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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

• phase_reaction_ZZZ refers to one of the phase-specific raction groups listed in Reaction models, e.g., liquid_reaction_ZZZ, solid_reaction_ZZZ.

• 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_KMM

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. Input as reaction index major.

Unit: \(~mol^{-1}~m^{-3}\)

Type: double

Range: \(\mathbb{R}\)

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

MM_KI_C

(Optional)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

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

MM_PRE_K

(Optional) Factor (\(\neq 0\)) before component for multiplying with Michaelis-Menten kinetics. The index \(k\) corresponds to the component acting on reaction \(j\). Note that components acting as substrates can not defined as prefactor components. Input as reaction index major.

Unit: None

Type: double

Range: \(\mathbb{R}\)

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

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
]