Abstract
We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model, the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division dynamics of the compartment. Bistability in the dynamics of the autocatalytic set results in a protocell that can exist with two distinct growth rates. Stochasticity in chemical reactions plays the role of mutations and causes transitions from one growth regime to another. We show that the system exhibits 'natural selection', where a 'mutant' protocell in which the autocatalytic set is active arises by chance in a population of inactive protocells, and then takes over the population because of its higher growth rate or 'fitness'. The work integrates three levels of dynamics: intracellular chemical, single protocell, and population (or ecosystem) of protocells.
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