Self-Consistent Approaches for the Protein Folding Problem: Kinetics and Equilibrium Properties of Random Copolymers

We address the problem of protein folding by studying a model of random copolymers with a Gaussian distribution of quenched disorder in the monomers' hydrophobicity. We develop the Gaussian self-consistent method in kinetics with the effective potentials depending on the disorder variables, which are further integrated out perturbatively. As an alternative, at equilibrium, we also suggest a version of a variational approach in the replica space. These methods allow us to achieve a unified description of the extended coil, liquid-like, frozen and folded globular states, as well as of the kinetic transformations between them. We discuss the role of the finite-size effects and the optimization of the disorder distribution for improving the folding properties of random sequences. We believe that the final resolution of these issues may shed light on the protein folding puzzle.