Poolman 2000 CBB model

import numpy as np

def model(
    time: float,
    variables: list[float], 
):
    _3PGA, BPGA, GAP, DHAP, FBP, F6P, G6P, G1P, SBP, S7P, E4P, X5P, R5P, RUBP, RU5P, atp = variables
    CO2__dissolved_ = 0.2
    nadph = 0.21
    protons = 0.000012589254117941661
    A_P = 0.5
    NADP_ = 0.5
    Pi_tot = 15
    E0_rubisco_carboxylase = 1
    kcat_rubisco_carboxylase = 2.72
    km_rubisco_carboxylase_RUBP = 0.02
    km_rubisco_carboxylase_CO2__dissolved_ = 0.0107
    ki_rubisco_carboxylase_3PGA = 0.04
    ki_rubisco_carboxylase_FBP = 0.04
    ki_rubisco_carboxylase_SBP = 0.075
    ki_rubisco_carboxylase_pi = 0.9
    ki_rubisco_carboxylase_nadph = 0.07
    kre_phosphoglycerate_kinase = 800000000
    keq_phosphoglycerate_kinase = 0.00031
    kre_gadph = 800000000
    keq_gadph = 16000000
    kre_triose_phosphate_isomerase = 800000000
    keq_triose_phosphate_isomerase = 22
    kre_aldolase_dhap_gap = 800000000
    keq_aldolase_dhap_gap = 7.1
    kre_aldolase_dhap_e4p = 800000000
    keq_aldolase_dhap_e4p = 13
    E0_fbpase = 1
    kcat_fbpase = 1.6
    km_fbpase_s = 0.03
    ki_fbpase_F6P = 0.7
    ki_fbpase_pi = 12
    kre_transketolase_gap_f6p = 800000000
    keq_transketolase_gap_f6p = 0.084
    kre_transketolase_gap_s7p = 800000000
    keq_transketolase_gap_s7p = 0.85
    E0_SBPase = 1
    kcat_SBPase = 0.32
    km_SBPase_s = 0.013
    ki_SBPase_pi = 12
    kre_ribose_phosphate_isomerase = 800000000
    keq_ribose_phosphate_isomerase = 0.4
    kre_ribulose_phosphate_epimerase = 800000000
    keq_ribulose_phosphate_epimerase = 0.67
    E0_phosphoribulokinase = 1
    kcat_phosphoribulokinase = 7.9992
    km_phosphoribulokinase_RU5P = 0.05
    km_phosphoribulokinase_atp = 0.05
    ki_phosphoribulokinase_3PGA = 2
    ki_phosphoribulokinase_RUBP = 0.7
    ki_phosphoribulokinase_pi = 4
    ki_phosphoribulokinase_4 = 2.5
    ki_phosphoribulokinase_5 = 0.4
    kre_g6pi = 800000000
    keq_g6pi = 2.3
    kre_phosphoglucomutase = 800000000
    keq_phosphoglucomutase = 0.058
    pi_ext = 0.5
    km_ex_pga = 0.25
    km_ex_gap = 0.075
    km_ex_dhap = 0.077
    km_N_translocator_pi_ext = 0.74
    km_N_translocator_pi = 0.63
    kcat_N_translocator = 2
    E0_N_translocator = 1
    km_ex_g1p_G1P = 0.08
    km_ex_g1p_atp = 0.08
    ki_ex_g1p = 10
    ki_ex_g1p_3PGA = 0.1
    ki_ex_g1p_F6P = 0.02
    ki_ex_g1p_FBP = 0.02
    E0_ex_g1p = 1
    kcat_ex_g1p = 0.32
    km_atp_synthase_adp = 0.014
    km_atp_synthase_pi = 0.3
    kcat_atp_synthase = 2.8
    E0_atp_synthase = 1
    adp = A_P + - atp
    nadp = NADP_ + - nadph
    pi = Pi_tot + - DHAP + - E4P + - F6P + - G1P + - G6P + - GAP + - R5P + - RU5P + - S7P + - X5P + - _3PGA + - atp + - 2 * BPGA + - 2 * FBP + - 2 * RUBP + - 2 * SBP
