Photosynthesis across African cassava germplasm is limited by Rubisco and mesophyll conductance at steady state, but by stomatal conductance in fluctuating light

Summary Sub-Saharan Africa is projected to see a 55% increase in food demand by 2035, where cassava (Manihot esculenta) is the most widely planted crop and a major calorie source. Yet, cassava yield in this region has not increased significantly for 13 yr. Improvement of genetic yield potential, the basis of the first Green Revolution, could be realized by improving photosynthetic efficiency. First, the factors limiting photosynthesis and their genetic variability within extant germplasm must be understood. Biochemical and diffusive limitations to leaf photosynthetic CO2 uptake under steady state and fluctuating light in 13 farm-preferred and high-yielding African cultivars were analyzed. A cassava leaf metabolic model was developed to quantify the value of overcoming limitations to leaf photosynthesis. At steady state, in vivo Rubisco activity and mesophyll conductance accounted for 84% of the limitation. Under nonsteady-state conditions of shade to sun transition, stomatal conductance was the major limitation, resulting in an estimated 13% and 5% losses in CO2 uptake and water use efficiency, across a diurnal period. Triose phosphate utilization, although sufficient to support observed rates, would limit improvement in leaf photosynthesis to 33%, unless improved itself. The variation of carbon assimilation among cultivars was three times greater under non-steady state compared to steady state, pinpointing important overlooked breeding targets for improved photosynthetic efficiency in cassava.


