  Efficient automatic protein classification is of central importance in
genomic annotation. As an independent way to check the reliability of the
classification, we propose a statistical approach to test if two sets of
protein domain sequences coming from two families of the Pfam database are
significantly different. We model protein sequences as realizations of Variable
Length Markov Chains (VLMC) and we use the context trees as a signature of each
protein family. Our approach is based on a Kolmogorov--Smirnov-type
goodness-of-fit test proposed by Balding et al. [Limit theorems for sequences
of random trees (2008), DOI: 10.1007/s11749-008-0092-z]. The test statistic is
a supremum over the space of trees of a function of the two samples; its
computation grows, in principle, exponentially fast with the maximal number of
nodes of the potential trees. We show how to transform this problem into a
max-flow over a related graph which can be solved using a Ford--Fulkerson
algorithm in polynomial time on that number. We apply the test to 10 randomly
chosen protein domain families from the seed of Pfam-A database (high quality,
manually curated families). The test shows that the distributions of context
trees coming from different families are significantly different. We emphasize
that this is a novel mathematical approach to validate the automatic clustering
of sequences in any context. We also study the performance of the test via
simulations on Galton--Watson related processes.
