Lipid flow through fusion pores connecting membranes of different tensions

When two membranes fuse, their components mix; this is usually described as a purely diffusional process. However, if the membranes are under differen t tensions, the material will spread predominantly by convection. We use st andard fluid mechanics to rigorously calculate the steady-state convective flux of lipids. A fusion pore is modeled as a toroid shape, connecting two planar membranes, Each of the membrane monolayers is considered separately as incompressible viscous media with the same shear viscosity, eta(s) The t wo monolayers interact by sliding past each other, described by an intermon olayer viscosity, eta(r), Combining a continuity equation with an equation that balances the work provided by the tension difference, Delta sigma, aga inst the energy dissipated by flow in the viscous membrane, yields expressi ons for lipid velocity, upsilon, and area of lipid flux, Phi. These express ions for upsilon and Phi depend on Delta sigma, eta(s), eta(r), and geometr ical aspects of a toroidal pore, but the general features of the theory hol d for any fusion pore that has a roughly hourglass shape. These expressions are readily applicable to data from any experiments that monitor movement of lipid dye between fused membranes under different tensions. Lipid veloci ty increases nonlinearly from a small value for small pore radii, r(p), to a saturating value at large r(p), As a result of velocity saturation, the f ur increases linearly with pore radius for large pores. The calculated lipi d flux is in agreement with available experimental data for both large and transient fusion pores.