Increased bundle‐sheath leakiness of CO₂ during photosynthetic induction shows a lack of coordination between the C₄ and C₃ cycles

Summary

• Use of a complete dynamic model of NADP‐malic enzyme C₄ photosynthesis indicated that, during transitions from dark or shade to high light, induction of the C₄ pathway was more rapid than that of C₃, resulting in a predicted transient increase in bundle‐sheath CO₂ leakiness (ϕ).

• Previously, ϕ has been measured at steady state; here we developed a new method, coupling a tunable diode laser absorption spectroscope with a gas‐exchange system to track ϕ in sorghum and maize through the nonsteady‐state condition of photosynthetic induction.

• In both species, ϕ showed a transient increase to > 0.35 before declining to a steady state of 0.2 by 1500 s after illumination. Average ϕ was 60% higher than at steady state over the first 600 s of induction and 30% higher over the first 1500 s.

• The transient increase in ϕ, which was consistent with model prediction, indicated that capacity to assimilate CO₂ into the C₃ cycle in the bundle sheath failed to keep pace with the rate of dicarboxylate delivery by the C₄ cycle. Because nonsteady‐state light conditions are the norm in field canopies, the results suggest that ϕ in these major crops in the field is significantly higher and energy conversion efficiency lower than previous measured values under steady‐state conditions.

Introduction

Photosynthetic energy conversion efficiency (ε _c), the efficiency with which crops convert intercepted radiation into biomass, is a major limitation to the yield potential for both C₃ and C₄ crops (Zhu et al., ^{2008, 2010}; Long et al., ²⁰¹⁵). The ε _c of C₄ species has the intrinsic advantage of minimizing energy loss to photorespiration under most conditions, compared with C₃ species (Long & Spence, ²⁰¹³). Although only 3% of species use the C₄ pathway, they account for 23% of terrestrial gross primary productivity (Sage et al., ²⁰¹²). C₄ species are also overrepresented in agricultural production in which just three C₄ crops (maize, sugarcane and sorghum) account for 32% of global production (Long & Spence, ²⁰¹³; FAO et al., ²⁰²⁰). All three are from a single C₄ evolutionary clade, tribe Andropogoneae, and use the NADP malic enzyme (ME) for decarboxylation in the bundle sheath. Despite high productivity, even under optimum conditions, these C₄ crops still fall well short of the theoretical maximum energy conversion efficiency of 6% in the field (Zhu et al., ^{2008, 2010}; Dohleman & Long, ²⁰⁰⁹). Understanding the limitations to realizing the theoretical maximum in field conditions is key to increasing the productivity of C₄ crops.

C₄ photosynthesis includes a light energy‐driven CO₂‐concentrating mechanism that increases the CO₂ concentration around Ribulose‐1,5‐bisphosphate carboxylase/oxygenase (Rubisco) in bundle‐sheath cells, competitively inhibiting the oxygenation reaction, with the result that photorespiration is almost eliminated under normal conditions (Hatch, ^{1978, 1987}; Edwards & Walker, ¹⁹⁸³; Keeley & Rundel, ²⁰⁰³; Sage, ²⁰⁰⁴). Compared with C₃ photosynthesis, C₄ photosynthesis requires two additional ATP per CO₂ assimilated in the regeneration of phosphoenolpyruvate (PEP), the initial acceptor molecule for CO₂ in the mesophyll. However, as the bundle sheath is not hermetically sealed, an inevitable consequence of the high [CO₂] gradient formed between bundle sheath and mesophyll cells is leakiness (ϕ). Leakiness describes the proportion of carbon fixed by PEP carboxylase (PEPC) and released by decarboxylation in the bundle sheath that diffuses back to the mesophyll. A variety of methods have estimated an average ϕ of 0.2 in C₄ NADP‐ME species when measured at steady state in high light (Kromdijk et al., ²⁰¹⁴). This means that for every five CO₂ molecules released by decarboxylation of malate in the bundle sheath, one will diffuse back to the mesophyll, raising the cost per net CO₂ assimilated by 0.5 ATP. Minimizing ϕ requires close coordination between the C₃ and C₄ cycles. Any elevation of ϕ indicates some lack of coordination between the two photosynthetic cycles and therefore a loss of photosynthetic efficiency (Henderson et al., ¹⁹⁹²).

Although previous studies of C₄ leakiness have focused on steady‐state conditions (Bellasio & Griffiths, ²⁰¹⁴; Kromdijk et al., ²⁰¹⁴; von Caemmerer & Furbank, ²⁰¹⁶), leaves in crop fields are seldom under steady‐state conditions; instead these crop species experience frequent fluctuations in environmental conditions, especially light intensity. Intermittent cloud cover, the movement of leaves, and the changing solar angle over the course of a day cause dramatic and often abrupt changes in the light environment, including sunflecking within the crop canopy (Pearcy, ¹⁹⁹⁰; Zhu et al., ²⁰⁰⁴; Slattery et al., ²⁰¹⁸; Ohkubo et al., ²⁰²⁰; Sakoda et al., ²⁰²⁰; Wang et al., ²⁰²⁰; Qiao et al., ²⁰²¹; Long et al., ²⁰²²). The planting densities of these crops are increasing such that self‐shading and more frequent light fluctuations will continue to increase. Although light fluctuations at points on a leaf can occur in fractions of a second, the photosynthetic apparatus may require many minutes to adjust, potentially leading to losses of efficiency at the crop canopy level. This has led to a growing awareness of the need to address photosynthetic efficiency in fluctuating light (Hubbart et al., ²⁰¹²; McAusland et al., ²⁰¹⁶; Deans et al., ²⁰¹⁹; Acevedo‐Siaca et al., ²⁰²⁰; De Souza et al., ²⁰²⁰; McAusland & Murchie, ²⁰²⁰; Murchie & Ruban, ²⁰²⁰). Much progress has been made in understanding the dynamic response to light in C₃ plants in the past few years. Photosynthetic induction of C₃ plants during shade‐to‐sun transitions is mainly influenced by three factors: activation of Rubisco, the speed of stomatal opening, and activation of the enzymes involved in RuBP regeneration within the C₃ cycle (Pearcy, ¹⁹⁹⁴; Mott & Woodrow, ²⁰⁰⁰; Kaiser et al., ²⁰¹⁶; Slattery et al., ²⁰¹⁸; Taylor et al., ²⁰²²). Photosynthetic rate during induction is lower than that under steady‐state; however, the major factors limiting photosynthesis, primarily Rubisco activation and stomatal opening, vary among crop species and all represent a loss of potential efficiency (McAusland et al., ²⁰¹⁶; Taylor & Long, ²⁰¹⁷; Acevedo‐Siaca et al., ^{2020, 2021}; De Souza et al., ²⁰²⁰).

