Global-to-local representation and visualization of molecular surfaces using deformable models

Macromolecules such as proteins and enzymes are responsible for most of cellular functionality. Many molecular interactions, such as protein-protein interactions or protein-ligand binding, occur at what can be defined as the molecular surface. The topology of the molecular surface is often complex, containing various geometric features such as clefts, cavities, tunnels, and flat regions. These geometric features coupled with non-geometric physicochemical properties influence surface-based molecular interactions. Consequently analysis of molecular surfaces is crucial in elucidating structure-property relationships of molecules. In this paper we propose a method for visualizing a molecular surface in a manner that preserves and elucidates salient features. The method involves mapping of a molecular surface to a standard spherical coordinate system. The ability to map arbitrary molecular surfaces to a standard coordinate system aids in comparison of surface features across different molecules. The mapping is accomplished by enclosing the molecular surface by a sphere, and then iteratively deforming the sphere until it converges by wrapping the entire molecular surface. This allows a one-to-one relationship to be established between points on the molecular surface and points on the surface of the sphere. The presence of discontinuities such as tunnels in the molecular surface can be identified by detecting collision between patches of the deforming sphere. Subsequently, the deformable surface is restored back to the sphere, retaining the mapping. Features and properties defined at the molecular surface are then mapped and visualized in the standard spherical coordinate system. The proposed approach has several key advantages. First, it allows a global-to-local visualization of molecular surfaces. Second, it facilitates comparison of specific features as well as collection of features within and across molecules by mapping them to a common coordinate system. Third, the method allows visualization of both geometric and non-geometric surface properties. Fourth, specific molecular characteristics can be visualized individually or in combination on-demand. Finally, and crucially the advantages offered by the proposed visualization do not involve simplification of the surface characteristics thereby ensuring that no loss of potentially important information occurs.