Supporting Information Notes S1
Code transcript for System Dynamics model of CAM
1. Dynamic input variables
(01)
"<NORMALISED PAR INPUT>": = GET XLS DATA ('Circadian inputs.xlsx', 'Circ',
'b', 'd4')
Units: Dmnl
Comment: Idealised curve imported from excel.
(02)
"<TEMPERATURE INPUT NORMALISED>": = GET XLS DATA ('Circadian
inputs.xlsx', 'Circ', 'b', 'c4')
Units: Dmnl
Comment: Idealised sinusoidal curve imported from excel.
(03)
<fp> PEPC activation state = INTEG (PEPC activation - PEPC deactivation, 0.2)
Units: Dmnl
Comment: Input was modelled from measured activation state (see txt).
(03a) PEPC activation = PEPC activation rate * Trigger variable
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(03b) PEPC activation rate = 2.6e-05
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(03c) PEPC deactivation = IF THEN ELSE (Time > "SWITCH A: PEPC off time", <fp>
PEPC activation state * PEPC deactivation rate * (1 - (Kid PEPC deactivated Dmnl
/ <fp> PEPC activation state)), 0)
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(03d) PEPC deactivation rate = 0.0008
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(03e) Trigger variable = IF THEN ELSE(Time < "SWITCH A: PEPC off time", IF THEN
ELSE (<fp> PEPC activation state fp >= 1, 0, 1), 0)
Units: Dmnl
(04)
<fc> Rubisco activation state = INTEG (Rubisco rate on-Rubisco rate off, 0)
Units: Dmnl
Comment: Input was modelled from measured activation state (see txt).
(04a) Rubisco rate = IF THEN ELSE(<fc > Rubisco activation state < 0.35, 0.0008, 2.5e05)
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(04b) Rubisco rate off = IF THEN ELSE (Time > Rubisco time switch off, 1/(86400(Rubisco time switch off)),0)
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(04c) Rubisco rate on = IF THEN ELSE (PAR lookup switch > "SWITCH B: Rubisco on
PAR", Rubisco rate, 0) * trigger
Units: 1/Second
Comment: Input was modelled from measured activation state (see txt).
(04d) Rubisco time switch off = 75000
Units: Second
Comment: Input was modelled from measured activation state (see txt).
(04e) trigger = IF THEN ELSE (Time < Rubisco time switch off, IF THEN ELSE( <fc>
Rubisco activation state >= 1, 0, 1), 0)
Units: Dmnl
Comment: Input was modelled from measured activation state (see txt).
2. Input constants
(05)
Acc INITIAL CONDITION = 34.73
Units: umol/m2
Comment: recalibrate after changing inputs, re-run simulation.
(06)
Aci INITIAL CONDITION =11498
Units: umol/m2
Comment: recalibrate after changing inputs, re-run simulation.
(07)
Asymptote1 = 100
Units: umol/m2
Comment: For Amv to approach 0 the model requires an arbitrarily small
number so as not to return error, hence 100 umol m-2
(08)
Asymptote2 = 10000
Units: umol/m2
Comment: Total malic acid levels approach this value at the end of Phase 4. Input
determind from titratable acidity measurements.
(09)
Cca pp CO2 ATMOSPHERE = 400
Units: ubar
Comment: Partial pressure of CO2 in atmosphere, 400 ubar = 400 ppm = 40.53
Pa
(10)
Conversion 1 = 0.025
Units: ubar*m2/umol
Comment: Conversion factor required to adjust for error arising from numerical
integration methodology.
(11)
Cwa pp H2O atmosphere = 13340
Units: ubar
Comment: Assumes constant atmospheric pressure 13,340 ubar = approx.. 10
g/m3
(12)
GLUCAN BUFFER 1Cs = 30000
Units: umol/m2
Comment: Reserve glucan/starch in 1Cs, approx. equal to 10000 G3Ps
(13)
gm MESOPHYLL CONDUCTANCE = 0.053
Units: umol/m2/Second/ubar
(14)
gsmax STOMATAL CONDUCTANCE = 0.06
Units: umol/m2/Second/ubar
(15)
Henrys law constant for CO2 solubility in water = 0.03445
Units: uM/ubar
Comment: Henry's Law: concentration = solubility * partial pressure Henry's
Law constant for CO2 solubility in water, s = 0.034 M Atm-1 = 0.03445 uM ubar1
(16)
Kc KCO2 RUBISCO = 10.8
Units: uM.
