Default Rate Law Classifications

Before the analysis, we classify each rate law into different categories (Xu, 2023). If a rate law does not belong to any of the default classes or the custom classification file provided, a warning will be raised.

The following categories are used for classifying rate laws:

• Zeroth order (ZERO): No reactant or product in the rate law. - Description: These reactions proceed at a constant rate regardless of the concentration of reactants or products. - Example:

  A -> B; k
  A = 10
  B = 0
  k = 0.1
  

• Uni-Directional Mass Action (UNDR): Direct, one-way reactions where all reactants influencing the rate law and resulting in a single product. - Description: These reactions follow the law of mass action for reactants. - Example:

  A + B -> C; k*A*B
  A = 10
  B = 5
  C = 0
  k = 0.01
  

• Uni-Directional Mass Action with an Activator (UNDR-A): Similar to UNDR but includes an essential activator. - Description: These reactions are influenced by the presence of an activator. - Example:

  A + B -> C; k*A*B*Activator
  A = 10
  B = 5
  C = 0
  Activator = 2
  k = 0.01
  

• Bi-Directional Mass Action (BIDR): Covers reversible reactions with all reactants and products in the rate law. - Description: These reactions are reversible and follow the law of mass action. - Example:

  A + B -> C + D; k1*A*B - k2*C*D
  A = 10
  B = 5
  C = 2
  D = 1
  k1 = 0.01
  k2 = 0.005
  

• Bi-Directional Mass Action with Activator(s) (BIDR-A): Reversible reactions with activators, including enzymes different from reactants and products. - Description: These reactions are reversible and influenced by activators or enzymes. - Example:

  A + B -> C + D; k1*A*B*Activator - k2*C*D
  A = 10
  B = 5
  C = 2
  D = 1
  Activator = 2
  k1 = 0.01
  k2 = 0.005
  

• Michaelis-Menten (MM): Describes enzymatic reactions based on substrate concentration, following specific Michaelis-Menten formulas without explicitly mentioning the enzyme. - Description: These reactions follow Michaelis-Menten kinetics. - Example:

  S => P; Vmax*S/(Km + S)
  E = 1
  S = 10
  P = 0
  Vmax = 1
  Km = 5
  

• Michaelis-Menten with explicit enzyme (MMcat): Michaelis-Menten model explicitly incorporating the enzyme in the reaction rate equation. - Description: These reactions explicitly include the enzyme in the Michaelis-Menten kinetics. - Example:

  S => P; Vmax*E*S/(Km + S)
  E = 1
  S = 10
  P = 0
  Vmax = 1
  Km = 5
  

• Allosteric and Inhibitors: Michaelis-Menten format affected by allosteric effects or inhibitors, altering reaction rates through enzyme or substrate modulation. - Description: These reactions are influenced by allosteric modulators or inhibitors. - Example:

  S => P; Vmax*S/(S + Km*(1 + Inhibitor/Ki))
  E = 1
  S = 10
  P = 0
  Inhibitor = 2
  Vmax = 1
  Km = 5
  Ki = 2
  

• Reversible Michaelis-Menten: Accounts for reaction reversibility in Michaelis-Menten format. - Description: These reactions are reversible and follow Michaelis-Menten kinetics. - Example:

  S => P; (Vf*S - Vr*P)/(Km + S)
  E = 1
  S = 10
  P = 0
  Vf = 1
  Vr = 0.5
  Km = 5
  

• Hill Equation: Describes enzyme kinetics in cooperative binding scenarios, relating reaction rate to substrate concentration through a sigmoidal curve. - Description: These reactions follow the Hill equation, describing cooperative binding. - Example:

  S => P; Vmax*S^n/(Kd^n + S^n)
  S = 10
  Vmax = 1
  Kd = 5
  n = 2
  

The details of the default rate law classifications can be found in the source code.