A 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

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 α + β 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 physicsbased 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.protein folding | structure symmetry | multi-domain packing P rediction of protein structures from amino acid sequence still remains an unsolved problem of computational biology. Although, since the famous experiments by Anfinsen (1), it is known that a protein adopts the structure which is the (kinetically reachable) global minimum of the free energy of a system, it is not straightforward to implement this physical principle in practice because of the inaccuracy of existing force fields and because of the enormous difficulty to search the conformational space of the system. Therefore, the most effective methods for protein-structure prediction nowadays are knowledge-based approaches, in which database information is incorporated explicitly into the procedure (2). These methods can be divided into three categories, namely, comparative (homology) modeling (3-5), in which the target sequence is compared with the sequences for which experimental structures are known and those structures are usually selected as candidate models for which the greatest similarity is observed; threading (6-8), in which the target sequence is superposed on structures from a database, and those which give the highest score (lowest pseudoenergy) are selected as candidate predictions; and, finally, the fragment-assembly or minithreading method developed by David Baker and colleagues (9, 10), in which the predicted structure is assembled from nine-residue fragments extracted from a protein-structure database, and knowledge-and physicsbased filters are applied at each asse...

Summary: Participating as the Cornell-Gdansk group, we have used our physics-based coarsegrained UNited RESidue (UNRES) force field to predict protein structure in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11). Our methodology involved extensive multiplexed replica exchange simulations of the target proteins with a recently improved UNRES force field to provide better reproductions of the local structures of polypeptide chains. All simulations were started from fully extended polypeptide chains, and no external information was included in the simulation process except for weak restraints on secondary structure to enable us to finish each prediction within the allowed 3-week time window. Because of simplified UNRES representation of polypeptide chains, use of enhanced sampling methods, code optimization and parallelization and sufficient computational resources, we were able to treat, for the first time, all 55 human prediction targets with sizes from 44 to 595 amino acid residues, the average size being 251 residues. Complete structures of six singledomain proteins were predicted accurately, with the highest accuracy being attained for the T0769, for which the CaRMSD was 3.8 Å for 97 residues of the experimental structure. Correct structures were also predicted for 13 domains of multi-domain proteins with accuracy comparable to that of the best template-based modeling methods. With further improvements of the UNRES force field that are now underway, our physics-based coarse-grained approach to protein-structure prediction will eventually reach global prediction capacity and, consequently, reliability in simulating protein structure and dynamics that are important in biochemical processes. Availability and Implementation: Freely available on the web at

A new approach to the calibration of the force fields is proposed, in which the force-field parameters are obtained by maximum-likelihood fitting of the calculated conformational ensembles to the experimental ensembles of training system(s). The maximum-likelihood function is composed of logarithms of the Boltzmann probabilities of the experimental conformations, calculated with the current energy function. Because the theoretical distribution is given in the form of the simulated conformations only, the contributions from all of the simulated conformations, with Gaussian weights in the distances from a given experimental conformation, are added to give the contribution to the target function from this conformation. In contrast to earlier methods for force-field calibration, the approach does not suffer from the arbitrariness of dividing the decoy set into native-like and non-native structures; however, if such a division is made instead of using Gaussian weights, application of the maximum-likelihood method results in the well-known energy-gap maximization. The computational procedure consists of cycles of decoy generation and maximum-likelihood-function optimization, which are iterated until convergence is reached. The method was tested with Gaussian distributions and then applied to the physics-based coarse-grained UNRES force field for proteins. The NMR structures of the tryptophan cage, a small α-helical protein, determined at three temperatures (T = 280, 305, and 313 K) by Hałabis et al. ( J. Phys. Chem. B 2012 , 116 , 6898 - 6907 ), were used. Multiplexed replica-exchange molecular dynamics was used to generate the decoys. The iterative procedure exhibited steady convergence. Three variants of optimization were tried: optimization of the energy-term weights alone and use of the experimental ensemble of the folded protein only at T = 280 K (run 1); optimization of the energy-term weights and use of experimental ensembles at all three temperatures (run 2); and optimization of the energy-term weights and the coefficients of the torsional and multibody energy terms and use of experimental ensembles at all three temperatures (run 3). The force fields were subsequently tested with a set of 14 α-helical and two α + β proteins. Optimization run 1 resulted in better agreement with the experimental ensemble at T = 280 K compared with optimization run 2 and in comparable performance on the test set but poorer agreement of the calculated folding temperature with the experimental folding temperature. Optimization run 3 resulted in the best fit of the calculated ensembles to the experimental ones for the tryptophan cage but in much poorer performance on the training set, suggesting that use of a small α-helical protein for extensive force-field calibration resulted in overfitting of the data for this protein at the expense of transferability. The optimized force field resulting from run 2 was found to fold 13 of the 14 tested α-helical proteins and one small α + β protein with the correct topologies; the average structu...

We show here that computer game players can build high-quality crystal structures. Introduction of a new feature into the computer game Foldit allows players to build and real-space refine structures into electron density maps. To assess the usefulness of this feature, we held a crystallographic model-building competition between trained crystallographers, undergraduate students, Foldit players and automatic model-building algorithms. After removal of disordered residues, a team of Foldit players achieved the most accurate structure. Analysing the target protein of the competition, YPL067C, uncovered a new family of histidine triad proteins apparently involved in the prevention of amyloid toxicity. From this study, we conclude that crystallographers can utilize crowdsourcing to interpret electron density information and to produce structure solutions of the highest quality.