Yokota 1985 photorespiration model

import numpy as np

def model(
    time: float,
    variables: list[float], 
):
    glycolate, glyoxylate, glycine, serine, hydroxypyruvate, H2O2 = variables
    kf_phosphoglycolate_phosphatase = 60
    E0_glycolate_oxidase = 1
    kcat_glycolate_oxidase = 100
    km_glycolate_oxidase_s = 0.06
    E0_glycine_transaminase = 1
    kcat_glycine_transaminase = 143
    km_glycine_transaminase_s = 3
    E0_glycine_decarboxylase = 0.5
    kcat_glycine_decarboxylase = 100
    km_glycine_decarboxylase_s = 6
    E0_serine_glyoxylate_transaminase = 1
    kcat_serine_glyoxylate_transaminase = 159
    km_serine_glyoxylate_transaminase_glyoxylate = 0.15
    km_serine_glyoxylate_transaminase_serine = 2.72
    E0_glycerate_dehydrogenase = 1
    kcat_glycerate_dehydrogenase = 398
    km_glycerate_dehydrogenase_s = 0.12
    E0_catalase = 1
    kcat_catalase = 760500
    km_catalase_s = 137.9
    vmax_glycolate_oxidase = E0_glycolate_oxidase * kcat_glycolate_oxidase
    vmax_glycine_transaminase = E0_glycine_transaminase * kcat_glycine_transaminase
    vmax_glycine_decarboxylase = E0_glycine_decarboxylase * kcat_glycine_decarboxylase
    vmax_serine_glyoxylate_transaminase = E0_serine_glyoxylate_transaminase * kcat_serine_glyoxylate_transaminase
    vmax_glycerate_dehydrogenase = E0_glycerate_dehydrogenase * kcat_glycerate_dehydrogenase
    vmax_catalase = E0_catalase * kcat_catalase
    phosphoglycolate_phosphatase = kf_phosphoglycolate_phosphatase
    glycolate_oxidase = (glycolate * vmax_glycolate_oxidase) / (glycolate + km_glycolate_oxidase_s)
    glycine_transaminase = (glyoxylate * vmax_glycine_transaminase) / (glyoxylate + km_glycine_transaminase_s)
    glycine_decarboxylase = (glycine * vmax_glycine_decarboxylase) / (glycine + km_glycine_decarboxylase_s)
    serine_glyoxylate_transaminase = (glyoxylate * serine * vmax_serine_glyoxylate_transaminase) / (glyoxylate * serine + (glyoxylate) / (km_serine_glyoxylate_transaminase_glyoxylate) + (serine) / (km_serine_glyoxylate_transaminase_serine) + (1) / (km_serine_glyoxylate_transaminase_glyoxylate * km_serine_glyoxylate_transaminase_serine))
    glycerate_dehydrogenase = (hydroxypyruvate * vmax_glycerate_dehydrogenase) / (hydroxypyruvate + km_glycerate_dehydrogenase_s)
    catalase = (H2O2 * vmax_catalase) / (H2O2 + km_catalase_s)
    dglycolatedt = +phosphoglycolate_phosphatase-glycolate_oxidase
    dglyoxylatedt = +glycolate_oxidase-glycine_transaminase-serine_glyoxylate_transaminase
    dglycinedt = +glycine_transaminase-2*glycine_decarboxylase+serine_glyoxylate_transaminase
    dserinedt = +glycine_decarboxylase-serine_glyoxylate_transaminase
    dhydroxypyruvatedt = +serine_glyoxylate_transaminase-glycerate_dehydrogenase
    dH2O2dt = +glycolate_oxidase-catalase
    return [dglycolatedt, dglyoxylatedt, dglycinedt, dserinedt, dhydroxypyruvatedt, dH2O2dt]

def all_derived(
    time: float,
    variables: list[float], 
):
    glycolate, glyoxylate, glycine, serine, hydroxypyruvate, H2O2 = variables
    kf_phosphoglycolate_phosphatase = 60
    E0_glycolate_oxidase = 1
    kcat_glycolate_oxidase = 100
    km_glycolate_oxidase_s = 0.06
    E0_glycine_transaminase = 1
    kcat_glycine_transaminase = 143
    km_glycine_transaminase_s = 3
    E0_glycine_decarboxylase = 0.5
    kcat_glycine_decarboxylase = 100
    km_glycine_decarboxylase_s = 6
    E0_serine_glyoxylate_transaminase = 1
    kcat_serine_glyoxylate_transaminase = 159
    km_serine_glyoxylate_transaminase_glyoxylate = 0.15
    km_serine_glyoxylate_transaminase_serine = 2.72
    E0_glycerate_dehydrogenase = 1
    kcat_glycerate_dehydrogenase = 398
    km_glycerate_dehydrogenase_s = 0.12
    E0_catalase = 1
    kcat_catalase = 760500
    km_catalase_s = 137.9
    vmax_glycolate_oxidase = E0_glycolate_oxidase * kcat_glycolate_oxidase
    vmax_glycine_transaminase = E0_glycine_transaminase * kcat_glycine_transaminase
    vmax_glycine_decarboxylase = E0_glycine_decarboxylase * kcat_glycine_decarboxylase
    vmax_serine_glyoxylate_transaminase = E0_serine_glyoxylate_transaminase * kcat_serine_glyoxylate_transaminase
    vmax_glycerate_dehydrogenase = E0_glycerate_dehydrogenase * kcat_glycerate_dehydrogenase
    vmax_catalase = E0_catalase * kcat_catalase
    phosphoglycolate_phosphatase = kf_phosphoglycolate_phosphatase
    glycolate_oxidase = (glycolate * vmax_glycolate_oxidase) / (glycolate + km_glycolate_oxidase_s)
    glycine_transaminase = (glyoxylate * vmax_glycine_transaminase) / (glyoxylate + km_glycine_transaminase_s)
    glycine_decarboxylase = (glycine * vmax_glycine_decarboxylase) / (glycine + km_glycine_decarboxylase_s)
    serine_glyoxylate_transaminase = (glyoxylate * serine * vmax_serine_glyoxylate_transaminase) / (glyoxylate * serine + (glyoxylate) / (km_serine_glyoxylate_transaminase_glyoxylate) + (serine) / (km_serine_glyoxylate_transaminase_serine) + (1) / (km_serine_glyoxylate_transaminase_glyoxylate * km_serine_glyoxylate_transaminase_serine))
    glycerate_dehydrogenase = (hydroxypyruvate * vmax_glycerate_dehydrogenase) / (hydroxypyruvate + km_glycerate_dehydrogenase_s)
    catalase = (H2O2 * vmax_catalase) / (H2O2 + km_catalase_s)
    return [vmax_glycolate_oxidase, vmax_glycine_transaminase, vmax_glycine_decarboxylase, vmax_serine_glyoxylate_transaminase, vmax_glycerate_dehydrogenase, vmax_catalase, phosphoglycolate_phosphatase, glycolate_oxidase, glycine_transaminase, glycine_decarboxylase, serine_glyoxylate_transaminase, glycerate_dehydrogenase, catalase]

