Where Does the Alignment Score Distribution Shape Come from?

Alignment algorithms are powerful tools for searching for homologous proteins in databases, providing a score for each sequence present in the database. It has been well known for 20 years that the shape of the score distribution looks like an extreme value distribution. The extremely large number of times biologists face this class of distributions raises the question of the evolutionary origin of this probability law. We investigated the possibility of deriving the main properties of sequence alignment score distributions from a basic evolutionary process: a duplication-divergence protein evolution process in a sequence space. Firstly, the distribution of sequences in this space was defined with respect to the genetic distance between sequences. Secondly, we derived a basic relation between the genetic distance and the alignment score. We obtained a novel score probability distribution which is qualitatively very similar to that of Karlin-Altschul but performing better than all other previous model.