  Finite mixture models are fitted to spherical data. Kent distributions are
used for the components of the mixture because they allow considerable
flexibility. Previous work on such mixtures has used an approximate maximum
likelihood estimator for the parameters of a single component. However, the
approximation causes problems when using the EM algorithm to estimate the
parameters in a mixture model. Hence the exact maximum likelihood estimator is
used here for the individual components. This paper is motivated by a
challenging prize problem in structural bioinformatics of how proteins fold. It
is known that hydrogen bonds play a key role in the folding of a protein. We
explore this hydrogen bond geometry using a data set describing bonds between
two amino acids in proteins. An appropriate coordinate system to represent the
hydrogen bond geometry is proposed, with each bond represented as a point on a
sphere. We fit mixtures of Kent distributions to different subsets of the
hydrogen bond data to gain insight into how the secondary structure elements
bond together, since the distribution of hydrogen bonds depends on which
secondary structure elements are involved.
