Abstract
The energetics underlying the expansion of fusion pores connecting biological or lipid bilayer membranes is elucidated. The energetics necessary to deform membranes as the pore enlarges, in some combination with the action of the fusion proteins, must determine pore growth. The dynamics of pore growth is considered for the case of two homogeneous fusing membranes under different tensions. It is rigorously shown that pore growth can be quantitatively described by treating the pore as a quasiparticle that moves in a medium with a viscosity determined by that of the membranes. Motion is subject to tension, bending, and viscous forces. Pore dynamics and lipid flow through the pore were calculated using Lagrange's equations, with dissipation caused by intra- and intermonolayer friction. These calculations show that the energy barrier that restrains pore enlargement depends only on the sum of the tensions; a difference in tension between the fusing membranes is irrelevant. In contrast, lipid flux through the fusion pore depends on the tension difference but is independent of the sum. Thus pore growth is not affected by tension-driven lipid flux from one membrane to the other. The calculations of the present study explain how increases in tension through osmotic swelling of vesicles cause enlargement of pores between the vesicles and planar bilayer membranes. In a similar fashion, swelling of secretory granules after fusion in biological systems could promote pore enlargement during exocytosis. The calculations also show that pore expansion can be caused by pore lengthening; lengthening may be facilitated by fusion proteins.