Table 1.

Parameters of the cell growth and microscale CO₂ transport model

Variable	Symbol	Unit	Value	Notes and references
Net rate of photosynthesis	A	µmol m−2 s−1	–	Calculated
Net hydration of CO 2 to bicarbonate	B	µmol m−3 s−1	–	Calculated
Concentration of CO 2 at CO 2 fixation site	C c	µmol m−3	–	Calculated
Concentration of bicarbonate at the CO 2 fixation site	C HCO3 −	µmol m−3	–	Calculated
Diffusivity of CO 2 (25 °C)	D l	m2 s−1	$1.89\times {10}^{-9}$	Lide, 1999
Diffusivity of CO 2 in cell wall	C CW	m2 s−1	3.78×10–10	Assuming effective porosity of 0.20 (Evans et al., 2009)
Diffusivity of H CO3 –	D HCO3 −	m2 s−1	1.17×10–9	Geers and Gros (2000)
Average thickness of tissue	d	µm	–	Calculated from the topologies
Ratio of final and initial resting lengths of walls	F	–	1 (spongy mesophyll) 1–10 (palisade mesophyll)	See the Materials and methods
Henry’s constant for CO 2 (25 °C)	H	–	0.83	Lide (1999)
Maximum rate of electron transport	J max	μmol m−2 s−1	233.23	‘Doloress’ tomato (Berghuijs et al., 2015)
Spring constant of cells aligned along maximum growth direction	k min	MN m−1	Calculated	See the Materials and methods
Turnover rate of carbonic anhydrase	k a	s−1	3×105	Pocker and Miksch (1978)
Michaelis–Menten constant for carbonic anhydrase hydration	K CO2	mol m−3	2.8	Hatch and Burnell (1990)
Equilibrium constant of carbonic anhydrase	K eq	mol m−3	5.6×10–7	Pocker and Miksch (1978)
Michaelis–Menten constant of Rubisco for CO 2	K m,c	mbar	267a	Berghuijs et al. (2015)
Michaelis–Menten constant for carbonic anhydrase hydration	K HCO3 −	mol m−3	34	Pocker and Miksch (1978)
Michaelis–Menten constant of Rubisco for O 2	K m,0	mbar	164a	Berghuijs et al. (2015)
Conversion efficiency of light to electron transport	K 2LL	–	0.357	Berghuijs et al. (2015)
Length of mesophyll surface exposed to air per leaf width	L m	–	–	Calculated
Length to width ratio of palisade mesophyll cells	L:W	–	–	Variable
Initial resting length of cell wall	l n,0	µm	Computed	Abera et al. (2013)
Maximum resting length of cell wall	l n,max	µm	Computed	Abera et al. (2013)
Oxygen concentration in stroma	O 2	mbar	210	Assumed
CO 2 permeability of chloroplast envelope	P CO2	m s−1	3.5×10–3	Gutknecht (1977), or variable
Mitochondrial respiration	R d	µmol m−2 s−1	2.65	Berghuijs et al. (2015)
Relative CO 2 /O 2 specificity for Rubisco	S C/O	mbar µbar−1	3.260	Berghuijs et al. (2015)
Thickness of cell wall	t cw	µm	0.128	Berghuijs et al. (2015)
Thickness of cytosol	t cy	µm	0.212	Berghuijs et al. (2015)
Thickness of membrane	T mem	µm	0.02	Tholen and Zhu (2011)
Rate of triose phosphate utilization	T p	µmol m−2 s−1	13.6	Berghuijs et al. (2015)
Carboxylation capacity of Rubisco	V c,max	µmol m−2 s−1	274	Berghuijs et al. (2015)
Concentration of carbonic anhydrase	X a	mol m−3	0.27	Tholen and Zhu (2011)
Angle expressing directionality of cell wall growth	α	–	Computed	Abera et al. (2013)
Anisotropy factor	β	–	0 (spongy mesophyll)	See the Materials and methods
			0–1 (palisade mesophyll)
Polarity of cell growth	λ	–	0≤λ≤1	See the Materials and methods
Convexity factor	θ	–	0.797	Berghuijs et al. (2015)
Time constant for length to reach maximum	τ	s	200 000	Assumed
CO 2 compensation point	Γ* a	µbar	0.5O2/SC/O	Berghuijs et al. (2015)

^a These parameters were converted into µmol m⁻³ liquid by multiplying by PH/RT, where P=101 325 Pa, H=0.83, R=8.314 m³ Pa K⁻¹ mol⁻¹, and T=298 °K.