Boundary flow induced membrane tubulation under turgor pressures

During clathrin-mediated endocytosis in yeast cells, a small patch of flat membrane is deformed into a tubular shape. It is generally believed that the tubulation is powered by actin polymerization. However, studies based on quantitative measurement of the actin molecules suggest that they are not sufficient to produce the forces to overcome the high turgor pressure inside of the cell. In this paper, we model the membrane as a viscous 2D fluid with elasticity and study the dynamic membrane deformation powered by a boundary lipid flow under osmotic pressure. We find that in the absence pressure, the lipid flow drives the membrane into a spherical shape or a parachute shape. The shapes over time exhibit self-similarity. The presence of pressure transforms the membrane into a tubular shape that elongates almost linearly with time and the self-similarity between shapes at different times is lost. Furthermore, the width of the tube is found to scale inversely to the cubic root of the pressure, and the tension across the membrane is negative and scales to the cubic root squared of the pressure. Our results provide a new mechanism to explain the deformation of membrane during endocytosis in addition to the actin polymerization.