Chain Length Scaling of Protein Folding Time.

Folding of protein-like heteropolymers into unique 3D structures is investigated using Monte Carlo simulations on a cubic lattice. We found that folding time of chains of length $N$ scales as $N^\lambda$ at temperature of fastest folding. For chains with random sequences of monomers $\lambda \approx 6$, and for chains with sequences designed to provide a pronounced minimum of energy to their ground state conformation $\lambda \approx 4$. Folding at low temperatures exhibits an Arrhenius-like behavior with the energy barrier $E_b \approx \phi |E_n|$, where $E_n$ is the energy of the native conformation. $\phi \approx 0.18$ both for random and designed sequences.