When grown under fluctuating light, two C₄ species (Setaria macrostachya and Amaranthus caudatus) showed a greater reduction in biomass than that observed in two C₃ species (Triticum aestivum and Celosia argentea) relative to growth under steady‐state light (Kubásek et al., ²⁰¹³). As rapid stomatal movement was reported in C₄ plants (Bellasio et al., ²⁰¹⁷; Ozeki et al., ²⁰²²), the biomass reduction suggests that C₄ species may be more vulnerable to efficiency losses under fluctuating light, perhaps because of the need to coordinate between the two photosynthetic cycles. This finding was challenged by Lee et al. (2022) who compared carbon assimilation during fluctuating light to steady‐state across six C₃ and six C₄ species. Whereas Kubásek et al. (2013) made measurements during photosynthetic induction, Lee et al. (2022) examined plants that were fully acclimated to high light and suggested that differences between the two studies could be a result of photosynthetic induction causing lower coordination between C₃ and C₄ cycles.

A dynamic modeling simulation of C₄ photosynthetic induction coupled with gas‐exchange measurements identified Rubisco activase, PPDK regulatory protein and stomatal conductance as the major limitations to the efficiency of NADP‐ME‐type photosynthesis during dark to high‐light fluctuations. The degree of influence of these limiting factors varied somewhat among single accessions of maize, sorghum and sugarcane (Wang et al., ²⁰²¹). Owing to the complex compartmentation of the photosynthetic reactions between mesophyll and bundle‐sheath cells, the gas‐exchange measurements in Wang et al. (2021) were not able directly to investigate the relationship between the C₄ and C₃ cycles or determine leakiness during induction. However, a higher leakiness was predicted during induction compared with the steady state, as activation of the C₄ dicarboxylate cycle appeared significantly faster than that of Rubisco in the bundle sheath, based on available kinetic data (Wang et al., ²⁰²¹).

Steady‐state ϕ increases only slightly with decreasing light and varies little when measured at different [CO₂], suggesting the C₃ and C₄ cycles are well coordinated under steady‐state conditions (Henderson et al., ¹⁹⁹²; Ubierna et al., ^{2011, 2013}; Bellasio & Griffiths, ²⁰¹⁴; Kromdijk et al., ²⁰¹⁴). However, little is known about how ϕ changes under nonsteady‐state conditions. Leakiness can be estimated by including measurements of photosynthetic carbon isotope discrimination (Kromdijk et al., ²⁰¹⁴). Estimates of leakiness using stable isotopes compare the theoretical model of photosynthetic discrimination (Δ¹³C) (Farquhar, ¹⁹⁸³; Farquhar & Cernusak, ²⁰¹²) with measured photosynthetic discrimination (Δ¹³C_obs) (Kromdijk et al., ²⁰¹⁴). Stable isotope discrimination can be estimated in real‐time using a tunable diode laser absorption spectroscope (TDL) coupled to a gas‐exchange system (Barbour et al., ²⁰⁰⁷). In steady‐state measurements of ϕ, the TDL cycles through a set of calibration gases, and the infrared gas analyzer (IRGA) reference and leaf chamber. The TDL remains on each sample for a period of c. 30 s, thus allowing a single measurement every c. 120–360 s, precluding continuous monitoring of the leaf chamber. Recently, Sakoda et al. (2021) and Liu et al. (2022) estimated mesophyll conductance in C₃ plants through induction using the steady‐state TDL method and were only able to measure c. 15 data points over a 30 min activation curve.

Here, we developed an experimental design that measures ϕ every c. 10 s over a 30 min induction. Based on our previous metabolic modeling (Wang et al., ²⁰²¹) we hypothesized that leakiness will be higher during activation of C₄ photosynthesis than during steady‐state conditions. The hypothesis is tested directly here from near‐continuous Δ¹³C discrimination measurements through induction of photosynthesis in maize and sorghum.

Materials and Methods

Plant material and growth conditions

Sorghum (Sorghum bicolor L. Moench, Tx430) and maize (Zea mays L., B73) plants were grown in a controlled‐environment glasshouse at the University of Illinois at Urbana‐Champaign. Temperature in the glasshouse was 28°C : 24°C, day : night. Plants were grown in 20 l pots filled with peat‐and‐perlite growing medium (BM6; Berger, Saint‐Modeste, QC, Canada). Measurements were taken on plants at 40 d after planting. Plants were kept in darkness for ≥ 30 min before measurement. The youngest fully expanded leaf on the main stem, as indicated by a fully emerged ligule, was selected for enclosure into the controlled‐environment measurement chamber.

Gas‐exchange measurements

For sorghum, the leaf was placed in the opaque conifer chamber (LI‐6400‐22; Li‐Cor Environmental, Lincoln, NE, USA) with an integrated RGB light source (LI‐6400‐18; Li‐Cor Environmental) attached to a LI‐6400XT gas‐exchange system (Li‐Cor Environmental). The chamber was fitted with a leaf thermocouple (Omega Engineering Inc., Norwalk, CT, USA) (Fig. S1a). To minimize leakage from the chamber, an opaque flexible polymer sealant (Qubitac Sealant; Qubit Systems Inc., Kingston, ON, Canada) was applied around the chamber lips after enclosing the leaf (Fig. S1a). For maize, the leaf was placed in the large leaf and needle chamber (LI‐6800‐13; Li‐Cor Environmental) incorporating the large light source (LI‐6800‐03; Li‐Cor Environmental) (Fig. S1b). The flows to the reference and sample IRGAs were monitored to ensure that both analyzers received sufficient flow. Because maize has a large midvein, the sample chamber pressure was set to 0.1 kPa to ensure that any leaks were out of, not into, the sample chamber. The average (±SE) leakage from the chamber from all the maize measurements was 6.4 ± 1.9 μmol s⁻¹, which accounted for 2.1 ± 0.68% of the flow. For both species, the leaf was placed in the chamber in darkness with a leaf temperature of 27°C, CO₂ reference of 800 μmol mol⁻¹, an [O₂] of 21% and a flow rate of 300 μmol s⁻¹. We controlled reference [CO₂] to avoid artifacts caused by system adjustment. Reference CO₂ of 800 μmol mol⁻¹ was used to ensure that the sample [CO₂] during the measurement is not lower than the ambient CO₂. Leaf area was calculated as the product of the internal length of the chamber and the average of the width of the leaf at both ends of the chamber.

