Dissipative dynamics and the statistics of energy states of a Hookean model for protein folding

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean spring connecting pails or hydrophobic residues, reproduces the energy probability distribution of real proteins over a very large range of energies. We show that this system with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional Ornstein-Uhlenbeck process and giving rise Lo the so-called Wigner distribution. A tunably fine- or coarse-grained sampling of the energy landscape yields a family of distributions for the energies and energy spacings.