Energy landscapes and the collapse dynamics of homopolymers

What is the shape of the conformational free energy landscape for the collapse of a single homopolymer molecule? We model the dynamics of homopolymer collapse in a poor solvent to a state of high compactness using short self-avoiding walks on two-dimensional square lattices. The conformations are obtained by exhaustive enumeration. The time-evolution is modeled by an analytic transition matrix using Metropolis dynamics with two different move sets. A main finding is that the shape of the energy landscape depends strongly on the move set, suggesting the need to be cautious in interpreting kinetic sequences of events and shapes of landscapes in Monte Carlo polymer dynamics. For some of the collapse pathways, we observe two different rates: a fast collapse to nonoptimal compact states, then a much slower rearrangement to maximally compact conformations. This two-stage process resembles protein folding through compact intermediate states. But we note that the nature and existence of the kinetic traps strongly depends on the move set. In addition, we find that the "Levinthal paradox" argument for protein folding does not correctly predict the collapse time when applied to homopolymers.