Pressure-driven membrane inflation through nanopores on the cell wall

Walled cells, such as plants and fungi, compose an important part of the model systems in biology. The cell wall primarily functions to prevent the cell from over-expansion when exposed to water, and is a porous material distributed with nanosized pores on it. In this paper, we study the deformation of a membrane patch by an osmotic pressure through a nanopore on the cell wall. We find that there exists a critical pore size beyond which the membrane cannot stand against the pressure and would inflate out through the pore. The critical pore size scales exponentially with the membrane tension and the spontaneous curvature, and exhibits a power law dependence on the osmotic pressure. Our results also show that the liquid membrane expansion by pressure is mechanically different from the solid balloon expansion, and predict that the bending rigidity of the membrane in walled cells should be larger than that of the mammalian cells so as to prevent inflation through the pores on the cell wall.