Probabilistic description of protein alignments for sequences and structures

Finite-temperature local protein sequence alignment: percolation and free-energy distribution

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size-scaling analysis, we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter-driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities on the order 10(-64). It is well known that in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution (T>0). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.

Profile conditional random fields for modeling protein families with structural information

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 pair-wise 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.

Probabilistic alignment detects remote homology in a pair of protein sequences without homologous sequence information

Dynamic programming (DP) and its heuristic algorithms are the most fundamental methods for similarity searches of amino acid sequences. Their detection power has been improved by including supplemental information, such as homologous sequences in the profile method. Here, we describe a method, probabilistic alignment (PA), that gives improved detection power, but similarly to the original DP, uses only a pair of amino acid sequences. Receiver operating characteristic (ROC) analysis demonstrated that the PA method is far superior to BLAST, and that its sensitivity and selectivity approach to those of PSI-BLAST. Particularly for orphan proteins having few homologues in the database, PA exhibits much better performance than PSI-BLAST. On the basis of this observation, we applied the PA method to a homology search of two orphan proteins, Latexin and Resuscitation-promoting factor domain. Their molecular functions have been described based on structural similarities, but sequence homologues have not been identified by PSI-BLAST. PA successfully detected sequence homologues for the two proteins and confirmed that the observed structural similarities are the result of an evolutional relationship.