Monte Carlo Simulation of the β-Sheet–Random Coil Transition of a Homopolypeptide. I. Equilibrium Study

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Abstract
Monte Carlo simulation of the β-sheet – random coil conversion of a homopolypeptide chain was carried out on the basis of a model where successive two amino acid residues were assumed to change their states simultaneously and hence constituted a basic unit. Only three states were considered for each unit: extended, turn and coil. The conversion exhibited a transition between two states, random coil (C) and the β-sheet (B). In the transition region, two population maxima were always found, each corresponded to the local minimum of the free energy and there was an energy barrier between them. This behavior is characteristic of the all-or-none type transition. We have found that the nature of the first-order transition is retained in the case of a small system consisting of 100 units. The size of the cooperative unit was evaluated. According to the analytical theory of Kanô, a transition curve was obtained which was very close to the present one. This consistent result has suggested that equilibrium properties of the β-sheet-random coil transition are well evaluated with the mean field approximation. The matrix method of Mattice is also discussed.