Reduction of bundle sheath size boosts cyclic electron flow in C₄ Setaria viridis acclimated to low light

SUMMARY

When C₄ leaves are exposed to low light, the CO₂ concentration in the bundle sheath (BS) cells decreases, causing an increase in photorespiration relative to assimilation, and a consequent reduction in biochemical efficiency. These effects can be mitigated by complex acclimation syndromes, which are of primary importance for crop productivity but are not well studied. We unveil an acclimation strategy involving the coordination of electron transport processes. First, we characterize the anatomy, gas exchange and electron transport of C₄ Setaria viridis grown under low light. Through a purposely developed biochemical model, we resolve the photon fluxes and reaction rates to explain how the concerted acclimation strategies sustain photosynthetic efficiency. Our results show that a smaller BS in low‐light‐grown plants limited leakiness (the ratio of CO₂ leak rate out of the BS over the rate of supply via C₄ acid decarboxylation) but sacrificed light harvesting and ATP production. To counter ATP shortage and maintain high assimilation rates, plants facilitated light penetration through the mesophyll and upregulated cyclic electron flow in the BS. This shade tolerance mechanism, based on the optimization of light reactions, is possibly more efficient than the known mechanisms involving the rearrangement of carbon metabolism, and could potentially lead to innovative strategies for crop improvement.

Significance Statement

We mechanistically link the optical cross section of leaf compartments with the rate of electron transport, the engagement of cyclic electron flow, the relative rate of ATP and NADPH generation and fluxes through the carbon metabolism. The striking capacity of Setaria viridis to counter the decrease in light absorption in the bundle sheath with an increase of cyclic electron flow presents perhaps the most efficient mechanism of shade acclimation.

INTRODUCTION

Leaves of the majority of C₄ plants are organized in concentric cylinders: an external tube of mesophyll (M) cells surrounds a tube of bundle sheath (BS) cells, which wrap around the innermost vasculature (Figure 1). This spatial arrangement compels light and CO₂ entering C₄ leaves to pass through M cells before reaching the BS. CO₂ is hydrated to HCO₃ ⁻ by carbonic anhydrase in the M cytosol and then fixed by phosphoenolpyruvate carboxylase (PEPC) into C₄ acids, which may be transaminated or chemically reduced. C₄ acids diffuse to BS cells where they are decarboxylated, primarily by NADP‐malic enzyme (NADP‐ME), NAD‐malic enzyme (NAD‐ME), PEP carboxykinase (PEPCK), or by a combination of these. Decarboxylation provides higher CO₂ partial pressure at the site of ribulose 1,5‐bisphosphate carboxylase/oxygenase (Rubisco), thereby largely suppressing the competitive reaction with oxygen that leads to the wasteful process of photorespiration (Bellasio et al., ²⁰¹⁴; von Caemmerer & Furbank, ²⁰⁰³). For this function, C₄ photosynthesis is also referred to as a biochemical carbon‐concentrating mechanism (CCM). Pyruvate resulting from the decarboxylation of C₄ acids diffuses back to the M cells, where it is regenerated into PEP by pyruvate orthophosphate dikinase (PPDK), using two ATP molecules. Some of the CO₂ released in BS cells diffuses out to M cells (called leakage), which incurs an additional ATP cost of C₄ photosynthesis (Bellasio & Griffiths, ^2014a; Farquhar, ¹⁹⁸³; Henderson et al., ¹⁹⁹²).

Figure 1.

Light microscopy images of the leaf cross sections used for anatomical measurements from Setaria viridis grown under high light (1000 μmol m⁻² sec⁻¹, HL) or low light (300 μmol m⁻² sec⁻¹, LL). [Colour figure can be viewed at wileyonlinelibrary.com]

C₄ photosynthesis is highly sensitive to limiting light intensities. Under low irradiance, the generation of ATP and NADPH slows down, limiting both the reductive pentose phosphate (RPP) cycle and the C₄ cycle. Since activities of RPP and the C₄ cycle are tightly balanced (Kromdijk et al., ²⁰¹⁴) through light modulation (Bailey et al., ²⁰⁰⁷), a slowdown of C₄ acid diffusion into the BS inevitably results in a decrease of CO₂ concentration in BS cells (C _BS). Consequently, the ratio between CO₂ and O₂ concentration at the active sites of Rubisco decreases, favouring oxygenation over carboxylation, thereby lowering the biochemical efficiency (ATP per gross assimilation of CO₂) of C₄ photosynthesis (Furbank et al., ¹⁹⁹⁰; Ubierna et al., ²⁰¹³). In crop canopies, where up to 50% of the net CO₂ uptake is fixed by shaded leaves, (Baker et al., ¹⁹⁸⁸; Long, ¹⁹⁹³) light limitation plays an important role in decreasing canopy productivity (Kromdijk et al., ²⁰¹⁰), and understanding the acclimation strategies of C₄ metabolism to light limitation is critical for increasing crop production to meet rising demands for food and fodder (Bellasio & Griffiths, ^2014a; Evans et al., ¹⁹⁹¹).

Shading also limits C₄ photosynthesis at the cell level. M and BS cells both need light to power photosynthesis. The amount of light that can be harvested by the BS cell is limited by the size of the cell (i.e. by the BS optical cross section; Bellasio & Lundgren, ²⁰¹⁶) and by light absorption in the M (with the concentric organization, BS cells are in effect shaded, meaning that light harvesting in the M reduces the light available to reach BS cells; Kramer & Evans, ²⁰¹¹), and depends on light quality. Green light is not strongly absorbed by chlorophyll, meaning that it can easily reach the BS, whereas blue light is all taken up by the upper chloroplasts and preferentially excites M cells (Evans et al., ²⁰⁰⁷). M cells use light to produce ATP and NADPH through linear electron flow (LEF), engaging both photosystems (PSs), whereas BS cells of NADP‐ME plants are thought to produce mainly ATP through cyclic electron flow (CEF) around photosystem I (PSI). In this way, the relative absorption of excitation energy will influence the availability of ATP and NADPH. Bellasio and Griffiths (2014c) proposed that these environmentally driven shifts in ATP and NADPH production can be countered by adjusting ATP and NADPH consumption by carbon metabolism, with a surprising degree of flexibility, but only up to a defined limit, ultimately determining how the biochemical work is apportioned between the two cell types. However, the possibility that plants could respond to shift in energy availability by rearranging light reactions, in such a way that also the production of ATP and NADPH is regulated, received little attention.

We have recently shown that the photosynthetic apparatus of Setaria viridis, a model C₄ plant of NADP‐ME subtype, is rearranged in response to low light in a cell‐specific fashion, preferentially increasing the electron transport capacity of BS cells (Ermakova, Bellasio, et al., ²⁰²¹). We hypothesized that this was a response to a shortage of ATP in the BS, which could depend on increased consumption resulting from dark reactions or on a lower rate of production caused by a shortage of light. Here we resolve these drivers and their causal relationship. First, we measure the anatomical properties of leaves from S. viridis plants grown under high light (HL plants) and low light (LL plants), and estimate how these would influence the light harvesting of the M and the BS. Then, we conduct comprehensive gas‐exchange characterization under ambient and low‐O₂ conditions, with the concurrent determination of PSII and PSI effective quantum yields, to estimate biochemical parameters and conductance to CO₂ diffusion at the M/BS interface (g _BS). Finally, we develop a model integrating two electron transport chains with the light‐harvesting properties of M and BS to study how the apportioning of light and carbon metabolism shifts in LL plants, and how these changes affect biochemical efficiency. We demonstrate that the decreased light interception in BS cells is effectively counteracted by an increase of CEF, uncovering another important link between the biochemical properties and structural characteristics of C₄ leaves.

