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

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...

Recently, we developed a new approach to protein-structure prediction, which combines template-based modeling with the physics-based coarse-grained UNited RESidue (UNRES) force field. In this approach, restrained multiplexed replica exchange molecular dynamics simulations with UNRES, with the C-distance and virtual-bond-dihedral-angle restraints derived from knowledge-based models are carried out. In this work, we report a test of this approach in the 11th Community Wide Experiment on the Critical Assessment of Techniques for Protein Structure Prediction (CASP11), in which we used the template-based models from early-stage predictions by the LEE group CASP11 server (group 038, called "nns"), and further improvement of the method. The quality of the models obtained in CASP11 was better than that resulting from unrestrained UNRES simulations; however, the obtained models were generally worse than the final nns models. Calculations with the final nns models, performed after CASP11, resulted in substantial improvement, especially for multi-domain proteins. Based on these results, we modified the procedure by deriving restraints from models from multiple servers, in this study the four top-performing servers in CASP11 (nns, BAKER-ROSETTASERVER, Zhang-server, and QUARK), and implementing either all restraints or only the restraints on the fragments that appear similar in the majority of models (the consensus fragments), outlier models discarded. Tests with 29 CASP11 human-prediction targets with length less than 400 amino-acid residues demonstrated that the consensus-fragment approach gave better results, i.e., lower α-carbon root-mean-square deviation from the experimental structures, higher template modeling score, and global distance test total score values than the best of the parent server models. Apart from global improvement (repacking and improving the orientation of domains and other substructures), improvement was also reached for template-based modeling targets, indicating that the approach has refinement capacity. Therefore, the consensus-fragment analysis is able to remove lower-quality models and poor-quality parts of the models without knowing the experimental structure.