Introduction {#s1}
============

C~4~ plants have evolved a CO~2~-concentrating mechanism (CCM) that enables the elevation of CO~2~ around the active sites of Rubisco by a combination of anatomical and biochemical specialization ([@CIT0034]). C~4~ photosynthesis has independently evolved \>60 times, providing one of the most widespread and effective solutions for remedying the catalytic inefficiency of Rubisco ([@CIT0047]; [@CIT0010]). The key carboxylases in C~4~ plants are localized to different cellular compartments. Phospho*enol*pyruvate carboxylase (PEPC) is localized to the cytosol of mesophyll cells and Rubisco to the chloroplasts of bundle sheath cells. For the CCM to operate effectively, PEPC activity must exceed Rubisco activity to balance leakage of CO~2~ out of the bundle sheath compartment. This maintains a high bundle sheath CO~2~ level but prevents wasteful overcycling of the mesophyll CO~2~ 'pump' ([@CIT0056]). As PEPC utilizes HCO~3~^−^ and not CO~2~, the first committed enzyme of the C~4~ pathway is carbonic anhydrase (CA) which catalyses the reversible conversion of CO~2~ and HCO~3~^−^ in the cytosol of mesophyll cells. C~4~ acids produced by PEPC then diffuse into the bundle sheath cells where they are decarboxylated, supplying CO~2~ for Rubisco.

Within higher plants, there are multiple forms of the α-CA, β-CA, and γ-CA families which share little sequence homology ([@CIT0043]). β-CAs are the most prevalent CA family in land plants. CA is an abundant enzyme in C~3~ plants, representing up to 2% of the soluble leaf protein ([@CIT0044]). In C~3~ plants, the role of CA is unclear ([@CIT0003]) as it does not appear to limit photosynthesis but does influence stomatal conductance, guard cell movement, and amino acid biosynthesis ([@CIT0036]; [@CIT0019]; [@CIT0021]).

It has long been contended that the uncatalysed rate of CO~2~ conversion to HCO~3~^−^ is insufficient to support C~4~ photosynthetic flux ([@CIT0035]; [@CIT0003]). This hypothesis was supported by experiments in the C~4~ dicot *Flaveria bidentis*, where antisense plants with \<10% of wild-type CA activity required high CO~2~ for growth and showed reduced CO~2~ assimilation rates ([@CIT0057]; [@CIT0011]). However, in the C~4~ monocot *Zea mays* mutant plants with reduced CA activity (3% of wild type), no limitation to CO~2~ assimilation rates at ambient CO~2~ was observed ([@CIT0050]). CA activity has been shown to vary widely between species ([@CIT0012]), and it is unclear whether CA activities are limiting at high CO~2~ assimilation rates, as has previously been suggested ([@CIT0035]; [@CIT0031]).

We examined the role of CA in the model C~4~ monocot species *Setaria viridis* (green foxtail millet). *Setaria viridis* is closely related to agronomically important C~4~ crops including *Z. mays* (maize), *Sorghum bicolor* (sorghum), and *Saccharum officinarum* (sugarcane) ([@CIT0007]). It is an ideal model species due to its rapid generation time, small stature, high seed production, diploid status, and small genome that is sequenced and publicly available ([@CIT0020]; [@CIT0007]; [@CIT0040]). Here we used a stable transformation approach to examine the role of CA in *S. viridis* and could show that *S. viridis* is a useful model species that lends itself to molecular manipulation of the C~4~ photosynthetic pathway. Two constructs both targeting the major leaf β-CA (Si003882m.g) were used to generate three independent transformed lines with reduced CA activity. A strong correlation between the CO~2~ assimilation rate at low *p*CO~2~ and CA activity was observed. Our combined measurements of mesophyll conductance and CA activity suggest that increasing mesophyll conductance may be an important way to increase the CO~2~ assimilation rate at low intercellular *p*CO~2~, as may occur under drought.

Materials and methods {#s2}
=====================

Plant growth conditions {#s3}
-----------------------

T~1~ seeds were incubated in 5% liquid smoke (Wrights) for 24h to promote germination, and germinated in garden soil mix fertilized with Osmocote (Scotts, Australia) in small containers before being transferred to individual 2 litre pots. Plants were grown in controlled environmental chambers, irradiance 500 µmol photons m^−2^ s^−1^, 16h photoperiod, 28 °C day, 24 °C night, 2% CO~2~. Pots were watered daily.

Construct generation {#s4}
--------------------

Two different constructs were used to generate three lines of reduced CA activity. First, an RNAi was targeted to the primary leaf β-CA Si003882m which generated lines 2.1 and 5.3. A region of Si003882m.g was amplified by PCR using gene-specific primers ([Supplementary Table S1 at *JXB* online](#sup1){ref-type="supplementary-material"}) and reverse-transcribed RNA from *S. viridis* leaves ligated into pENTR/D-TOPO (ThermoFisher), and verified by sequencing. The fragment was inserted via a double Gateway system LR reaction (Invitrogen) into the hairpin RNAi binary vector pSTARGATE ([@CIT0032]) to form a stem--loop region under the control of the ubiquitin promoter/intron (UBI) and octopine synthase (OCS) terminator to form the RNAi vector pSG/*CAa*.

Secondly, an overexpression approach, which resulted in gene silencing, generated the third transformed line, 1.1. The coding sequence of the maize β-CA gene (GRMZM2G348512), *ZmCA2* ([@CIT0050]), was amplified by reverse transcription--PCR (RT--PCR) from total RNA extracted from B73 maize. Total RNA was isolated using hot acid phenol and chloroform, and then treated with RQ1 RNase-free DNase (Promega). The reverse transcription and PCRs were performed as per the manufacturer's protocols with Superscript II (ThermoFisher) and Phusion High-Fidelity DNA polymerase (NEB), respectively (for primers, see [Supplementary Table S1](#sup1){ref-type="supplementary-material"}). The sequence encoding an AcV5 epitope tag ([@CIT0039]) was added to the C-terminal end of *ZmCA2*. The resulting *ZmCA2* amplicon was cloned into pENTR/D-TOPO and verified by sequencing. LR Gateway cloning (ThermoFisher) was used to insert the *ZmCA2* coding sequence into the overexpression vector, pSC110. pSC110 was created by Gibson Assembly ([@CIT0029]) from two modified pMDC164 vectors ([@CIT0015]), kindly provided to us by Udo Gowik (Heinrich-Heine University, Dusseldorf, Germany). *ZmCA2* expression from pSC110 was driven by the B73 *ZmPEPC* promoter. pSC110 and pSC110/*ZmCA2* were verified by sequencing.

Both constructs were transformed into *Agrobacterium tumefaciens* strain AGL1 for stable plant transformation.

