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.