A diffusion process-controlled Monte Carlo method for finding the global energy minimum of a polypeptide chain. I. Formulation and test on a hexadecapeptide

Finding the global energy minimum region of a polypeptide chain, independently of the starting conformation and in a reasonable computational time, is of fundamental interest. To approach this problem, a new Monte Carlo method is proposed and applied to the hexadecapeptide model Ac-(AAQAA)3Y(NH2), in which the global energy minimum conformation, an α helix, is known. In order to reduce the available conformational space, the backbone dihedral angles φ and ψ are restricted to a discrete set of ten regions and the side chains are modeled by a two-point representation. The energy used in these off-lattice simulations is of Amber type with a simplified hydrophobic potential. The novelty of the method is that, prior to the minimization of the energy, the move from the current conformation to the next must satisfy a kinetic requirement. The kinetic requirement is that there exists an upper bound on the escape time from the current conformation. From diffusion consideration it is shown that the escape time correlates with the angular deviations of the residues. The effectiveness of the approach is illustrated by a total of 25 biased simulations (i.e., using specific probabilities for the ten φ–ψ regions) and five unbiased simulations (i.e., the 10 regions are equiprobable before application of the kinetic requirement), starting from various conformations. It is found that all biased and unbiased simulations find the global minimum energy structure in ∼102–103 Monte Carlo steps, although the estimated probability of getting the full α helix is ∼10−11–10−16.