Isotopic gas‐exchange measurement

The gas‐exchange system was coupled to a TDL (model TGA 200A; Campbell Scientific Inc., Logan, UT, USA) to measure [¹²CO₂], [¹³CO₂] and δ¹³C (Bowling et al., ²⁰⁰³; Pengelly et al., ²⁰¹⁰; Ubierna et al., ²⁰¹³; Jaikumar et al., ²⁰²¹). For sorghum, the reference line for the LI‐6400XT was split on the back of the sensor head so that a portion of the reference gas was diverted to the TDL. The exhaust gas from the leaf chamber was taken from the match port on the chamber, fitted with a three‐way valve to allow the gas to go to either the TDL or the match valve on the LI‐6400XT (Fig. S1a). For maize, the TDL was connected to the LI‐6800 reference air stream using the reference port on the back of sensor head while the port on the front of the head supplied air from the leaf chamber (Jaikumar et al., ²⁰²¹; Fig. S1b). CO₂‐free air (N₂/O₂) with a known [O₂] was created by mixing two gas streams using precision mass flow controllers (Omega Engineering Inc.). A portion of this N₂/O₂ air traveled to the gas‐exchange system while the remainder was used as CO₂‐free air in calibration to correct for drift in the TDL over the course of the measurements. The TDL was calibrated using the concentration series method by diluting a 10% CO₂ gas cylinder into the N₂/O₂ stream to produce three different [CO₂] of the same isotopic composition (Pengelly et al., ²⁰¹⁰; Tazoe et al., ²⁰¹¹; Ubierna et al., ²⁰¹³; Jaikumar et al., ²⁰²¹). The measurement sequence cycled through eight gas streams in the following sequence: CO₂‐free air, followed by three different CO₂ concentrations of the same isotopic signature, air from a calibration tank with a known [¹²CO₂], [¹³CO₂], and δ¹³C composition (NOAA Global Monitoring Laboratory, Boulder, CO, USA), the IRGA reference and leaf chamber air streams, and the IRGA reference again. Each step had a duration of 20 s, except for the leaf chamber air, which had a duration of 600 s with a total cycle time of 740 s. Measurements were collected at a 10 Hz interval and averaged over 10 s as a single data point. The first 10 s of each gas stream was excluded to produce a single data point, except for the sample line which produced 59 data points each cycle. Instrument performance, including Allan deviations and instrument precision, are presented in Notes S1.

When the TDL switched to measuring the gas from the leaf chamber, the irradiance incident on the leaf was changed from 0 to 1800 μmol quanta m⁻² s⁻¹. The gas‐exchange system was set to auto‐log at 10 s intervals over the course of 30 min. Dark respiration rate was recorded before illumination.

Calculations of photosynthetic discrimination (Δ¹³C) and leakiness (ϕ)

Instantaneous online determination of observed photosynthetic discrimination (Δ¹³C_obs; Table 1) was calculated according to Evans & von Caemmerer (2013):

$${\mathrm{\Delta }}^{13}{\mathrm{C}}_{\mathrm{obs}}=\frac{1000\xi \left({\mathrm{\delta }}^{13}{\mathrm{C}}_{\text{samp}}-{\mathrm{\delta }}^{13}{\mathrm{C}}_{\mathrm{ref}}\right)}{1000+{\mathrm{\delta }}^{13}{\mathrm{C}}_{\text{samp}}-\xi \left({\mathrm{\delta }}^{13}{\mathrm{C}}_{\text{samp}}-{\mathrm{\delta }}^{13}{\mathrm{C}}_{\mathrm{ref}}\right)}$$ (Eqn 1)

where δ¹³C_samp and δ¹³C_ref are the carbon isotope compositions of the leaf chamber and reference air, respectively, and ξ is:

$$\xi =\frac{C_{\mathrm{ref}}}{C_{\mathrm{ref}}-C_{\text{samp}}}$$ (Eqn 2)

C _ref and C _samp are the [CO₂] of dry air entering and exiting the leaf chamber, respectively, as measured by the TDL. For each measurement sequence, we averaged the [CO₂] and δ¹³C of the reference air measured before and after the measurement of leaf chamber air.

Table 1.

List of symbols used in the text for calculating leakiness in maize and sorghum.

Variable	Definition	Units	Equations/value/reference
a	Fractionation across the stomata	‰	4.4 (Craig, 1953; a s in Ubierna et al., 2013, 2018)
a b	Fractionations across the boundary layer	‰	2.9
$\overline{a}$	Weighted fractionation across the boundary layer and stomata in series	‰	Eqn 18 (Ubierna et al., 2013, 2018)
Α	Rate of photosynthesis	μmol m−2 s−1	Measured
b 3	13C fractionation during carboxylation by Rubisco, including respiration and photorespiration fractionations	‰	Eqn 13 (Farquhar, 1983)
$b_3^{\prime }$	13C fractionation during carboxylation by Rubisco	‰	30
b 4	Net fractionation by CO2 dissolution, hydration and phosphoenolpyruvate carboxylase (PEPC) including respiratory fractionation	‰	Eqn 14 (Farquhar, 1983)
$b_4^{\prime }$	Net fractionation by CO2 dissolution, hydration and PEPC activity dependent upon temperature	‰	Eqn 15
C a	Ambient CO2 partial pressure	Pa	Measured in μmol mol−1 air
C bs	CO2 partial pressure in the bundle‐sheath cells	Pa	Eqn 7
C i	CO2 partial pressure at the intercellular airspace	Pa	Measured in μmol mol−1 air
C s	CO2 partial pressure at the leaf surface	Pa	Measured in μmol mol−1 air
C ref	CO2 concentration of the dry air exiting the leaf chamber	μmol mol−1	Measured
C samp	CO2 concentration of the dry air exiting the leaf chamber	μmol mol−1	Measured
e	13C fractionation during decarboxylation	‰	0 (Evans & von Caemmerer, 2013; Ubierna et al., 2013)
e′	13C fractionation during decarboxylation including the effect of a respiratory substrate isotopically distinct from recent photosynthate	‰	Eqn 16
E	Rate of transpiration	mol m−2 s−1	Measured
f	13C fractionation during photorespiration	‰	1.6‰ (Ubierna et al., 2013)
$g_{\mathrm{ac}}^{\mathrm{t}}$	Total conductance to CO2 diffusion including boundary layer and stomatal conductance	mol m−2 s−1	Measured
g bs	Bundle‐sheath conductance to CO2	mol m−2 s−1	0.00113 (Brown & Byrd, 1993)
J t	Total electron transport rate	μmol m−2 s−1	Eqn 3 (von Caemmerer, 2000)
O m	O2 partial pressure in the mesophyll cells	Pa	21.2 Pa atmospheric pressure
O s	O2 partial pressure in the bundle‐sheath cells	Pa	Eqn 11 (von Caemmerer, 2000)
R d	Leaf mitochondrial respiration in the light assumed to equal the rate of respiration in the dark	μmol m−2 s−1	Measured
R m	Rate of mesophyll cell respiration in the light	μmol m−2 s−1	R m = 0.5R d
s	Fractionation during leakage from the bundle‐sheath cells	‰	1.8 (Henderson et al., 1992)
t	Ternary effect	‰	Eqn 17
V c	Rubisco carboxylation rate	μmol m−2 s−1	Eqn 9 (von Caemmerer, 2000)
V o	Rubisco oxygenation rate	μmol m−2 s−1	Eqn 10 (von Caemmerer, 2000)
V p	PEP carboxylation rate	μmol m−2 s−1	Eqn 8 (von Caemmerer, 2000)
x	Fraction of J t allocated to the C4 cycle		0.4 (von Caemmerer, 2000)
α	Fraction of PSII activity in the bundle sheath		0 (von Caemmerer, 2000)
δ13Cgatm	Isotopic signature of growth CO2	‰	−8
δ13Cref	Isotopic signature of the CO2 entering the leaf chamber	‰	Measured
δ13Csamp	Isotopic signature of the CO2 exiting the leaf chamber	‰	Measured
ξ	Ratio of the 12CO2 mole fraction in the dry air coming into the gas‐exchange cuvette over the difference in 12CO2 mole fractions of air in and out of the cuvette	unitless	Eqn 2
Δ13Cobs	Observed 13C photosynthetic discrimination	‰	Eqn 1
ϕ is	Leakiness estimated assuming infinite mesophyll conductance	Unitless	Eqn 12