derived = all_derived
y0 = {"glycolate": 0.09, "glyoxylate": 0.7964601770483386, "glycine": 8.999999999424611, "serine": 2.5385608670239126, "hydroxypyruvate": 0.009782608695111009, "H2O2": 0.010880542843616855}
    

\begin{align*}
      \frac{d glycolate}{dt} &= kf\_phosphoglycolate\_phosphatase \\
  & - \frac{glycolate \cdot vmax\_glycolate\_oxidase}{glycolate + km\_glycolate\_oxidase\_s}\\ 
\frac{d glyoxylate}{dt} &= \frac{glycolate \cdot vmax\_glycolate\_oxidase}{glycolate + km\_glycolate\_oxidase\_s} \\
  & - \frac{glyoxylate \cdot vmax\_glycine\_transaminase}{glyoxylate + km\_glycine\_transaminase\_s} \\
  & - \frac{glyoxylate \cdot serine \cdot vmax\_serine\_glyoxylate\_transaminase}{glyoxylate \cdot serine + \frac{glyoxylate}{km\_serine\_glyoxylate\_transaminase\_glyoxylate} + \frac{serine}{km\_serine\_glyoxylate\_transaminase\_serine} + \frac{1}{km\_serine\_glyoxylate\_transaminase\_glyoxylate \cdot km\_serine\_glyoxylate\_transaminase\_serine}}\\ 
\frac{d glycine}{dt} &= \frac{glyoxylate \cdot vmax\_glycine\_transaminase}{glyoxylate + km\_glycine\_transaminase\_s} \\
  & - 2 \cdot \frac{glycine \cdot vmax\_glycine\_decarboxylase}{glycine + km\_glycine\_decarboxylase\_s} \\
  & + \frac{glyoxylate \cdot serine \cdot vmax\_serine\_glyoxylate\_transaminase}{glyoxylate \cdot serine + \frac{glyoxylate}{km\_serine\_glyoxylate\_transaminase\_glyoxylate} + \frac{serine}{km\_serine\_glyoxylate\_transaminase\_serine} + \frac{1}{km\_serine\_glyoxylate\_transaminase\_glyoxylate \cdot km\_serine\_glyoxylate\_transaminase\_serine}}\\ 
\frac{d serine}{dt} &= \frac{glycine \cdot vmax\_glycine\_decarboxylase}{glycine + km\_glycine\_decarboxylase\_s} \\
  & - \frac{glyoxylate \cdot serine \cdot vmax\_serine\_glyoxylate\_transaminase}{glyoxylate \cdot serine + \frac{glyoxylate}{km\_serine\_glyoxylate\_transaminase\_glyoxylate} + \frac{serine}{km\_serine\_glyoxylate\_transaminase\_serine} + \frac{1}{km\_serine\_glyoxylate\_transaminase\_glyoxylate \cdot km\_serine\_glyoxylate\_transaminase\_serine}}\\ 
\frac{d hydroxypyruvate}{dt} &= \frac{glyoxylate \cdot serine \cdot vmax\_serine\_glyoxylate\_transaminase}{glyoxylate \cdot serine + \frac{glyoxylate}{km\_serine\_glyoxylate\_transaminase\_glyoxylate} + \frac{serine}{km\_serine\_glyoxylate\_transaminase\_serine} + \frac{1}{km\_serine\_glyoxylate\_transaminase\_glyoxylate \cdot km\_serine\_glyoxylate\_transaminase\_serine}} \\
  & - \frac{hydroxypyruvate \cdot vmax\_glycerate\_dehydrogenase}{hydroxypyruvate + km\_glycerate\_dehydrogenase\_s}\\ 
\frac{d H2O2}{dt} &= \frac{glycolate \cdot vmax\_glycolate\_oxidase}{glycolate + km\_glycolate\_oxidase\_s} \\
  & - \frac{H2O2 \cdot vmax\_catalase}{H2O2 + km\_catalase\_s}
    \end{align*}