Here we present simulation results in which we have shown that osmotic-induced division is a feasible mechanism of vesicle self­replication. In this framework, the non-uniform distribution of osmotic pressures along the membrane is related to the non-uniform, enzyme-driven metabolite distribution inside the vesicle. These pressure changes are generated by the interaction of Turing­like instabilities with vesicle dynamics. They are able to induce the correct vesicle deformation and eventually cell division. After division, the metabolism regenerates the initial conditions and new division cycle starts again. 

Figure 1. Osmotic pressures in an ideal vesicle. These heterogeneous pressures can deform the membrane, eventually triggering membrane fission. Arrows indicate if the total pressure is compressive (the equator) or expansive (the poles). Models of cell replication must somehow create such spatially uneven pressure distribution.

In our model we propouse a well defined chemical mechanism mechanism coupled with vesicle 
growth, which generates the appropriate osmotic pressure distribution along the membrane (see figure 1). 

	Figure 2 The basic protocell model considered. It involves the presence of a membrane together with two basic molecules which interact.

This model can be described by this set of ODEs:

Numerical calculations in a rigid circular container show the emergence of non-uniform metabolites g₁ and g₂ distribution (see figure 3).

	Figure 3 Spatial distributions of morphogen concentrations g1 and g2, confined within a rigid circular container.

As a result of the previous set of interactions, the concentration change until they achieve a steady state. In figure 3 an example of the spatial distribution of g₁ and g₂ is shown. As expected from a symmetry­breaking phenomenon, the two morphogens get distributed in separated spatial domain. Each one tends to concentrate in one of the poles. These effects, coupled with membrane growth, will be exploited to design an active mechanism for controlled membrane division. A second component of our model involves membrane growth. The cell membrane will grow as a consequence of the continuous input of molecules or aggregates available from an external source. As a consequence of this process, the boundary (which allows diffusion with the external enviroment) in not rigid anymore. The effects of these mechanisms can be numerically analyzed. Figure 4 shows these numerical results, where membrane deformation is osmotically induced and can arrive to membrane division. 

		Figure 4. Evolution of the concentrations profiles of g1 and g2 coupled with the membrane expansion process. Here we can see that after a transient, two peaks emerge (a) indicating two maximal concentrations of g1 and g2 . As the simulation proceeds, the peaks separate (b­c) as the membrane (not shown) gets deformed. In (d) we shaw the two concentration profiles right after cell splitting.