Model for electrocurvature phase transitions in lipid bilayers driven by flip-flop asymmetry

The active transfer of phospholipids between membrane leaflets (flip-flop), mediated by (adenosine triphosphate) ATP-dependent enzymes such as flippases and floppases, is a key regulator of membrane asymmetry and curvature. However, the theoretical understanding of curvature generation driven by flip-flop under external perturbations remains incomplete. Here we present a mesoscopic thermodynamic model in which lipid asymmetry couples to membrane curvature via a Landau-type free energy, with curvature as the order parameter and transmembrane voltage as the control parameter. This framework predicts an electrically driven phase transition analogous to a ferroelectric transition. The model reproduces field-induced bistability, critical susceptibility divergence, and hysteresis, with numerical simulations revealing thickness-dependent curvature thresholds and robust curvature-memory effects. These results clarify how electric-field-driven lipid redistribution governs membrane shape and suggest strategies for voltage-controlled nanoscale memory and shape encoding.