Statistical Modelling and Simulation Using the Fisher-Bingham Distribution

Abstract

One simplified view of a protein main chain is that it consists of a sequence of amino acids, represented by points centered at their Cα atoms, separated by bonds of constant length. This representation is called the protein’s Cα trace. The “shape” of the protein is determined by the angles between two, and the dihedral angles between three, successive bonds. An equivalent view is that the shape is determined by a sequence of unit vectors or points on the sphere. Since the orientation of each bond represents a direction in three-dimensional space, we see that it is important to have statistical tools to understand and fit data on the sphere.