Membrane wetting by biomolecular condensates is facilitated by mobile tethers.

Biomolecular condensates frequently rely on membrane interactions for localization, recruitment, and chemical substrates. These interactions are often mediated by membrane-anchored tethers, a feature overlooked by traditional wetting models. Using a surface free-energy framework that couples surface tension with tether density, we solve for the contact angle and tether density in a spherical cap geometry, generalizing the Young-Dupré equation. While the contact angle retains its force-balance form, the tether density depends nontrivially on the form and strength of tether-condensate interactions. We solve for this dependence within a simple interaction model, and find a wetting phase diagram with a transition from non-wetting to partial to complete wetting over a biologically realistic parameter range. This work provides a quantitative framework for characterizing condensate-membrane interactions, uncovering potential mechanisms by which membranes mediate cellular organization and function.