Models for Relaxation in Glasses and Protein Channels

Abstract

Generally speaking, similarities of relaxation in glasses and biomolecules are due to the fact that in both cases a very large number of molecular configurations is involved in the relaxation processes¹. A characteristic feature of relaxation in such complex systems is the non-exponential time dependence of the relaxation functions; in the case of glasses the measured relaxation functions are usually well described by Kohlrausch’s fractional-exponential formula. One of the first models for non-exponential relaxation in glasses and undercooled melts was Glarum’s defect-diffusion model². An extension of the model, in which the molecular units visited by a defect relax with a finite rate, is presented. It is shown that a related defect-diffusion model can be applied successfully to the relaxation processes in ionic channels in protein molecules, which lead to a non-exponential distribution of the closed times of the channels. Considering the special case of a closed-time distribution following a power law, a general model for the gating kinetics of ionic channels is formulated, which is characterized by a waiting-time distribution. The waiting-time distribution is found to follow the same power law.