Consider the following reaction scheme: , where is the substrate, is an enzyme catalyst, is the enzyme-substrate complex, which decomposes to give the product , and is the enzyme. This enzymatic reaction takes place in a batch reactor and the governing differential-algebraic system of equations is:

.

The initial conditions are: , , , and

These equations can be solved using the Mathematica built-in function, NDSolve. This approach is the rigorous one.

Another method, called the quasi-steady-state assumption, considers that . The resulting governing equations are:

, where .

This model is referred to as Michaelis-Menten kinetics. An analytical solution is possible for this model and is given by:

The reaction rate constants , , and are expressed in , and , respectively.

This Demonstration shows the substrate concentration, [S], (red curve) and the product concentration, [P], (blue curve) versus time obtained using the exact approach. The bold dots correspond to the quasi-steady-state approach. Agreement between both methods is obtained and justifies the utilization of the pseudo-steady-state hypothesis, which is also called the quasi-steady-state approach.