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Quantitative Biology, Molecular Networks, q-bio.MN,Mathematics, Dynamical Systems, math.DS
Abstract:
Modelling the Calvin cycle of photosynthesis leads to various systems of
ordinary differential equations and reaction-diffusion equations. They differ
by the choice of chemical substances included in the model, the choices of
stoichiometric coefficients and chemical kinetics and whether or not diffusion
is taken into account. This paper studies the long-time behaviour of solutions
of several of these systems, concentrating on the ODE case. In some examples it
is shown that there exist two positive stationary solutions. In several cases
it is shown that there exist solutions where the concentrations of all
substrates tend to zero at late times and others (runaway solutions) where the
concentrations of all substrates increase without limit. In another case, where
the concentration of ATP is explicitly included, runaway solutions are ruled
out.
