Fundamentally all biological processes are molecular in nature. So, it is essential to understand biomolecules and their interactions to gain better insight into living systems. Proteins are constituted of chains of small building blocks called amino acids. These chains of amino acids fold in 3D space to define structure of a protein. It is known that structure of biomolecules plays an important role in defining its function. Biomolecular structures contain complex features such as pockets and protrusions on the surface, internal cavities and voids, channel and tunnel like structures connecting external surface to functional sites buried deep inside the molecule. Analysis of these features is very important for understanding of structure-function relationships, engineering new proteins with required functional properties, or designing inhibitors for existing proteins.
Proteins are often represented in space-fill model as a union of balls, where each ball corresponds to an atom (See Figure 1). This model is ideal for application of geometric and topological techniques for detailed analysis. For example, geometric algorithms have been developed for extraction of molecular surface which is extremely important in the study of any protein. Similarly, for accurate measurement of molecular volumes, identification and characterization of empty space within a molecule, methods from computation geometry and topology are applied. This project is a contribution to this area of research with special focus on integrated geometric and topological methods for visual analysis of cavities and channels in biomolecules.
With increasing availability of structures of large proteins and protein complexes at atomic detail through advancements in the field of crystallography, there is a need of designing faster and more space efficient algorithms for their analysis. Another driver for the need of efficient geometric algorithms is the availability of larger molecular dynamics trajectories, which are essentially time varying molecular structures. Designing algorithms to address these challenges is the second major focus of this project.
In the first part, we describe two methods: one for extraction and visualization of biomolecular channels, and the other for extraction of cavities in uncertain data. We also describe the two software tools based on the proposed methods targeted at the end-user, the biologists. These two web server tools publicly available for use are called ChExVis and RobustCavities. In the second part, we describe efficient parallel algorithms for two geometric structures widely used in the study of biomolecules. One of the structures we discuss is discrete Voronoi diagram which finds applications in channel visualization, while the other structure is alpha complex which is extremely useful in studying geometric and topological properties of biomolecules.