  Evolution in its course found a variety of solutions to the same optimisation
problem. The advent of high-throughput genomic sequencing has made available
extensive data from which, in principle, one can infer the underlying structure
on which biological functions rely. In this paper, we present a new method
aimed at extracting sites encoding structural and func- tional properties from
a set of protein primary sequences, namely a Multiple Sequence Alignment. The
method, called Critical Variable Selection, is based on the idea that subsets
of relevant sites cor- respond to subsequences that occur with a particularly
broad frequency distribution in the dataset. By applying this algorithm to in
silico sequences, to the Response Regulator Receiver and to the Voltage Sensor
Domain of Ion Channels, we show that this procedure recovers not only
information encoded in single site statistics and pairwise correlations but it
also captures dependencies going beyond pairwise correlations. The method
proposed here is complementary to Statistical Coupling Analysis, in that the
most relevant sites predicted by the two methods markedly differ. We find
robust and consistent results for datasets as small as few hundred sequences,
that reveal a hidden hierarchy of sites that is consistent with present
knowledge on biologically relevant sites and evo- lutionary dynamics. This
suggests that Critical Variable Selection is able to identify in a Multiple
Sequence Alignment a core of sites encoding functional and structural
information.
