Geometrical Detection of Pathways in Protein Structures LeadingAmong More Binding Sites

In this paper, we present a novel algorithm for the detection of pathways connecting two or more specific user defined binding sites, which are deeply buried in a protein macromolecule. These pathways can play an important role in the protein reactivity and overall behavior. However, our new algorithm can be generalized and used for computation of pathways inside an arbitrary set of spheres in three-dimensional space, leading through an ordered set of user-defined sites. Our approach is based on the localized Voronoi diagram approach and the Delaunay triangulation. The greatest benefit of our approach is its independence on the size of the input data set. This is achieved by using only a subset of all atoms in the macromolecule in each phase. This substantially reduces the size of the processed space. The method can also be utilized for determination whether pathways wide and straight enough exist among determined binding sites. This information then serves as the guideline for assessing the migration of products of chemical reaction between these binding sites.