A relationship between membrane properties forms the basis of a selectivity mechanism for vesicle self-reproduction

Self-reproduction and the ability to regulate their composition are two essential properties of terrestrial biotic systems. The identification of non-living systems that possess these properties can therefore contribute not only to our understanding of their functioning but also hint at possible prebiotic processes that led to the emergence of life. Growing lipid vesicles have been previously established as having the capacity to self-reproduce. Here it is demonstrated that vesicle self-reproduction can occur only at selected values of vesicle properties. We treat as an example a simple vesicle with membrane elastic properties defined by a membrane bending modulus kappa and spontaneous curvature C0, whose volume variation depends on the membrane hydraulic permeability Lp and whose membrane area doubles in time Td. Vesicle self-reproduction is described as a process in which a growing vesicle first transforms its shape from a sphere into a budded shape of two spheres connected by a narrow neck, and then splits into two spherical daughter vesicles. We show that budded vesicle shapes can be reached only under the condition that Td Lpkappa C0(4)> or =1.85. Thus, in a growing vesicle population containing vesicles of different composition, only the vesicles for which this condition is fulfilled can increase their number in a self-reproducing manner. The obtained results also suggest that at times much longer than Td the number of vesicles with their properties near the "edge" in the system parameter space defined by the minimum value of the product Td Lpkappa C0(4), will greatly exceed the number of any other vesicles.