CAM emerges in a leaf metabolic model under water-saving constraints in different environments

Crassulacean Acid Metabolism (CAM) evolved in arid environments as a water-saving alternative to C3 photosynthesis. There is great interest in engineering more drought-resistant crop species by introducing CAM into C3 plants. However, one of the open questions is whether full CAM or alternative water-saving flux modes would be more productive in the environments typically experienced by C3 crops. To study the effect of temperature and relative humidity on plant metabolism we coupled a time-resolved diel model of leaf metabolism to an environment-dependent gas-exchange model. This model allowed us to study the emergence of CAM or CAM-like behaviour as a result of a trade-off between leaf productivity and water-saving. We show that vacuolar storage capacity in the leaf is a major determinant of the extent of CAM and shapes the occurrence of phase II and IV of the CAM cycle. Moreover, the model allows us to study alternative flux routes and we identify mitochondrial isocitrate dehydrogenase (ICDH) and an isocitrate-citrate-proline-2OG cycle as a potential contributor to initial carbon fixation at night. Simulations across a wide range of environmental parameters show that the water-saving potential of CAM strongly depends on the environment and that the additional water-saving effect of carbon fixation by ICDH can reach up to 4% for the conditions tested.


29
Increasing aridity threatens agricultural productivity not only in hot and dry climates but also in 30 temperate regions where extreme weather conditions are becoming more frequent 1 . Thus, 31 the development of water-use efficient crop varieties is of utmost importance to maintain food 32 security 2 . Several plant lineages living in arid environments have evolved CAM 33 photosynthesis, a water-saving mode of C-fixation in which CO2 uptake into the mesophyll cell 34 and fixation by RuBisCO are temporally separated 3 . In CAM photosynthesis the stomata open 35 at night and CO2 is fixed and stored in the vacuole in the form of a carboxylic acid such as 36 malate or (iso-)citrate 4-7 . During the day the stored CO2 is remobilized for fixation by RuBisCO 37 in the chloroplast, accompanied by the accumulation of storage carbohydrates. This cycle is 38 considered to be an energetically expensive, but water-use-efficient, alternative to direct day-39 time CO2-fixation by RuBisCO (C3 photosynthesis) 8,9 . 40 The implementation of CAM photosynthesis into a C3 crop plant is a promising 41 engineering target for two reasons: first, all enzymes required for the CAM cycle are already 42 present in C3 plants (although specific isoforms with different regulatory properties are required 43 10 ); and second, some facultative CAM species, such as ice plant (Mesembryanthemum 44 crystallinum), can be induced to switch from C3 to CAM photosynthesis by a number of 45 environmental factors such as drought or high-salinity 8,11 suggesting that it should be possible 46 to engineer CAM into a C3 leaf. However, CAM photosynthesis is usually considered to be advantageous in hot and arid climates where water-use efficiency (WUE) is a strong 48 determinant for plant growth and where the suppression of photorespiration through carbon 49 concentration behind closed stomata becomes a considerable factor that balances the 50 additional cost of running the expensive CAM cycle 12 . To test this hypothesis, in a previous 51 study, we investigated the energetics and productivity of CAM and found that despite 3-fold 52 higher energy consumption at night, the additional cost of running a CAM cycle can be 53 balanced by the carbon-concentrating effect of carboxylic acid decarboxylation behind closed 54 stomata during the day 13 . 55 Here we addressed a different question: what are the metabolic and morphological 56 limitations to implementing a water-saving CAM or CAM-like mechanism in a C3 leaf and what 57 is the extent of the water-saving effect in different environments? To address this question, 58 we constructed a time-resolved, large-scale metabolic leaf model and coupled it to a gas-59 exchange model that includes the two main determinants of water-loss through the stomata 60 the temperature (T) and the relative humidity (RH). This environment-coupled model was 61 used to investigate emergent flux modes when water-saving constraints are applied in addition 62 to high productivity. 63 64

