Michaelis-Menton Meets the Market. Group Members. Jeff Awe Jacob Dettinger John Moe Kyle Schlosser. Overview. Introduction to continuous modeling Biological Modeling Nutrient absorption The Michaelis-Menton equation Deriving the Michaelis-Menton equation
The Michaelis-Menton Equation
The following Reaction Equations represent the process of passing nutrient molecules into a cell:
Let following symbols denote concentrations:
As you can see,
Which implies, is a constant.
Thus let .
Substitute into our differential equations to eliminate :
Assume that we are at a steady state, thus,
Solve for and plug into
Which gives us our Michaelis-Menton equation:
•Blood alcohol concentrations are complicated and vary from person to person. The state trooper is probably unlikely to accept as an excuse that John said it would be OK in his math models presentation.•It is also a bad idea to feed a squirrel beer.
BAC is measured as grams of alcohol per 100 mL of blood. Alcohol is distributed evenly in all of the water in a person’s body.Blood is 81.57% water.
With blood alcohol, the concentration of alcohol is much higher than the number of receptors, so the rate of alcohol elimination is basically a constant.The average person eliminates alcohol at the rate of about 7.5 grams / hour, although it can range from 4 - 12.
If you drink at a constant rate the amount of alcohol in your body would then be just the amount your are drinking per hour minus the amount your are metabolizing per hour multiplied by the number of hours you’ve been at it.All we need now to calculate BAC is the amount of water in your body.
The amount of water in a person is roughly proportional to their weight. This constant is then adjusted because blood is not 100% water.For males, you divide by 3.1 times weight in pounds. For females it is 2.5.
So if an average male person of weight w pounds averages c grams of alcohol per hour, then their BAC at time t would be: (c-7.5)t/(3.1w)For a female(because they have less water on average) it would be: (c-7.5)t/(2.5w)(c≥7.5 and t≥0)
A course in Mathematical Modeling by Douglas Mooney & Randell Swift, MAA Publications 1999“The Calculation of Blood Alcohol Concentration” http://www.vicroads.vic.gov.au/road_safe/safe_first/breath_test/BAC/BACReport.htmlDr. Deckelman (a source of tons of information)