Model

This model studies the Michaelis–Menten kinetics and compares it to a standard, enzyme-catalyzed mass action reaction.

Michaelis–Menten kinetics is one of the most important models for enzyme-substrate interactions. It is used to study the kinetics in a wide array of biological functions, such as the immune response.

While a mass action model of an enzyme-substrate interaction would go through a intermediate step with an enzyme-substrate complex, Michealis–Menten kinetics assumes that this complex rapidly enters quasi steady state and can be approximated. This eliminates the need to measure the formation rate of this complex, which is infeasible in practice.

The example model consists of two separate reaction models. The upper, larger model follows mass action kinetics, having an enzyme that binds to the substrate, creating an enzyme-substrate complex before transforming the substrate into product. The smaller model follows Michaelis–Menten kinetics, with its reaction rate formula representing the enzyme reaction seen in the mass action model.

Simulation

Simulating the model will give the possibility to see how well the Michaelis–Menten model agrees with the mass action one (which is more biologically correct).

Simulate the model by clicking the Simulate button:

If the models do not seem to agree, try to increase the kCat constant, which represents the product formation from the enzyme-substrate complex. The higher the kCat, the better the models should agree. You can also change other parameters and initial conditions. This can be done in the Parameters tab. Change the corresponding initial concentration and then click the Simulate button again.

In order to get the full experience of this example, you need a desktop Wolfram Language product. A free trial download is available at www.wolfram.com/mathematica/trial/

For the full example, open the accompanying notebook MichaelisMenten.nb.