65
Model construction 66 Light availability and gas exchange (CO2, water vapour) are major determinants of the 67 metabolic behaviour of a plant leaf. To model the interplay between leaf productivity and water-68 loss through transpiration we extended a previous diel flux-balance modelling framework 13 in 69 two ways. First, we increased the temporal resolution from a binary day-night scenario to 70 modelling a 24 time-step diel cycle, where each interval represents one hour of the day. The 71 time-resolution in the models was achieved by coupling 24 copies of the model in way that a 72 range of metabolites (starch, sugars, amino acids, carboxylic acids, and nitrate) were allowed 73 to accumulate and subsequently be degraded in the plastid and vacuole, respectively. For 74 each of these metabolites we introduced linker fluxes which transfer the accumulated 75 metabolite from one time interval to the next. Upper bounds were placed on the quantity of 76 carboxylic acids and other compounds that were allowed to accumulate in the vacuole based 77 on vacuole size and leaf anatomy (leaf thickness and porosity) for average C3 and CAM 78 leaves. Secondly, we coupled the metabolic model to a simplified gas-diffusion model which 79 allows us to compute water-loss through the stomata according to the CO2 demand of the 80 metabolic system and the environmental conditions (T and RH). A detailed description of the 81 model construction and the exchange constraints is given in the Materials and Methods 82 section. The resulting time-resolved, environment-coupled model enabled us to simulate the 83 effect of the diel light curve, T and RH on leaf metabolism and was used to study the trade-84 offs between leaf productivity and water-use efficiency ( Figure 1). 85 In this study we considered the metabolism of a mature leaf and started the analysis 86 by using the maximization of phloem output over the course of the day as the primary 87 objective. This optimality criterion led the metabolic system to synthesize storage compounds 88 in the light which were then used to sustain night-time metabolic processes such as phloem 89 output, maintenance, and nitrogen assimilation in an overall optimal manner. In accordance 90 with the metabolic mode of the system, the model predicted changing CO2-demand and -91 depending on T and RHwater-loss by transpiration over the course of the day. Conversely, 92 we could fix phloem output to a given value (equal to or less than the maximum value) and 93 used minimization of water-loss as a driving force to act on the metabolic system. These 94 constraints led to the prediction of water-saving flux modes while maintaining high productivity. 95 96

97
A time-resolved diel model simulates dynamics of C3 metabolism 98 To establish a reference model for a mature leaf operating under optimal conditions we began 99 our analysis by simulating an energy-limited scenario (due to the maximisation of phloem 100 output for a fixed light input) without water-saving constraints. We simulated a typical summer 101 day in a temperate climate with a maximum T of 26°C and a maximum RH of 0.8 (Figure 2A). 102 We used a light curve that peaks at a moderate intensity of 250 μmol m -2 s -1 and follows a 103 normal distribution with a day length of 12 hours. As a second optimization criterion we 104 minimized the metabolic flux sum 14 . This objective was used as a proxy for the cost of 105 providing the enzymes for the active reactions. Applying it as a second optimality criterion left 106 the objective value, here the phloem output, unaltered, but chose the flux distribution with the 107 least enzymatic cost from a set of alternatives. 108 Using this setup, the model predicted a total phloem output of 41.3 mmol m -2 leaf d -1 . 