(17)
Kia activated K for malic acid inhibition of PEPC = 8000
Units: uM
(18)
Kid PEPC deactivated Dmnl = 0.05
Units: Dmnl
Comment: Kid is given as a fraction of Kia in dimensionless units (Dmnl)
(19)
Kp KCO2 PEPC = 12
Units: uM
(20)
Malic acid efflux = 40
Units: umol/(m2*Second)
Comment: Rapid efflux of 40 umol m-2 s-1 such that not rate limiting to
decarboxylase activity
(21)
MAXIMUM PAR = 2000
Units: umol/m2/Second
(22)
SUCCULENCE = 3.4
Units: umol/m2/uM
Comment: Succulence, assume mass is water so kg/m2 = L/m2 uM = umol/L,
therefore conversion from umol/m2 leaf area to uM concentration is = 1/
succulence
(23)
Tmax TEMPERATURE MAX = 30
Units: deg C
(24)
Tmin TEMPERATURE MIN = 15
Units: deg C
(25)
Vcmax VMAX RUBISCO = 19
Units: umol/m2/Second
(26)
Vdmax MAX DECARBOXYLATION RATE = 9
Units: umol/m2/Second
Comment: Estimated from the maximum gradient of ‘de-acidification’ during PII
and PIII.
(27)
Vm MITOCHONDRIAL RESPIRATION RATE = 0.6
Units: umol/m2/Second
(28)
Vpmax VMAX PEPC = 23
Units: umol/m2/Second
(29)
Xvmax MAX C4 and VACUOLE CAPACITY = 150000
Units: umol/m2
Comment: Estimated from maximum measured titratable acidity.
3. Switch Inputs
(30)
SWITCH A: PEPC off time = 43200
Units: Second
(31)
SWITCH B: Rubisco on PAR = 300
Units: umol/m2/Second
(32)
SWITCH C tonoplast decarboxylation PAR = 1000
Units: umol/m2/Second
4. Flow variables
(33)
Je rate carbohydrate exported = IF THEN ELSE (G3Ps in 1Cs Ac > (3 * Xvmax
MAX C4 and VACUOLE CAPACITY) + Glucan buffer, (Vg Gluconeogenesis of PEP1
+ Vc C3 carboxylase activity - Vm CO2 mitochondrial respiration - Vh Hydrolysis
for PEP1), 0)
Units: umol/(m2*Second)
Comment: This expression allows the export of carbohydrate to occur only when
reserves for the maintenance of CAM are met. All parameters are in 1Cs.
(34)
Jm Mesophyll CO2 flux = gm MESOPHYLL CONDUCTANCE * (Cci ppCO2
intercellular space - Ccc ppCO2 cytosol ubar)
Units: umol/m2/Second
(35)
Jme tonoplast malic acid efflux = IF THEN ELSE (PAR lookup switch > SWITCH C
tonoplast decarboxylation PAR, Malic acid efflux * (1 - (Asymptote1 / Amv
Accumulation malic acid vacuole)),0)
Units: umol/m2/Second
(36)
Jmi Tonoplast malic acid influx = IF THEN ELSE (PAR lookup switch < SWITCH C
tonoplast decarboxylation PAR, Vp C4 carboxylase activity * (1 - (Amv
Accumulation malic acid vacuole / (Xvmax MAX C4 and VACUOLE CAPACITY))),
0)
Units: umol/m2/Second
(37)
Js Stomatal CO2 flux = gs CO2 Stomatal conductance * (Cca pp CO2 atmosphere Cci ppCO2 intercellular space)
Units: umol/m2/Second
(38)
Jmt Rate total malic acid accumulation = Vp C4 carboxylase activity - Vd
Decarboxylation rate
Units: umol/m2/Second
(39)
Vc C3 carboxylase activity = (Vcmax VMAX RUBISCO * (Ccc concCO2 cytosol
umol)) / (Kc KCO2 RUBISCO + (Ccc concCO2 cytosol umol)) * <fc> Rubisco
activation state
Units: umol/m2/Second
Comment: Vc is the product of Michaelis-Menten enzyme kinetics and Rubisco
activation state.