Callus induction and plant transformation {#s5}
-----------------------------------------

Stable transformation of *S. viridis* (accession A10.1) was carried out as described by [@CIT0007]. Seed coats were mechanically removed from mature *S. viridis* seeds to improve germination. Seeds were sterilized before plating on callus induction medium \[CIM; 4.3g l^−1^ Murashige and Skoog (MS) salts, pH 5.8, 10ml l^−1^ 100× MS vitamins stock, 40g l^−1^ maltose, 35mg l^−1^ ZnSO~4~·7H~2~O, 0.6mg l^−1^ CuSO~4~·5H~2~O, 4g l^−1^ Gelzan, 0.5mg l^−1^ kinetin, 2mg l^−1^ 2,4-D\]. After 4 weeks in the dark at 24 °C, any seedling structures or gelatinous calli were removed and remaining calli transferred to fresh CIM. After a further 2 weeks, calli were divided and replated onto fresh CIM. One week later, transformations were performed.

AGL1 containing the construct of interest were grown in the presence of 50 µg l^−1^ kanamycin and 50 µg l^−1^ rifampicin at 28 °C to OD~600~=0.5 and then resuspended in CIM without Gelzan and hormones. Acetosyringone (200mM) and synperonic \[0.01% (w/v)\] were added to the *Agrobacterium* solution before incubating the calli in the medium for 5min at room temperature. The calli were blotted dry on sterile filter paper and incubated at 22 °C for 3 d in the dark. The calli were then transferred to selective CIM (CIM containing 40mg l^−1^ hygromycin, 150mg l^−1^ timentin) and incubated in the dark at 24 °C for 16 d. Calli were then transferred to selective plant regeneration medium (PRM) containing 4.3g l^−1^ MS salts, pH 5.8, 10ml l^−1^ 100× MS vitamins, 20g l^−1^ sucrose, 7g l^−1^ Phytoblend, 2mg l^−1^ kinetin, 150mg l^−1^ timentin, 15mg l^−1^ hygromycin. Calli were maintained at 24 °C under a 16h light:8h dark photoperiod and a light intensity of 60 µmol photons m^−2^ s^−1^. Developing shoots were transferred to selective rooting medium (RM) containing 2.15g l^−1^ MS salts, pH 5.7, 10ml l^−1^ 100× MS vitamins, 30g l^−1^ sucrose, 7g l^−1^ Phytoblend, 150mg l^−1^ timentin, 20mg l^−1^ hygromycin. Shoots that survived and developed roots were genotyped using primers against the hygromycin phosphotransferase gene ([Supplementary Table S1](#sup1){ref-type="supplementary-material"}) by PCR, and positive transformants were transplanted to soil.

Selection of plants for analysis {#s6}
--------------------------------

The progeny of three independent T~0~ transformation events were analysed for CA hydration rates ([Supplementary Fig. S1](#sup1){ref-type="supplementary-material"}). One T~1~ plant with low CA hydration rates was selected from each transformation event (labelled 5.3, 2.1, and 1.1) and its progeny (T~2~) used for all future analysis. Two sets of experiments were performed on the T~2~ plants. First, gas exchange and biochemical analysis on lines 5.3, 2.1, and 1.1 ([Table 1](#T1){ref-type="table"}) and, secondly, gas exchange and oxygen discrimination on lines 5.3 and 1.1 ([Table 2](#T2){ref-type="table"}). Each T~2~ plant was genotyped prior to experiments using primers against the hygromycin phosphotransferase gene ([Supplementary Table S1](#sup1){ref-type="supplementary-material"}). The progeny of a plant which went through the *S. viridis* transformation process and tested negative for the hygromycin phosphotransferase gene were used as null controls.

###### 

Physiological and biochemical characteristics of CA transformants under ambient CO~2~ conditions

Net CO~2~ assimilation rate (*A*), stomatal conductance (*g*~s~), mesophyll *p*CO~2~ (*C*~m~), the rate constant of CA hydration (*k*~CA~), and enzyme activities were measured from the uppermost, fully expanded leaf of 5-week-old plants grown at 2% CO~2~. Gas exchange measurements were made at 25 °C leaf temperature, flow rate at 500 µmol m^−2^ s^−1^, and irradiance of 1500 µmol photons m^−2^ s^−1^. Three T~2~ plants from three different transformation events were measured.

             *A*          *g* ~s~       *C* ~m~        *k* ~CA~      Rubisco      PEPC           NADP-ME
  ---------- ------------ ------------- -------------- ------------- ------------ -------------- ------------
  **Null**   22.5±0.6 a   0.19±0.01 a   132.4±3.3 a    6.1±0.8 a     18.7±1.5 a   229.6±19.3 a   59.8±4.3 a
  **5.3**    21.7±2.6 a   0.2±0.02 a    118.9±13.1 a   3.3±0.2 b     18.8±1.8 a   249.3±24.6 a   54.5±5.8 a
  **2.1**    18.5±1.9 a   0.16±0.01 a   152.9±15.2 a   2.0±0.2 b,c   20.9±2.9 a   181.5±25.4 a   47.3±2.6 a
  **1.1**    19.1±1.2 a   0.19±0.02 a   153.9±4.4 a    0.8±0.1 c     19.7±1.8 a   180.3±18.4 a   43.6±3.9 a

Significant differences are based on one-way ANOVA and Tukey post-hoc analysis (SPSS statistics version 22; *P*=0.05).

###### 

Physiological characteristics of CA transformants at ambient CO~2~ measured using LI-6400XT coupled to a tunable diode laser

Net CO~2~ assimilation rate (*A*), stomatal conductance (*g*~s~), mesophyll *p*CO~2~ (*C*~m~), the ratio of intercellular to ambient *p*CO~2~ (*C*~i~/*C*~a~), the rate constant of CA hydration (*k*~CA~), online Δ^18^O discrimination, and the length of mesophyll cells exposed to intercellular airspace (*S*~m~) were measured on the uppermost, fully expanded leaf of 5-week-old plants grown at 2% CO~2~. Gas exchange measurements were made at 2% O~2~, 25 °C leaf temperature, flow rate at 500 µmol m^−2^ s^−1^, and irradiance of 1500 µmol photons m^−2^ s^−1^. Three T~2~ plants from two different transformation events were measured.

             *A*          *g* ~s~       *C* ~m~        *C* ~i~/*C*~a~   *k* ~CA~    Δ^18^O         *S* ~m~
  ---------- ------------ ------------- -------------- ---------------- ----------- -------------- ------------
  **Null**   30.0±1.4 a   0.30±0.03 a   144.6±5.9 a    0.39±0.03 a      8.4±0.7 a   18.0±1.4 a     10.2±0.4 a
  **5.3**    29.2±0.9 a   0.29±0.02 a   157.9±10.5 a   0.34±0.01 a      2.5±0.3 b   13.6±0.7 a,b   --
  **1.1**    24.5±1.6 a   0.26±0.03 a   178.1±13.5 a   0.43±0.02 a      0.8±0.2 b   10.9±0.6 b     10.2±0.9 a

Significant differences are based on one-way ANOVA and Tukey post-hoc analysis (SPSS statistics version 22; *P*=0.05).