109 Daily total water loss was predicted to be 116.4 mol m -2 leaf which is 2. To get a better overview of the metabolic behaviour over the course of the diel cycle 118 we examined the CO2 uptake, RuBisCO activity and the linker fluxes for starch and carboxylic 119 acids, respectively as shown in Figure 2B. The magnitude of a linker flux corresponds to the 120 amount of the stored metabolite, i.e. a flux of 1 μmol m -2 s -1 means that 3.6 mmol are available 121 for utilisation in subsequent time intervals in the model. Both, CO2 uptake (grey line) and 122 RuBisCO flux (orange) were predicted to follow the light curve and peaked at midday 123 coinciding with light availability. Carboxylic acid levels (magenta area) peaked before midday 124 and remained low from before sunset to dawn. Starch (green area) accumulated during day-125 time hours and was subsequently degraded to sustain metabolism at night. Overall, the 126 described flux patterns were characteristic for C3 leaf metabolism. From this starting point we 127 then asked the question: how will the metabolic fluxes change if we change the optimality 128 criterion from maximizing phloem output to minimizing water loss? 129 130 An optimality study reveals trade-offs between productivity and WUE 131 Computationally, the question of how a system's behaviour changes when operating between 132 competing objectives can be tackled by performing a Pareto analysis [16][17][18][19] . In our case phloem 133 output and water-saving represented two competing driving forces. We started the Pareto 134 analysis from the above described scenario of a mature leaf optimized for maximum phloem 135 output (i.e. 100% phloem output, here termed Pareto step 1). We then subsequently reduced 136 the required phloem output in 10%-steps and used minimization of water loss as the primary 137 optimization objective. Given this setup, we saw an almost linear decrease in water loss with 138 decreasing phloem output, hence we did not observe any significant water-saving mechanism 139 in our model ( Figure 2C top). Inspection of the CO2 uptake and RuBisCO reaction flux in the 140 model showed that with decreasing phloem output, the model closed the stomata during the 141 warmest and driest hours of the day, a phenomenon known as midday depression of 142 photosynthesis ( Figure 2D left column), which was accompanied by a very minor peak of CO2 143 uptake at night. 144 One possible explanation for the lack of water-saving metabolic modes in the model 145 was that the model was limited by the constraints we applied to mimic C3 leaf anatomy (e.g. 146 total vacuolar volume per unit of leaf). To test this, we examined the differences between C3 147 and CAM leaf anatomy and adjusted the vacuolar storage constraints accordingly. Using 148 morphological data for an average CAM leaf resulted in a 3.1-times larger vacuolar storage 149 capacity per unit leaf compared to a C3 leaf. (see Supplementary Text). When repeating the 150 Pareto analysis using this CAM-morphology, a non-linear relationship between productivity 151 and water loss emerged and the model predicted almost 50% water-saving at 70% of the 152 maximum phloem output ( Figure 2C bottom). It is worth noticing that the upper limit for the 153 vacuolar storage capacity had only a very minor impact on the maximum phloem output of the 154 model. The output at Pareto step 1 for the C3 leaf model was 99.7% of the phloem output of 155 the CAM leaf. Therefore, in subsequent analyses we directly compared between the two sets 156 of simulations. 157 What was causing the non-linearity in the relationship between productivity and water 158 loss? As in the C3-anatomy-constrained model, we observed a closure of the stomata and a 159 reduction of RuBisCO activity during the hottest and driest hours of the day. However, in 160 addition to these day-time changes to reduce water loss, we also observed a substantial peak 161 of CO2 uptake at night which was accompanied by an accumulation of carboxylic acids in the 162 vacuole at night and a greater amount of starch stored during the day and degraded at night. 163 ( Figure 2D  When investigating the CO2 uptake at different steps along the Pareto frontier it became 179 apparent that the model did not exhibit a full CAM-cycle ( Figure 2D middle columns). The 180 stomata closed only for a few hours in the day and re-opened only for a short period at night. 181 The sharp CO2 uptake peak at night-time can be explained by three factors. First, the applied 182 RH and T curves have a sharp local maximum and minimum (see Figure 2A). This occurs 183 where the lower and upper ends of the normal curves meet to close a diel cycle. Secondly, 184 our model is anticipating: i.e., the solution for time-point t depends on the environmental 185 parameters to be encountered at time-point t+1. Thirdly, the upper-bound on the rate of CO2 186 uptake was based on the largest CO2 uptake rates measured. Therefore, very high rates over 187 a short period were permitted, whereas in reality, under most conditions and in most species, 188 CO2 diffusion constraints would cause that CO2 is fixed at lower rates but for a longer duration. 