  Demixing of multicomponent biomolecular systems via liquid-liquid phase
separation (LLPS) has emerged as a potentially unifying mechanism governing the
formation of several membrane-less intracellular organelles ("condensates"),
both in the cytoplasm (e.g., stress granules) and in the nucleoplasm (e.g.,
nucleoli). While both in vivo experiments and studies of synthetic systems
demonstrate that LLPS is strongly affected by the presence of a macromolecular
elastic network, a fundamental understanding of the role of such networks on
LLPS is still lacking. Here we show that, upon accounting for capillary forces
responsible for network expulsion, small-scale heterogeneity of the network,
and its nonlinear mechanical properties, an intriguing picture of LLPS emerges.
Specifically, we predict that, in addition to the experimentally observed
cavitated droplets which fully exclude the network, two other phases are
thermodynamically possible: elastically arrested, size-limited droplets at the
network pore scale, and network-including macroscopic droplets. In particular,
pore size-limited droplets may emerge in chromatin networks, with implications
for structure and function of nucleoplasmic condensates.