Insertion number estimation {#s7}
---------------------------

DNA was isolated from a fully expanded leaf using a CTAB (cetyltrimethylammonium bromide) extraction buffer \[2% CTAB (v/v), 20mM Tris--HCl pH 8, 1.4M NaCl, 20mM EDTA, 1% polyvinylpyrrolidone (PVP)-40 (w/v), 0.2% (v/v) β-mercaptoethanol\] followed by extraction with phenol/chloroform/isoamylalcohol (25:24:1) and ethanol clean-up. DNA quality and quantity was determined using a NanoDrop spectrophotometer (Thermo Scientific).

IDNA genetics (UK) performed quantitative real-time PCR (qPCR) analysis to estimate the numbers of transgene copies in the CA transformed lines following the procedure described in [@CIT0005] with some modifications. The hygromycin phosphotransferase gene (with a FAM reporter) and the internal positive control (IPC, with a VIC reporter) were amplified together in a multiplex reaction (15min denaturation, then 40 cycles of 15s at 95 °C and 60s at 60 °C) in an ABI1900 real-time PCR machine. Fluorescence from the FAM and VIC fluorochromes was measured during each 60 °C step and the Ct values obtained. The difference between the Ct values for the hygromycin phosphotransferase gene and the IPC (the Delta Ct) was used to allocate the assayed samples into groups with the same gene copy number.

RNA extraction and reverse transcription--quantitative PCR (RT--qPCR) {#s8}
---------------------------------------------------------------------

Leaf discs (0.78cm^2^) frozen and stored at −80 °C were lysed using the Qiagen TissueLyser II. RNA was extracted using the Trizol extraction method and in the presence of RNase inhibitor (Ambion). DNA was removed using the TURBO DNA free kit (Ambion), and RNA quantity and quality were determined using a NanoDrop (Thermo Scientific).

RNA (200ng) was reverse transcribed into cDNA using Qiagen's RT^2^ HT First Strand cDNA synthesis kit. RT--qPCR and melt curve analysis were performed on a Viia7 Real-time PCR system using the Power SYBR green PCR Master Mix (Thermo Fisher) according to the manufacturer's instructions. Primers ([Supplementary Table S1](#sup1){ref-type="supplementary-material"}) were designed using Primer3 in Geneious R7.1.6, ensuring products spanned an intron. Primer amplification efficiencies were determined by the Ct slope method; efficiencies for all primer pairs were comparable (\~95%) and no amplification was detected in the no template control. Relative fold change was calculated by the ΔΔCt method, using the average of three nulls as reference, as described by [@CIT0041]. The geometric mean of the Ct values for three reference genes was used for normalization ([@CIT0052]). Statistics were performed with SigmaPlot (version 11.0).

Determination of enzyme activities {#s9}
----------------------------------

For CA activity, leaf discs (0.78cm^2^) were collected from the uppermost fully expanded leaf of 5-week-old *S. viridis* plants and frozen in liquid nitrogen. Soluble protein was extracted by grinding one frozen leaf disc in ice-cold glass homogenizers (Tenbroek) in 500 µl of extraction buffer \[50mM HEPES, pH 7.8, 1% (w/v) PVP, 1mM EDTA, 10mM dithiothreitol, 0.1% (v/v) Triton X-100, 2% (v/v) protease inhibitor cocktail (Sigma)\]. Crude extracts were centrifuged at 4 °C for 1min at 13 000 *g* and the supernatant collected for the soluble CA assay. Activity was measured on a membrane inlet mass spectrometer to measure the rates of ^18^O exchange from labelled ^13^C^18^O~2~ to H~2~^16^O at 25 °C ([@CIT0002]; [@CIT0057]). The hydration rates were calculated as described by [@CIT0037].

For Rubisco, PEPC, and NADP-malic enzyme (ME) activities, soluble protein was extracted from fresh leaf discs collected from leaves used for gas exchange analysis. Spectrophotometric assays were then performed as described previously ([@CIT0045], [@CIT0046]; [@CIT0049]).

Gas exchange measurements {#s10}
-------------------------

Net photosynthesis (*A*) was measured over a range of intercellular *p*CO~2~ (*C*~i~) on the uppermost, fully expanded leaf of 5-week-old *S. viridis* plants using a portable gas exchange system LI-COR 6400XT (LI-COR Biosciences). Measurements were made after leaves had equilibrated at 380 µbar, flow rate 500 µmol s^−1^, leaf temperature 25 °C, and irradiance 1500 µmol photons m^−2^ s^−1^. CO~2~ response curves were measured in a stepwise increase (3min intervals) in CO~2~ partial pressure 380, 0, 23.75, 47.5, 71.25, 95, 142.5, 190, 285, 380, 570, 760, and 950 µbar whilst maintaining leaf temperature and irradiance conditions.

Measurements of C^18^O^16^O discrimination (Δ^18^O) {#s11}
---------------------------------------------------

Simultaneous measurements of exchange of CO~2~, H~2~O, C^18^O^16^O, and H~2~^18^O were made by coupling two LI-6400XT gas exchange systems to a tunable diode laser (TDL: TGA200A, Campbell Scientific Inc., Logan, UT, USA) to measure C^18^O^16^O and a Cavity Ring-Down Spectrometer (L2130-i, Picarro Inc., Sunnyvale, CA, USA) to measure the oxygen isotope composition of water vapour. The system is essentially that described by [@CIT0051] except that the TGA100 was replaced by a TGA200A and the additional laser for water vapour measurements has been added together with a 16 port distribution manifold. To generate gas flows to the gas exchange systems, N~2~ and O~2~ were mixed by mass flow controllers (Omega Engineering Inc., Stamford, CT, USA) to generate CO~2~-free air with 2% O~2~. The humidity of incoming air was adjusted by varying the temperature of water circulating around a Nafion tube (Permapure, MH-110-12P-4) but was kept constant in this set of experiments to supply water vapour of a constant ^18^O composition. To supply flow to the TDL and the L2130-i from the sample and reference gas streams, two T junctions were inserted into the match valve tubing and in the reference line of the LI-6400XT, respectively. This allowed leaves of two plants to be measured in sequence, with each LI-6400XT sampled by the TDL at 4min intervals for 20s at the sample and reference line. The Picarro Cavity Ring Down spectrometer sampled for 3min, so that leaves were sampled at 6min intervals.

[Supplementary Fig. 5](#sup1){ref-type="supplementary-material"} shows the CO~2~ dependence of the standard error of δ^18^O of CO~2~ in the reference gas of repeated measurements on the TGA200A. The ^18^O isotopic composition of the CO~2~ calibration gas was 22.17±0.04‰ for Vienna mean oceanic water (VSMOW) and was checked against standards on an Isoprime mass spectrometer. We monitored the ^18^O composition of water vapour of the reference air streams daily, and the values were −6.07±0.08‰ and −6.34±0.08‰ (VSMOW) for LI-6400XT L1 and L2 references, respectively. We attribute the small difference between the reference lines to differences in the Nafion tubing. At the end of the experiment, the calibration of the Picarro L2130-i was confirmed by collecting water vapour samples from the gas stream of the LI-6400XT reference lines going to the Picarro as described by [@CIT0011] and assaying these water samples against standards on a Picarro 1102i, which was set up to measure the ^18^O isotopic composition of water samples.