189 These factors led to the observed behaviour where CO2 uptake showed a short burst when 190 water loss through transpiration was the lowest. 191 During the day, the stomata remained open for CO2 exchange during the early hours 192 of the day and re-opened in the evening hours before sunset. This behaviour was exhibited 193 for all Pareto steps meaning that night-time CO2-fixation alone was not sufficient to sustain the 194 required phloem output. The observed opening and re-opening of the stomata during the day 195 occurs in certain CAM species and is known as phase II and IV of the CAM cycle 3 . Night-time 196 stomata opening for CO2-uptake and day-time stomata closure are referred to as phases I and 197 III, respectively. Some CAM species show a remarkable plasticity with respect to these four 198 phases and the reasons for the occurrence and extent of these distinct patterns is still debated 199 [20][21][22] . Given the indication that vacuolar storage capacity had a major impact on the night-time 200 CO2 uptake pattern in the model and the fact that some CAM species exhibit a bi-phasic CAM 201 cycle we wondered if we might underestimate the vacuolar storage capacity of an average 202 CAM leaf. We therefore repeated the Pareto analysis using the same model but without any 203 vacuolar storage constraints. The results of this analysis are shown in Figure 2D, right column. 204 Without any limitation of the vacuolar storage capacity the model performed a bi-phasic full 205 CAM cycle at 70% of the maximum productivity and below i.e. the stomata remained closed 206 during the day and were open throughout the night, without the appearance of phase II and 207 IV of the CAM cycle. Therefore, our model suggested that keeping the stomata open for at 208 least a portion of the day was necessary to sustain a high productivity when vacuolar storage 209 capacity is limiting. 210 211

212
The occurrence of the four phases of CAM in our model raised the question of how metabolic 213 fluxes were distributed during these metabolically distinct phases. To analyse the underlying 214 flux modes in more detail we focused the analysis on a model with a vacuolar storage capacity 215 of a CAM leaf at 70% of maximum productivity (phloem output) optimized for water-saving. 216 We chose this value, as a yield penalty of 30% would be an acceptable trade-off if water usage 217 could be reduced by almost half. We followed the flux of CO2 (including bicarbonate) from the 218 stomata through the metabolic system by plotting time-resolved fluxes of all reactions that use 219 CO2 or bicarbonate as either a reactant or product ( Figure 3A left). During the day, RuBisCO 220 fixed the majority of CO2 available from gas-exchange and released by metabolic processes. 221 Cytosolic isocitrate dehydrogenase (ICDH), glycine oxidation in the photorespiratory pathway 222 (glycine decarboxylase), carbamate kinase in N metabolism and NADP-malic enzyme in the 223 cytosol were the main CO2-releasing processes during the day. To our surprise, we found that 224 night-time CO2 fixation in the model was shared between two enzymes -PEP-carboxylase 225 (PEPC) in the cytosol and ICDH in the mitochondria. While PEPC's role in CAM 226 photosynthesis is well established, mitochondrial ICDH activity has not been previously linked 227 to this metabolic cycle. In order for ICDH to be used for CO2 fixation it has to operate in the 228 reverse direction to its conventional direction in the TCA cycle. This is possible given an 229 appropriate mass action ratio (e.g. due to a high 2OG concentration) and indeed this reaction 230 has been shown to operate in the reverse direction in several in vivo metabolic flux studies in 231 developing rapeseed and soybean embryos 23-25 . ICDH has also been suggested as a 232 kinetically acceptable option for synthetic carbon fixation pathways (ΔG = 21 kJ mol -1 at pH 7, 233 ionic strength of 0.1 M, and reactant concentrations of 1 mM 26,27 ). For convenience, we refer 234 to this reaction as ICDHrev. 