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arXiv · 1411.6772

On necessary and sufficient conditions for proto-cell stationary growth

Erwan Bigan·Stéphane Douady·Jean-Marc Steyaert
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Abstract

We consider a generic proto-cell model consisting of any conservative chemical reaction network embedded within a membrane. The membrane results from the self-assembly of one of the chemical species (membrane precursor) and is semi-permeable to some other chemical species (nutrients) diffusing from an outside growth medium into the proto-cell. Inside the proto-cell, nutrients are metabolized into all other chemical species including the membrane precursor, and the membrane grows in area and the proto-cell in volume. Investigating the conditions under which such a proto-cell may reach stationary growth, we prove that a simple necessary condition is that each moiety be fed with some nutrient flux; and that a sufficient condition for the existence of a stationary growth regime is that every siphon containing any species participating in the membrane precursor incorporation kinetics also contains the support of a moiety that is fed with some nutrient flux. These necessary and sufficient conditions hold regardless of chemical reaction kinetics, membrane parameters or nutrient flux diffusion characteristics.

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Erwan Bigan, Stéphane Douady, Jean-Marc Steyaert. 2014-11-25. On necessary and sufficient conditions for proto-cell stationary growth. https://arxiv.org/abs/1411.6772

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