Introduction
Rising global population coupled with increased urbanization is predicted to increase food demand by 60% by 2050. Demand increase will be greatest in Sub-Saharan Africa where the population is expected to double by 2050 (van Ittersum et al., 2016;United Nations, 2017). In this region, where cassava (Manihot esculenta Crantz) is the most widely planted crop (FAOSTAT, 2019a), food demand is projected to rise by 55% within just 15 yr (World Bank, 2017). For a variety of cultural and pragmatic reasons, cassava is also the preferred staple food source for many smallholder farmers who constitute the bulk of the population. Dependence on cassava in Africa is underlined by the fact that it accounts for a higher proportion of food consumption per person than any staple in any part of the world (i.e. 0.4 kg per person d -1 ) (Henry et al., 2004). This makes cassava virtually irreplaceable in the fight against hunger in this key and most vulnerable region of the world (Nassar & Ortiz, 2010). Its importance as a cash crop has also increased with more widespread usage by industry (Kleih et al., 2013;Uchechykwu-Agua et al., 2015). For smallholder farmers, increased yields mean that when family needs are exceeded, the surpluses can be sold to provide other household needs. However, cassava yield in Sub-Saharan Africa has not increased over the last 13 yr (De Souza et al., 2017;FAOSTAT, 2019b). Moreover, the genetic progress achieved in breeding programs for increased yield has slowed significantly in recent years (Ceballos et al., 2016). In Africa, the focus of research and breeding programs has necessarily been on disease and pest resistance, as these are major threats to yield increase (Alene et al., 2018). Improved droughttolerant plants can also enhance its productivity in African soils, despite the fact that cassava already has a relatively high yield under drought conditions (Okogbenin et al., 2013). However, increasing yield also depends on increasing genetic yield potential, that is the yield that can be achieved in the absence of pests, disease, water and nutrient limitations. While this might seem of limited value for a crop like cassava, which is often nutrient-, water-or disease-limited, experience with other crops has shown that raising the genetic yield potential not only increases the maximum yields achieved in a region but also increases the minimum yields, that is those achieved under limiting conditions (Koester et al., 2014).
Increased yield potential can be achieved by improving photosynthetic efficiency (Long et al., 2006). Comparing the photosynthetic rates between landraces and improved lines, there is no evidence that photosynthesis in cassava has been improved through breeding (De Souza et al., 2017;De Souza & Long, 2018). Indeed, the conversion efficiency in cassava, which reflects its photosynthetic rates, is just one-seventh of the theoretical value for C 3 plants (De Souza et al., 2017). The validation that increased photosynthetic efficiency can improve yield potential in cassava has been shown by Free Air CO 2 Enrichment (FACE) experiments. Under open-air field CO 2 concentration elevation, leaf photosynthesis was increased by 30%, resulting in a doubling in cassava yield (Rosenthal et al., 2012). This shows that, if photosynthetic efficiency can be genetically improved in cassava, yield potential will also be substantially increased.
Genetic improvements depend on an understanding of the pre-existing diversity for a particular desired trait within an available germplasm. For bioengineering strategies, it is also key to understand the limitations of the desirable trait to design suitable approaches to overcome identified limitations. In cassava, it is remarkable that the genetic variability in photosynthesis is barely known and limitations have not been analyzed (Ceballos et al., 2004). Although the diversity in steady-state photosynthesis of South American cassava cultivars has been evaluated (El-Sharkawy, 2006, 2016, very little is known about African germplasm (De Souza et al., 2017;De Souza & Long, 2018).
Under steady-state conditions, in vivo biochemical and diffusive limitations to leaf photosynthesis may be deduced from the response of net leaf CO 2 uptake under saturating light (A sat ) to intracellular CO 2 concentrations (c i ) . These limitations are the apparent maximum in vivo Rubisco activity (V cmax ), maximum electron transport rate (J max ) and the maximum rate of triose phosphate utilization (V TPU ). Mesophyll conductance to CO 2 diffusion (g m ) is obtained by combining the A/c i curves with modulated Chl fluorescence (Harley et al., 1992;. In a previous study, steady-state photosynthesis in four African cassava cultivars was found to be limited by V cmax , which suggested that Rubisco activity and/or g m were restricting CO 2 uptake (De Souza & Long, 2018). While these results provided an indication that there was genotypic variation, they did not account for the full range of quantitative limitations of photosynthesis and indicated the need for evaluation of a larger number of farmer-preferred cultivars to provide a more realistic assessment of the photosynthetic limitations under steady-state conditions. Improvement of photosynthetic efficiency has focused almost entirely on steady-state and light-saturating conditions. However, in field crop canopies including that of cassava, lighting is almost never at steady-state due to continuous fluctuations in light (Pearcy, 1990). Although cassava is grown in tropical and subtropical environments where the intensity of sunlight is high, the amount of direct light received by a leaf reduces progressively with the depth into the canopy. A leaf in the shade of another receives about 1/10 th of the light of one in full sun (Zhu et al., 2004). Leaf area indices of cassava crops in Sub-Saharan Africa may average little more than 2 (Biratu et al., 2018), so does shading matter? Zhu et al. (2004) show, assuming a random distribution of leaves, that even on a clear sky day, a second layer of leaves will experience over 20 shade-sun transitions during the course of a day, simply due to intermittent shading by other leaves as the sun crosses the sky over the course of a day. Furthermore, cassava in Sub-Saharan Africa is often intercropped with grains that grow faster and mature earlier (Mutsaers et al., 1993), imposing more frequent shading. Additionally, in this region intermittent cloud cover is common during the wet growing seasons (Bourassa et al., 2005), promoting further incidence of shade-sun transitions. While there is limited information on steady-state photosynthesis and its limitations in cassava, to our knowledge there is none on photosynthetic limitations under fluctuating light conditions. Critically, when a leaf transitions from shade to full sunlight, there is a delay of minutes in achieving its maximum photosynthetic rates. This delay can be caused either by the rate of activation of Rubisco (Mott & Woodrow, 2000;Soleh et al., 2016), the rate of stomatal opening or both (Allen & Pearcy, 2000;McAusland et al., 2016). Depending on how slow this transition is, it adversely affects daily photosynthetic carbon gain resulting in lower biomass production. In wheat, for instance, the slow photosynthetic adjustment from shade to sun was calculated to result in a 21% loss of net canopy CO 2 assimilation and productivity (Taylor & Long, 2017). Considering the converse situation, when a leaf transitions from light to shade, photosynthesis declines immediately while stomatal responses are much slower, lowering by c. 20% the intrinsic efficiency of water use (Lawson & Blatt, 2014). On such transitions, it also takes many minutes for photosynthesis to acclimate to the lower light conditions, and over the course of a growing season this can cost 20-40% of potential productivity (Zhu et al., 2004;Kromdijk et al., 2016). In cassava, there is no information on how photosynthesis and stomatal conductance respond to fluctuations in light, nor what limits the speed of adjustment and, in turn, efficiency. This information would be crucial for developing strategies to improve carbon gain and water-use efficiency in this crop.
In addition to the physiological measurements, mechanistic models of photosynthetic metabolism provide a means to test hypotheses related to different in vivo dynamic behaviors, and provide a broader guide to assess quantitatively the value of varying individual traits affecting photosynthetic efficiency (Zhu et al., 2007(Zhu et al., , 2013. Previous model predictions have determined potential routes for improvements in photosynthesis (Zhu et al., 2004;Long et al., 2006) that were later successfully translated to yield increases (Lefebvre et al., 2005;Kromdijk et al., 2016;South et al., 2019). This approach is used here, integrating physiological and biochemical measurements to then predict modifications that could improve photosynthetic efficiency, and by how much.
Here we quantified limitations to photosynthesis in 13 African farm-preferred and high-yielding cassava cultivars under steadystate and fluctuating light conditions, aiming to determine the potential for improving cassava photosynthetic efficiency. A metabolic model of photosynthesis in cassava was developed using the measurements to explore the underlying traits that could give the largest improvements in photosynthetic and wateruse efficiencies, with a focus on nonsteady-state conditions.
For both experiments, all cultivars were propagated in vitro and transferred to the glasshouse as previously described by De Souza & Long (2018). Plants were grown in 14-liter pots, which allowed a plant biomass : pot size ratio of 1 g (DM) dm À3 , which is suggested to avoid any pot size limitation to growth (Poorter et al., 2011). Air temperature in the glasshouse was 28 AE 4°C, water vapor pressure deficit (VPD) was 1.5 AE 0.6 kPa and the average light intensity was 1200 AE 500 lmol m À2 s À1 . In each experiment, three to four biological replicates (individual plants) of each cultivar were measured in a completely randomized experimental design. Pots were distributed with 25 cm spacing and their positions in the glasshouse were re-randomized every 4-5 d to circumvent confounding cultivar with any environmental variation within the glasshouse. Plants were watered to pot capacity every 2-3 d allowing the soil surface to dry between the watering. Measurements were taken on plants 40 d after transplantation. At that stage, plants had, on average, 16.3 g of total biomass (Supporting Information Fig. S1).