235 Analysis of the linker fluxes revealed that citrate and/or isocitrate were the sole 236 carboxylic acid to accumulate at night (Accumulation of either citrate or isocitrate or of both 237 carboxylic acids resulted in the same phloem output and water-saving.). Additionally, two 238 amino acids accumulated -Asn during the night and Pro during the day ( Figure 3B left). None 239 of the other linker reactions in the vacuole carried a significant flux. Closer inspection of the 240 metabolic fluxes revealed an alternative CO2 fixation pathway where both PEPC and ICDH 241 contribute to night-time CO2-fixation. An overview of the reactions involved is shown in Figure  242 4A. 243 At night, when the stomata are open and CO2 can enter the leaf, PEPC catalyses the 244 fixation of CO2 to PEP (marked as (I) in Figure 4A). High enzyme costs might outweigh the water-saving effect of alternative flux routes 314 The occurrence of specific metabolic patterns was not only determined by water-use efficiency 315 but also by the cost for enzyme synthesis. In our analysis, this metabolic investment was only 316 indirectly considered by minimizing the metabolic flux sum after the leaf productivity and water 317 loss had been determined. Therefore, flux minimization did not represent a competing 318 objective on the Pareto frontier and a slightly more water-efficient solution with a high 319 enzymatic investment (high flux sum) would always be preferred over a slightly worse 320 performing mechanism with less enzyme investment. To account for this bias, we considered 321 the metabolic flux sum for the three models -ICDHrev, ICDHirrev, and ICDHirrev, Cit_night From these analyses we made the following observations: Overall, we found that for the 350 investigated environmental conditions, the relative water loss at 70% productivity with respect 351 to a C3 leaf ranged between 31 and 67 % and the additional water-saving effect of ICDHrev 352 reached up to 4%. As an example, the results for a set of simulations for a maximum light 353 intensity of 250 μmol m -2 s -1 , a 12:12 day:night-time ratio and a fixed RHmax of 0.9 are shown 354 in Figure 5B and will be analysed further.

356
Absolute water loss is the highest for high T and low RH values. The model predicted the 357 highest absolute water loss for low RH and high T. This behaviour was to be expected from 358 the gas-diffusion relationship between the system's demand for CO2 and the resulting water 359 loss through transpiration. In Figure 5B this relationship is illustrated by the orange heatmaps, 360 which represent the absolute water loss experienced by both models -ICDHrev (left) and 361 ICDHirrev (middle) for all analysed combinations of Tmin (y-axis) and Tmax (x-axis) values for three 362 different RHmin values (0.3, 0.5, 0.7). The darker the colours the higher absolute water loss. 363 For example, at RH between 0.5 and 0.9, Tmin = 10°C and Tmax between 20 and 30°C water 364 loss increased by 60 and 61%, respectively. Furthermore, we observed that the day-time 365 temperature Tmax was the main driver for water loss as the colour gradient changed more along 366 the x-axis than along the y-axis. This could be explained by the occurrence of phase II and IV 367 of the CAM cycle in our model. During these two phases the stomata opened during the day 368 and water-loss was much higher than at night in phase I. This was also reflected in the effect 369 of relative humidity on water loss. We found that the effect of the day-time humidity RHmin on 370 the absolute water loss was stronger than the effect of RHmax (A comparative plot for changing 371 RHmax is shown in the Supplementary Text, Figure 2). For example, water loss was 1.9-fold 372 higher at RHmin = 0.3 as compared to RHmin = 0.7 at Tmin = 10°C, Tmax = 30°C and RHmax= 0.9. 373 The difference in the absolute water loss between model ICDHrev and model ICDHirrev was 374 largest for combinations of low Tmin and high Tmax (darkest areas in the green heatmap in Figure  375 5B) and for the highest ΔRH value, i.e. RHmin = 0.3 and RHmax = 0.9. Therefore, with respect 376 to absolute water-saving, model ICDHrev outperformed model ICDHirrev the most for high day-377 and low night-time temperatures and large RH differences between day and night. 378 379 Relative water loss is the highest for small diel temperature (ΔT) and high RH changes (ΔRH). 