Model protein conformations via pair correlation functions, distance matrix, and embedding algorithm

Abstract

A method of constructing three-dimensional structures of model protein conformations is presented. The method consists of self-consistent field integral equations for pair correlation functions of constituent units in a heteropolymer chain and the use of the distance matrix and the embedding algorithm for constructing conformations. The pair correlation functions obey integral equations that are derived from the Kirkwood hierarchy by applying closure approximations; they appear as a generalized form of the liquid-state Percus–Yevick integral equation. Model protein sequences that exhibit the formation of secondary-like patterns and tertiary-like structures are examined. These structural features are formed at low temperatures and they are stabilized by strong hydrogen bonding forces. To obtain the structure in three dimensions, the method of distance geometry is used to refine the distance matrix of a folded structure which is then embedded in the three-dimensional space by an embedding algorithm.