Scaling of folding properties in Go models of proteins

Insights about scaling of folding properties of proteins are obtained by studying folding in heteropolymers described by Go-like Hamiltonians. Both lattice and continuum space models are considered. In the latter case, the monomer-monomer interactions correspond to the Lennard-Jones potential. Several statistical ensembles of the two- and three-dimensional target native conformations are considered. Among them are maximally compact conformations which are confined to a lattice and those which are obtained either through quenching or annealing of homopolymers to their compact local energy minima. Characteristic folding times are found to grow as power laws with the system size. The corresponding exponents are not universal. The size related deterioration of foldability is found to be consistent with the scaling behavior of the characteristic temperatures: asymptotically, the folding temperature becomes much lower than the temperature at which glassy kinetics become important. The helical conformations are found to have the lowest overall scaling exponent and the best foldability among the classes of conformations studied. The scaling properties of the Go-like models of the protein conformations stored in the Protein Data Bank suggest that proteins are not optimized kinetically.