  A generic model of a random polypeptide chain, with discrete torsional
degrees of freedom and Hookean springs connecting pairs of 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 to 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.
