Analysis of the Morphological Features of Protein Spatial Structure

Abstract

Protein function is mainly determined by its structure. For example, the interaction between ligands and receptors demands a match between their shapes. In this chapter we discuss morphological features of protein spatial structures using geometrical methods. The shape description of a binding pocket on the protein surface using geometrical tools is given, including a spatial polyhedron, the hypergraph and depth analysis. Furthermore, we generalize the rolling sphere method, and present several new concepts, such as the γ-accessible radius and γ-function in a spatial particle system, which connects with the biological concepts such as hydrophobicity using precise mathematical notions. We provide a recursive algorithm for the γ-function. The proof of the relative theorem and reasoning behind the computational formulas are given in the last section.