The purpose of this study was to determine the potentials of mean force (PMF) of the interactions between models of like-charged and between models of charged and nonpolar amino acid side chains in water to design improved side chain-side chain interaction potentials for our united residue UNRES force field for protein-structure prediction. Restrained molecular dynamics with the AMBER force field, the TIP3P model of water, and the Ewald summation were used to carry out simulations, and the weighted histogram analysis method (WHAM) was used to calculate the PMFs as functions of solute-solute distances. The following types of systems were considered to model the interactions between like-charged side chains and the interactions between charged and nonpolar side chains: (i) a pair of positively charged ions (potassium, ammonium, and guanidine, respectively); (ii) a pair of negatively charged ions (chloride and acetate, respectively), and (iii) pairs of methane with potassium, ammonium, and chloride ions, respectively. Additionally, a pair of potassium and chloride ions was included for comparison with the work of other authors. Except for the pair of acetate ions, where the PMF curve exhibited all-repulsive behavior, a minimum or two coalescing minima with positive PMF values appeared for pairs of like-charged ions. In the potassium-chloride ion pair, a contact and a solvent-separated minimum was observed. Comparison of our results with those obtained by other authors showed that including Ewald summation in computing electrostatic interactions has substantial influence on the PMFs of like-charged ions; for oppositely charged ions including Ewald summation only causes deepening of the contact minimum. It was found that the appearance of the minimum in the PMFs of likecharged ion pairs is caused by a high degree of ordering of water molecules and counterions between the solutes at this distance. The solvent contribution to the PMFs of pairs of charged and nonpolar solutes is positive in all cases; the most unfavorable contribution was observed for the methane-chloride ion pair. The results demonstrate that the use of all-repulsive potentials for the interactions between like-charged and between charged and nonpolar side chains in the UNRES force field is essentially correct, but the distance dependence should be more long range in the like-charged side chain interaction potential, because the PMF curves of like-charged ion pairs are reasonably fitted with a combination of r -1 , r -2 , and r -3 terms (r being the distance between the centers of the mass), while they are not reproduced well with combinations of r -6 and r -12 terms of the present version of UNRES.

Simple analytical functions consisting of electrostatic, polarization, Lennard-Jones or modified Lennard-Jones, and cavity terms are proposed to express the potentials of mean force analytically for spherical particles interacting in water. The cavity term was expressed either through the molecular-surface area of the solute or by using the Gaussian-overlap model of hydrophobic hydration developed in paper 1 of this series. The analytical expressions were fitted to the potentials of mean force of a methane homodimer, heterodimers composed of a methane molecule, and an ammonium cation or a chloride anion, respectively, and dimers consisting of two chloride anions, two ammonium cations, or a chloride ion and an ammonium cation. The potentials of mean force for these dimers were determined by umbrella-sampling molecular dynamics simulations with the AMBER 7.0 force field with TIP3P water either in our earlier work or in this work. For all systems, the analytical formulas fitted the potentials of mean force very well. However, using the molecular-surface area to express the cavity term provided a good fit only when the nonbonded interactions were expressed by an all-repulsive modified Lennard-Jones potential but also resulted in non-physical values of some of the parameters. Conversely, the use of our new Gaussian-overlap-based expression for the cavity term provided a good fit to the potentials of mean force (PMFs) with Lennard-Jones nonbonded potential, and the values of all parameters were physically reasonable.

Protein structure refinement from comparative models with the goal of predicting structures at near-experimental accuracy remains an unsolved problem. Structure refinement might be achieved with an iterative protocol where the most native-like structure from a set of decoys generated from an initial model in one cycle is used as the starting structure for the next cycle. Conformational sampling based on the coarse-grained SICHO model, atomic level of detail molecular dynamics simulations, and normal-mode analysis is compared in the context of such a protocol. All of the sampling methods can achieve significant refinement close to experimental structures, although the distribution of structures and the ability to reach native-like structures differs greatly. Implications for the practical application of such sampling methods and the requirements for scoring functions in an iterative refinement protocol are analyzed in the context of theoretical predictions for the distribution of protein-like conformations with a random sampling protocol.

In recent years, there have been significant advances in the field of computational protein design including the successful computational design of enzymes based on backbone scaffolds from experimentally solved structures. It is likely that large-scale sampling of protein backbone conformations will become necessary as further progress is made on more complicated systems. Removing the constraint of having to use scaffolds based on known protein backbones is a potential method of solving the problem. With this application in mind, we describe a method to systematically construct a large number of de novo backbone structures from idealized topological forms in a top–down hierarchical approach. The structural properties of these novel backbone scaffolds were analyzed and compared with a set of high-resolution experimental structures from the protein data bank (PDB). It was found that the Ramachandran plot distribution and relative γ- and β-turn frequencies were similar to those found in the PDB. The de novo scaffolds were sequence designed with RosettaDesign, and the energy distributions and amino acid compositions were comparable with the results for redesigned experimentally solved backbones. Proteins 2010. © 2009 Wiley-Liss, Inc.

Graphical abstractHighlights► The problem of protein prediction from sequence is difficult and incompletely solved. ► We show that a new method based on correlated mutations in a multiple sequence alignment, filtered through a process to extract direct contacts provide powerful constraints on selecting the correct fold in a large number of well constructed decoy models.