Soliton driven relaxation dynamics and protein collapse in the villin headpiece

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen's thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.