Statics, metastable states and barriers in protein folding: A replica variational approach

TL;DR

This paper uses a replica variational approach to analyze the free energy landscape of protein folding, identifying key transition temperatures and the nature of metastable states, providing insights into folding dynamics and barriers.

Contribution

It introduces a replica variational formalism combined with a random contact interaction model to characterize folding, glass, and transition states in protein energy landscapes.

Findings

Identification of dynamic and static transition temperatures T_A and T_K.

Characterization of metastable states and their growth with decreasing temperature.

Discussion of folding scenarios based on phase diagrams and transition states.

Abstract

Protein folding is analyzed using a replica variational formalism to investigate some free energy landscape characteristics relevant for dynamics. A random contact interaction model that satisfies the minimum frustration principle is used to describe the coil-globule transition (characterized by T_CG), glass transitions (by T_A and T_K) and folding transition (by T_F). Trapping on the free energy landscape is characterized by two characteristic temperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which are similar to those found in mean field theories of the Potts glass. 1)Above T_A, the free energy landscape is monotonous and polymer is melted both dynamically and statically. 2)Between T_A and T_K, the melted phase is still dominant thermodynamically, but frozen metastable states, exponentially large in number, appear. 3)A few lowest minima become thermodynamically dominant below T_K, where the polymer is totally frozen. In the temperature range between T_A and T_K, barriers between metastable states are shown to grow with decreasing temperature suggesting super-Arrhenius behavior in a sufficiently large system. Due to evolutionary constraints on fast folding, the folding temperature T_F is expected to be higher than T_K, but may or may not be higher than T_A. Diverse scenarios of the folding kinetics are discussed based on phase diagrams that take into account the dynamical transition, as well as the static ones.