Prewetting of Critical Membranes & Collapsed Polymers

Many intracellular proteins demix into coexisting liquid phases in response to varying cellular conditions. Some, such as those found in growth factor & immune signaling, phase-separate exclusively on the plasma membrane in response to ligand; other nuclear proteins condense exclusively on the 'surface' of chromatin to regulate gene expression. These "surface densities" are typically stable at concentrations far lower than those required without a lower-dimensional template. The surfaces that template these condensates -- chromatin and the plasma membrane -- are poised near phase-transition themselves - in the case of the plasma membrane, near a critical point. Here we propose a minimal theory for phase separation at biological surfaces by cytoplasmic & nuclear proteins. We show that templating surfaces themselves prone to transitions, such as the fluid plasma membrane and dynamically compressible chromatin, significantly expand a regime of "surface-only" phase transitions known as prewetting. We offer two pictures of what a prewetting transition offers to cellular functions. At the plasma membrane we find that prewetting enhances the specificity and sensitivity of signaling networks; in genomic contexts prewetting facilitates precise localization of regulatory machinery