EXTRACTING THE ENERGY BARRIER DISTRIBUTION OF A DISORDERED SYSTEM FROM THE INSTANTANEOUS NORMAL-MODE DENSITY-OF-STATES - APPLICATIONS TO PEPTIDES AND PROTEINS

A general method for estimating the statistical barrier height distrib ution in a disordered system is presented. The method is based on the interpretation of the temperature dependence of the instantaneous norm al mode density of states. An integral equation is derived which relat es the fraction of unstable instantaneous normal modes at a particular temperature to the intrinsic distribution of one-dimensional energy b arriers g(E) for the 3N - 6 internal degrees of freedom in the system. We argue that the overall distribution of multidimensional barriers o n the potential energy hypersurface Gamma(E) is a Gaussian distributio n with a mean and variance which can be calculated from the intrinsic barrier height distribution g(E). A technique for solving the integral equation is presented and applied to derive the energy barrier distri bution for the isobutyrl-val-ala(2)-methylamide tetrapeptide, the S-pe ptide of ribonuclease A, and the bovine pancreatic trypsin inhibitor. We compare our results with the random energy model and suggest how pa rameters for the statistical Hamiltonian used in that theory might be derived using computer simulation.