The next phase in the development of 13C isotopically non-stationary metabolic flux analysis

This viewpoint devises recommendations for future studies utilizing 13C isotopically non-stationary metabolic flux analysis to characterize plant metabolism. Most importantly, it highlights the necessity for model validation.

C isotopically non-stationary metabolic flux analysis ( 13 C-INST-MFA) is an emerging technique for estimations of metabolic fluxes and pool sizes. Within the plant sciences, two studies utilizing this technique to characterize carbon metabolism have been published so far. Here, I examine these studies carefully. Readers unfamiliar with 13 C-INST-MFA will obtain a critical understanding of the method and its findings. Readers working with 13 C-INST-MFA are recommended to enter a phase of model validation to devise clear-cut protocols enabling robust estimations of specific fluxes.

Realistic reaction networks
In 13 C-INST-MFA, a list of coded reactions specifies by which routes carbon can move from labelled or unlabelled sources through metabolic networks into sinks (Fig. 1). The reaction network of both studies allows direct export of 3-phosphoglycerate (3PGA) from chloroplasts to the cytosol. In the light, however, 3PGA export is believed to be restricted due to the chloroplast to cytosol pH gradient (Flügge et al., 1983, and references therein). Additionally, cytosolic reactions catalysed by glyceraldehyde-3-phosphate dehydrogenase and phosphoglycerate kinase are missing [conversion of glyceraldehyde 3-phosphate to 1,3-bisphosphoglycerate to 3PGA; triose phosphate (TP) to 3PGA]. Thus, 13 C flux into glycolysis and the tricarboxylic acid cycle may follow unrealistic routes and has no cytosolic connection with sucrose biosynthesis. Furthermore, fractional refixation of respired CO 2 is not considered (Loreto et al., 1999), and numerous reversible reactions were programmed as irreversible, or vice versa. This includes reactions of the Calvin-Benson cycle catalysed by phosphoglycerate kinase and glyceraldehyde-3-phosphate dehydrogenase (conversion of 3PGA to 1,3-bisphosphoglycerate to glyceraldehyde 3-phosphate; 3PGA to TP), fructose bisphosphatase (conversion of fructose 1,6-bisphosphate to fructose 6-phosphate; FBP to F6P), and fructose-bisphosphate aldolase [conversion of dihydroxyacetone phosphate and erythrose 4-phosphate (E4P) to sedoheptulose 1,7-bisphosphate; TP and E4P to SBP]. Lastly, mesophyll chloroplasts reportedly lack enolase (van der Straeten et al., 1991;Prabhakar et al., 2009;Fukayama et al., 2015). Thus, stromal conversion of 3PGA to phosphoenolpyruvate (PEP) is likely to be infeasible, and fatty acid biosynthesis probably relies on PEP import from the cytosol. Future studies are encouraged to implement more realistic reaction networks representing carbon metabolism with all its intrinsic restrictions and freedom. Incorporation of cytosolic glyceraldehyde-3-phosphate dehydrogenases and phosphoglycerate kinase may enhance the utility of the model since these reactions proposedly constitute a central hub in leaf energy metabolism (Wieloch, 2021).

Constrained fluxes
INCA allows users to constrain fluxes and pool sizes, for example based on independent physiological measurements This paper is available online free of all access charges (see https://academic.oup.com/jxb/pages/openaccess for further details) or theoretical considerations. Users may specify constants or intervals, or choose not to impose any constraints. In all models (both studies), net CO 2 assimilation was fixed at predetermined values scaling fluxes up to reasonable values (supporting interpretation of results) while maintaining flux ratios. Additionally, study 1 fixed the absolute flux into starch ( Fig.  1, ν Starch ) and flux ratios between sucrose and amino acid biosynthesis according to physiological measurements. Similarly, study 2 fixed absolute fluxes into starch, sucrose (ν Sucrose ), and amino acid biosynthesis, and the ratio of Rubisco oxygenation to carboxylation. This practice is potentially problematic since it may affect modelled flux ratios. Additionally, the necessity for constraints poses an important question. If large fluxes need to be fixed (ν Starch , ν Sucrose , and ν O /ν C ), can one rely on 13 C-INST-MFA to return credible results for unconstrained fluxes including smaller fluxes of interest (ν OPPP )? Thus, future studies are encouraged to present models without constraints alongside constrained models to show that data-driven flux estimation is feasible. Ideally, 13 C data should drive the estimations with a minimum of imposed constraints.

