APPLICATION OF THE DIFFUSION EQUATION METHOD FOR GLOBAL OPTIMIZATION TO OLIGOPEPTIDES

The diffusion equation method (DEM) for global optimization, previously applied to simple mathematical functions and to clusters of argon atoms, is modified here for a conformational analysis of two peptides, terminally-blocked alanine and the pentapeptide Met-enkephalin. In this modification, the diffusion equation is solved in the space of the Cartesian coordinates of all atoms of the molecule, and the solution is then examined on the manifold that corresponds to fixed bond lengths and bond angles [a constraint that is characteristic of the ECEPP (Empirical Conformational Energy Program for Peptides) potential function]. The DEM involves a deformation of the potential surface until a "time" t0, at which only one minimum remains, and then a time-reversing procedure to t = 0, where the original surface is attained. The modified method was able to locate the global minimum for terminally-blocked alanine, and regions near the global minimum for Met-enkephalin, in a very small amount of computer time [< 1 min for terminally-blocked alanine and approximately 20 min (approximately 10 min to test that the time t0 has been reached, and approximately 10 min for the time-reversing procedure) for Met-enkephalin on one processor of an IBM 3090 computer]; these times are much shorter than those for the MCM and EDMC algorithms developed in this laboratory. Finally, a discussion is presented of the statistical weights for a minimum-energy conformation, and it is shown that the DEM takes the entropic factor into account correctly in the classical approximation.