    vmax_rubisco_carboxylase = E0_rubisco_carboxylase * kcat_rubisco_carboxylase
    vmax_fbpase = E0_fbpase * kcat_fbpase
    vmax_SBPase = E0_SBPase * kcat_SBPase
    vmax_phosphoribulokinase = E0_phosphoribulokinase * kcat_phosphoribulokinase
    vmax_ex_pga = E0_N_translocator * kcat_N_translocator
    N_translocator = 1 + (1 + (km_N_translocator_pi_ext) / (pi_ext)) * ((DHAP) / (km_ex_dhap) + (GAP) / (km_ex_gap) + (_3PGA) / (km_ex_pga) + (pi) / (km_N_translocator_pi))
    vmax_ex_g1p = E0_ex_g1p * kcat_ex_g1p
    vmax_atp_synthase = E0_atp_synthase * kcat_atp_synthase
    rubisco_carboxylase = (CO2__dissolved_ * RUBP * vmax_rubisco_carboxylase) / ((CO2__dissolved_ + km_rubisco_carboxylase_CO2__dissolved_) * (RUBP + km_rubisco_carboxylase_RUBP * (1 + (FBP) / (ki_rubisco_carboxylase_FBP) + (SBP) / (ki_rubisco_carboxylase_SBP) + (_3PGA) / (ki_rubisco_carboxylase_3PGA) + (nadph) / (ki_rubisco_carboxylase_nadph) + (pi) / (ki_rubisco_carboxylase_pi))))
    phosphoglycerate_kinase = kre_phosphoglycerate_kinase * (_3PGA * atp + - (BPGA * adp) / (keq_phosphoglycerate_kinase))
    gadph = kre_gadph * (BPGA * nadph * protons + - (GAP * nadp * pi) / (keq_gadph))
    triose_phosphate_isomerase = kre_triose_phosphate_isomerase * (GAP + - (DHAP) / (keq_triose_phosphate_isomerase))
    aldolase_dhap_gap = kre_aldolase_dhap_gap * (DHAP * GAP + - (FBP) / (keq_aldolase_dhap_gap))
    aldolase_dhap_e4p = kre_aldolase_dhap_e4p * (DHAP * E4P + - (SBP) / (keq_aldolase_dhap_e4p))
    fbpase = (FBP * vmax_fbpase) / (FBP + km_fbpase_s * (1 + (F6P) / (ki_fbpase_F6P) + (pi) / (ki_fbpase_pi)))
    transketolase_gap_f6p = kre_transketolase_gap_f6p * (F6P * GAP + - (E4P * X5P) / (keq_transketolase_gap_f6p))
    transketolase_gap_s7p = kre_transketolase_gap_s7p * (GAP * S7P + - (R5P * X5P) / (keq_transketolase_gap_s7p))
    SBPase = (SBP * vmax_SBPase) / (SBP + km_SBPase_s * (1 + (pi) / (ki_SBPase_pi)))
    ribose_phosphate_isomerase = kre_ribose_phosphate_isomerase * (R5P + - (RU5P) / (keq_ribose_phosphate_isomerase))
    ribulose_phosphate_epimerase = kre_ribulose_phosphate_epimerase * (X5P + - (RU5P) / (keq_ribulose_phosphate_epimerase))
    phosphoribulokinase = (RU5P * atp * vmax_phosphoribulokinase) / ((RU5P + km_phosphoribulokinase_RU5P * (1 + (RUBP) / (ki_phosphoribulokinase_RUBP) + (_3PGA) / (ki_phosphoribulokinase_3PGA) + (pi) / (ki_phosphoribulokinase_pi))) * (atp * (1 + (adp) / (ki_phosphoribulokinase_4)) + km_phosphoribulokinase_atp * (1 + (adp) / (ki_phosphoribulokinase_5))))
    g6pi = kre_g6pi * (F6P + - (G6P) / (keq_g6pi))
    phosphoglucomutase = kre_phosphoglucomutase * (G6P + - (G1P) / (keq_phosphoglucomutase))
    ex_pga = (_3PGA * vmax_ex_pga) / (N_translocator * km_ex_pga)