380 Next, we considered the relative water loss with respect to the C3 leaf which is illustrated in 381 the blue heatmaps ( Figure 5B). Here, we found that the relative water loss was the lowest for 382 combinations of low night-time temperatures and high day-time temperatures. This 383 observation could be explained by the fact that low night-time temperatures benefited the 384 water-saving for a CAM-like leaf but had little impact on the water-loss of a C3 leaf which closed 385 the stomata during the night. Conversely, this holds true for high day-time temperatures. We 386 also observed that high ΔRH values drove high water loss. Finally, the red heatmaps show 387 the difference in relative water loss with respect to the C3 model between model ICDHrev and 388 ICDHirrev. The plot reveals differences in the contribution of ICDHrev to the water-saving 389 potential of the CAM-cycle. As with the absolute water loss, the contribution was the highest 390 for environments with high day-time and low night-time temperatures and environments with 391 low RH values. However, in contrast to the difference in absolute water-saving, the difference 392 in relative water-saving was high across a large range of conditions (as can be seen by the 393 dark colours for most parameter combinations). This indicated that for most of the encountered 394 conditions ICDHrev can have a significant contribution to relative water-saving with respect to 395 a C3 plant. 396 397 Day length and light intensity impact water loss. In addition to T and RH, we investigated the 398 influence of different light intensities and day-light hours on water loss. We found a strong 399 effect of light intensity on the additional relative water-saving potential of running the isocitrate-400 citrate-proline-2OG cycle and we observed that for higher light intensities this effect 401 diminishes. Changing day-time hours also had an effect on the relative water-saving potential 402 of ICDHrev and can make a difference of up to 4% for short days where it only reached 2% for 403 long days. Plots showing the water loss as dependent on light intensity and day length are 404 shown in Supplementary Figure 3 and 4, respectively. 405 406

407
The time-resolved, environment-coupled model of leaf metabolism allowed us to study the 408 trade-offs between productivity and water-saving for different network configurations and 409 across different environmental conditions in a systematic manner. Our analysis led to three 410 main conclusions. First, the leaf's vacuolar storage capacity is a major determinant of the 411 extent of a CAM cycle and without engineering a higher vacuole to cytoplasm ratio it will be 412 unlikely that a full CAM cycle can be engineered into a C3 leaf. Secondly, the reversibility of 413 mitochondrial ICDH might contribute to initial carbon fixation at night-time. This operational 414 mode of the TCA cycle was previously demonstrated by metabolic flux analysis in rapeseed 415 and soybean embryos 23,24 but is a novel prediction with respect to nocturnal CO2 assimilation. 416 Thirdly, the water-saving effect of CAM strongly depends on the environment and the 417 additional water-saving effect of carbon fixation by ICDH can range between 0.1 and 4% for 418 the environmental conditions tested here. The additional water-saving contribution is largest 419 at lower light intensities and for broad ranges of temperature and relative humidity which 420 makes it an interesting candidate for metabolic engineering approaches as these should be 421 beneficial for many weather conditions typically encountered by C3 crops. 422 423 Reduced photorespiration due to daytime stomata closure can increase the water-424 saving potential of CAM leaves 425 426 Our previous study on CAM photosynthesis investigated the energetics and productivity of 427 metabolic networks operating in C3 and CAM. It was found thatdepending on the rates of 428 the carboxylase and oxygenase activities of RuBisCOthe productivity of a CAM network 429 could reach between 74 -100% of the C3 network 13 . In the analysis presented here, we 430 focused on the water-saving potential of CAM without considering the potentially positive effect 431 of carbon concentration behind closed stomata during the day. As we do not know how the 432 carboxylation to oxygenation ratio changes as we move along the Pareto frontier from open 433 stomata to partial and full closure during the daytime we used a constant value of 3:1. 434 Therefore the implications of our analysis can be regarded as a conservative estimate. Due to 435 the suppression of photorespiration in a leaf operating in CAM mode the actual water-saving 436 potential at the same productivity level is expected to be higher than calculated here. 437 438

ICDH might play a role in facultative CAM photosynthesis
