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.

In computing, informatics and other scientific disciplines, combinations of two or more systems have been shown to perform better than individual systems. Although combinations of multiple systems can be better than each individual system, it is not known when and how this is the case. In this paper, we focus on visual cognition systems. In particular, we conduct an experiment consisting of twenty trials, each focused on a pair of visual cognition systems. The data set is then analyzed using combinatorial fusion. Our results demonstrate that on average, combination of two visual cognition systems can perform better than individual systems only if the individual systems have high performance ratio and cognitive diversity. These results provide a necessary condition as to when two visual cognition systems should be combined to achieve better outcomes.

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Neuronal exocytosis is mediated by a Ca 2þ -triggered membrane fusion event that joins synaptic vesicles and presynaptic membrane. In this event, synaptotagmin I plays a key role as a Ca 2þ sensor protein that binds to and bends the presynaptic membrane with its C2B domain and, thereby, triggers membrane fusion. We report free energy calculations according to which C2B-induced membrane bending is preceded by a Ca 2þ -and membrane-dependent conformational transition, in which C2B attaches to the membrane, moves its C-terminal helix from the orientation seen in the membrane-free crystal/NMR structures as pointing away from the membrane (helix up), to an orientation pointing towards the membrane (helix down). In the C2B ''helix down'' state, lipid tails in the proximal membrane bilayer leaflet interact with the moved helix and become disordered, while tails in the distal leaflet, to keep in contact with the proximal leaflet, become stretched and ordered. The difference in lipid tail packing between the two leaflets results in an imbalance of pressure across the membrane and, thereby, causes membrane bending. The lipid disordering in the proximal membrane leaflet should facilitate Ca 2þ -triggered membrane fusion.

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