[A theory of heteropolymers with frozen random primary structure: properties of the globular state, coil-globule transitions and possible biophysical applications]

Abstract

A new approach to the problem of correspondence between primary structures of polypeptides and their tertiary structures is presented. This approach is based on the following statement of the problem: what will be the statistical properties of tertiary structures provided that the statistical properties of primary structures (e. g. the ratio of polar and unpolar residues) are given? It is discussed whether such statement is useful for the investigation of the prebiological evolution and protein folding. It is emphasized that the basic point here is to determine the configurational entropy of the chain, i. e., the number of foldings which lead to a given density distribution space. Hence, the auxiliary problem of the ideal heteropolymer collapse in the external field is considered. This problem is investigated numerically in the case when the field is localized in the small region in space. It is shown that such geometrical characteristics as the size of a globule are not sensitive to the details of primary structure when the chain is a random coil, and become sensitive to such details in the opposite globular case. These characteristics in the globular state can be described by the stable probability distribution function which does not depend upon chain length. Geometric characteristics of the chain exhibit especially strong dependence upon the primary structure in the region of coil-globule transition which is of the second order for the ensemble of chains.