This project combines research developments in computational geometry and biology. Accurate and robust methods have been developed for computing shapes and topologies of macromolecules. Complex computational methods have been developed for studying molecular recognition and rational drug design. Geometric tools have been applied to compute areas, volumes, cavities, and interfaces in proteins with a high degree of success. The goal now is to accomplish the important step of modeling and rapidly computing the shape of binding pockets. This approach is novel and based on a recent theoretical breakthrough in the geometric modeling of shape and complementary space. The geometric methods will be combined with newly possible methods for computing interaction energetics between proteins and substrates. The primary focus is on providing accurate and efficient computational tools for the rational exploration of substrate and drug binding pockets in proteins, and aiding rational drug design.