  We study statistical properties of interacting protein-like surfaces and
predict two strong, related effects: (i) statistically enhanced self-attraction
of proteins; (ii) statistically enhanced attraction of proteins with similar
structures. The effects originate in the fact that the probability to find a
pattern self-match between two identical, even randomly organized interacting
protein surfaces is always higher compared with the probability for a pattern
match between two different, promiscuous protein surfaces. This theoretical
finding explains statistical prevalence of homodimers in protein-protein
interaction networks reported earlier. Further, our findings are confirmed by
the analysis of curated database of protein complexes that showed highly
statistically significant overrepresentation of dimers formed by structurally
similar proteins with highly divergent sequences (superfamily heterodimers). We
predict that significant fraction of heterodimers evolved from homodimers with
the negative design evolutionary pressure applied against promiscuous homodimer
formation. This is achieved through the formation of highly specific contacts
formed by charged residues as demonstrated both in model and real superfamily
heterodimers