The electron transport flux (J _t) was calculated as (von Caemmerer, ²⁰⁰⁰; Ubierna et al., ²⁰¹³):

$$J_{\mathrm{t}}=\frac{-\mathrm{II}+\sqrt{{\mathrm{II}}^2-4·\mathrm{III}·\mathrm{I}}}{2·\mathrm{III}}$$ (Eqn 3)

where

$$\mathrm{I}=\left(1+\frac{R_{\mathrm{d}}}{A}\right)\left(R_{\mathrm{m}}-g_{\mathrm{bs}}{C}_{\mathrm{m}}-\frac{7g_{\mathrm{bs}}{\gamma }^{*}{O}_{\mathrm{m}}}{3}\right)+\left(R_{\mathrm{d}}+A\right)\left(1-\frac{7\alpha {\gamma }^{*}}{3\times 0.047}\right)$$ (Eqn 4)

$$\mathrm{II}=\frac{1-x}{3}\left[\frac{g_{\mathrm{bs}}}{A}\left(C_{\mathrm{m}}-\frac{R_{\mathrm{m}}}{g_{\mathrm{bs}}}-{\gamma }^{*}{O}_{\mathrm{m}}\right)-1-\frac{\alpha {\gamma }^{*}}{0.047}\right]-\frac{x}{2}\left(1+\frac{R_{\mathrm{d}}}{A}\right)$$ (Eqn 5)

$$\mathrm{III}=\frac{x-x^2}{6A}$$ (Eqn 6)

R _d is leaf mitochondrial respiration in the light, assumed to be equal to dark respiration, R _m (R _m = 0.5R _d) is the rate of mesophyll cell respiration in the light, and A is the rate of net CO₂ assimilation. C _m is CO₂ concentration in the mesophyll cells, which was assumed to equal measured C _i, γ ^* is half of the reciprocal of Rubisco specificity (0.000193; von Caemmerer et al., ¹⁹⁹⁴), O _m is the O₂ mol fraction in the mesophyll cells (210 000 μmol mol⁻¹), and x is the portion of ATP used by the C₄ cycle, assumed to equal 0.4 (von Caemmerer, ²⁰⁰⁰). The fraction of PSII activity in the bundle sheath (α) was assumed to be 0 for maize and sorghum (von Caemmerer, ²⁰⁰⁰). The bundle‐sheath conductance to CO₂ (g _bs) was set as 0.00113 mol m⁻² s⁻¹ (Brown & Byrd, ¹⁹⁹³).

We calculated the CO₂ partial pressure in the bundle‐sheath cells (C _s), PEP carboxylation rate (V _p), Rubisco carboxylation rate (V _c), oxygenation rate (V _o) and the O₂ partial pressure in the bundle‐sheath cells (O _s) using the following expressions (von Caemmerer, ²⁰⁰⁰):

$$C_{\mathrm{bs}}=\frac{{\gamma }^{*}{O}_{\mathrm{s}}\left[\frac{7}{3}\left(A+R_{\mathrm{d}}\right)+\frac{\left(1-x\right)J_{\mathrm{t}}}{3}\right]}{\frac{\left(1-x\right)J_{\mathrm{t}}}{3}-\left(A+R_{\mathrm{d}}\right)}$$ (Eqn 7)

$$V_{\mathrm{p}}=\frac{x{J}_{\mathrm{t}}}{2}$$ (Eqn 8)

$$V_{\mathrm{c}}=\frac{A+R_{\mathrm{d}}}{1-\frac{{\gamma }^{*}{O}_{\mathrm{s}}}{C_{\mathrm{bs}}}}$$ (Eqn 9)

$$V_{\mathrm{o}}=\frac{V_{\mathrm{c}}-A-R_{\mathrm{d}}}{0.5}$$ (Eqn 10)

$$O_{\mathrm{s}}=\frac{\mathit{\alpha A}}{0.047g_{\mathrm{bs}}}+O_{\mathrm{m}}$$ (Eqn 11)

We estimated leakiness, assuming infinite mesophyll conductance, using the model proposed by Ubierna et al. (2013):

$${\varphi }_{\text{is}}=\frac{C_{\mathrm{bs}}-C_{\mathrm{i}}}{C_{\mathrm{i}}}\frac{\left(1-t\right){\mathrm{\Delta }}^{13}{\mathrm{C}}_{\mathrm{obs}}{C}_{\mathrm{a}}-a^{\prime }\left(C_{\mathrm{a}}-C_{\mathrm{i}}\right)-\left(1+t\right)C_{\mathrm{i}}{b}_4}{\left(1+t\right)\left[b_3{C}_{\mathrm{bs}}-s\left(C_{\mathrm{bs}}-C_{\mathrm{i}}\right)\right]+a^{\prime }\left(C_{\mathrm{a}}-C_{\mathrm{i}}\right)-\left(1-t\right){\mathrm{\Delta }}^{13}{\mathrm{C}}_{\mathrm{obs}}{C}_{\mathrm{a}}}$$ (Eqn 12)

where C _a, and C _i are the ambient and intercellular CO₂ partial pressures, respectively, and t is the ternary effect (Farquhar & Cernusak, ²⁰¹²). The fractionation during leakage from the bundle‐sheath cells (s) is 1.8‰, and b ₃ and b ₄ were defined as (Farquhar, ¹⁹⁸³):

$$b_3=b_3^{\prime }-\frac{e^{\prime }{R}_{\mathrm{d}}}{V_{\mathrm{c}}}-\frac{f{V}_{\mathrm{o}}}{V_{\mathrm{c}}}$$ (Eqn 13)

$$b_4=b_4^{\prime }-\frac{e^{\prime }{R}_{\mathrm{m}}}{V_{\mathrm{p}}}$$ (Eqn 14)

where f is fractionation during photorespiration, assumed to be 11.6‰ (Lanigan et al., ²⁰⁰⁸). $b_3^{\prime }$ (30‰) is Rubisco fractionation, and $b_4^{\prime }$, the net fractionation by CO₂ dissolution, hydration and PEPC activity at 27°C, was calculated according to Mook et al. (1974), which is used by Henderson et al. (1992) and von Caemmerer et al. (2014):

$$b_4^{\prime }=\frac{-9.483\times 1000}{273+\left(T°\mathrm{C}\right)}+23.89+2.2$$ (Eqn 15)

We estimated e′, which is the ¹³CO₂ fractionation during decarboxylation and takes into account respiration that is isotopically distinct from recent photosynthate, as previously discussed (Wingate et al., ²⁰⁰⁷; Ubierna et al., ²⁰¹⁸):

$$e^{\prime }=e+{\mathrm{\delta }}^{13}{\mathrm{C}}_{\mathrm{ref}}-{\mathrm{\delta }}^{13}{\mathrm{C}}_{\text{gatm}}$$ (Eqn 16)

where e is the respiratory fractionation during decarboxylation, 0‰, δ¹³C_gatm is the isotopic signature of the CO₂ in the air where the plants were grown, assumed to be −8‰, and δ¹³C_ref is the isotopic signature of the measurement CO₂ and was between −10‰ and −6.5‰.

