Download Calculus Investigation

Calculus Investigation
The Michaelis-Menton Equation – Short Version
This project asks you to derive the Michaelis-Menton Equation from the
chemical/cellular mechanisms involved. This project deals with modeling at microscopic
level and with processes unfamiliar to the nonbiologist. The Michaelis-Menton Equation
is important in molecular biology and this problem introduces you to molecular modeling
which is very important in medical research. In bacterial growth models, when the
nutrient concentration is low, the bacterial growth rate is proportional to the
concentration; when the nutrient level is high, the growth rate is constant. The reason is
that nutrients must pass through the cell wall of a bacterium through a chemical process
(called transport) involving receptor sites. Receptors are a certain type of molecule on
the cellular membrane which bind with the nutrient molecules on one side of the cell wall
and break down on the other side of the cell wall to let nutrient through. This process is
shown in Figure 1.
Figure 1: Nutrients passing through a cell wall using receptors bound to the cell wall.
When the nutrient concentration is low, there are ample receptors so the rate of
processing is proportional to the amount of nutrient. When the nutrient concentration is
high, the receptors are working at maximum capacity so increasing the nutrient has no
additional effect. Saturation results from the limited number of receptors and the limited
rate at which their “conveyer-belt” mechanism can operate.
In this project, we will deal with the bacteria-nutrient model as outlined, but
notice that if the word "bacteria" were replaced by "liver cell" and the word "nutrient"
were replaced by "drug," then this discussion would also apply to the pharmacokinetic
use of Michaelis-Menton equation.