the most transferable and outperformed all previous versions of UNRES on the test set.

Studies of conformational changes of an arginine-binding protein from Thermotoga maritima in the presence and absence of ligand via molecular dynamics simulations with the coarse-grained UNRES force field

The arginine-binding protein (ArgBP) from the hyperthermophilic eubacterium Thermotoga maritima (TmArgBP) is responsible for arginine transport through the bacterial cell membrane. The protein binds a single molecule of l-arginine, which results in conformational changes due to hinge bending. Thereby, TmArgBP acquires one of two possible conformations: open (without the presence of the arginine ligand) and closed (in the presence of the arginine ligand). Here we report a molecular dynamics study of the influence of the presence or absence of the ligand on the dynamics of TmArgBP, using the coarse-grained UNRES force field. The results of our studies indicate that binding of the arginine ligand promotes a closed conformation, which agrees with experimental data. However, the sensitivity of the TmArgBP conformation to the presence of arginine decreases and the protein becomes more flexible with increasing temperature, which might be related to the functionality of this protein in the thermophilic organism T. maritima.

Prediction of protein structure with the coarse-grained UNRES force field assisted by small X-ray scattering data and knowledge-based information

A new approach to assisted protein–structure prediction has been proposed, which is based on running multiplexed replica exchange molecular dynamics simulations with the coarse‐grained UNRES force field with restraints derived from knowledge‐based models and distance distribution from small angle X‐ray scattering (SAXS) measurements. The latter restraints are incorporated into the target function as a maximum‐likelihood term that guides the shape of the simulated structures towards that defined by SAXS. The approach was first verified with the 1KOY protein, for which the distance distribution was calculated from the experimental structure, and subsequently used to predict the structures of 11 data‐assisted targets in the CASP12 experiment. Major improvement of the GDT_TS was obtained for 2 targets, minor improvement for other 2 while, for 6 target GDT_TS deteriorated compared with that calculated for predictions without the SAXS data, partly because of assuming a wrong multimeric state (for Ts866) or because the crystal conformation was more compact than the solution conformation (for Ts942). Particularly good results were obtained for Ts909, in which use of SAXS data resulted in the selection of a correctly packed trimer and, subsequently, increased the GDT_TS of monomer prediction. It was found that running simulations with correct oligomeric state is essential for the success in SAXS‐data‐assisted prediction.