Modeling the "glass" transition in proteins

A model of a protein as a disordered system of identical spherical particles (which imitate protein side chains) interacting with each other via a repulsive soft sphere potential U(r) infinity r(-beta) is constructed. The particles undergo the conformational motion (CM) within their own harmonic conformational potentials around some mean equilibrium positions ascribed by the tertiary structure of the protein. A first principles calculation of the positional correlation functions for the CM is carried out. The general analysis is exemplified by the case in which the mean equilibrium positions of the particles form a cubic tightly-packed (face- centered) lattice (each particle has 12 nearest neighbors) with the step b(hydr) =6.6 A (the average distance between the centers of mass of hydrated protein subunits). The model yields dramatic slowing down of the relaxation with the decrease of temperature followed by a sharp glass transition at some crossover temperature T(c) < 200 K. At the transition the liquid-like dynamic behavior (the correlation functions tend to zero with time) is altered by the glass-like one (the correlation functions tend with time to some non-zero limit). In the liquid-like region above the crossover temperature the relaxation exhibits distinct alpha-process following the beta-one. The glass transition results from the interaction of the particles. Thus the model suggests that namely direct interactions of the fragments of protein structure rather than protein-solvent interactions are the origin of the phenomenon of the glass transition. The known increase of T(c) up to 300 K at dehydration of the protein is attributed to the known concomitant compression of the globule upon drying by about 4-6% so that positions of individual atoms displace by about 0.6 A (modeled by the decrease of the step of the lattice b by 0.6 A so that b(dehydr)=6 A). The model suggests that the solvent influences the phenomenon of the glass transition indirectly determining the tertiary structure of the protein rather than via own freezing. In the model the transition from the liquid-like dynamic behavior to the glass-like one can be obtained even in a cluster containing a few particles. Thus the results of the model can be considered as an argument in favor of the point of view that the transition to the glassy behavior can take place for a very small domains of the protein comprising only several constituting fragments of its structure. The model predicts that for the dehydrated protein the alpha-relaxation process is strongly repressed.