RESULTS

Leaf anatomy and chlorophyll

In HL plants, BS chloroplasts were uniformly distributed inside the cells (Figure 1). In LL plants, BS chloroplasts had a clear centrifugal position, whereas M chloroplasts were specifically arranged along the cell walls, particularly in adaxial M cells. This was captured by the higher apparent absorbance of M cells of HL plants (Table 1). The increased number of chloroplasts in adaxial BS cells compared with abaxial BS cells was more prominent in LL plants. In line with the higher chlorophyll content in the BS of LL plants relative to the M, LL vascular bundles showed increased apparent absorbance (Table 1). LL leaves had 15% lower M thickness as well as 10% lower interveinal distance, compared with HL plants. The BS surface area per leaf area (S _BS) was 13% lower and the M surface area exposed to the intercellular airspace (S _M) was decreased by 35% in LL plants, compared with HL plants.

Table 1.

Anatomical and biochemical characteristics of leaves, mesophyll (M) and bundle sheath (BS) cells of Setaria viridis grown at high light (1000 μmol m⁻² sec⁻¹, HL) or low light (300 μmol m⁻² sec⁻¹, LL)

Characteristic	HL	LL
Height at vein (μm)	238 ± 12.2	205 ± 8.5*
Interveinal distance (μm)	181.5 ± 4.8	165 ± 4.8*
Abaxial mesophyll height (μm)	60.2 ± 3.3	46.0 ± 2.5*
Adaxial mesophyll height (μm)	68.8 ± 3.2	69.7 ± 3.7
Bundle sheath area (μm2)	9604 ± 1101	6719 ± 763*
Vein width (μm)	98.1 ± 6.5	89.1 ± 5.11
Chlorophyll (a + b) in the M (mmol m−2)	0.27 ± 0.01	0.38 ± 0.01*
Chlorophyll (a + b) in the BS (mmol m−2)	0.13 ± 0.01	0.25 ± 0.04*
Mesophyll surface area exposed to intercellular airspace, S M (m2 m−2)	14.13 ± 0.4	9.12 ± 0.5*
Bundle sheath cells surface area per unit of leaf area, S BS (m2 m−2)	2.21 ± 0.06	1.92 ± 0.04*
Leaf absorptance	0.789 ± 0.02	0.855 ± 0.04*
Mesophyll apparent absorbance (from micrograph luminance)	0.168 ± 0.01	0.117 ± 0.01*
Vascular bundle apparent absorbance (from micrograph luminance)	0.288 ± 0.01	0.344 ± 0.02*

Mean ± SE values are shown, n = 20 (except for: chlorophyll and leaf absorptance, n = 3; apparent absorbance, n = 6). Asterisks indicate statistically significant difference between two light regimes (P < 0.05).

Gas exchange and yield of photosystems

When the light response was measured at 420 μmol mol⁻¹ CO₂ and 21% O₂, no significant difference was found between HL and LL plants in CO₂ assimilation rate (A) or effective quantum yields of PSII, Y(II), and PSI, Y(I) (Figure 2). Yields of non‐photochemical losses in PSI as a result of donor, Y(ND), and acceptor Y(NA), side limitations did not differ between the two growth regimes (Figure 2g). At 2% O₂, no differences in light responses between HL and LL plants were detected (Figure 3).

Figure 2.

Measured and modelled gas exchange and photosystems yield under ambient O₂ level.

Symbols show response curves of CO₂ assimilation (a, b), quantum yield of photosystem II (c, d), quantum yield of photosystem I (e, f), and photosystem I donor side, Y(ND), and acceptor side, Y(NA), limitations (g, h) obtained for Setaria viridis grown under high light (HL, solid circles) or low light (LL, empty circles). Light curves measured under a reference CO₂ concentration of 420 μmol mol⁻¹ are shown in the left‐hand panels, and CO₂ response curves obtained under constant irradiance of 1000 μmol m⁻² sec⁻¹ are shown in the right‐hand panels. Mean ± SE, n = 3 biological replicates. C _M, CO₂ concentration in M cells. Corresponding curves obtained by switching the background gas to low O₂ are shown in Figure 3. Lines show modelled responses obtained through a combined biochemical model of light reactions and carbon metabolism of C₄ photosynthesis. Model parameters are listed in Table 2.

Figure 3.

Measured gas exchange and photosystems yield at 2% O₂.

Light curves measured under a reference CO₂ concentration of 420 μmol mol⁻¹ are shown in the left‐hand panels; CO₂ response curves obtained under constant irradiance of 1000 μmol m⁻² sec⁻¹ are shown in the right‐hand panels. Symbols show response curves of CO₂ assimilation (a, b), quantum yield of photosystem II (c, d), quantum yield of photosystem I (e, f), and photosystem I donor side, Y(ND), and acceptor side, Y(NA) limitations (g, h) obtained for Setaria viridis grown under high light (HL, solid circles) or low light (LL, empty circles). Mean ± SE, n = 3 biological replicates. C _M, CO₂ concentration in M cells.

CO₂ response curves were measured at a photosynthetic photon flux density (PPFD) of 1000 μmol m⁻² sec⁻¹, either at 21% or 2% O₂. No differences in CO₂ assimilation, Y(II), Y(I), Y(ND) or Y(NA) were significant between HL and LL plants, independently of O₂ level (Figures 2 and 3). Both HL and LL plants showed decreased Y(II) and increased Y(ND) at low C _M, probably representing an induction of non‐photochemical quenching in the PSII antennae in response to the acidification of the thylakoid lumen. The acidification of the thylakoid lumen is induced by the downregulation of ATP synthase activity in response to the reduced consumption of ATP by the RPP cycle (Kanazawa & Kramer, ²⁰⁰²). Interestingly, Y(NA) at low C _M was higher when measured at 2% O₂ (Figures 2h and 3h), pointing to a contribution of O₂ in oxidating PSI via photorespiration and/or O₂ photoreduction (Sagun et al., ²⁰²¹).

To aid the interpretation of light and CO₂ response curves, we fitted empirical and mechanistic models after Bellasio et al. (2016a). Fitted parameters in Table S1 show that, under ambient O₂, the main differences were dependent on a decrease of respiration under light (R _LIGHT), light compensation point (LCP), CO₂ compensation point (Γ) and BS conductance to CO₂ diffusion (g _BS) in LL plants. Curiously, the O₂ sensitivity of R _LIGHT, quantum yield, Y(CO ₂ ) _LL, and carboxylation efficiency was opposite between HL and LL plants. The decrease in photosynthetic efficiency in LL plants under low concentrations of O₂ supports a more important role of O₂ in the photoprotection of LL plants (Sagun et al., ²⁰²¹). A link between electron transport and R _LIGHT is known to exist (Buckley & Adams, ²⁰¹¹), but is not characterized in C₄ plants. Of the fitted quantities, only R _LIGHT and g _BS were retained for model parameterization, detailed below.

Modelling of light distribution, light reactions and dark metabolism

Using measured anatomical characteristics, the BS/M chlorophyll ratio and leaf absorptance (Table 1), we modelled light penetration through the leaf profile according to Bellasio and Lundgren (2016). The absorbed light (AB) in the BS relative to that absorbed in M was higher in HL plants: AB(BS/M) was 0.414 for HL and 0.343 for LL (Table 1). Next, to gain a comprehensive understanding of the photosynthetic metabolism, we used AB(BS/M), Y(II), g _BS and R _LIGHT (derived from the concurrent gas‐exchange and chlorophyll fluorescence measurements; Table S1), to parameterize a purposely derived model of light reactions and dark metabolism. The fraction of electron flow through PSI following CEF in M and BS (f _CycM and f _CycBS, respectively) was fitted to maximize assimilation, constrained to maintain PPDK and PEPCK activity in BS cells at zero to match immunoblotting (Figure 4).