Gas exchange and assessment of photosynthetic limitations under steady state
Leaf CO 2 assimilation and transpiration of the central foliole of the youngest fully expanded leaf was measured on 40 d old plants with a portable gas exchange system integrated with a leaf cuvette including a modulated Chl fluorometer and light source (LI-6400XT and Li-6400-40; Li-Cor, Lincoln, NE, USA). To define the response of leaf net CO 2 uptake to intracellular CO 2 concentration (A/c i curves), the leaf was acclimated to a saturating light intensity of 1500 lmol m À2 s À1 (c. 90% red and 10% blue light) and a CO 2 concentration of 400 lmol mol À1 inside the cuvette. After steady-states for both A and stomatal conductance (g s ) were obtained, the chamber inlet [CO 2 ] was varied according to the following sequence: 400,270,150,100,75,50,400,400,600,800,1100,1300 and 1500 lmol mol À1 . The gas exchange measurements were recorded simultaneously with modulated Chl fluorescence as a 10 s average after the conditions inside the cuvette were stable at each [CO 2 ]. The block temperature was set to 28°C, VPD inside the cuvette was maintained at 1.5 AE 0.3 kPa and the air flow at 300 lmol s À1 .
The apparent maxima of Rubisco carboxylation rate (V cmax ), regeneration of ribulose-1,5-biphosphate expressed as electron transport rate (J max ) and triose phosphate utilization (V TPU ) were calculated from the A/c i curves using the equations from von Caemmerer (2000). Before fitting the curves, values for each individual curve were corrected for diffusive leaks between the cuvette and external environment (Bernacchi et al., 2001). Calculated values were adjusted to 25°C, following the equations for temperature response as described by Bernacchi et al. (2001Bernacchi et al. ( , 2003 and McMurtrie & Wang (1993). Stomatal conductance and operating c i were obtained from the data points collected at 400 lmol mol À1 [CO 2 ]. The intrinsic water use efficiency (iWUE) was calculated by dividing A by g s at this same CO 2 concentration.
Mesophyll conductance (g m ) and [CO 2 ] inside the chloroplast (c c ) were calculated for ambient [CO 2 ] (c. 400 lmol mol À1 ) according to the variable J method (Harley et al., 1992). The CO 2 compensation point (Γ*) and respiration (R d ) values necessary for g m calculation were estimated for each replicate according to Moualeu-Ngangue et al. (2017). V cmax and J max , based on chloroplast [CO 2 ] derived from measured g m , were obtained by using a nonlinear analysis with the Marquart method (Moualeu-Ngangue et al., 2017).
To determine photosynthetic limitations under steady-state, the stomatal, mesophyll and biochemical relative limitations were calculated following Grassi & Magnani (2005). Values for Rubisco Michaelis constants for CO 2 (K c ) and for O 2 (K o ) in these calculations were from Bernacchi et al. (2001).

Gas exchange and quantification of diffusional and biochemical limitations under fluctuating light conditions
To evaluate the response of gas exchange in cassava under fluctuating light, two measurements were performed: photosynthetic response to the transition from deep shade to high light (i.e. induction curves), and photosynthetic response to the transition from high to low and back to high light (i.e. relaxation curves followed by induction curves). The measurements were performed on 35-40 d old plants using the same equipment described above for the steady-state measurements.
For the induction curves, plants were maintained in the dark overnight. Before the measurements, the central foliole of the youngest fully expanded leaf was acclimated to the conditions of the LI-6400 cuvette for 20 min, still in the dark. CO 2 concentration inside the cuvette was 400 lmol mol À1 , air temperature 28 AE 2°C and VPD 1.5 AE 0.3 kPa. After 20 min, leaves were preilluminated with 50 lmol m À2 s À1 (deep shade) of photosynthetic photon flux density (PPFD) for 5 min to induce photosynthesis. Then, the light was increased to PPFD of 1500 lmol m À2 s À1 for 30 min, simulating a shade-sun transition. Gas exchange parameters were recorded every 10 s. For each induction curve, the time to reach 50% of maximum photosynthesis (T 50A ), the time to reach 90% of maximum photosynthesis (T 90A ), the cumulative CO 2 fixation in the first 5 min after photosynthetic induction (CCF) and the time to reach 50% of maximum stomatal conductance (T 50gs ) were calculated. Maximum light-saturated leaf CO 2 uptake and maximum stomatal conductance in the induction curves were considered to be that obtained after 30 min under high light. Stomatal conductance at the beginning of induction (g sT0 ) was the last value obtained before increasing the light to 1500 lmol m À2 s À1 PPFD. To investigate the impact of the rate at which the stomata opened on the induction of photosynthesis, a similar induction curve was performed, using a low CO 2 concentration of 100 ppm inside the chamber during the deep shade period to maintain stomatal opening (Taylor & Long, 2017).
The variation in induction rates of three cultivars with contrasting responses were further evaluated with induction curves at five CO 2 concentrations (75, 150, 270, 400 and 600 lmol mol À1 CO 2 ). From these curves, usually referred to as dynamic A/c i curves (Soleh et al., 2016;Taylor & Long, 2017;Salter et al., 2019), V cmax and stomatal limitation under nonsteady-state conditions were calculated using the equations described by Soleh et al. (2016).
Acclimation of photosynthesis to shade, on a sun-shade transition, was characterized after a steady-state rate of leaf CO 2 uptake was obtained at 1500 lmol m À2 s À1 PPFD (c. 40 min). Once in steady-state, the light was decreased to 10% of the initial value (i.e. 150 lmol m À2 s À1 PPFD), and plants were kept under this light intensity for 40 min. Then, the light was increased to 1500 lmol m À2 s À1 PPFD again, for an additional 40 min. Gas exchange was recorded every 10 s. Rate constants were calculated for the increase in g s on transfer to 1500 lmol m À2 s À1 PPFD (k i ), and again for the decrease in g s on return to 150 lmol m À2 s À1 PPFD (k d ). Measured time series for stomatal conductance changes were fit to the following equation (Vialet-Chabrand et al., 2017): where g max is the maximum stomata conductance, g 0 is the minimum stomata conductance, t is time and k (k i or k d ) is the value calculated by the curve fitting function (fit) in MATLAB (The Mathworks, Natick, MA, USA).

