GEOMETRIC AND TOPOLOGICAL METHODS IN PROTEIN STRUCTURE ANALYSIS

Biology provides some of the most important and complex scientific challenges of our time. With the recent success of the Human Genome Project, one of the main challenges in molecular biology is the determination and exploitation of the three-dimensional structure of proteins and their function. The ability for proteins to perform their numerous functions is made possible by the diversity of their three-dimensional structures, which are capable of highly specific molecular recognition. Hence, to attack the key problems involved, such as protein folding and docking, geometry and topology become important tools. Despite their essential roles, geometric and topological methods are relatively uncommon in com-putational biology, partly due to a number of modeling and algorithmic challenges. This thesis describes efficient computational methods for characterizing and comparing molecu-lar structures by combining both geometric and topological approaches. Although most of the work described here focuses on biological applications, the techniques developed can be applied to other fields, including computer graphics, vision, databases, and robotics. Geometrically, the shape of a molecule can be modeled as (i) a set of weighted points