(40)
Vd Decarboxylation rate = IF THEN ELSE (PAR lookup switch > SWITCH C
tonoplast decarboxylation PAR, Vdmax MAX DECARBOXYLATION RATE * (1(Asymptote2/Amc Accumulation malic acid cytosol)), 0)
Units: umol/m2/Second
(41)
Vg Gluconeogenesis of PEP = IF THEN ELSE (Agc Accumulation glucan cytosol
from pyruvate < Xvmax MAX C4 and VACUOLE CAPACITY + 1, Vd
Decarboxylation rate, 0)
Units: umol/(m2*Second)
(42)
Vg Gluconeogenesis of PEP1 = Vg Gluconeogenesis of PEP*3
Units: umol/(m2*Second)
Comment:
Multiplied by 3 to get PEP gluconeogenesis in 1Cs
Malic acid --> pyruvate + CO2 (decarboxylated)
CO2 + RuBP --> 2 G3P, or 3 CO2 + 3 RuBP --> 6 G3P, of which 5 are recycled as
RuBP, leaving 1 net.
G3P FOR PYRUVATE: pyruvate --> PEP in chloroplast - PEP in chloroplast
transported to cytosol - PEP cytosol --> (gluconeogenesis) --> G6P - G6P
transported to chloroplast for glucan synthesis.
(43)
Vh Hydrolysis for PEP = Vh Hydrolysis for PEP1/3
Units: umol/(m2*Second)
(44)
Vh Hydrolysis for PEP1 = IF THEN ELSE (Agc Accumulation glucan cytosol from
pyruvate > 0, Vp C4 carboxylase activity * 3, 0)
Units: umol/(m2*Second)
Comment: Vp * 3 because 1 3C substrate PEP is require to fix 1 CO2
(45)
Vm CO2 mitochondrial respiration = Vm MITOCHONDRIAL RESPIRATION RATE
Units: umol/(m2*Second)
(46)
Vp C4 carboxylase activity = IF THEN ELSE (Agc Accumulation glucan cytosol
from pyruvate > 0, (Vpmax VMAX PEPC * (Ccc concCO2 cytosol umol)) / ((Ccc
concCO2 cytosol umol) + Kp KCO2 PEPC) * im malic acid inhibition of PEPC, 0)
Units: umol/m2/Second
Comment: If, then, else statement only allows C4 carboxylase activity when is
sufficient carbohydrate for hydrolysis is available. Vp is a function of MichaelisMenten enzyme kinetics and malic acid induced inhibition of PEPC.
3. State variables
(47)
Acc Accumulation CO2 cytosol = INTEG (Jm Mesophyll CO2 flux + Vm CO2
mitochondrial respiration + Vd Decarboxylation rate - Vc C3 carboxylase activity
- Vp C4 carboxylase activity, Acc INITIAL CONDITION)
Units: umol/m2
(48)
Aci Accumulation CO2 intercellular = INTEG (Js Stomatal CO2 flux - Jm Mesophyll
CO2 flux, Aci INITIAL CONDITION)
Units: umol/m2
Comment: This is a proxy due to limitations of numerical integration
methodology over time-step of 1 second. Values generated should not be
considered for analysis.
(49)
Ac G3Ps in 1Cs = INTEG (Vg Gluconeogenesis of PEP1 + Vc C3 carboxylase
activity - Vm CO2 mitochondrial respiration - Je rate carbohydrate exported - Vh
Hydrolysis for PEP1, (3*Xvmax MAX C4 and VACUOLE CAPACITY) + Glucan
buffer)
Units: umol/m2
Comment: The initial condition requires 3 x Xvmax for 1Cs + glucan in 1Cs. Note
that ‘Vg Gluconeogenesis of PEP1 is also in 1Cs.
(50)
Ae Accumulation exported carbohydrate 3Cs = INTEG (Je rate carbohydrate
exported/3, 0)
Units: umol/m2
Comment: Je / 3 for carbohydrate in G3Ps, initial value = 0.