Rubisco and Rubisco activase contents, Rubisco activity, total soluble protein and Chl assays
Leaf samples of 4 cm 2 were collected, snap frozen and stored at À80°C until analysis. Samples were homogenized using an icecold mortar and pestle in 0.6 ml of extraction buffer (50 mM Bicine-NaOH pH 8.2, 20 mM MgCl 2 , 1 mM EDTA, 2 mM benzamidine, 5 mM e-aminocaproic acid, 50 mM 2-mercaptoethanol, 10 mM dithiothreitol, 1% (v/v) protease inhibitor cocktail (Sigma-Aldrich), and 1 mM phenylmethylsulphonyl fluoride). After rapid (45-60 s) grinding, samples were clarified via centrifugation at 4°C, 14 700 g for 1 min. The supernatant was used immediately to determine the initial and total activity of Rubisco via incorporation of 14 CO 2 into acid-stable products at 25°C (Parry et al., 1997;Carmo-Silva et al., 2017). This involved a reaction mixture containing 100 mM Bicine-NaOH pH 8.2, 20 mM MgCl 2 , 10 mM NaH 14 CO 2 (9.25 kBq lmol À1 ), 2 mM KH 2 PO 4 and 0.6 mM RuBP. Assays of initial activity were started by the addition of 25 ll supernatant to the complete assay mixture, whilst total activity assays were started by addition of RuBP to the mixture 3 min after adding 25 ll of the supernatant, to allow full carbamylation of Rubisco in the presence of CO 2 and Mg 2+ before the assay. All reactions were quenched after 30 s by adding 100 µl of 10 M formic acid. Assay mixtures were dried at 90°C and 0.4 ml de-ionized water was added to re-dissolve the residue. Acid-stable 14 C was determined by scintillation counting (Packard Tri-Carb; PerkinElmer, Waltham, MA, USA) with the addition of 3.6 ml of scintillation cocktail (Gold Star Quanta, Meridian Biotechnologies, Epsom, UK). The incubation time for total activity was tested to ensure accurate determination of total activity (Sharwood et al., 2016), and 3 min was found to be sufficient. Rubisco activation state was calculated as the ratio of initial to total activity. A 100 ll aliquot of the same supernatant was incubated at room temperature for 30 min with 100 µl of buffer containing 100 mM Bicine-NaOH pH 8.2, 20 mM MgCl 2 , 20 mM NaHCO 3 and 1.2 mM (37 kBq lmol -1 ) [ 14 C]CABP (carboxyarabintol-1,5-bisphosphate), and Rubisco content was determined via [ 14 C]CABP binding (Sharwood et al., 2016).
Total soluble protein (TSP) was determined via a Bradford assay (Bradford, 1976). Chl determination followed the method described by Wintermans & de Mots (1965). A 20 ll aliquot of the homogenate was rapidly taken in duplicate before centrifugation and added to 480 ll ethanol, inverted to mix, and kept in the dark until all extractions were complete (Carmo-Silva et al., 2017). Chl content was determined by measuring absorbance using a microplate reader (SPECTROstar Nano; BMG LabTech, Aylesbury, UK).
To determine relative Rubisco activase content, an aliquot of the supernatant resulting from Rubisco analysis was mixed 1 : 1 with SDS-PAGE loading buffer (62.5 mM Tris-HCl, pH 6.8, 2% (w/v) SDS, 25% (v/v) glycerol, 0.01% bromophenol blue), mixed by pipetting and heated at 95°C for 4 min. Proteins were separated via SDS-PAGE (12% TGX gels, Bio-Rad), and transferred to a nitrocellulose membrane using a dry blotting system (iBlot2, ThermoFisher Scientific, Waltham, MA, USA) (Perdomo et al., 2018). Rubisco activase was detected using an antibody with broad specificity for both isoforms of the protein in higher plants (Feller et al., 1998), and a secondary fluoro-tagged antibody (IRDye800CW, Li-Cor Biosciences). Images were taken and protein amounts were quantified using a fluorescence imaging and analysis system (Odyssey FC; Li-Cor Biosciences). Due to uncertainty regarding the exact binding affinity of this antibody to cassava Rubisco activase, after densitometry of all samples, signal intensities were compared relative to the mean signal intensity of the entire dataset to provide relative quantification of the panel of cultivars.

Cassava photosynthesis model and photosynthetic simulations
To estimate the influence of stomata and Rubisco response on dynamic photosynthesis rate, a cassava photosynthesis metabolic model was developed. The model was constructed based on three pre-existing models: the C 3 photosynthesis model (Zhu et al., 2007), a simplified light reaction model; a Rubisco activase model (Mate et al., 1996;Zhu et al., 2013); and a dynamic stomatal conductance model (Vialet-Chabrand et al., 2017). The cassava model was implemented in MATLAB. The description of the equations used in the model are presented in Notes S1, and the code for this model is available at https://github.com/long-lab/Cassava_model.

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The model was parameterized using cassava values of V cmax , J max , k i , k d , Ball-Berry slope and intercept. Each one of these parameters was calculated from photosynthetic measurements obtained in different cultivars of cassava (Table S1). Ball-Berry slope and intercept were calculated from light curves (A/PPFD curves) obtained for each cultivar (Table S2). For these curves, temperature and VPD were as described for A/c i curves, and [CO 2 ] inside the chamber was kept at 400 lmol mol À1 . The measured V cmax was used as the maximum Rubisco activity in the C 3 photosynthesis model. A, transpiration (T), c i and g s were estimated under a fluctuating light cycle (see later Fig. S8a). The predicted water use efficiency (WUE) was calculated dividing A by T.

Statistical analysis
Differences between cultivars were tested by ANOVA or nonparametric methods (JMP Pro, version 12.0.1; SAS Institute, Cary, NC, USA). For all measured variables, normality was tested using the Shapiro-Wilk's test and the homoscedasticity using Brown-Forsythe's and Levene's tests. When the data met the criteria for normality and homoscedasticity assumptions, one-way ANOVA followed by a pairwise comparison (t-test) was applied. When those criteria were violated, Wilcoxon's nonparametric comparison was used. The threshold for statistical significance was P ≤ 0.05. The data were analyzed using a completely randomized block design, split over 2 yr. The extent of correlation between steady-state variables was evaluated using Pearson's correlation using the data of all cultivars.

