Dependence of the energies of fusion on the intermembrane separation: optimal and constrained

Abstract

We calculate the characteristic energies of fusion between planar bilayers as afunction of the distance between them, measured from the hydrophobic/hydrophilic interface of one of the two nearest, cis, leaves to the other. The two leaves of each bilayer are of equal composition; 0.6 volume fraction of a lamellar-forming amphiphile, such as dioleoylphosphatidylcholine, and 0.4 volume fraction of a hexagonal-forming amphiphile, such as dioleoylphosphatidylethanolamine. Self-consistent field theory is employed to solve the model. We find that the largest barrier to fusion is that to create the metastable stalk. This barrier is the smallest, about 14.6 $k_BT$, when the bilayers are at a distance about 20 percent greater than the thickness of a single leaf, a distance which would correspond to between two and three nanometers for typical bilayers. The very size of the protein machinery which brings the membranes together can prevent them from reaching this optimum separation. For even modestly larger separations, we find a linear rate of increase of the free energy with distance between bilayers for the metastable stalk itself and for the barrier to the creation of this stalk. We estimate these rates for biological membranes to be about 7.1 $k_BT$/nm and 16.7 $k_BT$/nm respectively. The major contribution to this rate comes from the increased packing energy associated with the hydrophobic tails. From this we estimate, for the case of hemagglutinin, a free energy of 38 k_BT for the metastable stalk itself, and a barrier to create it of 73 k_BT. Such a large barrier would require that more than a single hemagglutinin molecule be involved in the fusion process, as is observed.