BSCI 426/ BIOL 622     Fall '14 Problem Set 1

assigned: 09/04/2014
due: 09/11/2014

This problem will help you to understand how to explore the properties of a quantitative model.  It requires you to use a spreadsheet to facilitate the calculation and visualize the results.  If you are not familiar with the use of a spreadsheet, COME TO SEE ME RIGHT AWAY!

An amphiphile (or detergent) added to water disperses either into monomers or into a mixture of monomers and micelles depending on the total amount added.  The model I presented, if it is valid, should reflect the fundamental properties of this system, the existence of a critical micellar concentration (CMC).

1. Use a spreadsheet to generate a graph displaying the variation of monomer and micelle concentrations with the amount of amphiphile added to the solution. Plot the monomer concentration, [M], and the concentration of monomers in micelles, n*[Mn], versus the total effective monomer concentration in solution, [M] + n*[Mn]. This graph should be based on a mathematical model such as the one I presented in class. Explore the properties of this theoretical system by varying the number of monomers in the micelle, the binding constant, and the concentration range.  Make statements on the important properties of this system. For example, how do the choices of K and n effect the graph, the CMC?

P.S. Learning occurs as you struggle and overcome difficulties.  That's the point of the homework.  That's where most of the learning takes place.  However, if you seem unable to get beyond some stumbling block, don't hesitate to contact me.

P.P.S. Any calculating device has limits on its accuracy. In working with the quantitative model, you are raising numbers to large powers. This is a recipe for disaster. You can rearrange the expression to avoid this by bringing the number to be raised to a high power close to 1.

[Mn] = [M] * ([M]*K)^n-1