Glass transition of an amphiphilic random copolymer and relation to the Ising model of spin-glass

Abstract

We present the results of our study of the freezing transition of an amphiphilic random copolymer. We here confirm that a replica variational approach predicts a "scale"dependent freezing transition due to the connectivity of the chain. In addition we suggest that two systems, a random copolymer and an Ising spin-glass, can be directly related to each other on the mean-field level in the vicinity of the freezing transition. Both systems have the same type of effective free energy. The properties of replica symmetrical (RS) and replica symmetry broken (RSB) solutions are discussed. The latter has larger radius of gyration and effective free energy, and is less phase separated. It might be related to a globule with more than one hydrophobic core.

Phase Diagram of Random Heteropolymers

“…However, many other disordered systems, like spin glasses, exhibit a continuous glass transition (in the ''overlap'' parameter, q l ). This has recently been predicted for the random amphiphilic chain [12], as does our analysis for a certain class of correlated sequences. The folding properties of a given heteropolymer will be crucially affected by the type of glass transition it undergoes, since the dynamics (e.g., the aging behavior) are rather different in these two scenarios [11].…”

“…On lowering the temperature, these preferences grow and result in increasing correlations at larger distances. This effect might be related to the scaledependent freezing predicted in [12,13] and the intermediate glass phase found in the numerics of [10].…”

“…The following family of correlation functions for a chain of length N proves very useful [12]: C l t; t w N ÿ1 P i hr i;l t r i;l t w i. Here r i;l r il ÿ r i and r i is the spatial position of the ith monomer of the chain.…”

Glassy phases in random heteropolymers with correlated sequences

“…20,21 In a series of papers exploiting a Gaussian variational technique to deal with the dynamics of heteropolymers, copolymers in particular, a much richer phase diagram was proposed, where the ultimate REM-like folding to a unique ground state is preceded by a less structured but still frustrated glassy phase. This is more in line with recent scenarios proposing a freezing that proceeds gradually from small scales to larger and larger structures.…”

A variational approach to the localization transition of heteropolymers at interfaces

“…This would imply a breaking of the ergodicity of the system, in contrast with simple intuitive arguments. The Gaussian variational approach has been thought to be effective in describing correctly the physics of disordered frustrated systems [16][17][18][19]. We deem therefore a quite interesting issue to try to evidentiate RSB with Monte Carlo simulations, or to understand why the Gaussian variational method fails in predicting it, if this should be the case.…”