Cassava photosynthetic limitations under steady state
Light-saturated net leaf CO 2 uptake (A sat ) in cassava cultivars ranged from 20.3 to 24.8 lmol m À2 s À1 , a total variation of 20% between cultivars (Table 1). A similar 20-24% range of variation was also observed for V cmax and J max calculated from the response of A sat to c i , and V cmax calculated from c c (V cmax,Cc ) ( Table 1). Because estimation of c c cannot be calculated by the variable J method when there is triose phosphate limitation due to the decrease in electron transport rate (Harley et al., 1992), values of J max,Cc could not be calculated for cassava plants in this experiment. However, under high c i the effect of g m on A sat is small (Harley et al., 1992). The operating efficiency of photosystem II (PSII) photochemistry (φPSII), which is usually correlated with the variation on A sat , varies c. 25% among cassava cultivars with an average of 0.22 across the cultivars (Fig. S2). The operating c i values for all cultivars were below the transition in the A/c i response from Rubisco limitation to electron transport limitation ( Fig. 1), indicating that all of the cassava cultivars are Rubiscolimited at current atmospheric [CO 2 ]. Stomatal conductance (g s ) varied from 0.25 to 0.34 mol m À2 s À1 leading to a 26.5% of variation in intrinsic water use efficiency (iWUE) among cultivars (Table 1). Cultivar TMS97/2205 had the highest iWUE whereas TMS96/1632 and TMS01/1412 had the lowest iWUE values out of the cultivars surveyed (Table 1). Corroborating the data presented above, calculation of relative photosynthetic limitation by the method of Grassi & Magnani (2005) showed that, despite no significant differences among cultivars (Fig. S3), at current atmospheric [CO 2 ] in vivo Rubisco activity accounted for about 43% of the total limitation across all cultivars, while stomatal conductance accounted for 16% (Fig. 2). Mesophyll conductance (g m ) did not vary significantly among cultivars (Fig. S4). However, it did account for a similar proportion (i.e. 41%) of the total limitation to photosynthesis across cultivars in cassava (Fig. 2). Additionally, g m was positively correlated to A sat (r = 0.27, P = 0.042; Table S3).
For most cultivars, A did not increase significantly when measured at c i higher than 700 lmol m À2 s À1 (Fig. 1). Except for TMS98/0505 and TMS97/2205, which increased photosynthesis by 7.7% and 5.1%, respectively, from a c i of c. 800 lmol mol À1 to a c i of c. 1250 lmol mol À1 , all other cultivars showed, on average, only a 2.6% increase in photosynthesis under c i higher than 700 lmol mol À1 . The lack of increase in photosynthesis with an increase in c i suggests that a TPU limitation is present in the majority of cassava cultivars evaluated in this study. This is shown by the observed concomitant reduction in J PSII (6-16%) with increasing c i (Fig. 1). There was a significant 15% variation in V TPU , which ranged from 9.9 to 11.65 lmol m À2 s À1 (Table 1). On average, V TPU for cassava was 10.8 lmol m À2 s À1 , suggesting a TPU utilization 44% above the average A sat observed across the cassava cultivars.
Rubisco content, Rubisco initial, total and specific activity, and Rubisco activation state varied significantly among cultivars ( Table 2). The variation in Rubisco content, and initial and total activity was positively correlated to A sat (r = 0.46, P = 0.001; r = 0.36, P = 0.012; and r = 0.36, P = 0.011, respectively; Table S3). Rubisco content also correlated with V cmax (r = 0.37, P = 0.009). Total Rubisco activase and fractions of a and b Rubisco activase isoforms did not vary significantly (Table 2). Chl a (Chla), b (Chlb), total Chl and the ratio of Chla/Chlb showed significant differences among cultivars (Table S4). Of these, Chla/Chlb ratio showed a significant correlation with A sat (r = 0.30, P = 0.029; Table S1). Variation in total soluble protein content (TSP) and in the ratio of TSP to Chl (TSP/Chl) content between cultivars (Table S4) did not correlate with variation in A sat (Table S3).

Dynamic photosynthesis and its limitations in cassava
Induction of photosynthesis on transfer from deep shade (50 lmol m À2 s À1 PPFD) to high light (1500 lmol m À2 s À1 PPFD) was at significantly different rates across the cassava cultivars (P < 0.0001; Fig. 3a). TMS98/0505 showed the fastest induction, reaching 50% and 90% of the steady-state A sat after 3 and 11 min, respectively. TME693 had the slowest induction rates with more than 10 and 21 min to reach, respectively, 50% and 90% of steady-state A sat (Fig. 3a; Table 3). These differences in photosynthetic induction rates translated to a variation of 65% in CCF (Table 3), which correspond closely to stomatal opening, as represented by g s (Fig. 3b; Table 3). Both stomatal conductance at the beginning of the induction (g sT0 ) and time to reach 50% of the final steady-state g s (T 50gs ) had a significant correlation with CCF (r = À0.60, P < 0.0001 and r = 0.52, P < 0.0001). Despite the differences in induction rates, after 30 min the photosynthetic rates of all cultivars reached similar values to those obtained at steady-state ( Fig. S5; Table 1). During photosynthetic induction, iWUE also varied among cultivars (Fig. 3d). During the first 5 min of induction, iWUE in TME7 was two-fold greater than in TMS 98/0505.
The role of g s on the speed of photosynthetic induction was investigated on the three selected cultivars by keeping the stomata open in low light, by reducing the chamber [CO 2 ] to 100 lmol mol À1 during the low light phase. Here, induction in high light was far more rapid and did not differ between cultivars (Fig. 4c). Differences in the speed of induction were therefore due to differences in the speed of stomatal opening.
Biochemical and stomatal limitations during induction in cassava were further estimated by measuring photosynthetic induction under different CO 2 concentrations. With these data, A/c i curves were fit for different time points during the inductions (Fig. S6), and V cmax and stomatal limitation were calculated (Fig. 5). The initial phase of the A/c i curves increased with induction for the three cultivars, and no significant differences were observed (Fig. S6). This was reflected in a nonsignificant difference in V cmax calculated for this phase across these cultivars (Fig. 5a), suggesting that Rubisco activity is not responsible for the differences observed during the induction. Nevertheless, the operating c i in all three cultivars is in the Rubisco-limited part of the A/c i curve throughout induction (Fig. S5), indicating that the induction response in cassava cultivars is overall Rubisco-limited. Stomatal limitation during induction is higher in TME693 than in TMS98/0505 (Fig. 5b), especially during the first 5 min (Fig. 5c) where there is a 20% difference (P = 0.034) between the two cultivars. Corroborating this, c i during the first 5 min of induction under ambient [CO 2 ] was 15.5% lower than the c i at steady-state (Fig. 3c). Stomatal limitation in TME693 decreased after c. 15 min of induction and, after this period, it was similar to that of the other two cultivars (Fig. 5b).
On transfer from high light to shade, A decreased instantaneously but g s required more than 20 min to reach steady state in all cassava cultivars (Fig. S7). Consistent with the differences in induction described above, TME693 showed low values of both rate constants for g s : the rate constant controlling increase on shade to sun transition (k i ) and that controlling decrease on sun to shade transition (k d ) (Table S1). By contrast, TMS01/1412, which had similar rates of photosynthesis induction to TMS98/ 0505 (Table 3; Fig. S5), showed the highest k i and a high k d (Table S1). However, a correspondence between k d and k i was not apparent across all cultivars.