Figure 4.

Protein assays.

Fluorescent micrographs of pyruvate orthophosphate dikinase (PPDK) localization on the leaf cross sections of Setaria viridis grown under low light (LL) and high light (HL). Fluorescence signals are pseudo‐coloured: green, PPDK labelled with secondary antibodies conjugated with Alexa Fluor 488; blue, calcofluor white‐stained cell walls. BS, bundle sheath cells; M, mesophyll cells. Below micrographs: immunodetection of PEP carboxykinase (PEPCK) in leaf protein extracts of S. viridis loaded on leaf area basis; a leaf sample from Zea mays was used as a positive control. Three biological replicates were loaded for HL and LL plants. [Colour figure can be viewed at wileyonlinelibrary.com]

Initially, we replicated in silico the leaf gas‐exchange measurements under the ambient O₂ level (Figure 2). For both light and CO₂ response curves, the trends of CO₂ assimilation and Y(II) were captured well by the model. For assimilation, R ² was 0.98 and 0.97 for the light curves or 0.95 and 0.81 for the A/C _i curves of HL and LL plants, respectively. For Y(II), R ² was 0.86 and 0.96 for the light curves or 0.91 and 0.76 for the A/C _i curves of HL and LL plants, respectively. In the light response curves, the model captured a hyperbolic decrease of the measured Y(I) at high irradiance (Figure 2e) but not the initial dip at low irradiance. However, the modelled Y(I) was similar to the trend of 1 − Y(ND), perhaps only capturing Y(I) available through electron input from PSII but not accounting for the loss of Y(I) through the unavailability of acceptors, i.e. Y(NA). In CO₂ exported to the M for reduction a higher fraction of the total 3PGA produced in the BS response curves, the hyperbolic increase of Y(I) was captured, but Y(I) was slightly underestimated for C _M values greater than 20 μmol mol⁻¹. Predicted Y(I) did not differ between HL and LL plants.

Next, we carried out a simulation of photosynthetic biochemistry using the specific parameterization of growth light regimes (Table 2). LL plants had a 60% lower rates of the reactions of the assimilatory metabolism, as a result of the lower energy availability (Table 3, to aid comparison between light regimes we also expressed fluxes in multiples of gross assimilation). With the lower NADPH availability, LL plants exported a higher fraction of the total 3‐phosphoglyceric acid (PGA) produced in the BS to the M (42% and 35%, respectively; Table 3). PGA is then reduced to trioses diffusing back to the BS. The rates of Rubisco carboxylation (V _C) and PEP carboxylation (V _P, which corresponds to the rate of malate export to BS cells and the backflux of pyruvate) were lower in LL plants. The decrease in V _P caused a 25% decrease in CO₂ concentration in the BS that was reflected by a higher ratio of Rubisco oxygenation relative to carboxylation (V _O/V _C, 4.9% in HL plants and 5.4% in LL plants; Table 3). However, there was a general increase in PSII efficiency in LL plants that overweighed the effect on V _O/V _C. As a result, the average quantum yield increased 38% on the basis of absorbed light (from 0.04 to 0.055 CO₂/quanta), and as much as 43% on the basis of incident light (from 0.031 to 0.044 CO₂/quanta), in LL plants compared with HL plants. LL plants gained more on the basis of incident light because of their higher leaf absorptance (captured in the measurements by s′, Table S1, and in the model inputs by s ₀, Table 2).

Table 2.

Model inputs and sources

Symbol	Description	Unit	HL	LL	Source
PPFD or I inc	Photosynthetic photon flux density	μmol m−2 sec−1	1000 or variable	1000 or variable	Equal to measurements
C M	CO2 concentration in M cells	μmol mol−1	Variable or 400	Variable or 400	–
O M	O2 concentration in M cells	μmol mol−1	210 000	210 000	Equal to ambient
g BS	Bundle sheath conductance to CO2 diffusion	mmol m−2 sec−1	0.0018	0.0012	Gas‐exchange curve fitting
γ*	Half the reciprocal Rubisco specificity		0.00031	0.00031	Boyd et al. (2015)
R LIGHT	Respiration in light	μmol m−2 sec−1	1.93	1.18	Gas‐exchange curve fitting
Chl(BS/M)	Chlorophyll (a + b) in the BS relative to M	$\left(\frac{\text{mmol}{\mathrm{m}}^{-2}\text{leaf}}{\text{mmol}{\mathrm{m}}^{-2}\text{leaf}}\right)$	0.48	0.66	Spectroscopic measurements (Table 1)
AB(BS/M)	Fraction of light absorption in BS cells relative to M cells		0.414	0.343	Light penetration and anatomy model (Bellasio & Lundgren, 2016)
Y(II) 0	Yield of PSII extrapolated under zero PPFD and infinite C M		0.76	0.73	1.04 × Y(II) LL
s 0	Lumped energy conversion coefficient when f Cyc = 0 (Yin et al., 2009), similar to αβ in other notations	e−/quanta	0.440	0.463	Fitted for $\frac{\mathrm{d}{\mathit{GA}}_{\mathrm{LOW}}}{\frac{1}{3}Y{\left(\mathit{II}\right)}_{\mathrm{LOW}}\mathrm{d}{I}_{\mathrm{Inc}}}=s^{\prime }$
f PSEUDO NR M	Fraction of J 1 used by nitrate reduction in M cells		0.01	0.01	Assumed low for simplicity
f PSEUDO NR BS	Fraction of J 1 used by nitrate reduction in BS cells		0.01	0.01	Assumed low for simplicity
f Q	Fraction of J 1 going through the Q‐cycle		1	1	(Yin & Struik, 2012)
H	Stoichiometry of ATP synthase:protons required to synthesize ATP	h+/ATP	4.67	4.67	Hahn et al. (2018); Vollmar et al. (2009)
Y(I) LL	Yield of PSI extrapolated under zero PPFD		1	1	Yin and Struik (2012)
f NDH M	Fraction of CEF through the NDH complex in the M		0.4	0.4	See Parameterization
f NDH BS	Fraction of CEF through NDH in BS cells		0.7	0.7	See Parameterization
f Cyc M	Fraction of J 1 following CEF in M cells		Fitted to max A	Fitted to max A
f Cyc BS	Fraction of J 1 following CEF in BS cells		Fitted to max A	Fitted to max A
αC	Slope of the non‐rectangular hyperbola used to model f(CO2)		0.15	0.15	Fitted to fluorescence
V 0C	y‐intercept of the non‐rectangular hyperbola used to model f(CO2)		1	1	Assumed 1 for simplicity
θC	Curvature of the non‐rectangular hyperbola used to model f(CO2)		0.3	0.3	Fitted to fluorescence
αV	Slope of the non‐rectangular hyperbola used to model f(PPFD)		0.0004	0.0004	Fitted to fluorescence
V 0V	y‐intercept of the non‐rectangular hyperbola used to model f(PPFD)		1	1	Assumed 1 for simplicity
θV	Curvature of the non‐rectangular hyperbola used to model f(PPFD)		0.8	0.8	Fitted to fluorescence
f PH	Fraction of PEP produced by PEPCK that is hydrolysed		–	–	Irrelevant because f PEPCK = 0
f PEPCK	Fraction of the activity of PECK relative to the maximum (that is the fraction of J ATP BS not used by the RPP and PCO cycle)		0	0	Immunoblotting (Fig. 2)
f RLIGHT	fraction of respiration in the light in BS cells relative to leaf level		0.5	0.5	von Caemmerer (2000)
f CS	Fraction of carbohydrate synthesis in BS cells		0.5	0.5	Bellasio (2017)
f MDH M	Fraction of M activity of MDH, relative to its maximum, defines the transition between NAD‐ME and NADP‐ME		1	1	John et al. (2014)

Table 3.

