An electric potential difference across the plasma membrane is common to all living cells and is crucial for the generation of action potentials for cell-to-cell communication. Beyond excitable nerve and muscle, bioelectric signals conjugated with the transmembrane potential control many cell behaviors such as migration, orientation, and proliferation, which play crucial role in embryogenesis, would healing, and cancer progression. The mechanisms of cellular responses to electric stimuli are virtually unknown. An electricitycentered view, epitomized by the Hodgkin-Huxley model, focuses on the voltage-dependent ion channels. However, in recent years membrane mechanics is emerging as a potentially important player: membrane deformations are detected to co-propagate with action potentials, several ion channels have been found to be both voltage-gated and mechanosensitive, and lipid rafts have been implicated as electrosensors. Assessment of the relevance of these membrane-related effects in bioelectric phenomena requires fundamental understanding of the coupling between membrane morphology, stresses, and voltage, which is limited. To fill this void, the team proposes a combined theoretical and experimental study of biomimetic membranes with transmembrane potential induced by an externally applied electric fields. Specifically, the project seeks to determine how an electric potential elicits membrane responses such a stretching or compression, curvature, and phase transitions, and vice versa, how changes in the membrane morphology modulate the transmembrane potential. Mathematically, these are challenging free boundary problems exhibiting complex dynamics. Continuum theory will be used to model the ions transport, motion of a charged lipid membrane interface and the surrounding liquids. A computational method is proposed to solve these complicated transient three-dimensional free-boundary problems. Experimentally, using giant unilamellar vesicles (GUVs) as a model membrane system the PI will develop novel methodologies to probe the dynamic coupling between shape and voltage of biomembranes. The techniques will be based on the flickering spectroscopy (analysis of the thermally driven micron- and sub-micron membrane undulations) and GUV deformation in applied electric fields. Membranes with broad range of compositions mimicking biological membranes will be investigated. The experimental results will inform the mathematical models in terms of relevant physics and material parameters, and vice versa, the theories will guide the experiments.