Fundamentals of massive automatic pairwise alignments of protein sequences: theoretical significance of Z-value statistics

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Abstract
Motivation:Different automatic methods of sequence alignments are routinely used as a starting point for homology searches and function inference. Confidence in an alignment probability is one of the major fundamentals of massive automatic genome-scale pairwise comparisons, for clustering of putative orthologs and paralogs, sequenced genome annotation or multiple-genomic tree constructions. Extreme value distribution based on the Karlin–Altschul model, usually advised for large-scale comparisons are not always valid, particularly in the case of comparisons of non-biased with nucleotide-biased genomes (such that of Plasmodium falciparum). Z-values estimates based on Monte Carlo technics, can be calculated experimentally for any alignment output, whatever the method used. Empirically, a Z-value higher than ∼8 is supposed reasonable to assess that an alignment score is significant, but this arbitrary figure was never theoretically justified. Results: In this paper, we used the Bienaymé–Chebyshev inequality to demonstrate a theorem of the upper limit of an alignment score probability (or P-value). This theorem implies that a computed Z-value is a statistical test, a single-linkage clustering criterion and that 1/Z-value2 is an upper limit to the probability of an alignment score whatever the actual probability law is. Therefore, this study provides the missing theoretical link between a Z-value cut-off used for an automatic clustering of putative orthologs and/or paralogs, and the corresponding statistical risk in such genome-scale comparisons (using non-biased or biased genomes).

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