Phase diagram analysis of random heteropolymers with composition specific and quenched cross-links

Abstract

We study the conformational organization of a novel class of soft matter, random heteropolymers (RHPs) with composition specific and quenched cross-links by replica field theory. These technologically relevant materials carry an essentially quenched sequence distribution of disparate segments, and also a fixed distribution of composition specific cross-links. The chain connectivity of the linear RHPs is captured most generally by a continuous microscopic RHP Hamiltonian, while the quenched character of the cross-links is enforced by spatial constraints on segments of a prescribed composition, and by allowing fluctuations in the total number of composition specific cross-links around an experimentally controlled average. The replica theory, a formalism widely used in the study of linear RHPs, is extended in the present work to analysis of systems with multiform disorder that have interdependent disorder components. By numerically analyzing the free energy and its stability we predict the occurrence of frozen phase formation wherein few conformations are sampled. By systematically varying the sequence/cross-link fluctuations, temperature, and the RHP interaction parameters we show that two conformational transitions can occur in the frozen phase. The low temperature conformational transition resembles to a large extent the reduction in chain conformations which occurs during the folding of proteins with fixed disulfide bonds. The frozen phase domain microstructure formation is discussed in context of the recently elucidated phase diagram of a close related system, RHPs with annealed cross-links. Explicit connection is made with possible experiments and computer simulations methods to test our predictions.