An improved functional form for the temperature scaling factors of the components of the mesoscopic UNRES force field for simulations of protein structure and dynamics.

Abstract

Coarse-grained or mesoscopic models of proteins and the corresponding force fields are of great importance because they enable us to reduce the folding simulation time by several orders of magnitude compared to the all-atom approach and, consequently, reach the millisecond time scale of simulations. In the coarse-grained UNRES model for simulations of protein structure and dynamics, developed by our group, each amino acid residue is represented by a united side chain and a united peptide group located in the middle between the two neighboring alpha-carbon atoms, which assist only in the definition of the geometry. The prototype of the UNRES force field has been defined as a potential of mean force or restricted free-energy function corresponding to averaging out the degrees of freedom not present in the coarse-grained representation, which has further been approximated by a truncated Kubo cumulant series to enable us to derive analytical expressions for the corresponding terms. This force field should depend on temperature, and in its simplest form, a term corresponding to the cumulant of order n should be multiplied by f(n) = 1/T(n-1). The temperature dependence has been introduced in recent work ( J. Phys. Chem. B , 2007 , 111 , 260 - 285 ), and in order to prevent too steep a variation with temperature, the factors at the nth order cumulant terms were assumed to have a form f(n) = ln[exp(1) + exp(-1)]/ln{exp[(T/T(0))(n-1)] + exp[-(T/T(0))(n-1)]}, where T(0) = 300 K is the reference temperature. In this work, we have introduced a modified scaling factor f(n) = ln[exp(c) + exp(-c)]/ln{exp[c(T/T(0))(n-1)] + exp[-c(T/T(0))(n-1)]}, where c is an adjustable parameter, and determined c by fitting the analytical approximation of the temperature dependence of the virtual bond torsional term corresponding to rotation about the C(alpha)...C(alpha) virtual bond in terminally blocked dialanine to the respective potential of mean force calculated from the MP2/6-31G(d, p) ab initio energy surfaces of terminally blocked alanine (Ac-Ala-NHMe) and, independently, by optimizing it to obtain a sharp heat capacity curve and the lowest ensemble-averaged root-mean-square deviation over the C(alpha) atoms of 1GAB used as a training protein. Both approaches gave consistent results, and c = 1.4 has been selected as the optimal value of this parameter. The force field with the new temperature scaling factors has been optimized using 1GAB as the training protein. The new force field has been tested on a series of medium size alpha-helical proteins and found to perform better than that with the original temperature scaling factors.