    ex_gap = (GAP * vmax_ex_pga) / (N_translocator * km_ex_gap)
    ex_dhap = (DHAP * vmax_ex_pga) / (N_translocator * km_ex_dhap)
    ex_g1p = (G1P * atp * vmax_ex_g1p) / ((G1P + km_ex_g1p_G1P) * ((1 + (adp) / (ki_ex_g1p)) * (atp + km_ex_g1p_atp) + (km_ex_g1p_atp * pi) / (F6P * ki_ex_g1p_F6P + FBP * ki_ex_g1p_FBP + _3PGA * ki_ex_g1p_3PGA)))
    atp_synthase = (adp * pi * vmax_atp_synthase) / ((adp + km_atp_synthase_adp) * (km_atp_synthase_pi + pi))
    d_3PGAdt = +2*rubisco_carboxylase-phosphoglycerate_kinase-ex_pga
    dBPGAdt = +phosphoglycerate_kinase-gadph
    dGAPdt = +gadph-triose_phosphate_isomerase-aldolase_dhap_gap-transketolase_gap_f6p-transketolase_gap_s7p-ex_gap
    dDHAPdt = +triose_phosphate_isomerase-aldolase_dhap_gap-aldolase_dhap_e4p-ex_dhap
    dFBPdt = +aldolase_dhap_gap-fbpase
    dF6Pdt = +fbpase-transketolase_gap_f6p-g6pi
    dG6Pdt = +g6pi-phosphoglucomutase
    dG1Pdt = +phosphoglucomutase-ex_g1p
    dSBPdt = +aldolase_dhap_e4p-SBPase
    dS7Pdt = -transketolase_gap_s7p+SBPase
    dE4Pdt = -aldolase_dhap_e4p+transketolase_gap_f6p
    dX5Pdt = +transketolase_gap_f6p+transketolase_gap_s7p-ribulose_phosphate_epimerase
    dR5Pdt = +transketolase_gap_s7p-ribose_phosphate_isomerase
    dRUBPdt = -rubisco_carboxylase+phosphoribulokinase
    dRU5Pdt = +ribose_phosphate_isomerase+ribulose_phosphate_epimerase-phosphoribulokinase
    datpdt = -phosphoglycerate_kinase-phosphoribulokinase-ex_g1p+atp_synthase
    return [d_3PGAdt, dBPGAdt, dGAPdt, dDHAPdt, dFBPdt, dF6Pdt, dG6Pdt, dG1Pdt, dSBPdt, dS7Pdt, dE4Pdt, dX5Pdt, dR5Pdt, dRUBPdt, dRU5Pdt, datpdt]

def all_derived(
    time: float,
    variables: list[float], 
):
    _3PGA, BPGA, GAP, DHAP, FBP, F6P, G6P, G1P, SBP, S7P, E4P, X5P, R5P, RUBP, RU5P, atp = variables
    CO2__dissolved_ = 0.2
    nadph = 0.21
    protons = 0.000012589254117941661
    A_P = 0.5
    NADP_ = 0.5
    Pi_tot = 15
    E0_rubisco_carboxylase = 1
    kcat_rubisco_carboxylase = 2.72
    km_rubisco_carboxylase_RUBP = 0.02
    km_rubisco_carboxylase_CO2__dissolved_ = 0.0107
    ki_rubisco_carboxylase_3PGA = 0.04
    ki_rubisco_carboxylase_FBP = 0.04
    ki_rubisco_carboxylase_SBP = 0.075
    ki_rubisco_carboxylase_pi = 0.9
    ki_rubisco_carboxylase_nadph = 0.07
    kre_phosphoglycerate_kinase = 800000000
    keq_phosphoglycerate_kinase = 0.00031
    kre_gadph = 800000000
    keq_gadph = 16000000
    kre_triose_phosphate_isomerase = 800000000
    keq_triose_phosphate_isomerase = 22
    kre_aldolase_dhap_gap = 800000000
    keq_aldolase_dhap_gap = 7.1
    kre_aldolase_dhap_e4p = 800000000
    keq_aldolase_dhap_e4p = 13
    E0_fbpase = 1
    kcat_fbpase = 1.6
    km_fbpase_s = 0.03
    ki_fbpase_F6P = 0.7
    ki_fbpase_pi = 12
