Kinetic modelling
Kinetic modelling, unlike FMEA, can be used to describe changes in metabolite concentrations overtime. A set of mass-balanced reactions can be described by ordinary differential equations which capture the system dynamics (Saa and Nielsen, 2017; Herrmann et al., 2019a). Here, we used kinetic modelling to assess how changes in flux correspond to changes in metabolite concentrations. Kinetic modelling is not practical with large networks so, rather than using a genome-scale model we constructed a minimal model based on a sub-set of reactions (Fig. 1; Table S1). For simplicity we did not consider compartmentalization in the kinetic model. Kinetic reactions were set up in COPASI (Version 4.27.217). Rates of photosynthesis and respiration (Fig. 2b,c; Fig. S1) were set as independent variables for Col-0, fum2 , and C24 plants, after being converted to μmol CO2 (gDW)-1s-1 (Fig. S2). We initially parametrized the model to fit the measured average diurnal carbon fluxes to starch, malate, and fumarate for control conditions (Fig. 3) using simple mass action kinetics (Abegg, 1899). All other metabolites were assumed not to accumulate in the leaf and were constrained to concentrations between 0-0.0005 μmol CO2 (gDW)1 s-1. The rate of carbon export (Fig.1) was allowed to adjust freely, accounting for any remaining carbon. Using the Hooke and Jeeves (1961) parameter estimation algorithm, with an interation limit of 10 000, a tolerance of 10-8 and a rho of 0.2, we found a model solution for which estimated concentration values fell within the uncertainty ranges of the experimentally measured values. We used an Arrhenius constant to capture temperature-dependence and allowed the effective Q10 to vary between 1.0-3.0 in order to fit the model to the measured starch, malate, and fumarate concentrations at T = 5 °C and T = 30 °C (Fig. 3). The Arrhenius constant describes an exponential increase of reaction rates with temperature (Arrhenius, 1889); it is most commonly reported for a 10 °C change in temperature, known as Q10 , with aQ10 = 2 being typical for enzyme catalysed reactions (Elias, 2014). Without implementing any regulatory mechanisms, we were able to find a solution for which the concentration values estimated by the model fell within the uncertainty ranges of the experimentally measured values (Fig. S3). It is important to note that the effective Q10, as represented in our model, quantifies a possible temperature sensitivity of a reaction rather than the intrinsic properties of enzymes.