Statistical distributions of optimal global alignment scores of random protein sequences

The inference of homology from statistically significant sequence similarity is a central issue in sequence alignments. So far the statistical distribution function underlying the optimal global alignments has not been completely determined.

In this study, random and real but unrelated sequences prepared in six different ways were selected as reference datasets to obtain their respective statistical distributions of global alignment scores. All alignments were carried out with the Needleman-Wunsch algorithm and optimal scores were fitted to the Gumbel, normal and gamma distributions respectively. The three-parameter gamma distribution performs the best as the theoretical distribution function of global alignment scores, as it agrees perfectly well with the distribution of alignment scores. The normal distribution also agrees well with the score distribution frequencies when the shape parameter of the gamma distribution is sufficiently large, for this is the scenario when the normal distribution can be viewed as an approximation of the gamma distribution.

We have shown that the optimal global alignment scores of random protein sequences fit the three-parameter gamma distribution function. This would be useful for the inference of homology between sequences whose relationship is unknown, through the evaluation of gamma distribution significance between sequences.