    kre_transketolase_gap_f6p = 800000000
    keq_transketolase_gap_f6p = 0.084
    kre_transketolase_gap_s7p = 800000000
    keq_transketolase_gap_s7p = 0.85
    E0_SBPase = 1
    kcat_SBPase = 0.32
    km_SBPase_s = 0.013
    ki_SBPase_pi = 12
    kre_ribose_phosphate_isomerase = 800000000
    keq_ribose_phosphate_isomerase = 0.4
    kre_ribulose_phosphate_epimerase = 800000000
    keq_ribulose_phosphate_epimerase = 0.67
    E0_phosphoribulokinase = 1
    kcat_phosphoribulokinase = 7.9992
    km_phosphoribulokinase_RU5P = 0.05
    km_phosphoribulokinase_atp = 0.05
    ki_phosphoribulokinase_3PGA = 2
    ki_phosphoribulokinase_RUBP = 0.7
    ki_phosphoribulokinase_pi = 4
    ki_phosphoribulokinase_4 = 2.5
    ki_phosphoribulokinase_5 = 0.4
    kre_g6pi = 800000000
    keq_g6pi = 2.3
    kre_phosphoglucomutase = 800000000
    keq_phosphoglucomutase = 0.058
    pi_ext = 0.5
    km_ex_pga = 0.25
    km_ex_gap = 0.075
    km_ex_dhap = 0.077
    km_N_translocator_pi_ext = 0.74
    km_N_translocator_pi = 0.63
    kcat_N_translocator = 2
    E0_N_translocator = 1
    km_ex_g1p_G1P = 0.08
    km_ex_g1p_atp = 0.08
    ki_ex_g1p = 10
    ki_ex_g1p_3PGA = 0.1
    ki_ex_g1p_F6P = 0.02
    ki_ex_g1p_FBP = 0.02
    E0_ex_g1p = 1
    kcat_ex_g1p = 0.32
    km_atp_synthase_adp = 0.014
    km_atp_synthase_pi = 0.3
    kcat_atp_synthase = 2.8
    E0_atp_synthase = 1
    adp = A_P + - atp
    nadp = NADP_ + - nadph
    pi = Pi_tot + - DHAP + - E4P + - F6P + - G1P + - G6P + - GAP + - R5P + - RU5P + - S7P + - X5P + - _3PGA + - atp + - 2 * BPGA + - 2 * FBP + - 2 * RUBP + - 2 * SBP
    vmax_rubisco_carboxylase = E0_rubisco_carboxylase * kcat_rubisco_carboxylase
    vmax_fbpase = E0_fbpase * kcat_fbpase
    vmax_SBPase = E0_SBPase * kcat_SBPase
    vmax_phosphoribulokinase = E0_phosphoribulokinase * kcat_phosphoribulokinase
    vmax_ex_pga = E0_N_translocator * kcat_N_translocator
    N_translocator = 1 + (1 + (km_N_translocator_pi_ext) / (pi_ext)) * ((DHAP) / (km_ex_dhap) + (GAP) / (km_ex_gap) + (_3PGA) / (km_ex_pga) + (pi) / (km_N_translocator_pi))
    vmax_ex_g1p = E0_ex_g1p * kcat_ex_g1p
    vmax_atp_synthase = E0_atp_synthase * kcat_atp_synthase
    rubisco_carboxylase = (CO2__dissolved_ * RUBP * vmax_rubisco_carboxylase) / ((CO2__dissolved_ + km_rubisco_carboxylase_CO2__dissolved_) * (RUBP + km_rubisco_carboxylase_RUBP * (1 + (FBP) / (ki_rubisco_carboxylase_FBP) + (SBP) / (ki_rubisco_carboxylase_SBP) + (_3PGA) / (ki_rubisco_carboxylase_3PGA) + (nadph) / (ki_rubisco_carboxylase_nadph) + (pi) / (ki_rubisco_carboxylase_pi))))
    phosphoglycerate_kinase = kre_phosphoglycerate_kinase * (_3PGA * atp + - (BPGA * adp) / (keq_phosphoglycerate_kinase))
    gadph = kre_gadph * (BPGA * nadph * protons + - (GAP * nadp * pi) / (keq_gadph))