Gas exchange was measured on the uppermost fully expanded leaf of 5-week-old *S. viridis* plants at 25 °C, and leaves were equilibrated at ambient CO~2~ (380 µbar), irradiance 1500 µmol photons m^−2^ s^−1^, and 2% O~2~. The flow rate was 200 µmol s^−1^. CO~2~ concentration was adjusted from 380 to 760, 570, 380, and 190 µbar at 1h intervals. Immediately following gas exchange measurements, leaf discs were collected and stored at −80 °C until measurements of CA activity were made.

Calculations of C^18^O^16^O (Δ^18^O) discrimination and mesophyll conductance (*g*~m~) {#s12}
--------------------------------------------------------------------------------------

Discrimination against ^18^O in CO~2~ during photosynthesis, Δ^18^O, was calculated from the isotopic composition of the CO~2~ entering δ~in~ and exiting δ~out~ the leaf chamber and the CO~2~ concentration entering *C*~in~ and exiting *C*~out~ (all measured with the TDL) ([@CIT0022]; [@CIT0004];):

Δ

18

O

=

ξ

(

δ

o

u

t

−

δ

i

n

)

1

\+

δ

o

u

t

−

ξ

(

δ

o

u

t

−

δ

i

n

)

where ξ=*C*~in~/*C*~in~--*C*~out~. Sample streams were passed through a Nafion drying tube before entering the TDL, and CO~2~ values presented are all at zero water vapour concentration.

Following the derivation by [@CIT0004] and [@CIT0025] photosynthetic Δ^18^O discrimination was used to calculate *p*CO~2~ in the mesophyll cytosol, *C*~m~, with the assumption that *C*~m~ is equal to the *p*CO~2~ at the site of CO~2~--H~2~O exchange and assuming that cytosolic CO~2~ is in full isotopic equilibrium with local cytosolic water. This allowed *g*~m~ to be calculated from

g

m

=

A

/

(

C

i

−

C

m

)

C

m

=

C

i

(

δ

i

−

a

w

−

δ

A

(

1

\+

a

w

)

δ

c

−

a

w

−

δ

A

(

1

\+

a

w

)

)

Equation 3 is the same as equation 21 of [@CIT0004], and is a rearrangement of equation 18 of [@CIT0025] using their notation. The oxygen isotope ratios are expressed relative to the standard, (VSMOW) $$. Intercellular *p*CO~2~ is denoted by *C*~i~, and *a*~w~ is the discrimination against C^16^O^18^O during liquid phase diffusion and dissolution (0.8‰).

The isotopic composition of CO~2~ being assimilated, δ~A~, is given by

δ

A

=

δ

a

−

Δ

18

O

1

\+

Δ

18

O

,

where δ~a~ is the isotopic composition of ambient air (in our case δ~a~=δ~out~).

The oxygen isotope composition of CO~2~ in the intercellular airspaces, δ~i~, including ternary corrections proposed by [@CIT0025], is given by

δ

i

=

δ

i

o

\+

t

\[

δ

A

(

C

a

C

i

\+

1

)

−

δ

a

C

a

C

i

\]

1

\+

t

where *C*~a~ is the *p*CO~2~ in the ambient air. The ternary correction factor, *t*, is given by

t

=

(

1

\+

a

18

b

s

1000

)

E

2

g

a

c

where *g*~ac~ is the total conductance to CO~2~, *E* the transpiration rate, and *a*~18bs~ is the weighted discrimination of C^16^O^18^O diffusion across the boundary layer and stomata in series given by:

a

18

b

s

=

(

C

a

−

C

s

)

a

18

b

−

(

C

s

−

C

i

)

a

18

s

(

C

a

−

C

i

)

where *C*~s~ is the *p*CO~2~ at the leaf surface and *a*~18s~ and *a*~18b~ are the discriminations against C^16^O^18^O through stomata and the boundary layer (8‰ and 5.8‰, respectively).

The isotopic composition of intercellular CO~2~ ignoring ternary corrections is given by

δ

i

o

=

δ

A

(

1

−

C

a

C

i

)

(

1

\+

a

18

b

s

)

−

C

a

C

i

(

δ

a

−

a

18

b

s

)

\+

a

18

b

s

To calculate *C*~m~, we assume that the isotopic composition of CO~2~ in the cytosol, δ~c~, is the isotopic composition of CO~2~ equilibrated with cytosolic water, δ~cw~, and

δ

cw

=

δ

w

\+

ε

w

where δ~w~ is the stable oxygen isotope composition of water in the cytosol at the site of evaporation and ε~w~ is the isotopic equilibrium between CO~2~ and water (dependent on temperature *T*~K~ in K ([@CIT0004], and references therein).

ε

w

(

‰

)

=

17604

T

K

−

17.93

Calculation of the isotopic composition of water at the site of evaporation from the isotopic composition of transpired water {#s13}
-----------------------------------------------------------------------------------------------------------------------------

The isotopic composition of water at the site of evaporation, δ~w~, can be estimated from the Craig and Gordon model of evaporative enrichment ([@CIT0014]; [@CIT0026])

δ

w

=

δ

t

\+

ε

\*

\+

ε

k

\+

e

a

e

i

(

δ

w

a

−

ε

k

−

δ

t

)

where ε\* is the equilibrium fractionation during evaporation, ε~k~ is the kinetic fractionation during vapour diffusion in air, δ~t~ is the oxygen isotopic composition of transpired water, *e*~a~/*e*~i~ is the ratio of ambient to intercellular vapour pressure, and δ~a~ is the isotopic composition of ambient air. ε\* is dependent on temperature:

ε

\*

=

2.644

−

3.206

(

10

3

T

K

)

\+

1.534

(

10

6

T

K

2

)

ε~k~ is dependent on stomatal and boundary layer conductances and associated fractionation factors ([@CIT0004], and references therein):

ε

k

=

28

g

s

−

1

\+

19

g

b

−

1

g

s

−

1

\+

g

b

−

1

The isotopic composition of transpired water δ~t~ can be calculated from mass balance knowing the isotopic composition of the water entering δ~win~ and exiting δ~wout~ the leaf chamber (measured with the Picarro) and the water vapour concentration entering *w*~in~ and exiting *w*~out~ (measured with the LI-6400XT):

δ

t

=

(

δ

w

o

u

t

(

1

−

w

i

n

)

−

δ

w

i

n

w

i

n

w

o

u

t

(

1

−

w

o

u

t

)

)

w

o

u

t

w

o

u

t

−

w

i

n

Calculation of the proportion of mesophyll cytosolic CO~2~ in equilibration with leaf water, θ {#s14}
----------------------------------------------------------------------------------------------

If *C*~m~ is known, it is possible to calculate the isotopic composition of cytosolic CO~2~ from measurements of Δ^18^O using equation 18 from [@CIT0025]:

δ

c

=

δ

A

(

1

−

C

i

C

m

)

(

1

\+

a

w

)

\+

C

i

C

m

(

δ

i

−

a

w

)

\+

a

w

.

