Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion.

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.