Glassy phases in random heteropolymers with correlated sequences

Abstract

We develop an analytic approach for the study of lattice heteropolymers and apply it to copolymers with correlated Markovian sequences. According to our analysis, heteropolymers present three different dense phases depending upon the temperature, the nature of the monomer interactions, and the sequence correlations: (i) a liquid phase, (ii) a "soft glass" phase, and (iii) a "frozen glass" phase. The presence of the intermediate "soft glass" phase is predicted, for instance, in the case of polyampholytes with sequences that favor the alternation of monomers. Our approach is based on the cavity method, a refined Bethe-Peierls approximation adapted to frustrated systems. It amounts to a mean-field treatment in which the nearest-neighbor correlations, which are crucial in the dense phases of heteropolymers, are handled exactly. This approach is powerful and versatile; it can be improved systematically and generalized to other polymeric systems.

Exact solution of a RNA-like polymer model on the Husimi lattice

“…As observed in the previous section, we thus obtain a nativelike state which does not correspond to a well-defined secondary structure, but rather to a variety of structures. 40,41 Let us also compare our results with two other recent works on similar models, which conversely take into account excluded volume. 5,7,[37][38][39] Even in this case, the low temperature glasslike phase does not correspond to a fixed structure, but the usual claim is that it would be able to describe average RNA properties.…”

RNA-like polymer model: Exact calculation on the Bethe lattice

“…This may be indeed a reason for our qualitatively different results. In order to investigate this issue in more detail, it would be interesting to extend the Bethe lattice analysis to the case of a random heterogeneous sequence, making use the recently proposed cavity method [31], along the lines traced by Montanari, Müller, and Mezard, for the selfavoiding heteropolymer [35,36].…”

Mean-field behavior of the negative-weight percolation model on random regular graphs

“…If the phase transition is continuous the density on the coexistence line vanishes. Studies of interacting heteropolymers have confirmed this statement [40,41]. We shall therefore develop a formalism allowing to compute the average density of monomers on a point, ψ, as function of the inverse temperature β, the chemical potential µ and the amount of disorder ρ.…”

“…The polymer problem can be studied using the cavity method as developed in [40,41]. Here, we shall use only the replica symmetric cavity method as we have not found any evidence for sizeable replica symmetry breaking effects.…”