    triose_phosphate_isomerase = kre_triose_phosphate_isomerase * (GAP + - (DHAP) / (keq_triose_phosphate_isomerase))
    aldolase_dhap_gap = kre_aldolase_dhap_gap * (DHAP * GAP + - (FBP) / (keq_aldolase_dhap_gap))
    aldolase_dhap_e4p = kre_aldolase_dhap_e4p * (DHAP * E4P + - (SBP) / (keq_aldolase_dhap_e4p))
    fbpase = (FBP * vmax_fbpase) / (FBP + km_fbpase_s * (1 + (F6P) / (ki_fbpase_F6P) + (pi) / (ki_fbpase_pi)))
    transketolase_gap_f6p = kre_transketolase_gap_f6p * (F6P * GAP + - (E4P * X5P) / (keq_transketolase_gap_f6p))
    transketolase_gap_s7p = kre_transketolase_gap_s7p * (GAP * S7P + - (R5P * X5P) / (keq_transketolase_gap_s7p))
    SBPase = (SBP * vmax_SBPase) / (SBP + km_SBPase_s * (1 + (pi) / (ki_SBPase_pi)))
    ribose_phosphate_isomerase = kre_ribose_phosphate_isomerase * (R5P + - (RU5P) / (keq_ribose_phosphate_isomerase))
    ribulose_phosphate_epimerase = kre_ribulose_phosphate_epimerase * (X5P + - (RU5P) / (keq_ribulose_phosphate_epimerase))
    phosphoribulokinase = (RU5P * atp * vmax_phosphoribulokinase) / ((RU5P + km_phosphoribulokinase_RU5P * (1 + (RUBP) / (ki_phosphoribulokinase_RUBP) + (_3PGA) / (ki_phosphoribulokinase_3PGA) + (pi) / (ki_phosphoribulokinase_pi))) * (atp * (1 + (adp) / (ki_phosphoribulokinase_4)) + km_phosphoribulokinase_atp * (1 + (adp) / (ki_phosphoribulokinase_5))))
    g6pi = kre_g6pi * (F6P + - (G6P) / (keq_g6pi))
    phosphoglucomutase = kre_phosphoglucomutase * (G6P + - (G1P) / (keq_phosphoglucomutase))
    ex_pga = (_3PGA * vmax_ex_pga) / (N_translocator * km_ex_pga)
    ex_gap = (GAP * vmax_ex_pga) / (N_translocator * km_ex_gap)
    ex_dhap = (DHAP * vmax_ex_pga) / (N_translocator * km_ex_dhap)
    ex_g1p = (G1P * atp * vmax_ex_g1p) / ((G1P + km_ex_g1p_G1P) * ((1 + (adp) / (ki_ex_g1p)) * (atp + km_ex_g1p_atp) + (km_ex_g1p_atp * pi) / (F6P * ki_ex_g1p_F6P + FBP * ki_ex_g1p_FBP + _3PGA * ki_ex_g1p_3PGA)))
    atp_synthase = (adp * pi * vmax_atp_synthase) / ((adp + km_atp_synthase_adp) * (km_atp_synthase_pi + pi))
    return [adp, nadp, pi, vmax_rubisco_carboxylase, vmax_fbpase, vmax_SBPase, vmax_phosphoribulokinase, vmax_ex_pga, N_translocator, vmax_ex_g1p, vmax_atp_synthase, rubisco_carboxylase, phosphoglycerate_kinase, gadph, triose_phosphate_isomerase, aldolase_dhap_gap, aldolase_dhap_e4p, fbpase, transketolase_gap_f6p, transketolase_gap_s7p, SBPase, ribose_phosphate_isomerase, ribulose_phosphate_epimerase, phosphoribulokinase, g6pi, phosphoglucomutase, ex_pga, ex_gap, ex_dhap, ex_g1p, atp_synthase]

derived = all_derived
