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Michaelis Menten kinetics

Group /input/model/unit_XXX/reaction - REACTION_MODEL = MICHAELIS_MENTEN

For information on model equations, refer to Michaelis Menten kinetics.

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 \(K^{c}_{I_{k}}\).

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 for uncompetitive inhibition \(K^{uc}_{I_{k}}\).

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
 ]