Statistical mechanics on the space of kinetic folding pathways

Abstract

We introduce a general scheme to assign statistical weights to alla priori pathways in conformation space for an aggregate of interacting particles that undergoes a series of unimolecular events in a limited time frame. Illustrations of such systems are biopolymers that fold intramolecularly or macromolecules of biological relevance that exert their function onto themselves through a series of structural rearrangements under the severe time constraints imposed by enzymatic timing. We endow the space of kinetically controlled pathways with a regular measure induced by a stochastic process built upon a complex potential energy landscape. This process simulates the progressive and opportunistic exploration of basins of attraction of critical points in the molecular potential energy. The derivation is general and holds for any diffusion-like process subject to time constraints and governed by thermal fluctuations upon a complex energy landscape. Within this framework, the ensemble of physically relevant kinetically arrested states becomes a cross-section of the ensemble of pathways at a fixed instant.