This thesis investigates the use of parametric representations of protein surface shape as a computational method of recognising similar and complementary protein surfaces. Both two-dimensional and three-dimensional shape parametrisations are described. The 2D parametrisation is constructed as an expansion of real spherical harmonic basis functions. These may be augmented by special shape-scaled radial functions, using the Laguerre polynomials, to give a novel 3D parametric "surface skin" representation.
Using the special rotational properties of the spherical harmonic functions, the 2D parametric surfaces of a pair of proteins may be rotated into superposition rapidly and accurately. In a similar manner, complementary arrangements of a pair of proteins are generated by finding orientations which maximise the degree of overlap between opposing pairs of 3D skins, thus "docking" the two surfaces. This novel approach to the "protein docking problem" has the form of a six-dimensional Fourier correlation. Protein docking using parametric skins is at least as accurate as comparable three-dimensional grid-based Fourier docking correlations, but is around two orders of magnitude faster.