DETERMINISTIC GLOBAL OPTIMIZATIONFOR PROTEIN STRUCTURE PREDICTIONJohn

Deterministic global optimization plays an essential role in the solution of many diicult problems with applications ranging from economics and operations research to computational chemistry and molecular biology. In this chapter we explore the application of deterministic global optimization approaches to problems related to protein structure prediction. Due to the complex nature of protein interactions, energy landscapes which model these systems display huge numbers of local minima often separated by high energy barriers. Since the number of local minima is vast, the corresponding formulation has earned the simple yet suggestive title of \multiple-minima" problem. Based on the complexity of the energy hypersurface, there is an obvious need for the development of eeective global optimization techniques. In this work, we have focused on the development of such global optimization methods through the foundations of the BB deterministic global optimization approach. 1 2 1. INTRODUCTION Proteins are undoubtedly the most complex and vital molecules in nature. This complexity arises from an intricate balance of intra-and inter-molecular interactions which deene the native three-dimensional structure of the system, and subsequently its biological functionality. Recent advances in genetic engineering have heightened the interest in research related to understanding the dynamics and predicting the equilibrium native protein folding and docking conformations. The ability to predict these structures is of great theoretical interest, especially in the elds of biophysics and biochemistry. Moreover, the applications of such knowledge also promise to be exciting. For example, the ability to predict these structures would greatly increase our understanding of hereditary and infectious diseases and aid in the interpretation of genome data. Such knowledge would also likely revolutionize the process of de novo drug design. Annnsen's thermodynamic hypothesis (Annnsen et al., 1961) suggests that this native structure is in a state of thermodynamic equilibrium corresponding to the system with the lowest free energy. Experimental studies have since shown that, under native physiological conditions and after denaturation, globular proteins spontaneously refold to their unique, native structure (Kim and Baldwin, 1990). Understanding the transition of a protein from a disordered state to its native state deenes the protein folding problem. The use of computational techniques and simulations in addressing the protein folding and peptide docking problems became possible through the introduction of qualitative and quantitative methods for modeling these systems. The development of realistic energy models also established a link to the eld of global optimization, where, based on An-nsen's hypothesis, the quantity …