Tension-area relationship in compartmentalized crumpled plasma membrane: a mechanistic model and its implications

The plasma membrane is a liquid lipid bilayer containing both dissolved proteins and proteins anchoring the membrane to the underlying actin cortex. Membrane tension, a 2D analog of pressure in a 3D liquid, is believed to play a crucial role in organizing essential processes within cells and tissues. This, along with recent, conflicting data on the speed of membrane tension propagation, highlights the need for a comprehensive mechanical model to describe tension in the cortex-anchored plasma membrane as a function of transmembrane hydrostatic pressure difference and excess membrane area due to cortex contraction. In this study, we present a mechanical model of plasma membrane compartments, separated by "picket fences" of cortex-anchoring proteins permeable to lipids. Beyond hydrostatic pressure, the model incorporates the 2D osmotic pressure exerted by membrane-dissolved proteins. Our findings reveal that the tension-area relationship within a membrane compartment exhibits a seemingly paradoxical feature: in a specific range of membrane surface area, an increase in area leads to a rise in tension. We further model the tension-area relationship for an ensemble of membrane compartments, which exchange membrane area through shared borders, and discuss potential biological implications of this model.