An exactly solvable model for a beta-hairpin with random interactions

I investigate a disordered version of a simplified model of protein folding, with binary degrees of freedom, applied to an ideal beta-hairpin structure. Disorder is introduced by assuming that the contact energies are independent and identically distributed random variables. The equilibrium free-energy of the model is studied, performing the exact calculation of its quenched value and proving the self-averaging feature.

💡 Research Summary

The paper presents an analytically tractable statistical‑mechanical model of a β‑hairpin protein fragment in which the native contacts are assigned random interaction energies. The underlying microscopic degrees of freedom are binary variables σi∈{0,1} representing whether residue i is in the folded (1) or unfolded (0) state. Because a β‑hairpin consists of a set of nested contacts between residue i and its partner N‑i+1, the contact map has a hierarchical (nesting) structure that allows the partition function to be expressed through a simple recursion.

Randomness is introduced by assuming that each native contact energy εi is an independent identically distributed (i.i.d.) random variable drawn from a prescribed probability distribution P(ε). The Hamiltonian reads H(σ,ε)=−∑i εi σiσN‑i+1, and the canonical partition function for a given realization of the disorder is ZN(ε)=∑σ exp