Dynamical Systems Analysis of a Protocell Lipid Compartment

Abstract

This paper develops phase portraits explaining the dynamic behaviour of the lipid compartment in a recently proposed stochastic protocell model. The protocell model is being used to investigate - in a bottom-up way - the possible roots of cellular autonomy, and the lipid compartment sub-system plays an integral part in determining the cellular dynamic. Whilst motivation is to ground the early model simulation results, the analysis here also reveals an interesting finding: simple addition of an ’osmotic buffer’ to the lipid compartment not only widens it’s range of stability, but also causes a profound change in the deep dynamical structure of the whole cellular system. Relevant to the origins of life, this bifurcation increases the robustness of the compartment to perturbation and instantly grants a richer behavioural repertoire including more reliable divide cycles.