  Recent experimental results suggest that the E. coli chromosome feels a
self-attracting interaction of osmotic origin, and is condensed in foci by
bridging interactions. Motivated by these findings, we explore a generic
modeling framework combining solely these two ingredients, in order to
characterize their joint effects. Specifically, we study a simple polymer
physics computational model with weak ubiquitous short-ranged self attraction
and stronger sparse bridging interactions. Combining theoretical arguments and
simulations, we study the general phenomenology of polymer collapse induced by
these dual contributions, in the case of regularly-spaced bridging. Our results
distinguish a regime of classical Flory-like coil-globule collapse dictated by
the interplay of excluded volume and attractive energy and a switch-like
collapse where bridging interaction compete with entropy loss terms from the
looped arms of a star-like rosette. Additionally, we show that bridging can
induce stable compartmentalized domains. In these configurations, different
"cores" of bridging proteins are kept separated by star-like polymer loops in
an entropically favorable multi-domain configuration, with a mechanism that
parallels micellar polysoaps. Such compartmentalized domains are stable, and do
not need any intra-specific interactions driving their segregation. Domains can
be stable also in presence of uniform attraction, as long as the uniform
collapse is above its theta point.