This can then be compared with δ~cw~ (Equation 9), the isotopic composition of CO~2~ in equilibrium with water at the site of evaporation. We calculated mesophyll conductance, *g*~m~, in the *S. viridis* null plants assuming that δ~c~=δ~cw~ and then used this *g*~m~ to estimate *C*~m~ in the *S. viridis* transgenics to calculate the proportion of cytosolic CO~2~ in equilibration with leaf water, θ using equations developed by [@CIT0008]

θ

=

δ

c

−

δ

a

\+

a

18

(

1

\+

C

c

C

a

)

δ

c

w

−

δ

a

\+

a

18

(

1

\+

C

c

C

a

)

where *a*~18~ is the weighted discrimination of C^16^O^18^O diffusion across the boundary layer, stomata, and the liquid phase in series given by:

a

18

=

a

b

(

C

a

−

C

s

)

\+

a

s

(

C

s

−

C

i

)

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Leaf anatomical measurements and estimation of *g*~m~ from anatomical measurements {#s15}
----------------------------------------------------------------------------------

Fully expanded leaves from 5-week-old T~2~ plants, null and line 1.1, were collected and cut into \~0.5×2mm pieces. Leaf slices were fixed in 2.5% (v/v) glutaraldehyde, 2% (v/v) paraformaldehyde, 0.1M phosphate buffer, and 0.01% (v/v) Tween-20 under vacuum for 20min, then replaced with buffer containing no Tween-20 and fixed overnight at 4 °C. Leaf pieces were washed in phosphate buffer and post-fixed in 1% (w/v) osmium tetroxide for 2h. Fixed leaf pieces were then dehydrated in an ethanol series (10, 30, 50, 70, 80, 95, 100%) followed by infiltration with LR white. Leaf sections were finally placed in moulds filled with resin and baked at 60 °C for 24h. Sections of 0.5 µm thickness were cut using glass knives on a Reichert ultramicrotome, stained with toluidine blue, and heat fixed to glass slides. Slides were viewed using a Zeiss Axioskop light microscope at ×400 magnification. Three images were taken from each slide for analysis, each containing a leaf cross-section in the same orientation and showing at least two vascular bundles. Fiji quantification software ([@CIT0048]) was used to select regions of interest. Mesophyll surface area exposed to intercellular airspace to leaf area ratio (*S*~m~) was calculated using Equation 18 where CCF is the curvature correction factor of 1.43 ([@CIT0023]).

S

m

=

Length of mesophyll cells exposed to intercellular airspace

Interveinal distance

×

CCF

The values of *S*~m~ together with measurements of cell wall thickness and cytosol thickness were used to derive an estimate of *g*~m~ from anatomical parameters. The cell wall thickness (0.113±0.005 μm) was kindly estimated from transmission electron micrographs of *S. viridis* grown under similar conditions by Florence Danila ([@CIT0016]). Calculations followed equations 1--5 of [@CIT0054] using the membrane permeability of Gutknecht for a lipid bilayer of 3.5×10^--3^ m s^−1^ since only the plasma membrane needs to be transversed for diffusion of CO~2~ from he intercellular airspace to mesophyll cytosol ([@CIT0033]) and a cytosol thickness of 0.3 μm ([@CIT0054]). These calculations give a *g*~m~ of 0.68mol m^−2^ s^−1^ bar^−1^.

Statistical analysis {#s16}
--------------------

One-way ANOVAs with post-hoc Tukey test analyses were performed for all measurements of gas exchange and enzyme activities with *P*=0.05 using the IBM SPSS Statistics 22 package.

Results {#s17}
=======

Generation of transgenic S. viridis with reduced β-CA {#s18}
-----------------------------------------------------

In *S. viridis* we identified four β-CA genes: Si002140m.g (with one other isoform Si002148m), Si002669m.g, Si030616m.g (with two other isoforms Si030928m and Si030803m), and Si003882m.g. There is very low sequence identity between these β-CA genes, \~37% ([Supplementary Fig. S2](#sup1){ref-type="supplementary-material"}). Si003882m.g has been shown to be the major leaf β-CA ([@CIT0009]; [@CIT0038]).

Three independent transformation events resistant to hygromycin and with reduced CA activity were generated using two different approaches. First, one line (1.1) was generated through gene suppression upon transformation with the overexpression construct pSC110/*ZmCA2*. The coding sequences of *ZmCA2* and Si003882m.g show 87% identity ([Supplementary Fig. S3](#sup1){ref-type="supplementary-material"}). Most probably, expression of *ZmCA2* therefore caused suppression of the primary *S. viridis* β-CA gene, resulting in reduced CA activity in line 1.1. The second approach was to target Si003882m.g using the RNAi construct pSG/*CAa* which generated stably transformed lines from two different events (2.1 and 5.3). Plants were grown at high *p*CO~2~ for all experiments.

To determine the specificity of the RNAi construct and check which β-CA was suppressed in line 1.1, RT--qPCR was performed against the β-CAs in *S. viridis*. Expression of the primary leaf β-CA Si003882m.g was significantly down-regulated, between 83% and 96%, in lines from all three transformation events ([Fig. 1A](#F1){ref-type="fig"}). Transcript levels of Si030616m.g and Si002140m.g were unchanged relative to expression in the null plants ([Fig. 1B](#F1){ref-type="fig"}, [C](#F1){ref-type="fig"}) while Si002669m.g transcript was undetectable in all samples (data not shown). Therefore, expression of only the target β-CA gene was affected in the three transformed lines.

![Expression level of β-CA transcripts. (A) Si003882m.g, (B) Si002140m.g, and (C) Si030616m.g in null control and CA transformed lines 1.1, 2.1, and 5.3 as measured by RT--qPCR and analysed by ΔΔCt. Fold change relative to the null transformant is shown; bars represent mean fold change, and circles show the data range of T~2~ plants (*n*=5--7 plants) from each transformation event measured in triplicate. The dotted line indicates average null fold change. Expression level of the major leaf β-CA transcript Si003882m.g (A) is significantly lower compared with the null control in all three transformed lines, calculated using one-way ANOVA.](erw35701){#F1}

qPCR was used to estimate the number of insertions in the transgenic plants, based on the number of copies of the hygromycin phosphotransferase gene. Three T~2~ plants of the three lines were analysed and there were two, four, and more than four transgene insertions detected for plants of line 5.3, 2.1, and 1.1, respectively. The high copy number in the overexpressing line of 1.1 is the likely cause of the suppression of transcript accumulation.