Output of the combined light reaction and biochemical model of C₄ photosynthesis

Symbol	Description	HL		LL
		M	BS	M	BS
f Cyc	Fraction of electron flow through PSI (J 1) following CEF	0.01	0.783	0.08	0.866
C	CO2 concentration	400	4100	400	3100
I Inc	Incident light (PPFD)	707 (23.5)	293 (9.71)	223 (17.7)	77 (6.08)
I 2	Light absorbed by PSII	310 (10.0)	50 (1.63)	100 (7.54)	9.5 (0.718)
I 1	Light absorbed by PSI	238 (7.68)	176 (5.69)	79.1 (5.97)	51.9 (3.92)
J 2	Electron flow through PSII	151 (4.88)	25 (0.794)	63.8 (4.82)	6.07 (0.458)
J 1	Electron flow through PSI	153(4.92)	113 (3.65)	69.2 (5.22)	45.4 (3.43)
J NADPH	NADPH production rate (half the electron flow to NADPH)	58.8 (1.90)	7.09 (0.229)	27.4 (2.07)	0.948 (0.07)
J ATP	ATP production rate	97.9 (3.16)	80.2 (2.59)	44.2 (3.34)	32.5 (2.46)
V P	PEP carboxylation rate. In this study f MDHM = 1, so V P corresponds to the rate of malate flux to the BS, the rate of pyruvate flux to the M, the PPDK reaction rate in the M (PPDK reaction rate in the BS is fitted to be zero in this study) and the malic enzyme reaction rate	36.7 (1.18)	0	15.9 (1.20)	0
L	Leakage rate of CO2 out of the BS	−6.64 (−0.214)	6.64 (0.214)	−3.21 (−0.242)	3.21 (0.242)
Φ	Leakiness: CO2 leakage rate out of the BS relative to V P	−0.18	0.18	−0.20	0.20
VC	Rubisco rate of carboxylation	0	31.7 (1.02)	0	13.6 (1.03)
V O	Rubisco rate of oxygenation	0	1.54 (0.0496)	0	0.735 (0.0555)
PR	Rate of PGA reduction	22.2 (0.716)	43.0 (1.39)	11.5 (0.868)	16.4 (1.24)
DHAP RPP	Rate of DHAP entering the conversion phase of the RPP cycle	0	55.5 (1.79)	0	23.9 (1.81)
RuP Phosph	Rate of RuP phosphorylation	0	33.3 (1.07)	0	14.3 (1.08)
CS	Rate of carbohydrate synthesis	4.85 (0.156)	4.85 (0.156)	2.01 (0.152)	2.01 (0.152)
R Light	Rate of respiration in the light	0.95 (0.031)	0.95 (0.031)	0.590 (0.047)	0.590 (0.046)
PGA flux	Flux of PGA	22.5 (0.726)	−22.5 (−0.726)	11.7 (0.882)	−11.7 (−0.882)
DHAP flux	Flux of DHAP	−17.3 (−0.559)	17.3 (0.559)	−9.48 (−0.716)	9.48 (0.716)

The output shown is calculated at the growth PPFD (1000 for HL or 300 μmol m⁻² sec⁻¹ for LL), and expressed, except for f _Cyc and Φ (dimensionless) or C (μmol mol⁻¹), in μmol m⁻² sec⁻¹, and in brackets as a fraction of gross assimilation under growth light (30.97 for HL and 13.24 μmol m⁻² sec⁻¹ for LL plants).

DISCUSSION

Setaria viridis is a wild ancestor of Setaria italica (foxtail millet), a grain crop widely grown in China and India. It has gained favour for studying C₄ photosynthesis because it has a rapid life cycle, small stature, sequenced genome and an available genetic transformation method (Brutnell et al., ²⁰¹⁰; Ermakova, Osborn, et al., ²⁰²¹). As C₄ photosynthesis has evolved independently at least 70 times (Sage, ²⁰¹⁷), diverse biochemical configurations exist in C₄ plants, and characterizing different strategies of shade acclimation is a prerequisite for identifying the best targets for improving crop performance. While the anatomical responses of C₄ plants to shading are relatively uniform or consistent (Pengelly et al., ²⁰¹⁰; Ward & Woolhouse, ¹⁹⁸⁶), the biochemical strategies appear to be diverse.

We recently showed that S. viridis grown at limiting irradiance deployed a suite of protein‐level adjustments providing BS thylakoids with increased capacity for light harvesting and electron transport, pointing to an increased ATP demand in the BS (Ermakova, Bellasio, et al., ²⁰²¹). Here, we were interested in resolving whether the observed rearrangements were triggered by increased ATP consumption from dark reactions or by a lower rate of production, perhaps due to the anatomical acclimation to growth under low light. Although acclimation to LL generally entails a downregulation of photosynthetic potential, here gas‐exchange measurements showed that HL and LL plants reached strikingly similar rates of assimilation when measured at the same light or CO₂ levels. This intriguing invariance, which we repeatedly measured in plants from different growth batches, and that was previously observed independently in the same ecotype (Henry et al., ²⁰¹⁹), may be a particular feature of S. viridis. Detailed analysis of the response curves through model fitting (Table S1) revealed some contrasting acclimation strategies: LL plants had lower carboxylation efficiency and lower Y(II) _LL, but also lower respiration, than HL plants. We then characterized the leaf anatomy and found a reduction in BS size and in BS surface area per leaf area (S _BS) in LL plants. Our interpretation is that these anatomical changes contributed to the reduction of g _BS (von Caemmerer et al., ²⁰⁰⁸), here estimated by fitting gas exchange and fluorescence data obtained under ambient and low concentrations of O₂. The reduction of g _BS under LL conditions is consistent with previous results obtained through different proxies, including anatomy, isotopic discrimination, combined gas exchange and chlorophyll fluorescence (Pengelly et al., ²⁰¹⁰; Ubierna et al., ²⁰¹³). Interestingly, g _BS was shown to decrease both in plants grown under LL conditions (Bellasio & Griffiths, ^2014b) and in plants grown under HL conditions and subsequently transferred to LL, as occurs in crop canopies where older leaves are shaded by new growth (Bellasio & Griffiths, ^2014a).

