2014/11/25 by Erwan Bigan, Bigan, Erwan, Stéphane Douady +3
Biochemistry, Genetics and Molecular Biology · #FOS: Biological sciences #Molecular Networks (q-bio.MN) #q-bio.MN
paper · pdf · doi:10.48550/arxiv.1411.6772
Fifth International Workshop on Static Analysis and Systems Biology (SASB 2014), Munich, Sept 10, 2014. To be published in Electronic Notes in Theoretical Computer Science
arxiv created 2014/11/25 · arxiv updated 2014/11/26
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.