  A statistical model of protein families, called profile conditional random
fields (CRFs), is proposed. This model may be regarded as an integration of the
profile hidden Markov model (HMM) and the Finkelstein-Reva (FR) theory of
protein folding. While the model structure of the profile CRF is almost
identical to the profile HMM, it can incorporate arbitrary correlations in the
sequences to be aligned to the model. In addition, like in the FR theory, the
profile CRF can incorporate long-range pairwise interactions between model
states via mean-field-like approximations. We give the detailed formulation of
the model, self-consistent approximations for treating long-range interactions,
and algorithms for computing partition functions and marginal probabilities. We
also outline the methods for the global optimization of model parameters as
well as a Bayesian framework for parameter learning and selection of optimal
alignments.
