Exploiting differences in the energy budget among C4 subtypes to improve crop productivity

Summary C4 crops of agricultural importance all belong to the NADP‐malic enzyme (ME) subtype, and this subtype has been the template for C4 introductions into C3 crops, like rice, to improve their productivity. However, the ATP cost for the C4 cycle in both NADP‐ME and NAD‐ME subtypes accounts for > 40% of the total ATP requirement for CO2 assimilation. These high ATP costs, and the associated need for intense cyclic electron transport and low intrinsic quantum yield ΦCO2, are major constraints in realizing strong improvements of canopy photosynthesis and crop productivity. Based on mathematical modelling, we propose a C4 ideotype that utilizes low chloroplastic ATP requirements present in the nondomesticated phosphoenolpyruvate carboxykinase (PEP‐CK) subtype. The ideotype is a mixed form of NAD(P)‐ME and PEP‐CK types, requires no cyclic electron transport under low irradiances, and its theoretical ΦCO2 is c. 25% higher than that of a C4 crop type. Its cell‐type‐specific ATP and NADPH requirements can be fulfilled by local energy production. The ideotype is projected to have c. 10% yield advantage over NADP‐ME‐type crops and > 50% advantage over C3 counterparts. The ideotype provides a unique (theoretical) case where ΦCO2 could be improved, thereby paving a new avenue for improving photosynthesis in both C3 and C4 crops.


Fig. S1
The three classically-defined C4 subtypes classified according to decarboxylation enzymes Notes S1 Deriving the equation for quantum yield for CO2-assimilation (CO2), and equations for calculating parameters a and fCET from the measured CO2 Notes S2 Extending the model of Yin & Struik (2018) to accommodate the proposed mixed type Notes S3 Extending the C4 submodel in crop model GECROS to accommodate the C4 ideotype Table S1 Definitions and units of model symbols Table S2 Indicative values of model input parameters used in the analysis Table S3 Formulae for calculating cell-type-specific NADPH and ATP demands per CO2 assimilation in the mixed PEP-CK type proposed in Fig. 1 Figure S1 The three classically-defined C4 subtypes classified according to decarboxylation enzymes (a, NADP-ME; b, NAD-ME; and c, PEP-CK), and their minimum cell-type specific energy requirements assuming (i) no leakiness, (ii) 50% of the 3-PGA reduction takes place in M and BS cells each, and (iii) no photorespiration and alternative electron and ATP sinks (Reprinted by permission from Springer Nature, Ishikawa et al. 2016). Abbreviations and numbers are as given in Fig. 3. Notes S1 Deriving the equation for quantum yield for CO2-assimilation (CO2), and equations for calculating parameters a and fCET from the measured CO2 The model described below for the general mixed type as described in Fig. 1 is based on the model of Yin & Struik (2012) for electron-transported limited C4 photosynthesis in the NADP-ME and NAD-ME subtypes.
For any type of (C3 or C4) photosynthesis when involving two types of electron transport: linear and cyclic electron transport (LET and CET, respectively), the factor for excitation partitioning to PSII (2; see Table S1 for symbol definitions) can be expressed as (Yin & Struik 2012, their eqn A5): where fCET is the fraction of total PSI electrons that follow CET, and r2/1 is the PSII : PSI electron transport efficiency ratio.

