Publication Date



We develop and implement geometric methods to study three-dimensional structures of proteins, the knowledge of which is critical to the understanding of the molecules and their interactions. Delaunay and Laguerre methods, which concern sets of overlapping spheres and their interrelationships, are well suited to the study of molecules. We discuss and implement algorithms for the calculation of molecular volume, atomic solvent accessible surface areas, their gradients and discontinuities. This is used for a detailed analysis of parameters obtained by the implicit solvation method, Semi-Explicit Assembly (SEA). We introduce the concept of Laguerre-Intersection cells which consist of the intersection of the Laguerre tessellation and space-filling diagram. This method eliminates the need for explicit water molecules to cap infinite Laguerre cells of certain solvent accessible solute atoms. We discuss and implement a quick weighted Delaunay tetrahedrization algorithm which is tailored specifically to the aforementioned algorithms. Finally, we use concepts from continuum mechanics to study the motion of the HIV protease dimer.

Degree Name


Level of Degree


Department Name

Mathematics & Statistics

First Committee Member (Chair)

Evangelos A. Coutsias

Second Committee Member

Deborah Sulsky

Third Committee Member

Scott Mitchell

Fourth Committee Member

Tudor Oprea

Project Sponsors

National Institute of Health




Delaunay, Delaunay triangulation, Voronoi, Laguerre tessellation, Voronoi tessellation, implicit solvation, solvent accessible surface area, molecular volume, molecular surface area, strain

Document Type