Forces and stresses acting on fusion pore membrane during secretion.

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.