Gaussian self-consistent method for the kinetics of heteropolymers: A direction in studying the protein folding problem

We develop a Gaussian self-consistent method for the study of equilibrium and kinetics of conformational transitions of arbitrary heteropolymers in dilute solution. It is discovered that certain chain sequences possess an additional symmetry that leads to reduction of the number of dynamical variables and simplification of the equations. As an application of our general method we consider the problem for a periodic ring heteropolymer with the sequence ab constituted by monomers of two types with different second virial coefficients. We present numerical results for equilibrium and kinetics of this system on that subspace of the phase diagram where one group of monomers can become hydrophobic. We find an interesting physical phenomenon of a phase separation that accompanies the coil-to-globule transition. We believe that our approach may shed Light on the fundamental problem of protein folding; some of the results seem encouraging.