Positional statistical significance in sequence alignment

Beginning with the concept of near-optimal sequence alignments, we can assi gn a probability that each element in one sequence is paired in an alignmen t with each element in another sequence. This involves a sum over the set o f all possible pairwise alignments, The method employs a designed hidden Ma rkov model (HMM) and the rigorous forward and forward-backward algorithms o f Rabiner. The approach can use any standard sequence-element-to-element pr obabilistic similarity measures and affine gap penalty functions. This allo ws the positional alignment statistical significance to be obtained as a fu nction of such variables. A measure of the probabilistic relationship betwe en any single sequence and a set of sequences can be directly obtained. In addition, the employed HMM with the Viterbi algorithm provides a simple lin k to the standard dynamic programming optimal alignment algorithms.