Protocell Dynamics: Modelling Growth and Division of Lipid Vesicles Driven by an Autocatalytic Reaction

We study a computational model of a protocell, in which an autocatalytic reaction sustains itself inside a lipid vesicle. The autocatalytic reaction drives volume growth via osmosis. Membrane area grows due to addition of lipids from the environment. The membrane growth rate depends on the external lipid concentration and on the tension in the membrane. In the absence of division, a cell either reaches a state of homeostasis or grows to a point where the internal reaction collapses. If a cell becomes elongated, it can divide into two smaller spherical vesicles, conserving the total volume and area. We determine when it is energetically favorable for a large vesicle to divide. Division requires the buildup of a difference between the lipid areas on the outer and inner leaflets of the membrane. Division occurs most easily when the rate of flipping of lipids between leaflets is relatively slow. If the flipping is too fast, the parent cell grows large without dividing. There is a typical size at which division occurs, producing two daughter cells of unequal sizes. The smaller and larger daughters regrow to the same typical size before the next division. Protocells with an active metabolism reach a stable state where the internal autocatalytic reaction and the membrane growth are well balanced. Active protocells can grow and divide in conditions where an inactive vesicle without an internal reaction cannot.