Geometric Models of Protein Structure and Function Prediction

This chapter describes how protein structures are obtained experimentally and discusses methods for computing the geometry of protein molecules. There are primarily three experimental techniques for obtaining protein structures namely, X-ray crystallography, solution nuclear magnetic resonance (NMR), and recently freeze-sample electron microscopy (cryo-EM). The geometric model of macromolecule amenable to convenient computation is an idealized model, where the shapes of atoms are approximated by three-dimensional balls. The incremental algorithm developed in can be used to compute the weighted tetrahedrization for a set of atoms of different radii. The chapter outlines the algorithm for two-dimensional unweighted Delaunay triangulation. Evolution plays central roles in shaping up the function and stability of protein molecules. The method of analyzing residue substitution rates using continuous-time Markov models and the method of surface mapping of conservation entropy and phylogeny only scratches the surface of this important issue.