y0 = {"_3PGA": 0.6387788347932627, "BPGA": 0.0013570885908749779, "GAP": 0.011259431827358068, "DHAP": 0.24770748227012374, "FBP": 0.01980222074817044, "F6P": 1.093666906864421, "G6P": 2.5154338857582377, "G1P": 0.14589516537322303, "SBP": 0.09132688566151095, "S7P": 0.23281380022778891, "E4P": 0.02836065066520614, "X5P": 0.03647242425941113, "R5P": 0.06109130988031577, "RUBP": 0.2672164362349537, "RU5P": 0.0244365238237522, "atp": 0.43633201706180874}
    

\begin{align*}
      \frac{d 3PGA}{dt} &= 2 \cdot \frac{CO2 (dissolved) \cdot RUBP \cdot vmax\_rubisco\_carboxylase}{(CO2 (dissolved) + km\_rubisco\_carboxylase\_CO2 (dissolved)) \cdot (RUBP + km\_rubisco\_carboxylase\_RUBP \cdot (1 + \frac{FBP}{ki\_rubisco\_carboxylase\_FBP} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA} + \frac{nadph}{ki\_rubisco\_carboxylase\_nadph} + \frac{pi}{ki\_rubisco\_carboxylase\_pi}))} \\
  & - kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{3PGA \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_pga}\\ 
\frac{d BPGA}{dt} &= kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - kre\_gadph \cdot (BPGA \cdot nadph \cdot protons - \frac{GAP \cdot nadp \cdot pi}{keq\_gadph})\\ 
\frac{d GAP}{dt} &= kre\_gadph \cdot (BPGA \cdot nadph \cdot protons - \frac{GAP \cdot nadp \cdot pi}{keq\_gadph}) \\
  & - kre\_triose\_phosphate\_isomerase \cdot (GAP - \frac{DHAP}{keq\_triose\_phosphate\_isomerase}) \\
  & - kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & - kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - \frac{GAP \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_gap}\\ 
\frac{d DHAP}{dt} &= kre\_triose\_phosphate\_isomerase \cdot (GAP - \frac{DHAP}{keq\_triose\_phosphate\_isomerase}) \\
  & - kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & - \frac{DHAP \cdot vmax\_ex\_pga}{N\_translocator \cdot km\_ex\_dhap}\\ 
\frac{d FBP}{dt} &= kre\_aldolase\_dhap\_gap \cdot (DHAP \cdot GAP - \frac{FBP}{keq\_aldolase\_dhap\_gap}) \\
  & - \frac{FBP \cdot vmax\_fbpase}{FBP + km\_fbpase\_s \cdot (1 + \frac{F6P}{ki\_fbpase\_F6P} + \frac{pi}{ki\_fbpase\_pi})}\\ 
\frac{d F6P}{dt} &= \frac{FBP \cdot vmax\_fbpase}{FBP + km\_fbpase\_s \cdot (1 + \frac{F6P}{ki\_fbpase\_F6P} + \frac{pi}{ki\_fbpase\_pi})} \\
  & - kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & - kre\_g6pi \cdot (F6P - \frac{G6P}{keq\_g6pi})\\ 
\frac{d G6P}{dt} &= kre\_g6pi \cdot (F6P - \frac{G6P}{keq\_g6pi}) \\
  & - kre\_phosphoglucomutase \cdot (G6P - \frac{G1P}{keq\_phosphoglucomutase})\\ 
\frac{d G1P}{dt} &= kre\_phosphoglucomutase \cdot (G6P - \frac{G1P}{keq\_phosphoglucomutase}) \\
  & - \frac{G1P \cdot atp \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{adp}{ki\_ex\_g1p}) \cdot (atp + km\_ex\_g1p\_atp) + \frac{km\_ex\_g1p\_atp \cdot pi}{F6P \cdot ki\_ex\_g1p\_F6P + FBP \cdot ki\_ex\_g1p\_FBP + 3PGA \cdot ki\_ex\_g1p\_3PGA})}\\ 