The ternary effect (t) (Farquhar & Cernusak, ²⁰¹²) takes into account the effect of transpiration on the rate of CO₂ assimilation through the stomata and is calculated as:

$$t=\frac{\left(1+a^{\prime }\right)E}{2g_{\mathrm{ac}}^{\mathrm{t}}}$$ (Eqn 17)

where E is the rate of transpiration, $g_{\mathrm{ac}}^{\mathrm{t}}$ is the total conductance to CO₂ diffusion from the atmosphere to the intercellular airspace including boundary layer and stomatal conductance (von Caemmerer & Farquhar, ¹⁹⁸¹), and $a\text{'}$ denotes the combined fractionation factor through the leaf boundary layer and the stomata:

$$a\text{'}=\frac{a_{\mathrm{b}}\left(C_{\mathrm{a}}-C_{\mathrm{s}}\right)+a\left(C_{\mathrm{s}}-C_{\mathrm{i}}\right)}{C_{\mathrm{a}}-C_{\mathrm{i}}}$$ (Eqn 18)

where C _s is the leaf surface CO₂ partial pressure, a _b (2.9‰) is the fractionation occurring through diffusion in the boundary layer, and a (4.4‰) is the fractionation as a result of diffusion in air (Craig, ¹⁹⁵³).

The error associated with Δ¹³C_obs measurements

The error associated with Δ¹³C_obs was calculated according to Ubierna et al. (2018):

$$\text{Error}=\sqrt{2}\mathit{\xi X}$$ (Eqn 19)

where X is instrument precision (Notes S1). The error (%) was calculated as $\text{error}\left(\%\right)=\left(\text{error}/{\Delta }^{13}{\mathrm{C}}_{\mathrm{obs}}\right)\times 100.$

Instrument precisions during the measurements were 0.24‰ and 0.14‰ for sorghum and maize, respectively. We excluded all data points where the error in Δ¹³C_obs was > 50%. This occurred in the first 144 s for sorghum and the first 110 s for maize.

Data processing

A fully automatic data processing and leakiness calculation tool was developed in Matlab. The tool used the pretreated (LI‐6400XT and LI‐6800) data files and the raw TDL data to calculate the leakiness through the photosynthetic induction, with the equations described earlier. The TDL data were averaged every 10 s to match the gas‐exchange data and to reduce noise (Fig. S2). See the Data availability statement for access to this tool.

Correction of the system delay

System delays were caused by both the large volume of the leaf chambers and the gas path from leaf chamber to the TDL (see Methods S1 for further information). The time delay from leaf chamber to the TDL was estimated by pulsing the leaf chamber with high CO₂ and monitoring the time it took to observe the CO₂ spike in the TDL. A 5‐cm‐wide paper strip was clipped into the chamber sealed with opaque flexible polymer sealant (Qubitac Sealant) to mimic the effect of the leaf on flow and mixing. The [CO₂] was recorded every 2 s until the chamber outlet [CO₂] was stable at 400 μmol mol⁻¹ (Fig. S3). Three different flow rates were measured, 300, 500 and 700 μmol s⁻¹. For each flow rate, the measurements were repeated three times. Results were used to estimate the chamber volume (V _chamber) and time constant (τ), as defined later (https://www.licor.com/env/support/LI‐6400/topics/custom‐chamber.html).

Assuming the gas is well mixed in the chamber, for an open, flow‐through system, the [CO₂] in the chamber C(t) at time t is:

$$C\left(t\right)=C_{\text{in}}-\left(C_{\text{in}}-C_0\right)e^{\frac{-\mathit{tf}{V}_{\mathrm{m}}}{V_{\text{chamber}}}}$$ (Eqn 20)

where C ₀ is the initial chamber [CO₂], C _in is the incoming [CO₂], V _m is the molar volume of air, which was assumed to approximate an ideal gas at standard atmospheric pressure and 27°C, and is set as 24.6 l mol⁻¹, f is the air flow rate (s) and V _chamber is the chamber volume (l). Then, an ordinary differential equation model was used to estimate the system delay during photosynthetic induction measurement:

$$\frac{\mathrm{d}C}{\mathrm{d}t}=\frac{S_{\text{leaf}}\left(A_{\text{leaf}}\left(C\right)-A_{\text{leaf}}^{\prime }\right)}{V_{\text{chamber}}}{V}_{\mathrm{m}}$$ (Eqn 21)

where S _leaf is the leaf area, A _leaf (C) is the leaf carbon assimilation rate estimated by the gas‐exchange system at a given [CO_2ref], and $A_{\text{leaf}}^{\prime }$ is the actual carbon assimilation rate. Here we set it as:

$$A_{\text{leaf}}^{\prime }=A_{\mathrm{f}}\left(1-e^{-\frac{t}{{\tau }_{\mathrm{A}}}}\right)$$ (Eqn 22)

where A _f is the steady‐state photosynthesis rate at high light, τ _A is the time constant of the induction of photosynthesis, and A _f and τ _A were set as 40 μmol m⁻² s⁻¹ and 300 s, respectively, according to gas‐exchange measurements.

Rubisco activation estimation

If the photosynthetic rate is limited by Rubisco, the maximum Rubisco activity is:

$$V_{\text{cmax}}=A+R_{\mathrm{d}}$$ (Eqn 23)

Thus, the rate constant of Rubisco activation is equal to the rate constant of induction of CO₂ assimilation. A semilogarithmic plot of the difference between A and steady‐state CO₂ assimilation at 1800 μmol m⁻² s⁻¹ (A _f) as a function of time during photosynthetic induction was plotted (Fig. S4). The linear portion of the semilogarithmic plot reflects an exponential phase in the time course that is proposed to be limited primarily by Rubisco (Woodrow & Mott, 1993; Wang et al., ²⁰²¹). The slope of this linear portion is equal to the negative reciprocal of the time constant for CO₂ assimilation and Rubisco activation (τ _A  = τ _Rubisco). As Rubisco limits the later phase of the induction of C₄ crops, we used the measured photosynthetic rate between 300 and 900 s for this estimation.

Statistical analyses

Normal distribution and homogeneity of variances were tested by the Shapiro–Wilk and Levene tests, respectively. Student's t‐test was used to determine if the means of two datasets were significantly different from each other (P < 0.05). All statistical analyses used Python (v.3.7), Shapiro–Wilk test, Levene test and Student's t‐test were performed using the SciPy library. The piecewise function was fitted by linear and exponential goodness‐to‐fit regression (OriginPro v.2020; OriginLab, Northampton, MA, USA).

