  We demonstrate that Protein-Protein Interaction (PPI) networks in several
eucaryotic organisms contain significantly more self-interacting proteins than
expected if such homodimers randomly appeared in the course of the evolution.
We also show that on average homodimers have twice as many interaction partners
than non-self-interacting proteins. More specifically the likelihood of a
protein to physically interact with itself was found to be proportional to the
total number of its binding partners. These properties of dimers are are in
agreement with a phenomenological model in which individual proteins differ
from each other by the degree of their ``stickiness'' or general propensity
towards interaction with other proteins including oneself. A duplication of
self-interacting proteins creates a pair of paralogous proteins interacting
with each other. We show that such pairs occur more frequently than could be
explained by pure chance alone. Similar to homodimers, proteins involved in
heterodimers with their paralogs on average have twice as many interacting
partners than the rest of the network. The likelihood of a pair of paralogous
proteins to interact with each other was also shown to decrease with their
sequence similarity. This all points to the conclusion that most of
interactions between paralogs are inherited from ancestral homodimeric
proteins, rather than established de novo after the duplication. We finally
discuss possible implications of our empirical observations from functional and
evolutionary standpoints.
