Scaling of Folding Properties in Go Models of Proteins

Insights about scaling of folding properties of proteins are obtained bystudying folding in heteropolymers described by Go-like Hamiltonians. Bothlattice and continuum space models are considered. In the latter case, themonomer-monomer interactions correspond to the Lennard-Jones potential.Several statistical ensembles of the two- and three-dimensional targetnative conformations are considered. Among them are maximally compactconformations which are confined to a lattice and those which are obtainedeither through quenching or annealing of homopolymers to their compactlocal energy minima. Characteristic folding times are found to grow aspower laws with the system size. The corresponding exponents are notuniversal. The size related deterioration of foldability is found to beconsistent with the scaling behavior of the characteristic temperatures:asymptotically, the folding temperature becomes much lower than thetemperature at which glassy kinetics become important. The helicalconformations are found to have the lowest overall scaling exponent andthe best foldability among the classes of conformations studied. Thescaling properties of the Go-like models of the protein conformationsstored in the Protein Data Bank suggest that proteins are not optimizedkinetically.