  Statistical analysis of evolutionary-related protein sequences provides
insights about their structure, function, and history. We show that Restricted
Boltzmann Machines (RBM), designed to learn complex high-dimensional data and
their statistical features, can efficiently model protein families from
sequence information. We here apply RBM to twenty protein families, and present
detailed results for two short protein domains, Kunitz and WW, one long
chaperone protein, Hsp70, and synthetic lattice proteins for benchmarking. The
features inferred by the RBM are biologically interpretable: they are related
to structure (such as residue-residue tertiary contacts, extended secondary
motifs ($\alpha$-helix and $\beta$-sheet) and intrinsically disordered
regions), to function (such as activity and ligand specificity), or to
phylogenetic identity. In addition, we use RBM to design new protein sequences
with putative properties by composing and turning up or down the different
modes at will. Our work therefore shows that RBM are a versatile and practical
tool to unveil and exploit the genotype-phenotype relationship for protein
families.
