Application of the Ray-Representation and a Massively Parallel Special Purpose Computer to Problems of Protein Structure and Function: I. Methodology for Calculation of Molecular Contact Surface, Volume, and Internal Free Space

Methodology is developed to apply ray-representations to geometric analysis of space-filling models of protein structure. The following specific problems are treated. First, we define the ray-representation for fused-sphere models of proteins. Second, using the ray-representation, we treat computation of molecular contact surfaces in solution via Minkowski dilation and erosion. Third, we describe how all points of the molecular contact surface can be tagged according to their chemical properties. Fourth, we show how equivalence set methods can be applied to ray representations of proteins in order to identify internal empty spaces and classify their connectedness to the outside. Fifth, we develop filters to analyze the morphology of interstitial spaces in proteins which connect to the outside. Sixth, we discuss how Boolean algorithms can be used to determine whether water molecules identified in X-ray crystallography are inside, outside, or intersecting the boundary defined by the solvent accessible surface. Finally we discuss the computation of volume properties from ray-representations. A special purpose massively parallel computer is used to compute the ray-representation.