Model simulations
Values of V cmax , J max , k i , k d and Ball-Berry parameters calculated from each cassava cultivar (Table S1) were used to simulate carbon assimilation and stomatal response in two contrasting cultivars, TME693 and TMS01/1412 (Fig. 6). These simulations were done considering the dynamic changes in Rubisco activation (DyRac) and dynamic stomatal conductance response (DyGs). (2019) Ó 2019 The Authors New Phytologist Ó 2019 New Phytologist Trust www.newphytologist.com

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Incorporation of these two variables improved the model performance as judged by an improved match to the measured induction curves (Fig. S8). The model showed that accelerating stomatal response three times would increase average A 11% for TME693 and 7% for TMS01/1412, during the first 10 min of induction ( Fig. 6; Table S5). After 10 min of induction, and during low-and high-light phases, there was no significant impact (i.e. < 3%) of acceleration of stomatal response on A. However, New Phytologist acceleration in stomatal response decreased WUE c. 15% in TME693 over the first 30 min of photosynthesis induction. For TMS01/1412, this reduction was c. 12% during the first 20 min of induction. There was also a decrease in WUE by 8% during the first 20 min of high light for both cultivars. However, WUE increased by 20% in TME693 and by 13% in TMS01/1412 during the first 20-30 min of low light, by accelerating the speed of decline in g s three-fold ( Fig. 6; Table S5).
In a simulated cycle of low and high light applied to all cultivars (Fig. S9) there was an average of 13% loss of carbon assimilation and 5% of WUE resulting from the lags in stomatal response. Accelerating stomata opening and closure speed three times offset 6% of this carbon loss, and 2% of WUE (Fig. S9b).

Discussion
Overcoming photosynthetic limitations to improve photosynthetic efficiency at the leaf level has resulted in some large demonstrated increases in field crop productivity and WUE (Kromdijk et al., 2016;Glowacka et al., 2018;Simkin et al., 2019;South et al., 2019). Previous focus has been overwhelmingly on lightsaturated steady-state photosynthesis. However, in field crop canopies, half of carbon gain is under conditions where photosynthesis is light-limited and most leaves are rarely under steadystate light (Zhu et al., 2004;Taylor & Long, 2017;Papanatsiou et al., 2019). While steady-state measurements are valuable for quantification of biochemical limitations in vivo , dynamic measurements provide insight into the more frequent field condition, particularly in crops canopies, of how leaves respond to fluctuating light (Way & Pearcy, 2012). Indeed, variation between cassava cultivars in carbon assimilation under nonsteady-state conditions was three times that under steady-state conditions (Tables 1, 3), identifying important new traits and therefore opportunities for selection in improving cassava photosynthetic efficiency and yield potential. With the recent advances in genomic resources for cassava (Bredeson et al., 2016) and the development of large-scale breeding efforts

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New Phytologist (Maxmen, 2019), the incorporation of such traits into new cassava varieties may be accelerated to increase yield potential.

