A mathematical model of the carbon metabolism in photosynthesis. Difficulties in explaining oscillations by fructose 2, 6-bisphosphate regulation

A mathematical model of the pentosephosphate carbon reduction (PCR) cycle is presented. The internal structure of the model is consistent with and complements the known biochemical pathways in the PCR cycle, together with starch and sucrose synthesis. Individual enzymes are described by maximum rate (V$_m$), standard free energy change ($\Delta G'_0$) and Michaelis constant (K$_m$) values as parameters and rate-equations, symmetrical for the direct and reverse reactions. Enzymic control is included in the starch synthesis pathway (activation by phosphoglycerate (PGA)). inhibition by inorganic phosphate) and in the reactions of sucrose synthesis based on fructose 2.6-bisphosphate (F2.6BP) as a metabolite controlling the cytosolic fructose bisphosphatase (FBPase) activity. The phosphate translocator carries out the exchange of triose phosphates, orthophosphate and PGA. Ionic forms of metabolites are calculated in relation to pH and assumed to be the actual reacting substances. The significant concentration of the active sites of ribulose 1.5-bisphosphate (RuBP) carboxylase is taken into account. Light reactions are included only in the form of an ATPase the $\Delta G'_0$ of which is shifted towards ATP synthesis by the existing proton gradient. The behaviour of the model was studied with the aim of reproducing oscillations in photosynthesis. It is concluded that oscillations in photosynthesis cannot be caused by the fructose 2.6-bisphosphate control of sucrose synthesis alone, but that an additional control of photosynthetic rate must also be involved.