Quantum yield of CO2 assimilation in terms of NADPH
Total NADPH production rate (Jnadph) is where Iabs is absorbed irradiance, 2Iabs2 as a whole is the rate of LET, and 0.5 stands for mol NADPH produced per LET. NADPH demand per mol CO2 assimilation, dnadph, is nadph = 2 + 2 o/c + 5 n/c + (1 + ) (1 .3) where vo/c is the RuBP oxygenation : carboxylation ratio, vn/c is the nitrogen assimilation : RuBP carboxylation ratio,  is leakiness, and a is the term specific for any type involving PEP-CK as defined in Fig. 1 (i.e. the fraction of OAA that is reduced to malate using the NADPH of M cells for shuttling to BS cells to drive mitochondrial electron transport). Eqn (1.3) assumes that the process (other than RuBP carboxylation and oxygenation) that uses electrons of LET is predominantly nitrate reduction, requiring 10 mol electrons (equivalent to 5 mol NADPH) per nitrate reduction (Noctor & Foyer 1998). Note that electron requirement for nitrate reduction was lumped to the pseudocyclic electron fraction (fpseudo) in the model of Yin & Struik (2012). (1.5) Quantum yield of CO2 assimilation in terms of ATP Similar logic can be used to define equation ATP-dependent quantum yield of CO2 assimilation but this has more uncertain parameters. Total ATP production rate (Jatp) is where z is the factor of ATP production per LET when CET runs simultaneously, in which fQ is the fraction of electrons at plastoquinone that follow the Q-cycle (= 1 for C4 photosynthesis, Furbank et al. 1990), h is protons required per ATP synthesis (either 4 or 14/3), and fNDH is the fraction of CET that follows the NAD(P)H dehydrogenase (NDH)-dependent pathway.
Uncertainties exist with regard to whether fNDH should be included in the model, but here we include fNDH so that our model covers all scenarios (whereby the z factor was derived following the same procedure as described by Yin et al. 2004 where cstarch is ATP cost per carbon in starch synthesis (=0.167; Noctor & Foyer 1998), vr/c is day respiration to RuBP carboxylation ratio, and [2+a"-(n+1+a")a] is the net chloroplast ATP requirement to operate the C4 cycle for the mixed type (see Fig. 1). Eqn (1.7) assumes that 1 mol ATP per nitrate reduction (Noctor & Foyer 1998) comes from chloroplasts, although other ATP sources may also satisfy this ATP requirement.
Combining eqns (1.1, 1.6-1.7) and considering photorespiratory CO2 release give the equation for gross CO2 assimilation rate in terms of ATP (Ag,atp)

Relationships between parameters fCET and a
For the most efficient use of energy, neither NADPH nor ATP should be overproduced or under-utilised. A balance between NADPH and ATP in their production and utilisation is also metabolically important (Kramer & Evans 2011). To achieve that, CO2,nadph and CO2,atp where two lumped terms e = 4 + 4 o/c + 10 n/c and a = 3 + 3.5 o/c + 1 n/c + starch (1 − 0.5 o/c − r/c ) are introduced to make eqn (1.10a) shorter. Simplifying gives Solving eqn (1.10b) for fCET gives: Eqn (1.11) suggests a hyperbolic relationship that fCET decreases with increasing a (see the  (Table S2). This relationship means that a higher value of parameter a would generate more ATP via mitochondrial NADH oxidation and LET such that there is a lower requirement for CET to provide ATP in support of the C4 cycle.

Estimating parameters fCET and a from the measured CO2
Neither fCET nor a is amenable to direct experimental measurement. We developed equations to estimate them based on values of CO2, which can easily be measured experimentally.
Figure Theoretical relationship between the required fraction of cyclic electron transport (fCET) and parameter a, the fraction of oxaloacetate (OAA) that is reduced to malate in M cells for being shuttled to BS mitochondria where malate is decarboxylated by NAD-ME to release NADH that drives mitochondrial electron transport to generate ATP (here the ATP : NADH ratio n is assumed to be 3). The case where a = 0 and fCET = c. 0.5 represents the classically-defined NADP-ME or NAD-ME subtypes. The case where a = 0.5 and fCET = -0.48 represents the NH2-flux balanced type discussed in the main text. Values where either a or fCET < 0 are physiologically irrelevant, merely representing mathematical extrapolation of eqn (1.11). The type with only the NH2-flux balance has the high a (0.5), meaning high mitochondrial electron transport generated ATP; and this, combined with high LET that also produces some ATP, yields ATP surplus that would need a mathematically negative CET for a physiologically balanced NADPH:ATP ratio.
Notes S2 Extending the model of Yin & Struik (2018) to accommodate the proposed mixed PEP-CK type The model of Yin & Struik (2018) contains a simple module for light absorption by M and BS cells, and algorithms for both cell type-specific energy production and energy demand, and suits for three classically defined subtypes and other types. We now extend the model for algorithms to account for the proposed mixed PEP-CK type in Fig. 1.