Biochemical and mesophyll limitations play a major role in photosynthesis under steady state
Similar to other C 3 crops (Xiong et al., 2018), in cassava biochemical limitation at steady-state was 43% of the total photosynthetic limitation (Fig. 2). In vivo Rubisco activity, not regeneration of RuBP, accounted for this biochemical limitation under the current atmospheric [CO 2 ], as operating c i for all cultivars was below the transition from Rubisco to electron transport limitation, representing RubP regeneration limitation (Fig. 1). On average, Rubisco content in cassava was 1.6 g m À2 (Table 2). This is low compared to 3 g m À2 for wheat and 2.6 g m À2 for rice, under similar conditions of good nutrition (Theobald et al., 1998;Masumoto et al., 2005). Although the CO 2 specificity of Rubisco in cassava is slightly higher (S c/o at 25°C = 105.4 AE 1.8) than in both rice and wheat (S c/o at 25°C = 101 AE 2 and 100 AE 1.1, respectively), its carboxylation efficiency of Rubisco (k cat c /k c air ) is c. 30% lower (Orr et al., 2016). Lower content and efficiency would explain the lower V cmax in cassava (Table 1) compared to elite cultivars of soybean, wheat and rice (Masumoto et al., 2005;Driever et al., 2014;Koester et al., 2014). This difference between cassava and these other C 3 crops suggests that strategies proposed to improve Rubisco efficiency and quantity would have particular value with this crop (  (c) (d) Fig. 3 Changes in leaf carbon assimilation (A, µmol m À2 s À1 ) (a), stomatal conductance (g s , mol m À2 s À1 ) (b), internal CO 2 concentration (c i , µmol m À2 s À1 ) (c) and intrinsic water use efficiency (iWUE, µmol CO 2 mol H 2 O À1 ) (d) in cassava cultivars during photosynthetic induction. Relative values were calculated as the percentage of the value obtained after 30 min under high light. Low light was 50 µmol m À2 s À1 and high light 1500 µmol m À2 s À1 PPFD. Colored lines indicate the cultivars with contrasting responses: TME693 (yellow) and TMS98/0505 (green)) and cultivar TME7 (black), which were selected for further investigation. Gray lines represent the other 10 cultivars. Data represent means; n = 6 except for genotypes TMS98/0505 and TMS97/2205 where n = 3.

Ó 2019 The Authors
New Phytologist Ó 2019 New Phytologist Trust New Phytologist (2019) www.newphytologist.com 20% between-cultivar variation in V cmax found here, although less than the 35% and 55% observed in rice and soybean, respectively (Gu et al., 2012;Koester et al., 2014), still provides a basis for breeding a significant improvement in photosynthetic efficiency. Additionally, the advance in genomic resources can help to target overcoming the low genetic variation in cassava in Sub-Saharan Africa, which has been a consequence of the limited introductions into Africa (Bredeson et al., 2016).
Despite some uncertainties regarding the methods for g m estimation, the limitation to steady-state photosynthesis imposed by mesophyll conductance in this study approached that imposed by assimilation within the chloroplast (c. 41%, Fig. 2). This is more than double the limitation imposed by stomata (Fig. 2). Increasing g m is an attractive target for breeding or bioengineering, because it can increase photosynthesis without increasing transpiration (Flexas et al., 2008;Zhu et al., 2010). An extensive survey of South American cultivars showed that differences in photosynthesis, biomass and yield were closely associated with variation in g m . This is consistent with the correlation between g m and A sat found here for African cultivars (Table S3). However, there is no evidence that g m has been increased with breeding, with no significant difference between g m in landraces and improved lines (F = 0.02; P = 0.889) suggesting that efforts to increase g m in cassava might lead to a significant improvement in photosynthetic rate in this crop.
Simulations have shown that increasing either V cmax or g m could compensate for up to a 40% decrease in stomatal conductance to water vapor (g sw ) (Flexas et al., 2016). This would allow Table 3 Time to reach 50% of light-saturated leaf carbon assimilation (T 50A , min), time to reach 90% of light-saturated leaf carbon assimilation (T 90A , min), cumulative CO 2 fixation in the first 5 min after photosynthesis induction (CCF, lmol CO 2 ), stomatal conductance at the point of initiation of induction (g s T 0 , mol m À2 s À1 ), and time to reach 50% of maximum stomatal conductance (T 50gs , min) in cassava cultivars.

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New Phytologist a cultivar to maintain the same A sat while using 40% less water, that is a 40% increase in iWUE. Although manipulations in g m have been found to affect g s negatively in some other species (Hanba et al., 2004;Flexas et al., 2006), and g m showed a strong positive correlation with g s in soybean (Tomeo & Rosenthal, 2017), these two parameters were not significantly correlated in cassava (r = 0.14, P = 0.280; Table S3). A similar lack of correlation was also found across cultivars of wheat, supporting the contention that improved g m may be selected without impacting g s (Jahan et al., 2014;Barbour et al., 2016). In cassava this would not only increase A sat under optimal conditions, but increase its resilience to the frequent and increasing droughts affecting the major growing regions of Sub-Saharan Africa (Tadele, 2018).

Low capacity of TPU may limit photosynthetic improvements
While Rubisco and mesophyll conductance are the major limitations found in cassava under current atmospheric conditions, TPU limitation, which reflects the plant's ability to convert triose phosphates into sucrose and starch (Sharkey, 1985), can represent a major hurdle for improving photosynthesis in this crop. Eleven of the 13 cassava cultivars evaluated showed TPU limitation, at an A sat only slightly higher than the measured A sat at the current ambient [CO 2 ]. This was evident as a lack of any increase in A sat when c i exceeded 700 lmol m À2 s À1 and an observed decline in J PSII with increasing c i (Fig. 1) (Sharkey, 1985;. The average V TPU across the cassava cultivars was 10.8 lmol m À2 s À1 and only sufficient to support a maximum A sat of 32 lmol m À2 s À1 . Therefore, the maximum improvement in photosynthesis that could be bred or bioengineered could not exceed 33% without simultaneous improvement of V TPU . V TPU values here were similar to those found in a more limited subset of African cassava cultivars (De Souza & Long, 2018), and 25.5-42% lower than in rice, wheat and rye (Wullschleger, 1993;Jaikumar et al., 2013). Low rates of V TPU can be associated with reduced sink strength for growth or storage, or with insufficient capacity to synthesize sucrose and starch in the leaf Sharkey et al., 2007). Cassava produces large tuberous roots. Thus, it is not expected that a reduced sink strength would cause its low V TPU . However, tuberous roots start to develop only after 2-3 months of planting (De Souza et al., 2017), and it is known that the response of cassava varies with age, especially between pretuberous and tuberous growing phases (Gleadow et al., 2016). Our measurements were performed before 2 months, which would indicate a limitation during the plant's establishment phase (De Souza & Long, 2018). Nevertheless, failure to fully utilize photosynthetic potential, even before storage roots form, will be at the cost of canopy and root expansion during the critical establishment phase of the crop. Suggested strategies would be upregulation of ADPglucose pyrophosporylase in roots, and ADPglucose pyrophosphatase in leaves to enhance sucrose and starch synthesis (Ihemere et al., 2006;Jonik et al., 2012;Yang et al., 2016;Sonnewald & Fernie, 2018). These strategies may increase V TPU in cassava, and allow greater bioengineered or bred increases in photosynthesis.

