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Efficient automatic protein classification is of central importance ingenomic annotation. As an independent way to check the reliability of theclassification, we propose a statistical approach to test if two sets ofprotein domain sequences coming from two families of the Pfam database aresignificantly different. We model protein sequences as realizations of VariableLength Markov Chains (VLMC) and we use the context trees as a signature of eachprotein family. Our approach is based on a Kolmogorov--Smirnov-typegoodness-of-fit test proposed by Balding et al. [Limit theorems for sequencesof random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic isa supremum over the space of trees of a function of the two samples; itscomputation grows, in principle, exponentially fast with the maximal number ofnodes of the potential trees. We show how to transform this problem into amax-flow over a related graph which can be solved using a Ford--Fulkersonalgorithm in polynomial time on that number. We apply the test to 10 randomlychosen protein domain families from the seed of Pfam-A database (high quality,manually curated families). The test shows that the distributions of contexttrees coming from different families are significantly different. We emphasizethat this is a novel mathematical approach to validate the automatic clusteringof sequences in any context. We also study the performance of the test viasimulations on Galton--Watson related processes.

Testing statistical hypothesis on random trees and applications to the protein classification problem