CA and photosynthetic enzyme activity and leaf anatomy {#s19}
------------------------------------------------------

T~1~ progeny of the three independent transformation events showed a range of CA hydration rates as measured on the soluble leaf fraction on a membrane inlet mass spectrometer. Compared with the null control, lines 1.1, 2.1, and 5.3 had on average (*n*=7 T~2~ plants) an 87, 70, and 50% reduction of CA activity, respectively ([Fig. 2](#F2){ref-type="fig"}). The CA hydration rate in the null plants was 934±92 µmol m^−2^ s^−1^ as calculated at a mesophyll *p*CO~2~ (*C*~m~) of 140 µbar (Equation 2).

![Range of CA hydration rates at mesophyll *p*CO~2~ (*C*~m~) measured using a membrane inlet mass spectrometer in the null control and T~2~ plants from lines 5.3, 2.1, and 1.1.](erw35702){#F2}

The activities of the photosynthetic enzymes Rubisco, PEPC, and NADP-ME were unchanged in lines 5.3, 2.1, and 1.1 compared with the nulls ([Table 1](#T1){ref-type="table"}) and showed no correlation with CA hydration rates (one-way ANOVA and Tukey post-hoc analysis (SPSS statistics version 22; *P*=0.05).

No significant differences were observed for the surface area of mesophyll cells exposed to intercellular airspace per unit leaf area (*S*~m~) in embedded leaf sections of nulls (10.22±0.35 m^2^ m^−2^) and plants from line 1.1 (10.18±0.95 m^2^ m^−2^). These anatomical measurements were used to estimate an anatomical *g*~m~ of 0.68mol m^−2^ s^−1^ bar^−1^ (see the Materials and methods).

CA activity and CO~2~ assimilation rates {#s20}
----------------------------------------

The response of CO~2~ assimilation rate (*A*) to increasing intercellular *p*CO~2~ (*C*~i~) was investigated to examine the effect of reduced CA activity on CO~2~ assimilation rates ([Fig. 3](#F3){ref-type="fig"}). There were no statistical differences in the maximum rate of CO~2~ assimilation under ambient or high CO~2~ conditions between null control and progeny of transformant lines. At low *p*CO~2~, CO~2~ assimilation rates were reduced to varying degrees in the progeny of the transformed lines compared with the null control. Individuals of line 1.1 with the lowest CA hydration rate had the lowest initial slopes of the *AC*~i~ curves. The initial slopes of the *AC*~i~ and *AC*~m~ curve were plotted against the CA hydration rate constant (*k*~CA~; [Fig. 4](#F4){ref-type="fig"}). Mesophyll cytosolic *p*CO~2~, *C*~m~, was calculated from Equation 2, using the average null *g*~m~ (0.9mol m^−2^ s^−1^ bar^−1^) since there was no difference in *S*~m~. A strong correlation between the initial slope from the *AC*~m~ curve and *k*~CA~ was observed, with the initial slope increasing as CA hydration rates increase (*R*^2^=0.845; [Fig. 4](#F4){ref-type="fig"}). There was a curvilinear response between the initial slope of the *ACi* curves indicating other limitations. No difference in stomatal conductance (*g*~s~) was observed across a range of intercellular *p*CO~2~ between null controls and any of the transformed lines during the rapid measurements of CO~2~ responses ([Fig. 5](#F5){ref-type="fig"}).

![CO~2~ assimilation rate of transformed lines over a range of intercellular *p*CO~2~ (*C*~i~). Average of three T~2~ plants from each line. Plants were grown at 2% CO~2~, and the uppermost, fully expanded leaves of 5-week-old plants were measured using a LI-6400XT at 25 °C leaf temperature at an irradiance of 1500 µmol photons m^−2^ s^−1^. Arrows mark ambient *p*CO~2~ for each line; note that the dotted arrow is line 1.1.](erw35703){#F3}

![Relationship between the initial slope of the *AC*~m~ (triangles) or *AC*~i~ (circles) curves and the rate constant of CA hydration rates (*k*~CA~), *AC*~m~*R*^2^=0.846. Each point represents a measurement made on an individual leaf of a T~2~ plant.](erw35704){#F4}

![Stomatal conductance (*g*~s~) over a range of intercellular *p*CO~2~ (*C*~i~). Measurements were made concurrently with those in [Fig. 4](#F4){ref-type="fig"}.](erw35705){#F5}

Oxygen isotope discrimination measurements {#s21}
------------------------------------------

Oxygen (∆^18^O) isotope discrimination and CO~2~ assimilation rates were measured in response to changes in *p*CO~2~ using a LI-6400XT coupled to a TDL trace gas analyser to measure C^18^O^16^O and a Cavity Ring-Down Spectrometer to measure the oxygen isotope composition of water vapour. Transformed plants with reduced CA hydration rates had lower ∆^18^O compared with the nulls, but only line 1.1 was significantly lower ([Table 2](#T2){ref-type="table"}).

In the null controls, measurements of ∆^18^O were used to estimate conductance of CO~2~ from the intercellular airspace to the sites of CO~2~ and H~2~O exchange in the cytosol (*g*~m~) with the assumption that CO~2~ was in full isotopic equilibrium with leaf water in the cytosol (Equation 2; [Fig. 6](#F6){ref-type="fig"}). Although *g*~m~ appeared to increase with decreasing *C*~i~, there were no significant differences between *g*~m~ estimated at the different *C*~i~, and the average value was 0.94±0.06mol m^−2^ s^−1^ bar^−1^ ([Fig. 6B](#F6){ref-type="fig"}). *C*~i~--*C*~m~ indicates the drawdown of CO~2~ from the intercellular airspace to the site of fixation, and for the null controls there is an increasing gradient of *p*CO~2~ as *C*~i~ increases ([Fig. 6C](#F6){ref-type="fig"}).

![(A) CO~2~ assimilation rate, (B) mesophyll conductance (*g*~m~; Equation 2), and (C) *C*~i~--*C*~m~ over a range of intercellular *p*CO~2~ in null controls measured using a LI-6400XT coupled to a tunable diode laser. Plants were grown at 2% CO~2~ and the uppermost, fully expanded leaves of 5-week-old plants were measured at 25 °C leaf temperature, flow rate 200 µmol m^−2^ s^−1^, 2% O~2~ at an irradiance of 1500 µmol photons m^−2^ s^−1^.](erw35706){#F6}

∆^18^O at ambient *p*CO~2~ showed statistically significant differences between line 1.1 (with the lowest CA activity) and null plants ([Table 2](#T2){ref-type="table"}). When plotted against *C*~m~/*C*~a~, ∆^18^O measurements closely correspond to theoretical curves representing θ (Equation 16) under different scenarios either where cytosolic CO~2~ is at full isotopic equilibrium with the cytosolic water (null lines) or where there is only partial equilibrium (such as line 1.1; [Fig. 7](#F7){ref-type="fig"}). Calculated values for line 5.3 which showed a 50% reduction in CA activity relative to the null controls fell in between these two theoretical lines. This is illustrated again with theta (θ) of lines 1.1 and 5.3 over a range of *C*~m~ ([Fig. 8](#F8){ref-type="fig"}). When CO~2~ is at full isotopic equilibrium with the cytosolic water, θ would be 1, whereas in lines 1.1 and 5.3 (with reduced CA hydration rates relative to the null control) θ is \<1. There was no CO~2~ dependence of θ over the range of *p*CO~2~ measured.

