Effect of membrane potential on the mechanical equilibrium of biological membranes

Abstract

The mechanical equilibrium of a membranous sac, whose wall is sandwiched by two oppositely charged fluid layers, is investigated as a mathematical model of a living cell. In so doing, it is assumed that the space charge density in the inner and the outer charged fluid layer is constant. It is also assumed that the fluid inside and outside of the charged fluid layer is a perfect conductor. By solving Maxwell's equation, the electric field and the thickness of the inner and the outer charged fluid layer is determined as a function of the geometry of the sac. Then, the fluid pressure in the charged fluid layer is derived by considering the body force created by the electrostatic field. The condition of mechanical equilibrium of the sac membrane yields an equation which reveals the inter-relation between the geometry, the sac fluid pressure and the membrane potential. According to this equation, the change of membrane potential causes a deformation of the sac. If the wall of the membranous sac is permeable, increase (decrease) of the absolute value of the membrane potential results in swelling (shrinking) of the sac. On the other hand, the mechanical change of the sac volume results in the change of the membrane potential. This analysis provides also an explanation of how the red blood cell maintains the biconcave shape, when the red blood cell is assumed to be a fluid filled membranous sac with non-zero membrane potential.