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 the folding time of chains of length $N$ scales as $N^{\lambda }$ at the 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 a simple Arrhenius-like behavior.