Force-extension model of cellular membrane extrusion

Membrane extrusion experiments offer a powerful framework for investigating cell surface mechanics. However, providing a robust physical interpretation of the observed force-extension curves (FECs) remains a significant challenge. In this work, we introduce a minimal statistical-mechanical model for cellular membrane extrusion that accounts for discrete lipids, adhesion molecules, and the finite-size elasticity of the loading device. Focusing on a peeling geometry to isolate the essential physics of extrusion, we derive exact analytical expressions for the force-extension relations under two loading conditions: isometric (constant extension) and isotensional (constant force). Our results elucidate how lipid-lipid interactions, adhesion energies, and device stiffness govern the emergence of a mechanically induced conformational transition, providing a formal interpretation of the characteristic mechanical signatures reported in membrane-extrusion experiments, including force peaks, plateau regimes, and relaxation patterns. A central outcome of our analysis is that the isometric and isotensional conditions provide qualitatively different FECs of the same membrane system. This finding carries profound physical implications, suggesting that distinct experimental protocols applied to the same membrane may yield different mechanical responses.