The decrease in g _BS ameliorates the efficiency of C₄ photosynthesis. By hindering CO₂ leakage, it counters the decrease in CO₂ concentration in the BS and the increase of photorespiration occurring under LL (Kromdijk et al., ²⁰¹⁴). However, the associated reduction in BS size (Table 1) has the undesirable consequence of decreasing the light harvesting in BS cells, limiting ATP generation and decreasing the operational plasticity under changing light conditions (Bellasio & Lundgren, ²⁰¹⁶). LL plants deployed a concerted suite of responses to counter a potential ATP starvation in the BS. First, whereas in HL plants the M chloroplasts were dispersed, in LL plants the M chloroplasts were arranged along the cell walls (Figure 1), similar to that observed in Saccharum officinarum grown under LL (Sales et al., ²⁰¹⁸), which created optical gaps, resulting in a lower apparent absorbance of the M and thereby increasing the amount of light filtering through to the BS cells (Table 1), a phenomenon known as the ‘sieve effect’ (Terashima et al., ²⁰⁰⁹). Chloroplast arrangements differ depending on the species and the light quality and intensity. For instance, under midday illumination: Eleusine coracana was shown to aggregate M chloroplasts around the BS; Zea mays showed a dispersed arrangement, similar to that observed in S. viridis; and Sorghum bicolor created characteristic optical corridors spanning the whole leaf thickness, presumably aiding photoprotection, which was also observed in Z. mays but only under non‐physiological irradiance (3000–4000 μmol m⁻²  sec⁻¹) (Maai et al., ^{2020a, 2020b}; Yamada et al., ²⁰⁰⁹). Second, in LL leaves the BS had higher chlorophyll content (Table 1) and increased abundance of light‐harvesting complexes (LHC) I and II, compared with HL plants (Ermakova, Bellasio, et al., ²⁰²¹). Consistently, LL leaves had higher absorptance (Table 1) and fitting combined gas‐exchange and fluorescence data captured a higher s′, the parameter representing effective leaf level light interception lumped in with the yield of ATP generation (Table S1). Third, the potential of BS thylakoid membranes for ATP production increased as a result of the upregulation of PSI, cytochrome b ₆ f, ATP synthase and NDH (Ermakova, Bellasio, et al., ²⁰²¹). NDH has been shown to be essential for C₄ photosynthesis in reverse‐genetics studies (Ishikawa et al., ²⁰¹⁶; Peterson et al., ²⁰¹⁶) and is found to correlate with the ATP requirements of cell types in C₄ plants (Takabayashi et al., 2005).

Next, we were interested in resolving to what extent the observed reorganization of light‐harvesting and electron transport processes in LL plants was effective in countering the limitations to ATP generation caused by a smaller BS, and what modifications to the metabolism of BS and M were required to maintain invariant levels of assimilation (Figure 2). We developed a model encompassing explicit anatomy and separate electron transport chains in the BS and M, parameterized specifically for HL and LL plants. We found that the increased chlorophyll concentration was not sufficient to counter the effect of smaller BS cells and, overall, LL plants absorbed 40% less light in BS cells relative to the total (from 23% under HL to 14% under LL; Table 3). However, the higher proportion of CEF (f _Cyc) in the BS of LL plants (Figure S3; Table 3) could partially compensate for the decrease in light absorption, so that the predicted ATP production rate, relative to the total, only decreased by about 5% (from 45% in the BS of HL plants to 42% in the BS of LL plants; Table 3). The predicted changes in f _Cyc – an emerging property of the fitted model mainly resulting from the reduction in the size of the BS – are in line with the increased content of NDH detected in LL BS cells (Ermakova, Bellasio, et al., ²⁰²¹), again pointing to the key role of NDH in ATP production in BS cells. Hence, we demonstrated that: first, the upregulation of CEF (f _Cyc) is effective in mitigating decreased light interception in BS cells; and, second, that decreasing light interception in BS cells is a sufficient condition to require an increase of f _Cyc (Figure S3; Table 3). To our knowledge, this functional dependence was not demonstrated before, uncovering another important link between biochemical properties and the structural characteristics of C₄ leaves.

The NADPH production rate in BS cells relative to the total was predicted to decrease by 97% in LL plants (from 11% under HL to 0.3% under LL), driven both by the decrease in BS size and the increase in f _Cyc. This led to a 13% decrease in the rate of PGA reduction in BS cells relative to the total (from 66% under HL to 59% under LL), and a consequent relative increase of triose fluxes between M and BS cells in LL plants (Table 3). By means of LEF, PSII activity in BS cells not only supplies NADPH production, but also replenishes the CEF electrons leaking to various electron sinks downstream of PSI (explicitly accounted for in the model as pseudocyclic electron flow, but not varied in this study). In this model output, LEF in the BS was predicted to be 21 μmol m⁻² sec⁻¹ (14% of the total leaf rate for HL plants) and 5.59 μmol m⁻² sec⁻¹ (9% of the total leaf rate for LL plants) (Table 3). The actual PSII activity in the BS thylakoid membranes measured by Ermakova, Bellasio, et al. (2021) matched the value predicted for LL plants (it was approx. 7% of the leaf rate), but in HL plants it was half of the LL value, much lower than the model prediction. This suggests that the predicted value of J ₂ in the BS of HL plants cannot be supplied in vivo by electrons coming from water oxidation, but must be obtained via oxidation of NADPH, derived from malate imported from the M, through the NDH. This idea is supported by experimental observations. When supplied with malate, isolated BS strands of Z. mays retained PSI activity even in the presence of the PSII inhibitor. Further, the BS of Sorghum bicolor maintained CO₂ fixation under far‐red illumination, which is unable to excite PSII (Ivanov et al., ²⁰⁰⁵; Osmond, ¹⁹⁷⁴).

Theory shows that, under changing irradiance, flexibility in the apportioning of PGA reduction between BS and M cells can adjust the BS demand for NADPH, and the engagement of PEPCK and PPDK can attune the BS demand for ATP (Bellasio & Griffiths, ^2014c; Furbank, ²⁰¹¹). Because PEPCK consumes ATP generated in the M and is tightly regulated by ATP availability, the expression of PEPCK in NADP‐ME plants was predicted to increase light‐harvesting plasticity, i.e. the capacity to efficiently harvest light of a broad range of intensities and spectral qualities (Bellasio & Griffiths, ^2014c). Further, the activity of PPDK in the BS could compensate for a lack of PEPCK, making PEPCK engagement necessary when the activity of PPDK in the BS was reduced, and vice versa (Bellasio, ²⁰¹⁷). Indirect evidence supports these predictions. It was shown that low‐light‐acclimated NADP‐ME plants, like Z. mays and Saccharum officinarum, increased the total rate of PEPCK activity (Sales et al., ²⁰¹⁸) or the activity of PEPCK relative to PEPC (Sharwood et al., ²⁰¹⁴; Sonawane et al., ²⁰¹⁸), and increased the pool of inactive PEPCK (data made available by courtesy of B.V. Sonawane, personal communication), presumably available to be activated by changing light conditions (Bailey et al., ²⁰⁰⁷).

Uniquely, S. viridis did not express PEPCK under HL or LL conditions (Figure 4). Nor did we find detectable levels of PPDK in the BS (Figure 4), in line with previous reports (John et al., ²⁰¹⁴; Schlüter & Weber, ²⁰²⁰). Although Z. mays grown under LL overexpressed LHCII subunits and PsbD in BS cells (Drozak & Romanowska, ²⁰⁰⁶), it did not show increased oxygen activity or changes in the supramolecular organization of PSII (Rogowski et al., ²⁰¹⁹; Romanowska et al., ²⁰⁰⁶). In contrast, S. viridis had a striking plasticity in acclimating light reactions, probably sufficient to avoid the necessity to alter PEPCK and PPDK expression (Figure 4). Importantly, and in contrast to the nine species (four NADP‐ME species, including Z. mays and Sorghum bicolor, two NAD‐ME species and two PEPCK species) studied by Sonawane et al. (2018), the acclimation of light reactions in S. viridis did not compromise quantum yield (Table S1). Therefore, the outstanding capacity of S. viridis to rearrange light reactions under LL is a highly efficient acclimation strategy, setting S. viridis aside from other NADP‐ME plants and representing a so‐far overlooked innovation in C₄ evolutionary history.

