Kinetic Laws - HelikarLab/ode-app GitHub Wiki

The simulations performed are basically applying a particular Kinetic Law to a reaction and devising a rate for the reaction.

There are 3 Kinetic Laws currently available to use in the application:

• Law of Mass Action
• Michaelis-Menten Kinetics
• Hill Kinetics

Other than this you can define your own Custom Rate in the application.

The law of mass action is the proposition that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants.

Examples:

Take the reaction:

Reactant ==> Product

Rate of the above reaction according to Mass Action would be:

[Reactant] * k

• [Reactant] is concentration of the Reactant
• k is a parameter that governs the reaction

Similarly for a reversible reaction:

Reactant <==> Product

Rate of the above reaction according to Mass Action would be:

[Reactant] * k1 - [Product] * k2

• [Reactant] is concentration of the Reactant
• [Product] is concentration of the Product
• k1 is the forward parameter
• k2 is the backward parameter

Even though variations of this law exist for reactions with multiple reactants/products, this application only implements this law for reactions with a single reactant and product.

Michaelis–Menten kinetics is one of the best-known models of enzyme kinetics. The model takes the form of an equation describing the rate of enzymatic reactions, by relating reaction rate to the concentration of a substrate.

Lets take the following reaction as an example:

Enzyme + Substrate ==> Intermediate (E + S) ==> Product + Enzyme

Its formula is given by:

V = (Vmax * [Substrate]) / (Km + [Substrate])

• [Substrate] is concentration of the Substrate
• V is the reaction rate
• Vmax represents the maximum rate achieved by the system
• Km is the Michaelis constant and is numerically equal to the substrate concentration at which the reaction rate is half of Vmax

For reversible reactions:

Lets take the following reaction as an example:

Enzyme + Substrate <==> Intermediate (E + S) <==> Product + Enzyme

The formula for the above would be:

• [Substrate] is concentration of the Substrate
• [Product] is concentration of the Product
• V is the reaction rate
• V^fmax and V^rmax represent the maximum rate achieved by the system in the forward and reverse manner respectively.
• K^Sm and K^Pm is the Michaelis constant and is numerically equal to the substrate concentration at which the reaction rate is half of V^fmax and V^rmax respectively

Needs a description

Formula:

• [S] is concentration of the Substrate
• V is the reaction rate
• Vmax represents the maximum rate achieved by the system
• K_0.5 is the Michaelis constant and is numerically equal to the substrate concentration at which the reaction rate is half of Vmax
• n is Hill's co-efficient