Results

Leakiness during photosynthetic induction in sorghum

During the photosynthetic induction, sample [CO₂] declined rapidly from 820 μmol mol⁻¹ to a steady state of c. 450 μmol mol⁻¹ at c. 600 s (Fig. 1a). Photosynthetic discrimination (Δ¹³C_obs) was used to estimate leakiness (ϕ), declining from an initial 10‰ to c. 3.5‰ at 120 s, then rising to 5‰ at 300 s and finally declining to a steady state of c. 2.0‰ at c. 1500 s (Fig. 1b). As expected, ξ, a measure of the uncertainty in Δ¹³C_obs was high (15) when rates of photosynthesis were low and decreased as A increased through induction, to a steady state of 2.5 at c. 600 s (Fig. 1c). The error of Δ¹³C_obs was higher than 2‰ (50% of Δ¹³C_obs) in the first 100 s of the measurement and quickly declined to around 1.2‰ (30% of Δ¹³C_obs) by 200 s (Fig. 1d; Table N1 in Notes S1).

Fig. 1.

Measured carbon isotope discrimination during photosynthetic induction of sorghum (Tx430) using a tunable diode laser absorption spectroscope (TDL) coupled to a gas‐exchange system (LI‐6400XT). (a) Sample [CO₂]; (b) the observed leaf photosynthetic discrimination (Δ¹³C_obs); (c) ξ, an estimate of the uncertainty in Δ¹³C_obs and ϕ calculations; (d) error of Δ¹³C_obs going from dark to high light (1800 μmol m⁻² s⁻¹). Time 0 s refers to when the light was switched on. Open dots represent the data points where the error of Δ¹³C_obs was > 50%. The TDL was calibrated after every 600 s of measurement. The gas from leaf chamber was not measured during the calibration and the measurement of reference gas (140 s), which occurred from c. 490 to 640 s and c. 1215 to 1365 s. Leaf gas‐exchange and carbon discrimination of the youngest fully expanded leaf was measured on 40‐d‐old sorghum (Tx430) plant. The leaf was dark‐adapted for 30 min before the measurement. Each data point is the mean (±SE) of eight plants (n = 8).

In the first 120 s in high light (1800 μmol quanta m⁻² s⁻¹), leakiness (ϕ) in sorghum declined from 0.32 to c. 0.23; however, ϕ then increased to c. 0.35 at 300 s, before gradually decreasing and reaching a steady state of c. 0.18 (Fig. 2b) at c. 1500 s. The leakiness curve was fitted with a piecewise function. No obvious trend was found in the first segment (R‐squared (R ²) = 0.098; Fig. 2b), which is also the segment with the greatest error of Δ¹³C_obs. The second segment of the piecewise function showed linear growth (R ² = 0.81); during this time the error rapidly declined to < 50% of the associated measurement. The third segment was exponential decline (R ² = 0.93; Fig. 2b). The transition time point of the leakiness curve of sorghum occurred at c. 290 s. Excluding the initial 100 s of measurement, given its high error of Δ¹³C_obs, the average (±SE) ϕ was 0.237 ± 0.012 over the 1500 s period of induction, which was 32% higher than the steady‐state ϕ in high light (0.180 ± 0.015, P = 0.005; Fig. 4a (see later); Table S1), indicating a substantial loss of efficiency during induction, compared with the steady state. The average ϕ value over the first 600 s period of induction was 0.289 ± 0.022, which was 61% higher than the steady‐state ϕ (P < 0.001; Fig. 4a (see later); Table S1). The reference [CO₂] was set as 800 μmol mol⁻¹ to minimize the limitations induced by stomatal and mesophyll conductance of CO₂ to PEPC. In sorghum, intercellular [CO₂] (C _i) was always > 200 μmol mol⁻¹, and so assumed not to be limiting to PEP carboxylation (Fig. 2d). Stomatal conductance to water vapor increased from 0.04 to c. 0.57 mol m⁻² s⁻¹ through the induction (Fig. 2c). The time constant of photosynthetic induction (τ_A) between 300 and 900 s was 332 s, which was assumed to reflect the kinetics of Rubisco activation (Eqn 21; Fig. S4).

Fig. 2.

CO₂ assimilation and bundle‐sheath leakiness during photosynthetic induction of sorghum measured with an LI‐6400XT coupled to a tunable diode laser absorption spectroscope (TDL). (a) CO₂ assimilation rate (A). (b) Bundle‐sheath leakiness (ϕ, Eqn 12). Open dots represent the data points derived from values of observed discrimination that had large uncertainty (the error in the calculated Δ¹³C_obs was > 50% of its calculated value). (c) Stomatal conductance to water vapor (g _s). (d) Intercellular CO₂ concentration (C _i). The dotted vertical lines mark the time of highest leakiness, which was 286 s. t ₁ is the time constant (τ) of the exponential curve for leakiness. Time 0 s is when the light was switched on to 1800 μmol m⁻² s⁻¹. Each data point is the mean (±SE) of eight plants (n = 8).

Fig. 4.

The comparison between steady‐state and transient leakiness in sorghum (a) and maize (b). Steady state, the average leakiness after 1500 s; Mean_1500, the average leakiness over the 1500 s period of induction; Mean_600, the average leakiness of the first 600 s in the induction. The data points with the error of Δ¹³C_obs > 50% were excluded. Data of each replicate were listed in Tables S1, S2. P‐values were calculated using Student's t‐test. Black circles represent the outliers; black lines in boxes show the medians. Upper and lower whiskers represent the maximum and minimum values, respectively.

Leakiness during photosynthetic induction in maize

During the dark to high‐light transition, leakiness increased faster in maize than in sorghum (Figs 3b, S8; see later). Similar to the measurement of sorghum, the error associated with Δ¹³C_obs estimation was > 50% for the first 90 s (Fig. S5d open circles) and photosynthetic discrimination rose rapidly to c. 120 s before a slow decrease to the steady state (Fig. S5b). As with sorghum, ξ was high when rates of photosynthesis were low and decreased with increasing rates of assimilation to a steady state at c. 600 s (Fig. S5c). ϕ during the photosynthetic induction in maize was fitted with the piecewise function. The first segment of the piecewise function was linear growth (Fig. 3b). The first segment of the piecewise function was linear increase, and R ² of the linear regression was 0.57; however, the error of Δ¹³C_obs in this segment is large (Fig. S5d). After 110 s, ϕ during the induction can be fitted with an exponential decline function (Fig. 3b). The time constant of the exponential decline in ϕ was 540 s. The highest ϕ was c. 0.4 at 110 s. Excluding the initial 90 s of measurement, given its high error of Δ¹³C_obs, over the 1500 s period of induction, the average ϕ was 0.258 ± 0.006, which was 35% higher than the steady‐state ϕ at high light (0.191 ± 0.010). Average ϕ over the first 600 s period of induction was 0.315 ± 0.014, which was 65% higher than the steady state ϕ (P < 0.001; Fig. 4b; Table S2). As in the case of sorghum, intercellular [CO₂] (C _i) of maize was always > 200 μmol mol⁻¹ (Fig. 3d). Stomatal conductance to water vapor increased from 0.02 to about 0.4 mol m⁻² s⁻¹ through induction (Fig. 3c).

Fig. 3.