![Oxygen isotope discrimination (Δ^18^O) as a function of the ratio of mesophyll *p*CO~2~ to ambient *p*CO~2~ (*C*~m~/*C*~a~) in null and lines 5.3 and 1.1. Each point represents a measurement made on an individual leaf of a T~2~ plant. Triangular symbols represent measurements made at low *p*CO~2~. Theoretical curves represent the scenario where cytosolic CO~2~ is at full isotopic equilibrium with cytosolic water (θ=1, black) or under partial equilibrium (θ=0.5, grey) of ^18^O in the leaf. The equations for the curves are given by $$ and *a*~18~=5.85‰ and δ~c~--δ~a~=33‰ at full equilibration or *a*~18~=5.1‰ and δ~c~--δ~a~=15‰ ([@CIT0026]).](erw35707){#F7}

![Average isotopic equilibrium (theta, θ) over a range of mesophyll *p*CO~2~ in two reduced CA lines 5.3 (grey) and 1.1 (white). Measured values of θ were determined from Δ^18^O using Equation 16. Each point represents the average measurement of three T~2~ plants.](erw35708){#F8}

Discussion {#s22}
==========

*Setaria viridis* as a model species to study photosynthetic physiology in a C~4~ monocot {#s23}
-----------------------------------------------------------------------------------------

*Flaveria bidentis*, a readily transformable model C~4~ dicot, has been successfully used to study the regulation of C~4~ photosynthesis using antisense and RNAi technology ([@CIT0028]; [@CIT0042]; [@CIT0057]; [@CIT0046]). This work has been crucial in quantifying the rate-limiting steps in the C~4~ pathway by 'titrating' out levels of target enzymes by gene suppression and observing the effects on physiological characteristics of the resultant transgenics ([@CIT0028]). There are, however, important differences between C~4~ dicots and the C~4~ monocots which make up the majority of agriculturally important C~4~ species. *Setaria viridis* has emerged as a new model grass to study C~4~ photosynthesis in crops and related bioenergy species. *Setaria viridis* is an appropriate biochemical model species for *Z. mays* and *S. bicolor* as all three use NADP-ME as the primary decarboxylation enzyme. We generated transgenic *S. viridis* plants with reduced CA activity to compare the effect with previous results obtained with *F. bidentis* and *Z. mays* ([@CIT0057]; [@CIT0050]) and to explore the effect that a reduction in CA activity has on the initial slope of the *AC*~i~ and *AC*~m~ curves. In these lines, only the major leaf isoform of β-CA was reduced ([Fig. 1](#F1){ref-type="fig"}). The transgenic plants had a range of different CA activities ([Fig. 2](#F2){ref-type="fig"}), but showed no changes in PEPC and Rubisco activity ([Table 1](#T1){ref-type="table"}) or anatomical parameters ([Table 2](#T2){ref-type="table"}), making these plants ideal for exploring the role of CA activity in *S. viridis*.

Initial slope of *AC*~i~ curves in C~4~ plants {#s24}
----------------------------------------------

Models of C~4~ photosynthesis suggest that the initial slope of the *AC*~i~ curve is determined by three possible limitations: (i) the mesophyll conductance to CO~2~ diffusion from the intercellular airspace to the mesophyll cytosol (*g*~m~); (ii) the rate of CO~2~ hydration by CA; and (iii) the rate of PEP carboxylation ([@CIT0053]). However, it is not readily known which is the major limitation in C~4~ species. Studies with PEPC mutants from the C~4~ dicot *Amaranthus edulis* indicate that PEPC activity may not be the major limitation as a 60% reduction in PEPC leads to only a 20% reduction in the CO~2~ assimilation rate at ambient *p*CO~2~ accompanied by a small reduction in initial slope for the *AC*~i~ curves ([@CIT0018]; [@CIT0017]; [@CIT0013]). This study with *S. viridis* confirms that substantial reductions in CA activity are possible before a reduction in steady-state CO~2~ assimilation rate and initial slope of the *AC*~i~ curve are observed. This is in accordance with previous observations in *F. bidentis* and *Z. mays* ([@CIT0057]; [@CIT0050]).

The Michaelis--Menten constant for CO~2~ for CA is \>2mM (\~5% CO~2~) which makes it appropriate to quantify CA activity by its first-order rate constant ([@CIT0037]; [@CIT0035]) and simplifies species comparisons. In *S. viridis*, the lowest rate constant recorded was 0.8mol m^−2^ s^−1^ bar^−1^ compared with values of 0.1 for the *ca1ca2* double mutant in *Z. mays* and 0.47 for transgenic *F. bidentis* ([@CIT0057]; [@CIT0050]). With this low rate constant, *F. bidentis* had very low CO~2~ assimilation rates and the CO~2~ response curves did not saturate at high CO~2~. In contrast, for both *S. viridis* transgenics and *Z. mays* mutants, CO~2~ assimilation rates were only slightly less than in the controls, suggesting that *S. viridis* is more similar to *Z. mays* in its CA requirements. This suggests that these two monocot species can make better use of leaf CA activity or that *in vivo* CA activity is greater than that estimated *in vitro*.

Mesophyll conductance and the initial slope of *AC*~m~ curves {#s25}
-------------------------------------------------------------

Next, we used recently established techniques that utilize ^18^O discrimination measurements to quantify *g*~m~ in our null controls ([Fig. 6B](#F6){ref-type="fig"}; [@CIT0004]). This estimates the diffusion of CO~2~ from the intercellular airspace through the cell wall, plasma membrane, and cytosol to the sites of CA activity. At ambient *p*CO~2~, the *g*~m~ observed for the null plants were similar to those reported by [@CIT0004]. A key assumption for the calculation of *g*~m~ is that CA activity is not limiting and that CO~2~ is in isotopic equilibrium with HCO~3~^−^; consequently *g*~m~ was not measured in the transgenic lines with reduced CA activity. In C~3~ species, *g*~m~ (in this instance from the intercellular airspace to the chloroplast stroma) has been shown to be proportional to the chloroplast surface area appressing the intercellular airspace per unit leaf area ([@CIT0023]). [@CIT0024] hypothesized that in C~4~ species *g*~m~ may correlate with the mesophyll surface area exposed to intercellular airspace per unit leaf area (*S*~m~). Since *S*~m~ was similar between the nulls and line 1.1 plants, we assumed that *g*~m~ may also be similar between the plants. In C~3~ species, *g*~m~ has been shown to, in some instances, increase with decreasing *p*CO~2~ ([@CIT0027]; [@CIT0051]; [@CIT0001]). These changes to *g*~m~ which may be important in regulating and maintaining photosynthesis were also observed here in the *S. viridis* null plants, with *g*~m~ increasing slightly at low *p*CO~2~. However, because the differences in *g*~m~ at different *p*CO~2~ were not significant, we used the average *g*~m~ estimated for the null plants to calculate mesophyll cytosolic *p*CO~2~ (*C*~m~) in the transgenics.

