Emergent Surface Tension in Active Membranes Under Area Constraint

Abstract Biological membranes operate far from equilibrium due to the continuous activity of embedded proteins that generate forces and curvature stresses. These nonequilibrium processes alter membrane mechanics, yet the connection between microscopic activity and emergent properties such as surface tension remains unclear. Here, we develop a combined theoretical and computational framework to study an active fluid membrane under a fixed projected area constraint. Using a statistical mechanical formulation based on Helfrich curvature elasticity, we derive the fluctuation spectrum of a membrane driven by temporally correlated active forces and determine the effective surface tension self-consistently from excess area conservation. Two modes of activity are examined: direct normal forces and curvature-generating spontaneous curvature. Coarse-grained molecular dynamics simulations with a solvent-free membrane model validate the theoretical predictions. Activity enhances long-wavelength fluctuations and renormalizes membrane mechanics: direct forces significantly increase effective surface tension, while curvature-driven activity primarily redistributes excess area with smaller tension changes. Short-wavelength fluctuations remain bending-dominated. These results quantitatively link microscopic protein activity to emergent membrane mechanics, providing insight into how active processes regulate membrane stability and morphology.