Becker–Döring model of self-reproducing vesicles

Abstract

Important developments have been made recently in the experimental study of self-reproducing supramolecular systems based on micelles and vesicles (or liposomes); the processes are related to possible prebiotic transformations involving the forerunners of biological cells. Here we construct and study a kinetic model which describes both the formation and self-reproduction of vesicles. Until now, a detailed mechanistic understanding of vesicle formation has been lacking. Our approach is based on a novel generalisation of the Becker–Döring cluster equations which describe the stepwise growth and fragmentation of vesicular structures. The non-linear kinetic model we present is highly complex and involves many microscopic processes; however, by means of a systematic contraction of the complete set of kinetic equations to the macroscopic limit, we show that the model correctly captures the experimentally observed behaviour.