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

摘要

Protein folding is analyzed using a replica variational formalism toinvestigate some free energy landscape characteristics relevant for dynamics. Arandom contact interaction model that satisfies the minimum frustrationprinciple is used to describe the coil-globule transition (characterized byT_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 characteristictemperatures, one dynamic, T_A the other static, T_K (T_A> T_K), which aresimilar 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 dynamicallyand statically. 2)Between T_A and T_K, the melted phase is still dominantthermodynamically, 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 andT_K, barriers between metastable states are shown to grow with decreasingtemperature suggesting super-Arrhenius behavior in a sufficiently large system.Due to evolutionary constraints on fast folding, the folding temperature T_F isexpected to be higher than T_K, but may or may not be higher than T_A. Diversescenarios of the folding kinetics are discussed based on phase diagrams thattake into account the dynamical transition, as well as the static ones.