CO₂ assimilation and bundle‐sheath leakiness during photosynthetic induction of maize B73 measured with an LI‐6800 coupled to a tunable diode laser absorption spectroscope (TDL). (a) CO₂ assimilation rate (A). (b) Bundle‐sheath leakiness (ϕ, Eqn 12). Open dots represent data points derived from values of observed discrimination that had large uncertainty (the error in the calculated Δ¹³C_obs was > 50% of its calculated value). (c) Stomatal conductance to water vapor (g _s); and (d) intercellular CO₂ concentration (C _i). The dotted vertical lines mark the time of highest leakiness, which was 110 s. t ₁ is the time constant (τ) of the exponential curve for leakiness. Time 0 is when the light was switched on to 1800 μmol m⁻² s⁻¹. The TDL was calibrated after every 600 s of measurement. Each point is the mean (±SE) of six plants.

After 1800 s (30 min) in photosynthetic photon flux density of 1800 μmol m⁻² s⁻¹, maize and sorghum had similar rates of steady‐state CO₂ assimilation and leakiness (Fig. 5a,d), and there was no significant difference between the species in the time taken for A to reach 50% and 90% of the steady‐state value, IT50 and IT90, respectively (Fig. 5e,f). However, the rise in leakiness in sorghum was significantly more prolonged than in maize, as indicated by the time taken to reach the peak of leakiness during induction (Fig. 5b). The speed of exponential decay of ϕ was similar, and there was no significant difference between the two species in ϕ (Fig. 5c), which is the time constant of exponential decline segment of the leakiness function (Figs 2b, 3b; curve‐fitting parameter t ₁).

Fig. 5.

Mean and variation of steady‐state leakiness, the time to reach the maximum leakiness and the time constant of the exponential decay (τ _leakiness), steady‐state CO₂ assimilation rate (A), and IT50 and IT90 during the induction in sorghum and maize. (a) Average leakiness after 1500 s; (b) the time at the end of the linear growth segment of leakiness; (c) τ_leakiness, the time constant of exponential decline segment; (d) average A after 1500 s; (e) IT50, the time at which A reached 50% of the steady state; (f) IT90, the time at which A reached 90% of the steady state A. P‐values were calculated using Student's t‐test. Black circles represent the outliers; black lines in boxes show the medians; upper and lower whiskers represent the maximum and minimum values, respectively.

Discussion

Coordination between the C₃ and C₄ cycles was disrupted during photosynthetic induction

Coordination between the C₃ and C₄ cycles is essential to the high efficiency of C₄ photosynthesis. We estimated CO₂ leakiness with stable carbon isotopes by coupling a TDL to a gas‐exchange system. Leakiness (ϕ) is the proportion of CO₂ released by decarboxylation of dicarboxylates in the bundle sheath that leaks back to the mesophyll. Any variation in ϕ reflects the degree of coordination between the two cycles.

A complete metabolic model of NADP‐ME photosynthesis, incorporating activation of enzymes, stomatal induction and dynamic changes in metabolic pools predicted poor coordination and transient increase in ϕ during photosynthetic induction, as a result of a more rapid activation of PPDK in the mesophyll by the PPDK regulatory protein, than activation of Rubisco in the bundle sheath by Rubisco activase (Wang et al., ²⁰²¹). The transient increases in ϕ in both maize and sorghum observed here are fully consistent with this explanation.

Leaves in a crop canopy often face intense and rapid light changes (Zhu et al., ²⁰⁰⁴; Wang et al., ²⁰²⁰; Qiao et al., ²⁰²¹). Over this 1500 s period of induction, the average ϕ was > 30% higher than the steady‐state ϕ at high light for sorghum and maize. Leakiness over the first 600 s was 61% higher than the steady‐state ϕ for sorghum and 65% for maize. The lack of coordination between C₄ and C₃ cycles will substantially reduce the efficiency of C₄ photosynthesis at both leaf and canopy levels. Although the present study uses an extreme case of fluctuation (i.e. an immediate transfer from darkness to full sunlight), leaves in the canopy will frequently experience transfer from 10% to full sunlight (Long et al., ²⁰²²). A recent application of a high‐throughput assay of Rubisco activation has shown that deactivation on transfer to shade is very rapid, occurring within a minute (Taylor et al., ²⁰²²). So why has natural selection not removed this inefficiency? In the wild, many C₄ plants, including wild ancestors of maize and sorghum, are most abundant in hot semiarid and nutrient‐poor regions (De Wet, ¹⁹⁷⁸; Yang et al., ²⁰¹⁹). As a result, leaf canopies may be sparse, and cloud cover infrequent. In these conditions there will be fewer light fluctuations and little selective pressure to avoid these transient increases in ϕ. The dense modern crop canopies of maize and sorghum are recent in an evolutionary context, but here the losses as a result of these transient inefficiencies would be much greater.

Differences of transient leakiness between sorghum and maize during induction

The induction rate of CO₂ assimilation was similar between the two species, and a transient increase in leakiness was detected in both sorghum and maize (Figs 2a,b, 3a,b, S6). Leakiness reached a maximum significantly faster in maize than in sorghum (Fig. 5b), which most probably indicates faster activation of PPDK, possibly as a result of either more of its regulatory protein (PDRP) or a more efficient PDRP (Ashton et al., ¹⁹⁸⁴; Burnell & Chastain, ²⁰⁰⁶; Wang et al., ²⁰²¹). These results, consistent with the previous metabolic modeling of NADP‐ME C₄ photosynthesis, through induction suggest activation of Rubisco as the key limitation through induction and the primary cause of lost efficiency. Rubisco activase (Rca) appears to be an exceptionally heat‐labile protein, implicated in loss of photosynthetic efficiency at high temperatures (Crafts‐Brandner & Salvucci, ²⁰⁰⁰). This implies that the loss of efficiency in these key crops would be amplified by rising global temperatures. This loss of efficiency might be overcome by breeding or engineering an increase in Rca content, and in particular more high‐temperature‐tolerant isoforms (Carmo‐Silva & Salvucci, ²⁰¹³; Degen et al., ²⁰²¹). Kim et al. (2021). These studies have shown that the redox‐regulated Rca‐α isoform is expressed in sorghum, sugarcane, maize and Sateria only at temperatures > 42°C and the time course of Rca‐α corresponds to recovery of Rubisco activation and the rate of photosynthesis from heat shock. However, overall variation in Rca in C₄ crops has so far received little attention. Based on our estimation and previous studies, increasing the activity of Rca by either increasing Rca content or engineering a more efficient Rca would increase photosynthetic efficiency under constant and fluctuating light. Both now appear possible through bioengineering and possibly breeding (Long et al., ²⁰²²).