Extended model for cell-type-specific NADPH and ATP production
The model for cell-type-specific NADPH and ATP production uses the following measurable traits as input: (1) leaf chlorophyll content (mol m -2 ), (2) fraction of chlorophyll in BS cells, Now to accommodate the mixed type as described in Fig. 1, two modifications are needed. First, the term  in eqn (2.1) needs to be expanded from 2a for the classicallydefined PEP-CK subtype to: where two terms are added to 2a to account for the ATP required for PEP regeneration by PPDK for NAD(P)-ME or PEP-CK(PK) and PEP-CK(PP) pathways, respectively (see Fig. 1).
Applying the equation for the NH2-flux balance in Fig. 1 to eqn (2.4) gives: Second, eqn (2.2) for ATPadd should become: where (na-a) is the surplus of ATP from mitochondrial NADH oxidation that is not used for PEP-CK. This is necessary because, unlike the classically-defined PEP-CK subtype where ATP from the mitochondrial NADH oxidation just suffices to fuel PEP-CK, the mixed type has a surplus that would alleviate the requirement for CET.

Extended model for cell type-specific NADPH and ATP demand
Basic cell-type specific NADPH demands are 2(1-)+a(1+) and 2 for M and BS cells, respectively, for the classically defined PEP-CK subtype, where  is the fraction of 3-PGA reduction that takes place in BS cells (Yin & Struik 2018). Now for the mixed PEP-CK type proposed in Fig. 1, there is a need to consider possible extra amount of NADPH required in M cells to reduce OAA to malate in case of some NADP-ME decarboxylation. We denote b as the fraction of the second decarboxylation category in Fig. 2 (Yin & Struik 2018). Now for the mixed PEP-CK type proposed in Fig. 1, there are two additional sources of ATP demands for PEP regeneration by PPDK for NAD(P)-ME or PEP-CK(PK) and PEP-CK(PP) pathways, respectively; so the total ATP These cell-type-specific NADPH and ATP requirements for CCM and Calvin cycles, plus those required for photorespiratory cycle, nitrate reduction and starch synthesis, are summarised in Table S3.

Notes S3 Extending the C4 submodel in crop model GECROS to accommodate the C4 ideotype
The crop model GECROS (v4.0) was described by Yin & Struik (2017). Its submodel for C4 leaf photosynthesis was a modified version of the model of von Caemmerer & Furbank (1999). The basic equations relevant to our analysis here are electron transport limited rate of PEP carboxylation (Vp) and gross rate of CO2 assimilation (Ag): where J2 is total electron transport rate passing PSII and z is given in eqn (1.6), and where Cc is the level of CO2 at the carboxylating sites of Rubisco, O is the level of O2 at the same sites, * is the half of the inverse of Rubisco specificity for CO2, and fpseudo is the fraction of the total PSI electron flux for the basal pseudocyclic pathway (equivalent to accounting for the electron consumption by nitrate reduction as described in Supporting Notes S1 and S2).
Eqn (3.2), the NADPH-limited form for CO2 assimilation rate, was used because the equivalent ATP-limited form (as originally proposed for the C4 model) where x1 becomes (1- x)J2z/3 and x2 is 7*/3, would predict an increased rate of CO2 assimilation with increasing fCET, which is not physiologically logical (see Yin & Struik 2017).
To accommodate our C4 ideotype, the following revisions have to be made here: (1) Setting fCET to 0.
(2) Changing the chloroplastic ATP requirement for the CCM cycle () from 2 for malic-enzyme subtypes (von Caemmerer & Furbank 1999) to: for the ideotype (where n is the ATP:NADH ratio, 3 or 2.5; and a = 0.36 or 0.4, see the main text).
(3) Changing the factor for ATP partitioned to the CCM cycle (x) from 0.4 for the NAD(P)-ME subtypes (von Caemmerer & Furbank 1999) to: This gives that x is c. 0.16-0.17 for the ideotype (Table 1).
(4) Changing the stoichiometric coefficient in eqn 3.2 from 4 to (4 + 2a), i.e.: This accounts for the additional a mol NADPH required per mol CO2 assimilated.
All other algorithms and parameter values were the same as described by Yin &Struik (2017). Fraction of remaining OAA that follow the NAD(P)-ME or PEP-CK(PK) in Fig. 1 − a" Fraction of remaining OAA that follow the PEP-CK(PP) pathway in Fig. 1 − Ag Gross rate of CO2 assimilation mol m -2 s -1 Ag,atp ATP-determined gross rate of CO2 assimilation mol m -2 s -1 Ag,nadph NADPH-determined gross rate of CO2 assimilation mol m -2 s -1 Amax Light-saturated maximum net rate of leaf CO2 assimilation mol m -2 s -1 b Fraction of the a' part that belongs to the NADP-ME type (see Fig. 1