(51)
Agc Accumulation glucan cytosol from pyruvate = INTEG (Vg Gluconeogenesis of
PEP - Vh Hydrolysis for PEP, Xvmax MAX C4 and VACUOLE CAPACITY)
Units: umol/m2
(52)
Am malate accumulation = INTEG ("v.p - D", Asymptote2)
Units: umol/m2
(53)
Amc Accumulation malic acid cytosol = INTEG (Vp C4 carboxylase activity + Jme
tonoplast malic acid efflux - Jmi Tonoplast malic acid influx - Vd Decarboxylation
rate, 10000)
Units: umol/m2
Comment: initial value = 10,000 from measured titratable acidity level at
beginning of PI
(54)
Amv Accumulation malic acid vacuole = INTEG (Jmi Tonoplast malic acid influxJme tonoplast malic acid efflux, 0)
Units: umol/m2
Comment: initial value = 0
4. Ancilliary parameters
(55)
Actual PAR profile = MAXIMUM PAR*"<NORMALISED PAR INPUT>"
Units: umol/m2/Second
(56)
Ccc concCO2 cytosol umol = Acc Accumulation CO2 cytosol/succulence
Units: uM
Comment: To estimate the molar concentration of CO2, chlorenchyma tissue is
assumed aqueous. Succulence (kg/m2 leaf area) is therefore considered
equivalent to (L/m2)
(57)
Ccc ppCO2 cytosol ubar = Ccc concCO2 cytosol umol/Henrys law constant for
CO2 solubility in water
Units: ubar
Comment: Partial pressure = Concentration (umol/L) / Henrys Law solubility
constant for CO2 in H2O
(58)
Cci ppCO2 intecellular space = Aci Accumulation CO2 intercellular * Conversion
1
Units: ubar
Comment: Calculating Cci partial pressure required a conversion factor due to
error arising from numerical integration methodology used by VenSim software.
(59)
"CHECK ci/ca"= Cci ppCO2 intecellular space / Cca pp CO2 atmosphere
Units: Dmnl
Comment: Included to validate output.
(60)
Cmc conc malic acid cytosol = Amc Accumulation malic acid cytosol/succulence
Units: uM
(61)
Cwi Intercellular pp H2O = (6107.8 * EXP((17.2694 * T 24 hour temperature
profile)/(T 24 hour temperature profile + 238.3)))
Units: ubar
Comment: Assumes the intercellular space remains saturated levels.
(62)
gs CO2 Stomatal conductance = (gsmax STOMATAL CONDUCTANCE * sa
Stomatal aperture)+0.001
Units: umol/m2/Second/ubar
Comment: The ‘+.001’ was required so simulaitons do not crash with a divide 0
(63)
gsH2O Stomatal conductance = gs CO2 Stomatal conductance * 1.6
Units: umol/m2/Second/ubar
Comment Assume molecular mass inversely proportional to conductance,
conversion factor of 1.6 (Nobel 1988)
(64)
im malic acid inhibition of PEPC = 1 - (Cmc conc malic acid cytosol / (Ki PEPC
inhibition malic acid + Cmc conc malic acid cytosol))
Units: Dmnl
(65)
Ki PEPC inhibition malic acid = Kia activated K for malic acid inhibition of PEPC *
PEPC activation state fp
Units: uM
(66)
sa Stomatal aperture = IF THEN ELSE (Cca pp CO2 atmosphere < Cci ppCO2
intecellular space, 0.001, SQRT ((1 -(Cci ppCO2 intecellular space / Cca pp CO2
atmosphere))^2) * (Cwa pp H2O atmosphere / Cwi Intercellular pp H2O))
Units: Dmnl
Comment: If Cca < Cci this statement specifies minimum stomatal aperture of
0.001 Dmnl. Otherwise, sa is given by the gradient of ppCO2 in divided by
gradient of ppH2O out.
(67)
T 24 hour temperature profile = (((Tmax TEMPERATURE MAX - Tmin
TEMPERATURE MIN)) * " < TEMPERATURE INPUT NORMALISED>") + Tmin
TEMPERATURE MIN
Units: deg C