Based on the results of our recent work on the determination of the potentials of mean force of pairs of models of amino-acid side chains in water, in this work we make an attempt at introducing temperature-dependent side chain - side chain interaction potentials in our coarse-grained UNRES energy function. For hydrophobic pairs as well as oppositely-charged pairs, two functional forms are introduced, one of which implies a linear dependence of the free energy of interactions on temperature and the other one a hyperbolic-tangent dependence. The free energy of the interactions of other pairs is assumed to be independent of temperature. With the example of the N-terminal part of the B-domain of staphylococcal protein A, we demonstrate that, with this temperature dependence, the radius of gyration and the root-mean-square deviation from the native structure grow less steeply with temperature and the heat-capacity peak is lower than that obtained with temperature-independent side chain - side chain potentials. This demonstrates that ignoring the increase of the strength of hydrophobic interactions with increasing temperature in coarse-grained force fields is likely to result in grossly wrong predictions of the thermodynamics of folding and of the process of thermal unfolding made with such force fields.

United-residue models of polypeptide chains [3, 5, 19-22, 24, 31, 33] have long been of interest, because they enable one to carry out global conformational searches of proteins in real time, which in turn can facilitate ab initio protein structure predictions based solely on Anfinsen's thermodynamic hypothesis [1], according to which the native structure of a protein is a global minimum of its potential energy surface [32]. In the last few years, we developed a united-residue force field [20-22, 24], hereafter referred to as UNRES, in which a polypeptide chain is represented by a sequence of α-carbon (Cα) atoms linked by virtual bonds with attached united side chains (SC) and united peptide groups (p) located in the middle between the consecutive α-carbons (Figure 1). Only the united peptide groups and united side chains serve as interaction sites, the α-carbons serving to define the geometry.