439 Diel cycles of Pro accumulation have been previously observed in ice plant exposed to CAM-440 inducing salt stress. Under this stress condition Pro is known to act as an osmoprotectant. It 441 has been reported that Pro accumulation proceeded in an oscillating manner in which high 442 levels of Pro accumulated during the day (up to 16 μmol gFW -1 ), followed by a partially 443 degradation at night which led to steadily increasing Pro levels during the CAM-induction 444 phase 30 . The increase in Pro levels was accompanied by an increase in PEPCase mRNA up 445 to 10 days after stress exposure when PEPC mRNA has reached a full CAM level. This 446 oscillatory behaviour led the authors to the following statement "Changes of proline in light 447 and darkness suggested that proline plays an important role in addition to serving as an 448 osmolyte." but they offered no further explanation of what this role could be. We suggest that 449 in addition to its function as an osmoprotectant during the day, Pro degradation at night might 450 support C-fixation by supplying the substrate 2OG for citrate synthesis through ICDH in the 451 mitochondria. Once PEPC capacity has been induced to the level required for full CAM the 452 initial CO2-fixation proceeds via this enzyme, as it is kinetically superior, catalysing a 453 thermodynamically favourable reaction compared to ICDHrev (ΔG = -40kJ mol - increase in the palisade mesophyll and 2.0-to 2.5-fold increase in the spongy mesophyll in A. 520 thaliana. Assuming that the larger cell size is mainly driven by increased vacuolar volume the 521 reported increase would suffice to enable partial CAM with high water-saving potential. 522 Besides increased cell size, the authors also reported a significant decrease in cell wall 523 thicknessanother feature typically observed in CAM plants 36  Gas-exchange through the stomata was described by a linearized diffusion model 558 which predicts the water-loss depending on the metabolic model's demand for CO2, at a 559 particular T and RH. The input curves for T and RH are based on a normal distribution function 560 and allowed us to systematically scan a multidimensional parameter space by adjusting the 561 function parameters accordingly. 562 The model equations for optimizing phloem output and water-saving were solved as a 563 linear optimization problem (L1 norm). The subsequent minimization of the metabolic flux sum 564 was solved as a quadratic optimization problem (L2 norm) to select from a possible set of 565 multiple solutions, the one with the least variation in fluxes between time points. To exemplify 566 this, consider a three-time-step model with the flux sequence [1, 1 ,1], [2, 0, 1] and [3, 0, 0]. 567 When applying the L1 measure all three cases will be weighted with 3 although in the second 568 and third case more enzyme needs to be synthesized and degraded and therefore would be 569 costlier. The L2 distance yields values of 3, 5, and 9 and would therefore prefer the flux 570 distribution in which fluxes are equally split between the 3 phases. A derivation of the gas-571 water exchange relationship through the stomata, any further modelling assumptions, 572 parameter derivations, and auxiliary calculations are detailed in the Supplementary Text. allowed the transfer of storage compounds in the vacuole and the plastid between successive 580 models. Light uptake was constrained by the diel light curve. The day:night ratios of phloem 581 output and maintenance were set to 3:1 for each hour of the diel cycle, and N uptake was 582 constrained to a ratio of 3:2 based on previous estimates 50 . Upper right: The effect of 583 temperature T and relative humidity RH on stomatal water loss was modelled by a simplified 584 gas-diffusion equation. T and RH data determined the relationship between CO2 uptake and 585 water loss. In C3 plants stomata open during the day and CO2 uptake and water loss are high 586 due to high T and low RH. At night the stomata are closed and gas/water exchange is 587 minimized. In CAM plants stomata remain closed during the day and open at night allowing 588 high CO2 influx while having a low transpiration stream due to low T and high RH. Bottom: 589 Combining metabolic and gas-exchange models allows the trade-off between productivity and 590 water-loss to be studied as competing objectives on a Pareto frontier and reveals alternative 591 water-saving C-fixation mechanisms. 592 593