How sequence alignment scores correspond to probability models

Sequence alignment remains fundamental in bioinformatics. Pairwise alignment is traditionally based on ad hoc scores for substitutions, insertions, and deletions, but can also be based on probability models (pair hidden Markov models: PHMMs). PHMMs enable us to: fit the parameters to each kind of data, calculate the reliability of alignment parts, and measure sequence similarity integrated over possible alignments. This study shows how multiple models correspond to one set of scores. Scores can be converted to probabilities by partition functions with a “temperature” parameter: for any temperature, this corresponds to some PHMM. There is a special class of models with balanced length probability, i.e. no bias towards either longer or shorter alignments. The best way to score alignments and assess their significance depends on the aim: judging whether whole sequences are related versus finding related parts. This clarifies the statistical basis of sequence alignment.