CONCLUSION

Using a purposely developed model, parametrized with original anatomical, biochemical and gas‐exchange data, we analytically and mechanistically solved the causality link between anatomy and biochemistry. The optical cross section determined the absorption of light in the BS and the M, the rate of electron transport, the engagement of CEF and LEF, the rate of ATP and NADPH generation, and ultimately the apportioning of carbon metabolism between M and BS cells. To counter ATP starvation, S. viridis adjusted the electron transport processes, boosting cycling electron flow in the BS. Although quantifying the impact in field conditions will require additional experiments, the striking capacity of S. viridis to acclimate light reactions is perhaps the most efficient shade‐tolerance strategy, potentially leading to novel possibilities for crop improvement.

EXPERIMENTAL PROCEDURES

Plants

Setaria viridis plants (A10 ecotype) were grown in 2‐L pots filled with commercial soil mix (Debco, https://www.lovethegarden.com/au‐en/debco) supplemented with 1 g L⁻¹ of slow‐release fertilizer (Osmocote; Scotts, https://www.scotts.com). Plants were grown in controlled chambers with 28°C day, 24°C night, 60% humidity and 16 h of illumination at an intensity of 1000 or 300 μmol m⁻² sec⁻¹, provided by halogen incandescent lamps (42 W, 2800 K, warm white, clear glass, 630 lumens; CLA, http://www.clalighting.com.au) and Pentron Hg 4‐ft fluorescent tubes (54 W, 4100 K, cool white; Osram Sylvania, https://www.osram.us), and reached by hanging a shade cloth above some of the plants. Growth light spectra are shown in Figure S2. All measurements were performed on the youngest fully expanded leaves sampled before flowering, between 15 and 25 days after germination.

Leaf anatomy

Resin‐embedded cross sections were prepared and imaged according to Pengelly et al. (2010). Quantification of anatomical parameters was performed using imagej (https://imagej.nih.gov/ij) on an equal number of secondary and tertiary veins, as described by Bellasio and Lundgren (2016). Calculations of the M surface area exposed to the intercellular airspace (S _M) and the BS surface area per unit of leaf area (S _BS) were made as described by Pengelly et al. (2010) using the curvature correction factor of 1.43 from Evans et al. (1994). Apparent absorbance was calculated as the log10 of the ratio between the luminance of the background divided by the luminance of the tissue, both processed with imagej as described by Bellasio and Lundgren (2016) and averaged over two regions for n = 6 replicates. Leaf absorptance was the complement to one of leaf reflectance and transmittance, both measured with a Li‐Cor 1800‐12 integrating sphere (Li‐Cor, https://www.licor.com), coupled to a Li‐190S light sensor (Li‐Cor), following the manufacturer's instructions for calibration and calculations.

Chlorophyll

Total chlorophyll was extracted from frozen leaf discs ground using TissueLyser II (Qiagen, https://www.qiagen.com) in 80% acetone, buffered with 25 mm 4‐(2‐hydroxyethyl)‐1‐piperazineethanesulfonic acid (Hepes)‐KOH (pH 7.8). Chlorophyll a and b content was measured at 750, 663.3 and 646.6 nm, and calculated according to Porra et al. (1989). The fraction of total leaf chlorophyll in BS cells was determined from the chlorophyll a/b ratios in BS and M cells, as described by Ermakova, Bellasio, et al. (2021).

Western blotting and immunolocalization

Protein isolation from leaves, gel electrophoresis and Western blotting were performed as described by Ermakova et al. (2019). PEPCK antibodies (Agrisera, https://www.agrisera.com) were used according to the manufacturer's protocol.

Immunodetection of PPDK on lightly fixed leaf cross sections was performed according to (Ermakova, Arrivault, et al., ²⁰²¹). Sections were treated with 1:100 PPDK primary antibody (Karki et al., ²⁰²⁰), 1:200 Alexa Fluor 488‐conjugated goat anti‐rabbit secondary antibody (Life Technologies, now ThermoFisher Scientific, https://www.thermofisher.com) and 0.05% calcofluor white to stain cell walls. The fluorescence signal was captured with a Leica DM5500 microscope (Leica Microsystems, https://www.leica‐microsystems.com) equipped with a Leica DFC7000T camera using leica application suite 4.12. Fluorescence was detected at 505–565 nm for PPDK (excitation 490–510 nm, YFP Filter Cube; Leica) and at 450–490 nm for cell walls (excitation 330–370 nm, A4 Filter Cube; Leica).

Simultaneous gas exchange, chlorophyll fluorescence and P700 measurements

Gas exchange, fluorescence and P700⁺ absorbance changes were measured simultaneously with the set‐up of Bellasio and Farquhar (2019) on n = 3 biological replicates. Briefly, a portable gas‐exchange system (LI6400XT; Li‐Cor) was modified to operate at low CO₂ concentrations (see licor.com) and fitted with a 6400‐06 PAM2000 adapter (courtesy of Susanne von Caemmerer), holding a fibre probe in the upper leaf cuvette distant enough to minimize shading. Leaves were aligned without overlapping their edges to fill the cuvette. Light was provided by a bespoke red–blue light source, adjusted to provide approximately 90% red and 10% blue light, positioned to illuminate the leaf uniformly. Light intensity was measured through an in‐chamber gallium arsenide photodiode, calibrated using a Li‐250 light sensor (Li‐Cor). Neoprene gaskets were used on both sides of the cuvette. A mixture with 2% O₂ was prepared by mixing ambient air and N₂ using a bespoke gas mixing unit (kindly assembled by Suan Chin Wong). This mix of ambient air was CO₂‐scrubbed with soda lime and humidified to a dew point of 15–17°C upstream of the inlet to maintain water vapour pressure deficit around 1 kPa. CO₂ was added from a large cylinder (BOC, https://www.boc.com.au), using the CO₂ injection unit of the LI6400XT. Mass flow leaks (Boesgaard et al., ²⁰¹³) were monitored with a gas flow meter, as detailed by Bellasio et al. (2016b).

Both PSII and PSI yields were measured with a Dual PAM‐F (Walz, https://www.walz.com, courtesy of Dean Price). PSII activity was assessed with the pulse amplitude modulated fluorescence method using 620 nm measuring light of 9 μmol m⁻² sec⁻¹ (Schreiber et al., ¹⁹⁸⁶). The redox state of P700, the reaction centre of PSI, was assessed by detecting the absorbance of the cation at 830 nm with a dual wavelength unit (830/875 nm), following the method of Klughammer and Schreiber (1994). Saturating pulses of red light (635 nm) at 20 000 μmol m⁻² sec⁻¹ were used. First, P _M, the maximal level of P700⁺, was recorded upon the application of a saturating pulse on top of the far‐red light, and P ₀, the minimal P700⁺ signal, was recorded after that saturating pulse. Photosynthetic parameters (P, the steady‐state P700⁺ signal; P _M′, the maximal P700⁺ signal under light; F, the steady‐state fluorescence signal; F _M′, the maximal fluorescence signal under light) were monitored by the application of the saturating pulse at different irradiances, CO₂ and O₂ concentrations. The effective quantum yield of PSII, Y(II), was calculated according to Genty et al. (1989). The effective quantum yield of PSI, Y(I), and the non‐photochemical yields of PSI caused by donor, Y(ND), or acceptor, Y(NA), side limitation were calculated as described by Klughammer and Schreiber (2008).

