Monte Carlo simulation of folding transitions of simple model proteins using a chain growth algorithm

We have performed Monte Carlo simulations of folding transitions of model proteins on a simple cubic lattice with the Rosenbluth and Rosenbluth (1955) chain growth algorithm combined with Boltzmann weighting and multilink additions. We use a model proposed by Dill (1985) that represents the protein as a connected sequence of hydrophobic and hydrophilic beads on the lattice, with nearest-neighbor interactions between the constituent beads. The algorithm allows the calculation of equilibrium folding curves for arbitrary sequences of chain lengths of at least 48 in three dimensions. This is significantly longer than the maximum chain length for which equilibrium curves can be determined with the Metropolis (1953) based algorithms used in previous work. The thermal denaturation curve for the model is found to vary greatly with the sequence used, in some special cases approximating closely the sharpness observed for real proteins. These special sequences appear to be simple, periodic arrangements of beads. However, it seems that the unique or almost unique lowest energy states that exist for certain sequences of moderate length approaching the length of the simplest real proteins cannot be recovered in feasible simulation times with our particular model/algorithm combination.