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.