\frac{d SBP}{dt} &= kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & - \frac{SBP \cdot vmax\_SBPase}{SBP + km\_SBPase\_s \cdot (1 + \frac{pi}{ki\_SBPase\_pi})}\\ 
\frac{d S7P}{dt} &= - kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & + \frac{SBP \cdot vmax\_SBPase}{SBP + km\_SBPase\_s \cdot (1 + \frac{pi}{ki\_SBPase\_pi})}\\ 
\frac{d E4P}{dt} &= - kre\_aldolase\_dhap\_e4p \cdot (DHAP \cdot E4P - \frac{SBP}{keq\_aldolase\_dhap\_e4p}) \\
  & + kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p})\\ 
\frac{d X5P}{dt} &= kre\_transketolase\_gap\_f6p \cdot (F6P \cdot GAP - \frac{E4P \cdot X5P}{keq\_transketolase\_gap\_f6p}) \\
  & + kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - kre\_ribulose\_phosphate\_epimerase \cdot (X5P - \frac{RU5P}{keq\_ribulose\_phosphate\_epimerase})\\ 
\frac{d R5P}{dt} &= kre\_transketolase\_gap\_s7p \cdot (GAP \cdot S7P - \frac{R5P \cdot X5P}{keq\_transketolase\_gap\_s7p}) \\
  & - kre\_ribose\_phosphate\_isomerase \cdot (R5P - \frac{RU5P}{keq\_ribose\_phosphate\_isomerase})\\ 
\frac{d RUBP}{dt} &= - \frac{CO2 (dissolved) \cdot RUBP \cdot vmax\_rubisco\_carboxylase}{(CO2 (dissolved) + km\_rubisco\_carboxylase\_CO2 (dissolved)) \cdot (RUBP + km\_rubisco\_carboxylase\_RUBP \cdot (1 + \frac{FBP}{ki\_rubisco\_carboxylase\_FBP} + \frac{SBP}{ki\_rubisco\_carboxylase\_SBP} + \frac{3PGA}{ki\_rubisco\_carboxylase\_3PGA} + \frac{nadph}{ki\_rubisco\_carboxylase\_nadph} + \frac{pi}{ki\_rubisco\_carboxylase\_pi}))} \\
  & + \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))}\\ 
\frac{d RU5P}{dt} &= kre\_ribose\_phosphate\_isomerase \cdot (R5P - \frac{RU5P}{keq\_ribose\_phosphate\_isomerase}) \\
  & + kre\_ribulose\_phosphate\_epimerase \cdot (X5P - \frac{RU5P}{keq\_ribulose\_phosphate\_epimerase}) \\
  & - \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))}\\ 
\frac{d atp}{dt} &= - kre\_phosphoglycerate\_kinase \cdot (3PGA \cdot atp - \frac{BPGA \cdot adp}{keq\_phosphoglycerate\_kinase}) \\
  & - \frac{RU5P \cdot atp \cdot vmax\_phosphoribulokinase}{(RU5P + km\_phosphoribulokinase\_RU5P \cdot (1 + \frac{RUBP}{ki\_phosphoribulokinase\_RUBP} + \frac{3PGA}{ki\_phosphoribulokinase\_3PGA} + \frac{pi}{ki\_phosphoribulokinase\_pi})) \cdot (atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_4}) + km\_phosphoribulokinase\_atp \cdot (1 + \frac{adp}{ki\_phosphoribulokinase\_5}))} \\
  & - \frac{G1P \cdot atp \cdot vmax\_ex\_g1p}{(G1P + km\_ex\_g1p\_G1P) \cdot ((1 + \frac{adp}{ki\_ex\_g1p}) \cdot (atp + km\_ex\_g1p\_atp) + \frac{km\_ex\_g1p\_atp \cdot pi}{F6P \cdot ki\_ex\_g1p\_F6P + FBP \cdot ki\_ex\_g1p\_FBP + 3PGA \cdot ki\_ex\_g1p\_3PGA})} \\
  & + \frac{adp \cdot pi \cdot vmax\_atp\_synthase}{(adp + km\_atp\_synthase\_adp) \cdot (km\_atp\_synthase\_pi + pi)}
    \end{align*}