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Michaelis Menten kinetics

Group /input/model/unit_XXX(/particle_type_YYY)/phase_reaction_ZZZ/ - TYPE = MICHAELIS_MENTEN

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

Notes

• reaction_phase_ZZZ refers to one of the phase-specific reaction groups listed in Reaction models, e.g., reaction_bulk_ZZZ, reaction_solid_ZZZ, or reaction_particle_ZZZ (for particle type YYY).

• Some dimensions below depend on the hosting phase of this model instance:

  • Bulk phase or particle liquid phase: NVAR = NCOMP

  • Particle solid phase: NVAR = NTOTALBOUND (total number of bound states across all components)

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: \(\texttt{NREACT} \cdot \texttt{NVAR}\)

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: \(\texttt{NREACT} \cdot \texttt{NVAR} \cdot \texttt{NVAR}\)

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: \(\texttt{NREACT} \cdot \texttt{NVAR} \cdot \texttt{NVAR}\)

CADET Python Interface Example

This example shows the configuration of one Michaelis-Menten reaction system in bulk liquid phase. 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
input.model.unit_000.NREAC_LIQUID = 1
input.model.unit_000.reaction_liquid_000.type = 'MICHAELIS_MENTEN'

# Km values 2D array [reaction][components]
input.model.unit_000.reaction_liquid_000.mm_km = [
    [KM_a, 0.0]  # A is substrate
]

# Competitive inhibition constants - 3D array [reaction][components][components]
input.model.unit_000.reaction_liquid_000.mm_ki_c = [
    [
        [0.0, KI_b_a],  # Inhibition constant for A (Product inhibition B inhibits A)
        [0.0, 0.0],     # Inhibition constant for B (not active)
    ]
]

# Uncompetitive inhibition constants - 3D array [reaction][components][components]
input.model.unit_000.reaction_liquid_000.mm_ki_uc = [
    [
        [0.0, 0.0],  # Inhibition constant for A (not active)
        [0.0, 0.0],  # Inhibition constant for B (not active)
    ]
]

# Vmax values 1D array [reaction]
input.model.unit_000.reaction_liquid_000.mm_vmax = [vmax]

# Stoichiometry matrix 2D array [components][reaction]
input.model.unit_000.reaction_liquid_000.mm_stoichiometry = [
    [-1],
    [1]  # A -> B
]