  Lipid bilayer membranes are the fundamental biological barriers that permit
life.
  The bilayer dynamics largely participates in orchestrating cellular workings
and is characterized by substantial stability together with extreme plasticity
that allows controlled morphological/topological changes.
  Modeling and understanding the topological change of vesicle-like membrane at
the scale of a full cell has proved an elusive aim.
  We propose and discuss here a continuum model able to encompass the
fusion/fission transition of a bilayer membrane at the scale of a Large
Unilamellar Vesicle and evaluate the minimal free energy path across the
transition, inspired by the idea that fusion/fission-inducing proteins have
evolved in Nature towards minimal work expenditure.
  The results predict the correct height for the energetic barrier and provide
the force field that, by acting on the membrane, can induce the transition.
They are found in excellent agreement, in terms of intensity, scale, and
spatial localization with experimental data on typical protein systems at play
during the transition.
  The model may pave the way for the development of more complete models of the
process where the dynamics is coupled to the fluid internal and external
environment and to other applications where the topological changes do either
occur or should be prevented.
