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Phase transitions in heteropolymers with "secondary structure"

We study a model of a random heteropolymer with ``secondary structure'' at the level of mean field theory. The randomness in the polymer sequence is represented by a set of quenched disorder variables that describe the monomer-monomer interactions. The secondary structure is represented by a set of Ising-like thermodynamic variables that describe internal states of the monomers. The interactions between the monomers depend on the quenched disorder variables, on the thermodynamic secondary-structure state variables, and also on the polymer configuration. We find that the system can exist in different phases that depend on the heterogeneity and average strength of the interactions, and on the polymer flexibility. At high temperatures the polymer interconverts freely between configurations without a stable secondary structure. At intermediate temperatures there is a transition to phases with one or two (coexisting) stable secondary-structure motifs and with a large number of thermodynamically important spatial configurations. At low enough temperatures (determined by the polymer flexibility) the polymer undergoes a freezing transition into phases with a unique spatial configuration and one or two stable secondary-structure motifs.