Geometric representation and detection methods of cavities on protein surfaces

Abstract

Most living organisms are made up of cells, while cells are composed by molecules. Molecules play a fundamental role in biochemical processes that sustain life. The functions of a molecule depend not only on its interaction with other molecules, but also on the sites of its surface where such interactions take place. Indeed, these interactions are the driving force of almost all cellular processes. Interactions between molecules occur on specific molecular surface regions, called binding sites. The challenge here is to know the compatible sites of two coupling molecules. The compatibility is only effective if there is physico-chemical compatibility, as well as geometric compatibility in respect to docking of shape between the interacting molecules. Most (but not all) binding sites of a molecule (e.g., protein) correspond to cavities on its surface; conversely, most (but not all) cavities correspond to binding sites. This thesis essentially approaches cavity detection algorithms on protein surfaces. This means that we are primarily interested in geometric methods capable of identifying protein cavities as tentative binding sites for their ligands. Finding protein cavities has been a major challenge in molecular graphics and modeling, computational biology, and computational chemistry. This is so because the shape of a protein usually looks very unpredictable, with many small downs and ups. These small shape features on the surface of a protein are rather illusive because they are too small when compared to cavities as tentative binding sites. This means that the concept of curvature (a local shape descriptor) cannot be used as a tool to detect those cavities. Thus, more enlarged shape descriptors have to be used to succeed in determining such cavities on the surface of proteins. In this line of thought, this thesis explores the application of mathematical theory of scalar fields, including its topology, as the cornerstone for the development of cavity detection algorithms described herein. Furthermore, for the purpose of graphic visualisation, this thesis introduces a GPU-based triangulation algorithm for molecular surfaces.