As shown in [Fig. 4](#F4){ref-type="fig"}, a strong almost linear relationship was found between *AC*~m~ and *k*~CA~, whereas a saturating relationship was observed with *AC*~i~. This indicates that the CO~2~ assimilation rate is limited by cytosolic CA activity, with the relationship becoming clearer after accounting for *g*~m~. It is tempting to speculate that the differences between the two monocot species and *F. bidentis* relate to differences in limitations imposed by *g*~m~ which affects cytosolic *p*CO~2~ and hence *in vivo* CA activity, but this is not borne out by comparative measurements of *g*~m~ made by [@CIT0004]. CA activity increases with increasing pH, so variation in cytosolic pH can also contribute to variations in *in vivo* CA activity; however, these effects are not large ([@CIT0037]). The interaction of β-CA and a CO~2~-permeable aquaporin in *Arabidopsis thaliana* has indicated that CA can be localized near the plasma membrane rather than dispersed throughout the mesophyll cytosol ([@CIT0058]). This may also impact on CA activity and result in another difference between the C~4~ species. Other possibilities pertain to differences in anatomical characteristics of leaves. Both CA and PEPC are cytosolic enzymes, and differences in *S*~m~ may affect the efficiency with which CA is used. Our results suggest that increasing *g*~m~ may be an important way to increase the CO~2~ assimilation rate at low intercellular *p*CO~2~, a scenario that may, for example, occur under drought.

Oxygen isotope discrimination and the CO~2~ dependence of isotopic equilibrium {#s26}
------------------------------------------------------------------------------

As had previously been observed, Δ^18^O decreased with reductions in CA activity as CA facilitates the exchange of O~2~ between cytosolic water and CO~2~ ([Fig. 7](#F7){ref-type="fig"}; [@CIT0059]; [@CIT0011]). Previous reports, which have estimated the proportion of cytosolic CO~2~ in equilibrium with leaf water (θ) in C~4~ species, have generally assumed a relatively large *g*~m~ value and this then led to lower estimates of θ ([@CIT0011], [@CIT0012]). Here we assumed that in the *S. viridis* null plants there is sufficient CA for isotopic equilibrium to be reached, as discussed by [@CIT0004]. For comparison, we also estimated *g*~m~ from anatomical estimates of *S*~m~, and cell wall and cytosolic thickness following calculations outlined by [@CIT0054]. This gives a *g*~m~ value of 0.68mol m^−2^ s^−1^ bar^−1^ which is less than the value of 0.9mol m^−2^ s^−1^ bar^−1^ calculated from Δ^18^O measurements and highlights the anatomical constraints for CO~2~ diffusion dictated by the photosynthetic pathway in leaves of C~4~ plants ([@CIT0013]).

Reduction in CA activity led to significant reductions in θ but it is interesting to note that θ did not vary significantly with *p*CO~2~. This is explained by the fact that CA activity increases linearly with *p*CO~2~ so that although there is more CO~2~ that needs to equilibrate with leaf water, there is also proportionally more CA activity. The fact that neither transgenic line showed a CO~2~ dependence suggests that the decrease in the ratio of CA hydrations to PEP carboxylations is not affecting the isotopic equilibration of CO~2~ with leaf water. These results have important implications for the interpretation of the ^18^O signature of atmosopheric CO~2~ ([@CIT0061]; [@CIT0030]; [@CIT0060]).

Reduction of CA in *S. viridis* does not alter the stomatal reponse to CO~2~ {#s27}
----------------------------------------------------------------------------

The CO~2~ regulation of stomatal conductance remains an open question ([@CIT0021]). It has been previously shown that in the *ca1/ca4* double mutant of *A. thaliana*, the degree of stomatal closure in response to increasing *p*CO~2~ was reduced ([@CIT0036]; [@CIT0058]). It is clear that CA is part of a complex signal transduction network. However, nothing is currently known about the role of CA in stomatal CO~2~ responses in C~4~ species. In our study, where only one β-CA isoform was reduced, we found no change in the response of stomatal conductance to CO~2~. The *S. viridis* β-CA reduced here (Si003882m.g) has low sequence identity (\<50%) to all of the Arabidopsis β-CAs, but we would predict that multiple reductions in β-CA isoforms would be required to observe a similar stomatal phenotype in *S. viridis*.

Conclusion {#s28}
----------

Under current atmospheric conditions, CA activity was not rate limiting for C~4~ photosynthesis in *S. viridis.* At lower *C*~i~, which may, for example, occur under conditions of drought, our results suggest that *g*~m~ may pose a greater limitation than CA activity. However, it is important to investigate the role of CA on C~4~ photosynthesis under a range of environmental conditions such as high temperatures which have recently been suggested to deactivate CA activity in *S. viridis* ([@CIT0006]). Here we have shown that *S. viridis* is a useful model monocot C~4~ species that lends itself to molecular manipulation of the C~4~ photosynthetic pathway.

Supplementary Data {#s29}
==================

Supplementary data are available at *JXB* online.

Table S1. Primers used in this study

Figure S1. CA hydration rates at mesophyll *p*CO~2~ in the T~1~ plants.

Figure S2. Very low sequence identity (\~37%) between the four main *S. viridis* β-CAs.

Figure S3. High sequence identity (87%) of Si003882m.g to the *ZmCA2* (GRMZM2G348512).

Figure S4. CO~2~ assimilation rate of the TDL experiment.

Figure S5. Standard error of δ^18^O in the reference gas of repeated measurements with the TGA200A.

Supplementary Material
======================

###### 

Click here for additional data file.

We thank Jasper Pengelly for assisting with construct generation, Xueqin Wang for assisting with *S. viridis* transformations, Soumi Bala for help with biochemical assays, gas exchange, and TDL measurements, and Murray Badger for making the MIMS available for measurements of CA activity. We thank Hilary Stuart-Williams for calibrating standard gases and water samples, and Joyce van Eck and Tom Brutnell for helpful discussions regarding *S. viridis* transformations. We thank Joanne Lee and the Centre for Advanced Microscopy at ANU for technical assistance with microscopy. This research was supported by the Bill and Melinda Gates Foundation's funding for the C~4~ Rice consortium and by the Australian Research Council Centre of Excellence for Translational Photosynthesis (CE140100015). RES is funded by ARC DECRA (DE130101760).
