Electronic Supplementary Material
Appendix A
Determination of Vcmax and Vpmax
Values of Vcmax and Vpmax were determined following the methodology reported by Massad et al. (2007). This methodology involves solving a system of six non-linear equations derived from three basic functions obtained by combining the various relationships for the C4 photosynthetic pathway. The first equation (A1) represents the net CO2 assimilation in terms of CO2 level in the intercellular spaces and the mesophyll cells. The second (A2) and the third (A3) equations describe the Rubisco limited and PEP carboxylase limited rate of CO2 assimilation
(A1)
(A2)
(A3)
where Kc, Ko and Kp are the Michaelis–Menten constants for Rubisco carboxylation, oxygenation, and PEP carboxylation, respectively. Os and Ob are the oxygen concentration in the mesophyll and bundle sheath cells, respectively. gbs is the conductance of bundle sheath cells to CO2, and Cs and Cm are the concentration of CO2 in the bundle sheath and mesophyll cells, with respiration rates, respectively.
The values of Ko, Kc, Kp, γ*, Os, gi, and gbs are constants at a given temperature, and quantities for AN and Ci can be obtained from an AN-Ci relationships. Thus, this system has three equations and four unknowns, with the unknowns being Cs, Cm, Vcmax, and Vpmax. Values of Rd and Rm are assumed to be functions of Vcmax with Rd = 0.01Vcmax and Rm = 0.5Rd. To solve this system of equations, two sets of experimental points were selected on an AN-Ci curve, (AN1, CNi1) and (AN2, CNi2). Three equations were re-written for these two sets of points to obtain a system of six non-linear equations with six unknowns (A4 to A9).
(A4)
(A5)
(A6)
(A7)
(A8)
The six unknowns in this system of equations include, Cm1, Cm2, Cs1, Cs2, Vpmax, and Vcmax with the oxygen concentration in the bundle sheath cells (Os1 and Os2) derived from the oxygen concentration in the mesophyll cells as shown in the relationship (A10)
(A10)
where αO (0< αO <1) denotes the fraction of the O2 evolution occurring in the bundle sheath cells (Farquhar, 1983). Oxygen concentration in the mesophyll is derived from ambient oxygen concentration and the leaf temperature (Long, 1991)
(A11)
where TLeaf is the leaf temperature, and Oa is the ambient oxygen concentration. The AN1 and AN2 values and corresponding quantities for Ci1 and Ci2 were obtained from AN-Ci relationships taken during different times of the day. The Ci1 and Ci2 values were selected with CO2 mixing ratio values between 30 and 90 μmol mol-1, as stable results are obtained at lower CO2 mixing ratios corresponding with the linear part of the AN-Ci relationship (Massad et al., 2007). This analysis was done on AN-Ci functions obtained during different times of the day so that temperature relationships could be developed for Vpmax and Vcmax.
Determination of Jmax
To determine the Jmax values, rates of carbon assimilation resulting from Rubisco carboxylation (Vc) and PEP carboxylation (Vp) are required (see equations A12 and A13).
(A12)
(A13)
In equation A13, the term L represents the rate of CO2 leakage from bundle sheath to mesophyll cells (See Figure 1). L is defined as a function of conductance of bundle sheath cells and CO2 concentration gradient between bundle sheath and mesophyll cells (see equation A14).
(A14)
The electron transport limited expressions for Vc and Vp are defined in terms of the total electron transport (Jt) in the messophyll (Jm) and bundle sheath (Js) as shown in equations A15 and A16.
(A15)
(A16)
In equation A16, x denotes the partitioning factor of electron transport. Relationships between assimilation (AN) and electron transport rate can be rewritten by substituting the electron transport limited expressions of Vc (equation A15) and Vp (equation A16) in equation (A12) and equation (A13) to obtain
(A17)
(A18)
These two relationships (A17 and A18) along with (A1) form a system of three non-linear equations with three unknowns Cs, Cm and Jt. Once the value of Jt (equation A19) is obtained by solving the system of equations, the value of Jmax can be estimated by substituting the value of Jt for a specific light value (Farquhar & Wong, 1984).
(A19)
In the present study, bundle sheath respiration (Rd) was assumed to be 2.5 μmol (CO2) m-2 s-1. This was an average value derived from all the different AN-PAR relationships established based on field measurements. Mesophyll respiration was assumed to be half of the Rd following the results obtained by Massad et al. (2007).
Supplemental Figure A. Schematic representation of C4 photosynthesis (adapted from von Caemmerer 1999). The CO2 diffusing from the outside into the mesophyll cells is converted to bicarbonate (HCO3-) which is fixed by PEP carboxylase and transported into the bundle sheath where it can be either fixed by Rubisco in the photosynthetic carbon reduction cycle (PCR) or can leak (L) back into the mesophyll cells. The photosynthetic carbon oxidation (PCO) cycle which is involved in oxygenation of Rubisco is also represented along with mitochondrial respiration occurring in mesophyll (Rm) and bundle sheath cells (Rs).
Supplemental Figure A.
Supplemental Table A. Summary of all the photosynthetic model constants used in the determination of plant physiological variables
Constants / ValueKc at 298 K (Michaelis-Menten constant for CO2 Rubisco) / 650 μbar
Ko at 298 K (Michaelis-Menten constant for O2 Rubisco) / 450 mbar
Kp at 298 K (Michaelis-Menten constant for CO2 PEP carboxylase) / 80 μbar
gbs (Bundle sheath conductance to CO2) / 3 mmol m-2 s-1
gi (Mesophyll conductance to CO2) / 2 mol m-2 s-1
Θ (Empirical curvature factor) / 0.7 unitless
γ* (Half the reciprocal of Rubisco specificity / 0.000193 unitless
αO (Fraction of O2 evolved in mesophyll cell) / 0.5 unitless
abs (Leaf absorbance) / 0.85 unitless
f (Correction for spectral quality of light) / 0.15 unitless
Oa (Oxygen mixing ratio in the atmosphere) / 210000 μmol mol-1
Q10 Kc / 2.1 unitless
Q10 Ko / 1.2 unitless
Q10 Kp / 2.1 unitless
R* (Universal gas constant) / 8.314 J mol-1 K-1