Dirichlet mixtures: a method for improved detection of weak but significant protein sequence homology

We present a method for condensing the information in multiple alignments of proteins into a mixture of Dirichlet densities over amino acid distributions. Dirichlet mixture densities are designed to be combined with observed amino acid frequencies to form estimates of expected amino acid probabilities at each position in a profile, hidden Markov model or other statistical model. These estimates give a statistical model greater generalization capacity, so that remotely related family members can be more reliably recognized by the model. This paper corrects the previously published formula for estimating these expected probabilities, and contains complete derivations of the Dirichlet mixture formulas, methods for optimizing the mixtures to match particular databases, and suggestions for efficient implementation.