Chain length scaling of protein folding time: Beta sheet structures

We present comprehensive 3D lattice Monte Carlo simulations of the folding kinetics of two-turn antiparallel beta sheets. The model employed takes into account isotropic nonspecific interactions as in previous flexible heteropolymer models and also orientation-dependent monomer-monomer interactions, mimicking the formation of hydrogen bonds and chain rigidity. The chain length is varied from N=15 to 33. For each chain length, we calculate the fastest folding temperature, T-fast, folding temperature, T-fold, and glass-transition temperature, T-g. The time-averaged occupation probability of the native state is found to be nearly independent of N at all temperatures. The dependence of T-fast and T-fold on N is accordingly relatively weak. The temperature interval where the folding is fast rapidly decreases with increasing N. For the chain lengths chosen, T-fold slightly exceeds T-g. The dependence of the folding time tau(f) on N is well fitted by using the power law, tau(f)proportional to N-lambda. The exponent lambda is found to depend on temperature and on the distribution of nonspecific interactions in the chain. In particular, lambda=2.7-4.0 at T=T-fast and 5.2 at T slightly below T-fold. Evaluating tau(f) in real units at T near T-fold yields physically reasonable results. (C) 2000 American Institute of Physics. [S0021-9606(00)50526-1].