Polymer collapse facilitates protein phase-separation*

Nuclear proteins such as transcription factors demix into liquid-like droplets in-vitro, and in-vivo phase-separate at somewhat lower concentrations onto DNA & RNA polymers. Separately, long polymers can undergo extended to collapsed transitions as solvent conditions change, and spatial rearrangements of chromosomes in three-dimensions regulate transcription. Here we use approaches from statistical physics to explore a model where proteins with a propensity to phase-separate in 3D modulate the collapse transition of a long polymer. Our analysis reveals that the surface of a long polymer is best viewed as a compressible 'scaffold' onto which a bulk fluid can phase-separate. Demixing of the bulk fluid coincides with the polymer collapse transition, and the presence of a scaffold dramatically widens the regime in which these demixing transitions occur. Polymers lacking the collapse transition or fluidity do not see a similar degree of enhancement. A simple extension of our model allows us to understand how cells may use these scaffolded phases to integrate information for sensory tasks. We draw parallels to a recent model we proposed for clusters of cytoplasmic signaling molecules that phase-separate exclusively at the surface of the plasma membrane, itself near a 2D liquid-liquid critical point. In both long polymers & critical membranes, phase-transitions in a lower-dimensional surface mediate surface-localized demixing of a bulk fluid.