Four photosynthetic response curves (A/PPFD and A/C _i curves, under ambient and low concentrations of O₂) were measured at 25°C in day‐long experiments. A/C _i curves were measured first, under a PPFD of 1000 μmol m⁻² sec⁻¹ and imposing reference CO₂ concentrations of 20, 40, 60, 80, 100, 200, 300, 400, 500, 600, 800, 1000 μmol mol⁻¹ and a minimum of 120 sec between steps; A/PPFD curves were measured under reference CO₂ concentrations of 420 μmol mol⁻¹, imposing PPFDs of 1500, 1000, 200, 500, 150, 100, 75, 50, 30 μmol m⁻² sec⁻¹ and a minimum of 180 sec between steps. The order between ambient and low O₂ was inverted each day. The flow rate was 400 μmol sec⁻¹; CO₂ diffusion through the gaskets was compensated by lengthening the tubing of the LI6400XT reference gas (Bellasio & Farquhar, ²⁰¹⁹). Gas‐response curves were analysed using the protocol of Bellasio et al. (2016a). CO₂ concentration at the M carboxylation sites was calculated as C _M = C _i−A/g _M, where mesophyll conductance (g _M) was 1.5 and 1.2 mol m⁻² sec⁻¹ for HL and LL, respectively, derived by adjusting the data of Ubierna et al. (2017) for S _M (Table 1).

C₄ photosynthesis model

Biochemical models may include formulations describing a variety of processes (e.g. electron transport), but at any given time only the formulation describing the process that is limiting photosynthesis in that circumstance will be representative (outputs are called ‘actual’ rates), whereas others are not (outputs are called ‘potential’ rates; Farquhar et al., ¹⁹⁸⁰). The mismatch between formulations can sometimes be useful, for instance, to estimate stomatal conductance in C₃ (Farquhar & Wong, ¹⁹⁸⁴) and C₄ plants (Bellasio et al., ²⁰¹⁷), but typically it generates ambiguity in curve fitting (e.g. fluorescence; reviewed in Bellasio et al., ^2016b) and difficulties in locating the cut‐off points (Gu et al., ²⁰¹⁰). To avoid discontinuities, we merged enzyme limitations into a light‐limited model by introducing a function describing the quenching of Y(II) depending on C _M, analogous to the classical PPFD‐dependence of the electron transport rate. This function depends on the familiar biochemical quantities V _PMAX and K _P, but we have not derived an explicit expression at this stage.

The model is organized to simulate two compartments representing M and BS cells (Figure 5): each harvests light to drive a distinct electron transport chain (Note S1; Figure S1). In both electron transport chains, the ratio between the rates of ATP and NADPH production is varied via adjustment of CEF (through the parameter f _Cyc), which may flow through PGR5/PGRL1 or the NAD(P)H dehydrogenase‐like complex (NDH, adjusted through the parameter f _NDH). When f _Cyc is adjusted, the proportion of light absorbed by the photosystems varies to maintain invariance in the sum of the light absorbed by the two (equations described in supporting information of Yin et al., ²⁰⁰⁴). This is of key importance when modelling energetics and CEF engagement under limiting light (Bellasio, ²⁰¹⁹) because, otherwise, supplemental CEF would be driven by an increase in light absorbed (but s would be invariant, main text of Yin et al., ²⁰⁰⁴). The reducing power requirements for nitrogen reduction and for the water–water cycle are explicitly accounted for as a fraction of pseudo‐cyclic electron flow, after Yin and Struik (2012), but we did not use the functionality in this study. A key innovation is that the rate of oxygen evolution in the BS is calculated from the actual rate of electron transport in both compartments, instead of being assumed to scale to assimilation through the parameter α, as in all the models derived from Berry and Farquhar (1978).

Figure 5.

Schematic of the processes included in the model.

Metabolites are in black. Fluxes are depicted by black arrows and pink symbols that directly link to the equations reported in Notes S1–S4. Key processes are briefly described in bright green. The leaf is divided into mesophyll (M) and bundle sheath (BS) compartments. Incident PPFD (I _inc) may reach M (I _Inc M) or BS (I _Inc BS) cells, depending on anatomical characteristics and the size of the light‐harvesting machinery. A fraction I is absorbed by PSI or PSII (I ₁ or I ₂, respectively). Light reactions (for more details see Figure S1) result in the production of NADPH and ATP, which are consumed by carbon metabolism encompassing C₄ and C₃ activity. The C₄ cycle reactions appear in the middle of the M and BS compartments. CO₂ is initially hydrated to bicarbonate (the point of entry is highlighted in yellow) and fixed by PEP carboxylase (PEPC) at the rate V _P to form oxaloacetate (OAA). This may be reduced to malate (MAL) or to aspartate (ASP) through transamination (T), i.e. the exchange of amino groups with glutamate (GLU). MAL and ASP both diffuse to BS cells; MAL is decarboxylated with a concurrent reduction of NADP by malic enzyme (ME), whereas ASP is deaminated to OAA (the exchange of amino groups with alpha‐ketoglutarate (αKG) is implied) and may be decarboxylated by PEP carboxykinase (PEPCK) or by malic enzyme (ME). The regeneration of PEP is shared between M and BS cells, depending on energy availability. The C₃ metabolism appears at the bottom, partitioned between M and BS compartments. Rubisco carboxylation and oxygenation reactions (V _C and V _O) consume RuBP and produce PGA and PGLA and are fully compartmentalized to BS cells. PGLA is recycled through the photorespiration cycle, eventually regenerating PGA. This is consumed by respiration (R _LIGHT), assumed to be entirely supplied by newly assimilated PGA, and is reduced (PR) to triose phosphate (DHAP), which is a substrate of carbohydrate synthesis (CS). The final product of photosynthesis is a generic triose carbohydrate (highlighted in yellow). The majority of DHAP enters the sugar conversion phase of the reductive pentose phosphate (RPP) cycle, exclusive to the BS. Metabolites for which fluxes are calculated are listed in the middle and are assumed to be positive when occurring in the normal direction, indicated by the arrows. The excel workbook provided renders outputs according to this scheme. [Colour figure can be viewed at wileyonlinelibrary.com]

Both ATP and NADPH drive the reactions of carbon metabolism, described following Bellasio and Griffiths (2014c), McQualter et al. (2016) and Bellasio (2017). Although the NADPH available in the BS is consumed by the RPP and the photorespiratory cycles, the ATP available in the M and any ATP surplus in the BS are consumed by the C₄ cycle, until all the ATP and NADPH available have been consumed. In this way, the partitioning between cycles and the apportioning of metabolic work between M and BS cells emerges directly from the rate of ATP and NADPH produced by light reactions, instead of being assumed through the parameter x, as in all the approaches following Berry and Farquhar (1978). In contrast to Bellasio (2017), where all intermediate photosynthetic types were modelled, here C₄ photosynthesis is fully expressed, such that the glycine decarboxylase complex (GDC) and Rubisco are both fully compartmentalized to BS cells (Bellasio, ²⁰¹⁷). However, C₄ subtypes can be changed seamlessly, forming a continuous biochemical space that can be explored by varying two parameters: f _MDH, representing the engagement of MDH in M cells and governing the trajectory between the NADP‐ME subtype and the NAD‐ME subtype, and f _PEPCK, representing the capacity of PEPCK to consume the ATP available in BS cells and representing the level of PEPCK expression relative to other carboxylases (we will explore these functionalities in dedicated studies). In the decarboxylation of malate, the co‐products NADH and NADPH are assumed to be equivalent or interconvertible. This may be underpinned by an actual biochemical interconversion, mediated by the intercellular operation of the malate shuttle (Furbank, ²⁰¹¹), or simply by the capacity of malic enzyme (ME) to dock both cofactors, as suggested by early studies (Kanai & Edwards, ¹⁹⁷³).

