You're reading the documentation for a development version. For the latest released version, please have a look at v5.0.4.
Michaelis Menten kinetics¶
Group /input/model/unit_XXX/reaction - REACTION_MODEL = MICHAELIS_MENTEN
For information on model equations, refer to _michaelis_menten_kinetics_model.
MM_STOICHIOMETRY_BULK
Stoichiometric matrix \(S\). This matrix defines the quantitative relationships between reactants and products for each reaction in the system. Each entry \(S_{i,j}\) specifies the stoichiometric coefficient for component \(i\) in reaction \(j\). Negative values indicate consumption (substrate), while positive values indicate production (products). Input as reaction index major.
Unit: None
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NREACT} \cdot \texttt{NCOMP}\)
MM_VMAX
Maximum reaction rate \(v_{\mathrm{max},j}\) at substrate saturation for reaction \(j\). This parameter defines the upper limit of the reaction rate when the substrate concentration is sufficiently high such that the enzyme is saturated.
Unit: \(~mol^{-1}~m^{-3}~s^{-1}\)
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NREACT}\)
MM_KM
Michaelis constant \(K_{\mathrm{M},{i,j}}\) for reaction \(j\) and substrate \(i\). This constant represents the substrate concentration at which the reaction rate is half of its maximum value.
Unit: \(~mol^{-1}~m^{-3}\)
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NREACT}\)
MM_KI_C
Inhibition constant for competitive inhibition \(K_{I_{k}}\).
The index \(k\) corresponds to the inhibitors acting on substrate \(c_{i,j}\) in reaction \(j\), i.e. \(k = (j,i,k)\), where \(k\) is the index of the inhibitor. If \(K^{c}_{I_{k}} > 0\), the component inhibits the reaction.
Input as reaction index major.
Unit: \(mol^{-1}~m^{-3}\)
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NREACT} \cdot \texttt{NCOMP} \cdot \texttt{NCOMP}\)
MM_KI_UC
Inhibition constant uncompetitive inhibition \(K^{u}_{I_{k}}\).
- The index \(k\) corresponds to the inhibitors acting on substrate \(c_{i,j}\) in reaction \(j\), i.e. \(k = (j,i,k)\), where \(k\) is the index of the inhibitor.
Input as reaction index major.
Unit: \(mol^{-1}~m^{-3}\)
Type: double
Range: \(\mathbb{R}\)
Length: \(\texttt{NREACT} \cdot \texttt{NCOMP} \cdot \texttt{NCOMP}\)
Example configuration¶
This example shows the configuration of one Michaelis-Menten reaction system in CADET-Python. The system has two components A and B, where A is the substrate and B is the product. In addition to that the model includes:
A Michaelis constant
KM_a
,competitive inhibition constant of
KI_b_a
for B inhibiting A,and a maximum rate of
vmax
#Configure the reaction system
model.root.input.model.unit_001.reaction_model = 'MICHAELIS_MENTEN'
# Km values 2D array [reaction][components]
model.root.input.model.unit_001.reaction_bulk.mm_km = [
[KM_a, 0.0] # A is substrate
]
# Competitive inhibition constants - 3D array [reaction][components][components]
model.root.input.model.unit_001.reaction_bulk.mm_ki_c = [
[
[0.0, KI_b_a], # Inhibition konstant for A (Product inhibtion B inhibits A)
[0.0, 0.0], # Inhibition konstant for B (not active)
]
]
# Uncompetitive inhibition constants - 3D array [reaction][components][components]
model.root.input.model.unit_001.reaction_bulk.mm_ki_uc = [
[
[0.0, 0.0], # Inhibition konstant for A (not active)
[0.0, 0.0], # Inhibition konstant for B (not active)
]
]
# Vmax values 1D array [reaction]
model.root.input.model.unit_001.reaction_bulk.mm_vmax = [vmax]
# Stoichiometry matrix 2D array [components][reaction]
model.root.input.model.unit_001.reaction_bulk.mm_stoichiometry_bulk = [
[-1],
[1] # A -> B
]