Dynamics of Membrane Tension Propagation in Eukaryotic Cells

The propagation of membrane tension perturbations is a potentially critical mechanism in the mechanical signal transduction across the surfaces of living cells. Tethered proteins in the cell membrane play a crucial role in the propagation of the membrane tension. Intact cell membranes in eukaryotic cells possess unique characteristics, such as transmembrane proteins bound to the underlying cortex, rendering them immobile over timescales of minutes to hours. These immobile obstacles significantly alter the dynamics of lipid flow. While existing simplified lipid flow models provide fundamental insights into membrane tension dynamics, they fall short in accounting for complex phenomena like vesicle crumpling. To address this, we propose a more sophisticated model of lipid bilayers, solving the Stokes equations in a two-dimensional framework with embedded obstacles. We employ the finite element method and the FEniCS library to solve the weak form of the Stokes equations, providing a more accurate representation of membrane behaviour under physiological conditions.