Slow stomatal conductance limits carbon fixation during light fluctuations
After the transition from deep shade or low light to high light, cassava takes c. 20 min to reach photosynthetic rates comparable to steady state (Figs 3a, S5, S7). CCF over first 5 min varied by 286%, from 122 lmol CO 2 assimilated for TME693 to 349 lmol for TMS98/0505 (Table 3). What limits CCF in cassava? In tobacco, rice, soybean and wheat, Rubisco activation is the major limitation to induction (Hammond et al., 1998;Yamori et al., 2012;Soleh et al., 2016;Taylor & Long, 2017;Salter et al., 2019), whereas in cassava, it is the rate of stomatal opening (Figs 3, 5). While V cmax during induction was similar between the contrasting cultivars, stomatal limitation in the first 5 min varied substantially (Fig. 5). When stomatal limitation was effectively removed by artificially lowering the chamber [CO 2 ] during shade, differences between cultivars in the speed of induction were eliminated (Fig. 4).
The rate constant for g s increase (k i ) varied 47% between cultivars with an average value of 9.8 min (Table S1). By definition, the higher the k i the slower the rise in g s . The measured k i values for cassava were similar to those reported for tomato, wheat and common bean, but were 11 times higher than for rice, and three times higher than for maize (McAusland et al., 2016). Slow stomatal opening during induction can significantly affect CO 2 uptake and have a cumulative effect over a day and over a growing season, lowering yields (Reynolds et al., 1994;Fisher et al., 1998;Lawson & Blatt, 2014;Taylor & Long, 2017). Therefore, cultivars with an increased k i , or any genetic manipulation that would allow acceleration of opening would benefit photosynthesis in cassava. Our simulations showed that with a three-fold acceleration of k i , it is possible to increase photosynthetic carbon gain by 7-11% during the first 10 min after induction from deep shade ( Fig. 6; Table S5). The large, almost three-fold, differences found between cultivars during induction (Table 3) could therefore be exploited to improve cassava yield potential. Compared to just a 20% variation in steady-state photosynthesis (Table 1), this emphasizes nonsteady-state photosynthesis as an overlooked trait for improving cassava productivity.
Accelerating stomatal opening can cause a pronounced decrease in WUE. This is because rate of increase in transpiration through the stomata is higher than the rate of increase in CO 2 assimilation due to the intrinsic differences in water and CO 2 concentration gradients between the intracellular spaces and the external atmosphere (Lawson & Blatt, 2014). To counterbalance the decrease of WUE when k i is accelerated (Fig. 6; Table S5), it is also necessary to accelerate the rate of stomatal closing on sun to shade transitions. For the majority of cassava cultivars, the rate constants for g s decrease (k d ) were lower than for k i (Table S1), indicating that cassava stomata are faster to close than to open. Even so, the average value of k d in cassava is higher than for many other crops such as rice, maize, common beans, oat, tomato, sorghum and wheat (McAusland et al., 2016). Our modeling showed that a three-fold increase in k i and k d would increase WUE by 16-20% during the transition from high to low light depending on genotype ( Fig. 6; Table S5). Given a cycle of fluctuations in light similar to that observed in lower layers of the canopy, this increase in k i and k d would increase daily carbon assimilation by 6% without a significant change in WUE (Fig. S9). Importantly, 6% would be the minimum gain in productivity, as before canopy closure this would have a positive feedback by creating more leaf and, in turn, more canopy carbon gain. Thus, over the full growth cycle of cassava of 10-12 months (Lebot, 2009), a substantially higher gain in carbon would be expected while maintaining the current WUE.
Despite low genetic variability in the cassava of Sub-Saharan Africa, this study has identified opportunities to substantially improve photosynthetic carbon gain and increase WUE, particularly by giving attention to nonsteady-state photosynthetic traits. Fig. 6 Model simulated carbon assimilation rate (A), transpiration rate (T), intercellular CO 2 concentration (c i ) and stomata conductance (g s ) of cassava cultivars TME693 and TMS01/1412. Light in PPFD input is: 0 lmol m À2 s À1 in the first 30 min, 50 lmol m À2 s À1 from 30 to 35 min, 1500 lmol m À2 s À1 from 35 to 75 min, 150 lmol m À2 s À1 from 75 to 115 min, and 1500 lmol m À2 s À1 from 115 to 155 min. Cultivar names followed by k i *3 represent the simulation with a three-fold increase in the rate of stomatal opening and k i *3 k d *3 a three-fold increase in rates of both stomatal opening and closure.

Author contributions
APDS and SPL planned the research, APDS performed the experiments and analyzed the data, DJO and EC-S analyzed the material and data for Rubisco, Rubisco activase, protein and Chl, YW conducted the modeling, and APDS and SPL wrote the manuscript with the input of all the other authors.

Supporting Information
Additional Supporting Information may be found online in the Supporting Information section at the end of the article.         Notes S1 Cassava leaf photosynthesis and transpiration model description.

Table S1
Input parameters of cassava model of leaf photosynthesis and transpiration.

Table S4
Chl contents, total soluble protein content, fraction of total soluble protein present as Rubisco, and ratio of total soluble protein to Chl content in cassava cultivars.

Table S5
The effect of a three-fold acceleration of stomatal response on carbon assimilation rate and water use efficiency in cassava cultivars.
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