# Carmen E. Castaneda: Week 4

### Terminology

• Explain the following terms in your own words.
1. The Michaelis-Menten model of enzyme kinetics is a mathematical equation for enzyme kinetics, which is the study of chemical reactions that are catalyzed with enzymes.This sort of equations models the rate of enzyme activity versus the concentration of the substrate.
2. The experiment required for the Lineweaver-Burk approach to estimating parameters for Michealis-Menten is an inverse of the slope of the linear representation of the data shown by a Michaelis-Menten model.
3. Chemostat reactor is a system in which there is a flow into as well as out of the sytem at a specific rate.
4. Exponential growth is a growth rate which increases at a pretty fast paced in a small amount of time.

### Applying Michealis-Menten Models

• Consider a single substrate being converted to product.

E + SESE + P with an initial substrate concentration of 1.0 and an initial enzyme concentration of 0.05. Use the Michaelis-Menten matlab model to explore the following.

• Set k1 = 2.0, k-1 = 0.0. Plot the substrate dynamics for k2 = 1.0, k2 = 2.0, k2 = 5.0, k2 = 10.0 all on the same graph to see the effect of this parameter.

• Set k1 = 2.0, k-1 = 1.0. Plot the substrate dynamics for k2 = 1.0, k2 = 2.0, k2 = 5.0, k2 = 10.0 all on the same graph to see the effect of this parameter.

• Set k1 = 2.0, k-1 = 5.0. Plot the substrate dynamics for k2 = 1.0, k2 = 2.0, k2 = 5.0, k2 = 10.0 all on the same graph to see the effect of this parameter.

### Estimating Michaelis-Menten Parameters

• Consider the following data:

[S] = 11.0, 16.7, 20.0, 25.0, 33.3, 50.0

V = 0.00952, 0.01111, 0.01282, 0.01515, 0.01852, 0.02128

Apply the Lineweaver-Burk technique to determine Vmax and K.

After applying the Lineweaver-Burk technique we determined that the Vmax = 0.031550718 and K = 27.10932324.