# Modeling demo: enzyme kinetics

When using this demo, students can alter the reaction rate, substrate, or enzyme concentrations. The simulation motivates understanding what a basic mechanistic model of enzyme kinetics would consist of.

After running a simulation, the predicted dynamics of the product and substrate are plotted.

The model behind the simulation is:

$\frac{dS}{dt} = - r*E*S\\ \frac{dE}{dt} = 0\\ \frac{dP}{dt} = r*ES$

First I ask them a series of questions to motivate the model:

1. How is the amount is substrate changing?
2. When can substrate become product?
3. If you had no enzyme could you get a product?
4. How does the amount of enzyme change over time? I

Then I ask them to write how substrate and products change over time both mathematically and in English. In math language, $\frac{dE}{dt}$ means “enzyme changing over time”. For example,

$\frac{dS}{dt} = - r*E*S$

means “the change in substrate over time is decreasing with the reaction rate and the amount of substrate and enzyme.”