december, 1, 1998
This paper is not a theoritical study on the distribution of SW-scores
and Z-values. Rather, it presents a statistical analysis of Z-values
on large datasets of protein sequences, leading to a law of probability
that the experimental Z-values follow.
First, we determine the relationships between the computed Z-value, an estimation of its variance and the number of randomizations in the Monte-Carlo process. Then we illustrate that Z-values are less correlated to sequence lengths than SW-scores.
Then we show that pairwise alignments, performed on 'quasi-real' sequences (i.e. , randomly shuffled sequences of the same length and amino acid composition as the real ones) lead to Z-value distributions that statistically fit the extreme value distribution, more precisely the Gumbel distribution (global EVD, Extreme Value Distribution). However, for real protein sequences, we observe an over-representation of high Z-scores.
We determine first a cutoff value which separates these overestimated Z-values from those which follow the global EVD. We then show that the interesting part of the tail of distribution of Z-values can be approximated by another EVD (i.e., an EVD which differs from the global EVD) or by a Pareto law.
This has been confirmed for all proteins analysed so far, whether extracted from individual genomes, or from the ensemble of five complete microbial genomes comprising altogether 16956 protein sequences.
Keywords: Sequence alignment, Dynamic programming, Significance, Z-value, Gumbel distribution, Pareto distribution.