Metabolic Modelling
We used a metabolic model modified from that of Arnold and Nikoloski
(2014), as previously published (Herrmann, Dyson, Vass, Johnson, &
Schwartz, 2019). Specifically, the model was modified to ensure that
cytosolic fumarate could be produced from cytosolic malate (inclusion of
reversible cytosolic FUM reaction) and added “export reactions” to the
model (describing diurnal storage pools) for malate, fumarate and
starch, in addition to the already existing sucrose export.
Additionally, we added a cyclic electron transport reaction to the model
which was previously missing. We generated four models for each genotype
(Col-0 and fum2 ): 20oC; 4oC
on Day 0; 4oC on Day 7 of treatment; and one with
NADPH-limiting conditions. We constrained the models using metabolite
assays such that the beginning-of-day concentrations of fumarate,
malate, and starch subtracted from their respective end-of-day
concentrations equated to the diurnal flux over the eight-hour
photoperiod, consistent with an approximately constant rate of
accumulation of these metabolites seen experimentally (Dyson et
al. , 2016). We assumed a constant rate of photosynthesis through the
day (Dyson et al. , 2016) and converted the measured rates of
photosynthesis to cumulative diurnal fluxes of carbon intake
(mmol.gFW-1.Day-1), as previously
described by Herrmann et al. (2019) . Flux to sucrose was not
constrained but was used to estimate the remaining carbon which is
exported from the leaf during the day. We then used proteomics data to
further constrain the upper bounds of the flux reactions (Ramon, Gollub,
& Stelling, 2018). For each metabolic reaction we checked whether all
of the corresponding proteins were available in the data set; if so,
then those reactions were given an upper bound of the additive values of
all of the identified proteins, in case multiple isoforms exist. The
proteomic constraints of the Col-0 and fum220oC models we also applied to the respective
4oC Day 0 models, assuming that during the first day
of cold, changes in metabolic enzyme content are negligible (consistent
with measured total protein and photosynthetic capacity). Given that the
proteomics data are relative and not quantitative, we scaled all the
proteomics constraints to the lowest possible values for which we were
able to obtain model solutions across all models. In total, we
constrained the upper bounds of 101 reactions in each model. Proteomic
constraints were calculated as the averages of four biological
replicates for each treatment plus the standard error of those
measurements, thus accounting for measurement error. Because protein
presence does not necessarily equate to enzymatic activity, we set the
lower bounds for these reactions to zero for irreversible reactions and
to the negative value of the upper bound for reversible reactions.
Proteomic constraints were applied only to the “inner” model
reactions, whereas the metabolite and photosynthesis data were used to
set boundary conditions (i.e. influxes and effluxes). We the used flux
solutions, from a flux balance analysis maximizing carbon assimilation
via Rubisco within feasible model constraints, in order to eliminate
non-essential reactions which generate loops within the model, using the
loopless function in the cobra (version 0.10.1) package (Desouki,
Jarre, Gelius-Dietrich, & Lercher, 2015). The objective function is
irrelevant to the results presented in this paper and was only applied
to ensure that none of the pathways required for carbon metabolism
contained thermodynamically infeasible solutions. We then conducted flux
sampling on the loopless models using the CHRR algorithm in the MATLAB
toolbox as outlined in Herrmann et al. (2019). In order to
minimise observer bias, the flux sampling was performed without an
optimisation constraint for the control, Day 0 and Day 7 models. The
NADPH-limited models are the same as the control models, but here, in
addition to the experimental constraints, we set a minimum NADPH
production via linear electron transport as an objective function.