The high CO₂ concentration supplied to the leaf chamber in our experiment (Figs 1a, S6a) minimized diffusional limitations (stomatal and mesophyll) to photosynthesis. During induction, the CO₂ concentrations inside the leaf (C _i) were > 200 and 180 μmol mol⁻¹ for sorghum and maize, respectively (Figs 2d, 3d). Previous research (Wang et al., ²⁰²¹) demonstrated that at ambient CO₂ concentrations, slow stomatal opening during the middle phase of induction reduced both CO₂ assimilation rate and leakiness in three C₄ crops. The CO₂ concentration used for measurements should have had a negligible effect on leakiness determined for the fast response of stomata in sorghum but could have impacted values for the slower response of stomata seen in maize. Mesophyll conductance (g _m) could also be a limiting factor during induction. In this study, g _m was assumed to be infinite and constant. There are no experimental data on the variation of g _m during induction in C₄ species. However, the main resistances to CO₂ diffusion through, the cell wall and plasmalemma to the PEP carboxylase baring mesophyll cytoplasm, are probably unaffected by light, barring a Péclet effect with increasing outflow of water. This is a topic for subsequent investigation.

Energy‐use efficiency of C₄ crops under fluctuating light

The steady‐state ϕ values were c. 0.2 in maize and sorghum; thus 5.5 ATP are used to assimilate one CO₂. However, over the 1500 s period of the induction, the average ϕ was 0.25. Moreover, the average ϕ of the first 600 s was c. 0.30 in both sorghum and maize. The higher transient ϕ will have increased the ATP consumption of assimilating a CO₂ to 5.7 and 5.9, respectively. The energetic cost of CO₂ assimilation is therefore higher in fluctuating light than under steady‐state conditions. However, when light is in excess, as in induction, this will have little effect.

Variation in carbon assimilation during fluctuating light was previously observed by Lee et al. (2022) across four NADP‐ME grass species and may well arise from variation in the degree to which the C₄ and C₃ cycles are coordinated, as was shown here for maize and sorghum, but was not determined in their study. Being able to estimate variation in ϕ between species and genotypes during fluctuating light will be necessary for developing strategies to improve C₄ crop performance. Additionally, low‐growth‐light intensity increases steady‐state ϕ of shaded field‐grown M. × giganteus leaves, assuming the C _i in the bundle sheath is much higher than C _i in the ϕ estimation (Kromdijk et al., ²⁰⁰⁸). Although the underlying basis of the increased ϕ in shade‐adapted leaves may be different from the increased ϕ in fluctuating light, these leakages could be additive, which would further handicap the efficiency of leaves within C₄ canopies. We demonstrated a new experimental design with the TDL to estimate ϕ at high resolution and under transient conditions. This technique provides opportunities to investigate further the underlying causes of increased ϕ, as well as facilitating strategies to improve C₄ plant performance in fluctuating light.

A new experimental design for the TDL with a gas‐exchange system

The coupling of a TDL with a gas‐exchange system has been used to measure leakiness in C₄ plants under photosynthetic steady‐state conditions (Pengelly et al., ²⁰¹⁰; Ubierna et al., ^{2011, 2013}). Recent work has coupled gas‐exchange systems to a TDL to measure mesophyll conductance during induction curves (Sakoda et al., ²⁰²¹; Liu et al., ²⁰²²); however, these studies were only able to estimate mesophyll conductance every 120 s over the activation curve. Our method, allowing the TDL to remain on the leaf chamber for 600 s, enabled us to have a nearly continuous high‐resolution (10 s) dataset over a 30 min high‐light induction. This allowed the measurement of ϕ under nonsteady‐state conditions. The stability and precision of the instrument are critical to the accuracy of the estimation of ϕ (Fig. N1 in Notes S1). The error of our laser could be controlled within a limited range during the experiment, and the averaging time of 10 s significantly reduced the system noise and improved the prediction accuracy, with sufficient time resolution for the purposes of the questions asked in this study (Notes S1, laser performance). In the first c. 100 s of the induction, the error associated with Δ¹³C_obs estimation was > 50%, which indicated that our measurements were masked by instrument error. Thus, we minimized our interpretation of the leakiness values in this time frame. The error associated with photosynthetic discrimination (Δ¹³C_obs) was < 30% after 200 and 130 s for sorghum and maize, respectively, indicating that the error associated with the TDL was acceptable for the remainder of the induction. The error associated with the laser can change through time, environment and with retuning of the laser. These characters were verified for each laser and tested before each application. As CO₂ concentration around Rubisco (C _bs) should not be much higher than CO₂ in mesophyll (C _m) at the beginning of the induction, the complete calculation of leakiness (Eqn 12) was used instead of the simplified model that assumes the C _bs is much higher than C _m (Fig. S7). Additionally, we developed a program to calculate the leakiness automatically from raw carbon isotope and gas‐exchange data, which improved throughput of data analysis.

The accuracy of the measured gas‐exchange values was significantly improved by correcting for the time delay of the system (Figs S8, S9). The measuring noise of carbon isotope mole fractions was also constrained by averaging signals within every 10 s (Fig. N1 in Notes S1), and thus the noise in leakiness estimation was also reduced (Fig. S2), although the accuracy of the measurement was still limited by the precision of the gas‐exchange system and the TDL in the first c. 100 s after the illumination. We expect that our measurement experience and data‐processing program will help researchers to save time and develop new applications for this system.

Author contributions

The project was conceived by YW, SSS and SPL. YW and SSS performed the experiments. YW developed the data‐processing tool and analyzed the data. SSS developed the method for continual monitoring of leakage through induction. CJB and SSS set up the TDL. YW, SSS and SPL wrote the manuscript with insights from DRO, RAB and CJB. YW and SSS contributed equally to this work.

Supporting information

Fig. S1 Pictures of the setup for the two gas‐exchange systems used for the measurements.

Fig. S2 Increasing the time averaged for each data point from 1 to 10 s significantly limited the estimation noise of the leakiness.

Fig. S3 The [CO₂] of Li‐Cor 6400 opaque conifer chamber and Li‐Cor 6800 large leaf chamber (CO₂S) changes with the decrease of influx [CO₂] (CO₂R) from 800 to 400 μmol mol⁻¹.

Fig. S4 A semilogarithmic plot of the difference between the net CO₂ assimilation (A) and steady‐state net CO₂ assimilation at 1800 μmol m⁻² s⁻¹ (A _f) as a function of time.

Fig. S5 Estimated bundle‐sheath leakiness, Δ¹³C_obs and ξ during photosynthetic induction of maize B73 calculated from tunable diode laser absorption spectroscope coupled to a gas‐exchange system (LI‐6800).

Fig. S6 Bundle‐sheath leakiness during photosynthetic induction of maize B73 and sorghum Tx430.

Fig. S7 Estimated ϕ _is is and ϕ _i during photosynthetic induction of sorghum and maize.

Fig. S8 Time correction of CO₂ assimilation and bundle‐sheath leakiness during photosynthetic induction of sorghum.

Fig. S9 Time correction of CO₂ assimilation and bundle‐sheath leakiness during photosynthetic induction of maize.

Methods S1 Correction of the system delay.

Notes S1 Performance of tunable diode laser absorption spectroscope.

Table S1 Estimated values of leakiness and CO₂ assimilation rate (A) of each individual sorghum plant.

Table S2 Estimated values of leakiness and CO₂ assimilation rate (A) of each individual maize plant.

Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the New Phytologist Central Office.

Data availability

The data and code that support the findings of this study are available at doi: 10.13012/B2IDB‐1181155_V1.