Coupled dynamics of sequence selection and compactification in mean-field hetero-polymers

We study a simple solvable model describing the genesis of monomer sequences for hetero-polymers (such as proteins), as the result of the equilibration of a slow stochastic genetic selection process which is assumed to be driven by the competing demands of functionality and reproducibility of the polymer’s folded structure. Since reproducibility is defined in terms of properties of the folding process, one is led to the analysis of the coupled dynamics of (fast) polymer folding and (slow) genetic sequence selection. For the present meanfield model this analysis can be carried out using the finite-dimensional replica method, leading to exact results for (firstand second-order) transitions and to rich phase diagrams. PACS numbers: 61.41.+e, 75.10.Nr