GENERALIZED SIMULATED ANNEALING STOCHASTIC MOLECULAR OPTIMIZATION USING STOCHASTIC MOLECULAR OPTIMIZATION USING

INTRODUCTION

Molecular systems can exist in different conformational geometries, corresponding to different three- dimensional arrangements of atoms in a structure. The number of allowed conformations increases with molecular size. In particular, macromolecules of biological interest present a large number of the local minima (or local equilibrium conformations). Indeed, geometry optimization is a crucial, first step, in any molecular modeling strategy. The main obstacle in this field is to find global minimum and to not get trapped in one of the many local minima. The usual optimization methods applied to quantum and classical molecular physics are based on the gradient descent approach which indistinctly selects both global and local minima. Therefore, in locating the global minimum, brute-force has been the usual tool.

In order to overcome these difficulties, we propose a stochastic strategy to determine optimized geometries based on the Generalized Simulated Annealing (GSA) algorithm [1]. In this proposal the localization of the global minimum of any potential function (cost function) is obtained using the Monte Carlo method in an annealing procedure. This procedure maps various intermediary equilibrium states and goes at the end to the global minimum.

Our procedure consist in use the molecular conformational energy, obtained from a classical parameterized force field (THOR package [2], [3]), with the geometries obtained randomly for the GSA routine [4]. Following the Monte Carlo procedure, we introduce an artificial decreasing temperature which allows the storage of a local minima through I/O statement. In the end of the optimization process, the system will be inside the basin of the global minimum (or if there is degeneracy within one of the global minima).

The Stochastic Molecular Optimization (SMO) method is a promising step toward the understating of the behavior of macromolecules in terms of interactions on the atomic level. This method is appropriate to analyze the most probable macromolecular conformational state. As an additional bonus conformational energy hypersurface mapping results from the search for the global minimum conformation. Further, unlike usual Molecular Dynamics (MD) method, the SMO is force independent, i.e., we obtain the optimized conformation without calculating the force, only potential energy is involved. Therefore, we don't need to know the conformational energy gradient to arrive at equilibrium conformations.

In section 2, we present the GSA algorithm used for recovering the global minimum. In section 3, we discuss the computational code used by THOR for calculating the potential energy of geometries obtained randomly from the GSA routine. In section 4, we present results concerning some molecular structures of simple molecules (H O and H O ) and to polipeptides. We present conclusions in section 5.

GENERALIZED SIMULATED ANNEALING STOCHASTIC MOLECULAR OPTIMIZATION USING STOCHASTIC MOLECULAR OPTIMIZATION USING