  The presence of knots has been observed in a small fraction of single-domain
proteins and related to their thermodynamic and kinetic properties. The
exchanging of identical structural elements, typical of domain-swapped
proteins, make such dimers suitable candidates to validate the possibility that
mutual entanglement between chains may play a similar role for protein
complexes. We suggest that such entanglement is captured by the linking number.
This represents, for two closed curves, the number of times that each curve
winds around the other. We show that closing the curves is not necessary, as a
novel parameter $G'$, termed Gaussian entanglement, is strongly correlated with
the linking number. Based on $110$ non redundant domain-swapped dimers, our
analysis evidences a high fraction of chains with a significant intertwining,
that is with $|G'| > 1$. We report that Nature promotes configurations with
negative mutual entanglement and surprisingly, it seems to suppress
intertwining in long protein dimers. Supported by numerical simulations of
dimer dissociation, our results provide a novel topology-based classification
of protein-swapped dimers together with some preliminary evidence of its impact
on their physical and biological properties.

Soft Condensed Matter;Statistical Mechanics;Biomolecules