Statistical mechanics of a correlated energy landscape model for protein folding funnels

Abstract

Energetic correlations due to polymeric constraints and the locality of interactions, in conjunction with the apriori specification of the existence of a particularly low energy state, provides a method of introducing the aspect of minimal frustration to the energy landscapes of random heteropolymers. The resulting funnelled landscape exhibits both a phase transition from a molten globule to a folded state, and the heteropolymeric glass transition in the globular state. We model the folding transition in the self-averaging regime, which together with a simple theory of collapse allows us to depict folding as a double-well free energy surface in terms of suitable reaction coordinates. Observed trends in barrier positions and heights with protein sequence length, stability, and temperature are explained within the context of the model. We also discuss the new physics which arises from the introduction of explicitly cooperative many-body interactions, as might arise from side-chain packing and non-additive hydrophobic forces. Denaturation curves similar to those seen in simulations are predicted from the model.