The statistics of energy states of a Hookean model for proteins

Abstract

A generic model of a random polypeptide chain, with discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobia 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 with reflecting boundary conditions, and giving rise to distributions of the Wigner or inverse Gaussian form. A continuum approximation leads to a path integral formulation of the problem.