  Molecular interactions have widely been modelled as networks. The local
wiring patterns around molecules in molecular networks are linked with their
biological functions. However, networks model only pairwise interactions
between molecules and cannot explicitly and directly capture the higher order
molecular organisation, such as protein complexes and pathways. Hence, we ask
if hypergraphs (hypernetworks), that directly capture entire complexes and
pathways along with protein-protein interactions (PPIs), carry additional
functional information beyond what can be uncovered from networks of pairwise
molecular interactions. The mathematical formalism of a hypergraph has long
been known, but not often used in studying molecular networks due to the lack
of sophisticated algorithms for mining the underlying biological information
hidden in the wiring patterns of molecular systems modelled as hypernetworks.
  We propose a new, multi-scale, protein interaction hypernetwork model that
utilizes hypergraphs to capture different scales of protein organization,
including PPIs, protein complexes and pathways. In analogy to graphlets, we
introduce hypergraphlets, small, connected, non-isomorphic, induced
sub-hypergraphs of a hypergraph, to quantify the local wiring patterns of these
multi-scale molecular hypergraphs and to mine them for new biological
information. We apply them to model the multi-scale protein networks of baker
yeast and human and show that the higher order molecular organisation captured
by these hypergraphs is strongly related to the underlying biology.
Importantly, we demonstrate that our new models and data mining tools reveal
different, but complementary biological information compared to classical PPI
networks. We apply our hypergraphlets to successfully predict biological
functions of uncharacterised proteins.
