The structure of a random heteropolymer in a disordered medium: Ensemble growth simulation

We use Monte Carlo simulations to study the thermodynamics and structural behavior of random heteropolymers immersed in a disordered medium. Simulation results pertain to isolated heteropolymer chains with renormalized intrachain interactions determined by analytic averaging over the realizations of the external medium. Two situations are considered. In the first scenario, the random heteropolymer is such that segments of different type have a propensity to segregate, while in the second situation different types of segments prefer to be adjacent to each other. Polymer configurations are generated by the ensemble-growth Monte Carlo method wherein the slow-down effects that typically hinder dynamic Monte Carlo simulations of compact polymer states with strong interactions are alleviated. Our simulations show that for the case where the bare heteropolymer prefers to form segregated patterns, below a certain temperature, the random heteropolymer "folds" into a few dominant conformations with a segregated pattern of contacts. In the case where the bare heteropolymer favors mixing of different types of segments we find richer behavior. Here, our simulations show the existence of two frozen phases separated by a reentrant phase as temperature (or strength of the external disorder) is scanned. The heteropolymers in the two frozen phases are "folded" in different patterns (high T, mixed pattern; low T, segregated pattern). The physical reasons for these phenomena are elucidated based on our simulation results for structural features of the polymer. The results agree remarkably well with a simple mean-field theory, a fact that may be of some general consequence. Specific experiments are suggested to test the phenomena that we predict.