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

We explored the energy-parameter space of our coarse-grained UNRES force field for large-scale ab initio simulations of protein folding, to obtain good initial approximations for hierarchical optimization of the force field with new virtual-bond-angle bending and side-chain-rotamer potentials which we recently introduced to replace the statistical potentials. 100 sets of energy-term weights were generated randomly, and good sets were selected by carrying out replica-exchange molecular dynamics simulations of two peptides with a minimal α-helical and a minimal β-hairpin fold, respectively: the tryptophan cage (PDB code: 1L2Y) and tryptophan zipper (PDB code: 1LE1). Eight sets of parameters produced native-like structures of these two peptides. These eight sets were tested on two larger proteins: the engrailed homeodomain (PDB code: 1ENH) and FBP WW domain (PDB code: 1E0L); two sets were found to produce native-like conformations of these proteins. These two sets were tested further on a larger set of nine proteins with α or α + β structure and found to locate native-like structures of most of them. These results demonstrate that, in addition to finding reasonable initial starting points for optimization, an extensive search of parameter space is a powerful method to produce a transferable force field.

A proposed coarse-grained model of nucleic acids demonstrates that average interactions between base dipoles, together with chain connectivity and excluded-volume interactions, are sufficient to form double-helical structures of DNA and RNA molecules. Additionally, local interactions determine helix handedness and direction of strand packing. This result, and earlier research on reduced protein models, suggest that mean-field multipole-multipole interactions are the principal factors responsible for the formation of regular structure of biomolecules.

We review the coarse-grained UNited RESidue (UNRES) force field for the simulations of protein structure and dynamics, which is being developed in our laboratory over the last several years. UNRES is a physics-based force field, the prototype of which is defined as a potential of mean force of polypeptide chains in water, where all the degrees of freedom except the coordinates of α-carbon atoms and side-chain centers have been integrated out. We describe the initial implementation of UNRES to protein-structure prediction formulated as a search for the global minimum of the potential-energy function and its subsequent molecular dynamics and extensions of molecular-dynamics implementation, which enabled us to study protein-folding pathways and thermodynamics, as well as to reformulate the protein-structure prediction problem as a search for the conformational ensemble with the lowest free energy at temperatures below the folding-transition temperature. Applications of UNRES to study biological problems are also described.

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...

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Protegrin is an antimicrobial peptide with a β-hairpin structure stabilized by a pair of disulfide bonds. It has been extensively studied by solid-state NMR and computational methods. Here we use implicit membrane models to examine the binding of monomers on the surface and in the interior of the membrane, the energetics of dimerization, the binding to membrane pores, and the stability of different membrane barrel structures in pores. Our results challenge a number of conclusions based on previous experimental and theoretical work. The burial of monomers into the membrane interior is found to be unfavorable for any membrane thickness. Because of its imperfect amphipathicity, protegrin binds weakly, at most, on the surface of zwitterionic membranes. However, it binds more favorably onto toroidal pores. Anionic charge on the membrane facilitates the binding due to electrostatic interactions. Solid-state NMR results have suggested a parallel NCCN association of monomers in dimers and association of dimers to form octameric or decameric β-barrels. We find that this structure is not energetically plausible for binding to bilayers, because in this configuration the hydrophobic sides of two monomers point in opposite directions. In contrast, the antiparallel NCCN and especially the parallel NCNC octamers are stable and exhibit a favorable binding energy to the pore. The results of 100-ns simulations in explicit bilayers corroborate the higher stability of the parallel NCNC barrel compared with the parallel NCCN barrel. The ability to form pores in zwitterionic membranes provides a rationalization for the peptide's cytotoxicity. The discrepancies between our results and experiment are discussed, and new experiments are proposed to resolve them and to test the validity of the models.

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