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We present a simple mathematical model that captures the evolutionarycapabilities of a prebiotic compartment or protocell. In the model theprotocell contains an autocatalytic set whose chemical dynamics is coupled tothe growth-division dynamics of the compartment. Bistability in the dynamics ofthe autocatalytic set results in a protocell that can exist with two distinctgrowth rates. Stochasticity in chemical reactions plays the role of mutationsand causes transitions from one growth regime to another. We show that thesystem exhibits `natural selection', where a `mutant' protocell in which theautocatalytic set is active arises by chance in a population of inactiveprotocells, and then takes over the population because of its higher growthrate or `fitness'. The work integrates three levels of dynamics: intracellularchemical, single protocell, and population (or ecosystem) of protocells..

Multistable protocells can aid the evolution of prebiotic autocatalytic sets