The M and BS cells are connected by an exchange of metabolites (aspartate, ASP; alanine, ALA; dihydroxyacetone phosphate, DHAP; malate, MAL; phosphoenolpyruvate, PEP; 3‐phosphoglyceric acid, PGA; pyruvate, PYR; and CO₂) that diffuse obeying mass‐balance constraints. Diffusion is non‐limited, except that of CO₂, restrained by a finite conductance (g _BS) that allows higher CO₂ concentrations in BS cells (C _BS) based on classical underpinnings (Berry & Farquhar, ¹⁹⁷⁸). Glutamate and αKG do not diffuse directly between M and BS cells, but exchange amino‐ groups with ALA and PYR (Mallmann et al., ²⁰¹⁴; Pick et al., ²⁰¹¹; Schlüter et al., ²⁰¹⁹). If reactions can proceed in the opposite direction, they are assumed to proceed only in the direction with positive balance. Respiration is a shared process between M and BS cells. To avoid a futile cycle consisting of concurrent glycolysis and carbohydrate synthesis, respiration is assumed to be supplied by new assimilates (PGA), in line with Bellasio and Griffiths (2014c). The ATP and NADH produced during respiration are neglected, assumed to be consumed by basal metabolism. Any ATP and NADH residual imbalances produced during respiration in the light are absent, supported by the analysis of Buckley and Adams (2011), who proposed that they would be dissipated by alternative oxidases. The final product of photosynthesis is a generic triose carbohydrate, the destiny of which is not followed further by the model.

Details of the functions describing the reaction rates and CO₂ and O₂ concentrations in M and BS compartments are provided in Note S2, the balance of reducing power consumption and production in the M and BS are provided in Note S3 and metabolite flows are provided in Note S4. Model sensitivity analysis is shown in Table S2.

Parameterization

Parameters were either derived from measurements (in which case the data were randomized and averaged for HL and LL plants), taken from dedicated studies or assumed. Light penetration in the leaf was simulated through a separate optical model, freely downloadable from the supporting information of Bellasio and Lundgren (2016). The number of layers of adaxial M cells was 289 for HL plants and 340 for LL plants; the number of layers of the vein was 458 for HL plants and 435 for LL plants; the number of layers of abaxial M cells was 253 for HL plants and 225 for LL plants; the fraction of interveinal distances occupied by the vein was 0.56 for HL plants and 0.532 for LL plants, all derived from anatomical measurements (Table 1). The absorbance of the adaxial M cells was set to equal that of M cells following the observation that BS extensions are absent in S. viridis; the absorbance of the vein relative to M cells (k _VB/k _MI) was 1.65 for HL plants and 2.73 for LL plants, calculated by dividing the measured BS/M ratio of chlorophyll content per metre square of leaf, by the measured ratios of BS/M areas, 0.29 for HL and 0.24 for LL; reflectance was 0.067 for HL plants and 0.081 for LL plants (Table 1).

The combined model of light and dark reactions has 29 input quantities: three define the environmental characteristics, PPFD, C _M and O _M; 17 define light reactions, Y(II) ₀, s, f _{Pseudocyc NR M}, f _{Pseudocyc NR BS}, f _Q, h, Y(I) _LL f _NDH M, f _NDH BS, f _Cyc M, f _Cyc BS, α_C,V _0C, θ_C, α_V, V _0V, θ_V; six define dark reactions, f _PH, f _PEPCK, f _RLIGHT, f _CS, f _MDH; and three more, g _BS, AB(BS/M), R _LIGHT, are not grouped. AB(BS/M) was taken from the light penetration model described above, and R _LIGHT and g _BS were derived from gas‐exchange and fluorescence measurements with the procedure described by Bellasio et al. (2016a) (Table S1). Y(II) ₀ was derived by slightly increasing the maximum values of Y(II) _LL so that Eqn S11 would return Y(II) _LL under ambient CO₂ concentration and zero PPFD. α_C, V _0C, θ_C, α_V, V _0V and θ_V were derived by fitting the fluorescence data shown in Figure 2. s ₀ is the theoretical maximum value of s when f _Cyc is zero, adjusted for: $s^{\prime }=\frac{\mathrm{d}{\mathit{GA}}_{\mathrm{LOW}}}{\frac{1}{3}Y{\left(\mathit{II}\right)}_{\mathrm{LOW}}\mathrm{d}{I}_{\mathrm{Inc}}}$, modelled to fit measured values of s′ (Table S1). The Q cycle was assumed to be obligate, making f _Q = 1; Y(I) _LL was assumed to be 1, after Yin and Struik (2012). The behaviour of f _{Pseudocyc NR BS} and f _{Pseudocyc NR M} in response to CO₂ and PPFD is not well known, and therefore we assumed a low value for simplicity. The stoichiometry of the ATP synthase was set at h = 4.67 H⁺ per ATP in accordance with structural evidence (Hahn et al., ²⁰¹⁸; Vollmar et al., ²⁰⁰⁹). The operation of NDH is essential for C₄ photosynthesis, but estimates for electron flow through the complex have not yet been made, and are difficult to imagine. Here f _NDH was set to 0.4 in M cells and 0.7 in BS cells following the observation that NDH‐ and PGR5‐mediated electron flows are both operating in C₄ plants (Takabayashi et al., ²⁰⁰⁵), while keeping in mind that the relative ratio of NDH to PSI was higher in BS cells than in M cells (Ermakova, Bellasio, et al., ²⁰²¹). f _Cyc M and f _Cyc BS were fitted to maximize A at each light intensity, subject to the constraint that the activity of PPDK in BS cells is zero; fitted values are shown in Figure S3. f _RLIGHT and f _CS were set to 0.5 after von Caemmerer (2000) and Bellasio (2017). f _PEPCK was set to zero to match immunoblotting (Figure 4). f _PH is irrelevant under the previous assumption. f _MDH sets the transition between NAD‐ME and NADP‐ME subtypes and was assumed to be 1 (Gutierrez et al., ¹⁹⁷⁴; John et al., ²⁰¹⁴).

Statistical analysis

The relationship between the mean values for HL and LL plants was tested using a two‐tailed, heteroscedastic Student's t‐test, at P < 0.05 (microsoft excel® 2016; Microsoft, https://www.microsoft.com). Error propagation in the model was not analysed.

AUTHOR CONTRIBUTIONS

ME and CB conceived the project. CB developed the model and ran the simulation. CB and ME performed the experiments, analysed the data and wrote the article.

CONFLICT OF INTEREST

The authors declare that they have no conflicts of interest associated with this work.

OPEN DATA BADGES

This article has earned Open Data and Open Materials badges. Data are available in Supporting Information. Models are available on GitHub at: https://github.com/chandrabellasio/C4‐Electron‐Transportand‐biochemistry.

Supporting information

Figure S1. Schematic of the light reactions model.

Figure S2. Spectra of growth light.

Figure S3. The fitted fraction of CEF.

Table S1. C₄ photosynthesis parameters.

Table S2. Sensitivity analysis.

Note S1. A model for light reactions: ATP and NADPH production rate.

Note S2. Dark reactions and metabolite diffusion.

Note S3. Balancing NADPH demand in BS cells.

Note S4. Metabolite Fluxes between M and BS cells, and amino–group balancing.

DATA AVAILABILITY STATEMENT

Data are made available in Supporting Information, and the model coded in R and Microsoft Excel is freely available on GitHub at the link https://github.com/chandrabellasio/C4‐Electron‐Transportand‐biochemistry.