Statistical mechanis of correlated energy landscape models for random heteropolymers and proteins

Abstract

We study the role of correlations in the energy landscape of heteropolymers and proteins, specifically their role in the glass transition in random heteropolymers and the folding transition in minimally frustrated proteins. In the context of the glass transition, a correlated landscape results in a more gradual freezing into basins of extensive entropy, while not completely destroying the first-order jump in the order parameter until below a certain density. Quantities such as the glass transition temperature and the probability distribution of overlaps q are quantitatively similar to the results for an uncorrelated landscape or random energy model (REM), while the number of searchable basins at the glass transition (the Levinthal search) is significantly modified. For proteins, correlations provide a way to induce a funnel topography onto the energy landscape by the selection of a sequence with a particularly low energy configuration. The folding transition is weakly first order. The position of the transition state ensemble in the model is in accord with recent experimental results on denaturant effects on kinetics of small proteins.