FROZEN PHASES WITH REENTRANT TRANSITION FOR RANDOM HETEROPOLYMERS WITH COMPOSITION SPECIFIC AND ANNEALED CROSS-LINKS

A field theoretic formalism of random heteropolymers (RHPs) with compo sition specific cross-links that are annealed, is developed in this wo rk. This system can serve as a simple meaningful model of proteins wit h disulfide bonds. The agent that cross-links the macromolecules, as i n real proteins, is assumed to maintain an equilibrium cross-linking d ensity within the heteropolymer globule; this situation is reminiscent to in vivo reagent induced cross-linking, and protrudes the experimen tal desired control on formation and dissolution of cross-links. The s tarting point of our analysis, i.e. the random heteropolymer Hamiltoni an, captures both the chain connectivity and the essentially quenched nature of amino-acids distribution reminiscent of linear uncross-linke d polypeptides. The conformational statistics of the RHP is determined within the replica approach. For experimentally realizable values of the RHP interaction parameters, we predict the appearance of two froze n phases of RHPs wherein a small number of chain conformations of orde r O(1) are being sampled. At the interim between the two phases our ca lculation predicts the appearance of a re-entrant transition wherein t he number of chain conformations sampled is of order O(N). The occurre nce of the re-entrant transition is due to a tight competition between the intersegment interactions (measured by chi(F)), and the propensit y of composition specific and annealed cross-links to form (determined by the chemical potential of the cross-linking agent). We suggest how to traverse the re-entrant transition line, by chemically manipulatin g the competition of dissimilar interactions of the disparate segments , and the specific propensity of the peptides to cross-link, and also, we provide an explanation for the observation that in nature cross-li nking between alike rather than dissimilar segments is observed. (C) 1 997 American Institute of Physics.