#arnold4

FIX: CO2 O2 RuBP

#reactions
NADPH_prod:
 $pool = {1.0}NADPH
  chloroplast * NADPH_production(J, NADP, Nt)
PGA_cons:
 {1.0}PGA = {1.0}RuBP
  chloroplast * PGA_consumption(PGA, Rp, NADPH, Nt, Vcmax)
PGA_prod_Vc:
 {1.0}RuBP + {1.0}CO2 + {2.0}NADPH = {2.0}PGA
  chloroplast * carboxylation(Vc, Vj, Vp)
PGA_prod_Vo:
 {1.0}RuBP + {1.0}O2 + {2.0}NADPH = {1.5}PGA
  chloroplast * oxygenation(phi, Vc, Vj, Vp)


#parameters
Gamma = 3.74116898182615
J = 0.0307678189755062
Kc = 27.2372124161502
Ko = 16.5788431231261
Nt = 0.5
Rd = 0.0307674936008629
Rp = 3.2
TPU = 0.0307585098788555
Vcmax = 0.0307602623029146
gm = 0.0307740792044142
CO2 = 24.5
O2 = 21.0
RuBP = 2.0
chloroplast = 1.0


#initial values
NADPH = 0.21
PGA = 2.4


#assignment rules
!F phi = 0.21 * (gm * O2 / Ko) / ((gm * CO2 - v_c + Rd) / Kc)
!F v_c = (abs((abs(Vc + Vj) - abs(Vc - Vj)) / 2.0 + Vp) - abs((abs(Vc + Vj) - abs(Vc - Vj)) / 2.0 - Vp)) / 2.0
!F Vc = Vcmax * (CO2 - 1.0 / 2.0 * (CO2 + Kc * (1.0 + O2 / Ko) + (Vcmax - Rd) / gm - sqrt(pow(CO2 + Kc * (1.0 + O2 / Ko) + (Vcmax - Rd) / gm, 2.0) + 4.0 / gm * (Rd * (CO2 + Kc * (1.0 + O2 / Ko)) + Vcmax * (Gamma - CO2))))) / (CO2 - 1.0 / 2.0 * (CO2 + Kc * (1.0 + O2 / Ko) + (Vcmax - Rd) / gm - sqrt(pow(CO2 + Kc * (1.0 + O2 / Ko) + (Vcmax - Rd) / gm, 2.0) + 4.0 / gm * (Rd * (CO2 + Kc * (1.0 + O2 / Ko)) + Vcmax * (Gamma - CO2)))) + Kc * (1.0 + O2 / Ko))
!F Vp = 3.0 * TPU * ((CO2 - (3.0 * TPU - Rd) / gm) / (CO2 - (3.0 * TPU - Rd) / gm - Gamma))
!F NADP = Nt - NADPH
!F Vj = J / 4.0 * (CO2 - 1.0 / 2.0 * (CO2 + 2.0 * Gamma + (J - 4.0 * Rd) / (4.0 * gm) - sqrt(pow(CO2 + 2.0 * Gamma + (J - 4.0 * Rd) / (4.0 * gm), 2.0) + 4.0 / gm * (Rd * (CO2 + 2.0 * Gamma) + J / 4.0 * (Gamma - CO2))))) / (CO2 - 1.0 / 2.0 * (CO2 + 2.0 * Gamma + (J - 4.0 * Rd) / (4.0 * gm) - sqrt(pow(CO2 + 2.0 * Gamma + (J - 4.0 * Rd) / (4.0 * gm), 2.0) + 4.0 / gm * (Rd * (CO2 + 2.0 * Gamma) + J / 4.0 * (Gamma - CO2)))) + 2.0 * Gamma)