Abstract

The electrical properties of cellular membranes, particularly their capacitance, are fundamental to numerous biological processes, including signal transduction and cell-cell communication. This study addresses the theoretical and practical challenge of accurately measuring the electrical capacitance of a **deformed lipid membrane**, a common state in biological systems due to mechanical stresses or interactions with the cytoskeleton. Our objective was to derive precise corrections to the standard parallel-plate capacitor model when the membrane undergoes non-spherical or anisotropic deformation. Using a theoretical framework that integrates continuum mechanics with electrostatics, we developed a novel analytical model that accounts for changes in membrane surface area and thickness induced by mechanical strain. The key finding is a set of correction factors that depend on the principal radii of curvature and the membrane's elastic properties, demonstrating that deformation can significantly alter the measured capacitance, potentially leading to misinterpretations of membrane composition or state. These corrections are crucial for the accurate analysis of experimental data from techniques like patch-clamping or electromanipulation of giant unilamellar vesicles (GUVs), providing a more robust understanding of membrane biophysics under physiological and pathological conditions.