  Despite the wide existence of vesicles in living cells as well as their
important applications like drug-delivery, the underlying mechanism of vesicle
fusion/fission remains under debate. Here, we develop a constrained
self-consistent field theory (SCFT) which allows tracking the shape evolution
and free energy as a function of center-of-mass separation distance. Fusion and
fission are described in a unified framework. Both the kinetic pathway and the
mechanical response can be simultaneously captured. By taking vesicles formed
by polyelectrolytes as a model system, we predict discontinuous transitions
between the three morphologies: parent vesicle with a single cavity,
hemifission/hemifusion and two separated child vesicles, as a result of
breaking topological isomorphism. With the increase of inter-vesicle repulsion,
we observe a great reduction of the cleavage energy, indicating that vesicle
fission can be achieved without hemifission, in good agreement with simulation.
The force-extension relationship elucidates typical plasticity for separating
two vesicles. The super extensibility in the mechanical response of vesicle is
in stark contrast to soft particles with other morphologies such as cylinder
and sphere.
