A solvable model of secondary structure formation in random hetero-polymers

We propose and solve a simple model describing secondary structure formation in random hetero-polymers. It describes monomers with a combination of one-dimensional short-range interactions (representing steric forces and hydrogen bonds) and infinite-range interactions (representing polarity forces). We solve our model using a combination of mean-field and random-field techniques, leading to phase diagrams exhibiting second-order transitions between folded, partially folded and unfolded states, including regions where folding depends on initial conditions. Our theoretical results, which are in excellent agreement with numerical simulations, lead to an appealing physical picture of the folding process: the polarity forces drive the transition to a collapsed state, the steric forces introduce monomer specificity and the hydrogen bonds stabilize the conformation by damping the frustration-induced multiplicity of states.