Effects of constrained fluxes on fluxes of interest
In principle, constraining fluxes or pool sizes can affect estimates of fluxes or pool sizes of interest due to interconnectivities within the reaction network (Fig. 1). In study 2, ν O /ν C was constrained to be between 0.2 and 0.25. Modelling returned a ν O /ν C ratio of 0.2, and an R L and ν OPPP of 5.2 μmol CO 2 g -1 FW h -1 and 4.6 μmol CO 2 g -1 FW h -1 , respectively. When left unconstrained, modelling returned a physiologically unrealistic ν O /ν C ratio of 0.09, and an R L and ν OPPP of 12.1 μmol CO 2 g -1 FW h -1 and 10.5 μmol CO 2 g -1 FW h -1 , respectively. This indicates negative correlations between ν O /ν C and R L and ν O /ν C and ν OPPP (the lower photorespiration, the higher day respiration). Hence, fixing ν O /ν C at values >0.2 may cause R L →0 and ν OPPP →0. Note that under normal growth conditions, ν O /ν C ratios of 0.34 are common (Sharkey, 1988;Cegelski and Schaefer, 2006;Pärnik et al., 2007). Thus, future studies are encouraged to include sensitivity analyses investigating dependence between constrained fluxes and fluxes of interest.

Validation of results by independent methods
INCA-based 13 C-INST-MFA returns a comprehensive dataset containing estimates of (i) forward and reverse fluxes of all reactions and (ii) pool sizes of all metabolites specified in the reaction network (Fig. 1). Some of these items are accessible to other analytical techniques which, in principle, enables independent validation of 13 C-INST-MFA results. Study 1 made no attempt to confirm modelled ν O /ν C estimates by independent methods. However, estimated ratios were within the physiologically reasonable range. In contrast, study 2 tested the model estimate for R L (5.2 μmol CO 2 g -1 FW h -1 ) by the Laisk method which returned an R L estimate of 9.3 μmol CO 2 g -1 FW h -1 (Brooks and Farquhar, 1985). However, corresponding 95% confidence intervals showed no overlap (3.5-8.05 μmol CO 2 g -1 FW h -1 versus 8.1-10.7 μmol CO 2 g -1 FW h -1 ). Thus, these estimates are statistically different at the 0.05 significance level. Additionally, the model estimate for ν OPPP in chloroplasts was compared with an estimate of flux through the cytosolic OPPP (Sharkey et al., 2020). However, there is no reason to believe that these pathways carry the same flux. Thus, validation of estimates from 13 C-INST-MFA by independent methods has not yet been achieved. However, independently determined fluxes currently used as constraints (ν Starch and ν Sucrose ) can be utilized to test the method by leaving them unconstrained and comparing modelled and measured values. Additionally, ν O /ν C ratios may help to test the method since several alternative methods can provide independent estimates (Busch, 2013).

Metabolically inactive pools or injection of carbon from unlabelled sources
In 13 C-INST-MFA, 12 C is progressively flushed out of the metabolic network and replaced by 13 C from the labelling compound, such as 13 CO 2 (Fig. 1). Both studies reported fast initial labelling of metabolite pools. After several minutes, however, labelling slowed and, even after 1 h, a significant fraction of the pools remained unlabelled. This was attributed to metabolically inactive pools (i.e. metabolite pools disconnected from the flux of incoming 13 C) and modelled accordingly by including a dilution term for each metabolite (accounting for apparently constant offsets between measured and modelled 13 C enrichments). Alternatively, labelling lags may be explained in combination by breakdown of weakly labelled cytosolic sucrose into glucose and fructose, phosphorylation by hexokinase and fructokinase, and reinjection of glucose-6-phosphate-derived carbon into chloroplasts via a cytosolic OPPP not shown in Fig.  1 (Sharkey et al., 2020). Figure 2 shows reported 13 C enrichments of metabolites of the Calvin-Benson cycle, and starch and sucrose biosynthesis 1 h into 13 CO 2 labelling of Arabidopsis thaliana rosettes (Szecowka et al., 2013). Additionally, these authors reported subcellular distributions of metabolites given on the x-axis from fully plastidial (x=0) to fully cytosolic (x=1). Interestingly, plastidial metabolites are more strongly 13 C labelled than cytosolic metabolites. Metabolite distribution explains 55% of the labelling variability (P<0.01, n=11). Since it is not apparent why sizes of metabolically inactive pools would correlate with plastid-cytosol metabolite distribution, this corroborates the idea of injection of weakly labelled carbon into cytosolic metabolism. Future 13 C-INST-MFA studies are encouraged to further explore this by expanding their reaction networks by sucrose breakdown pathways and a cytosolic OPPP. Additionally, sucrose, glucose, and fructose are large carbon pools with significant vacuolar contributions (Szecowka et al., 2013). Thus, cytosol-vacuole transmembrane transport of these metabolites may need to be considered.