Engineering Approaches to Cholesterol-Linked Diseases

Engineering Approaches to Cholesterol-Linked Diseases

Problem Set

Steven P. Wrenn

Chemical Engineering

Summer, 2001

1. Go to the library (or use the Internet) to get and read the following journal article:

Carey, M.C. Critical tables for calculating the cholesterol saturation of native bile. Journal of Lipid Research, 19, 945-955 (1978) (i.e., Reference #4 in the Gallstone List of References).

Using the tables and polynomial functions in the article, determine (via calculation or interpolation or both) the value of the CSI for the following bile compositions:

Mole% Mole% Mole%

Total solids (g/dL) Lecithin Bile Salt Cholesterol

2 40 50 10

3 40 50 10

4 40 50 10

5 40 50 10

5 40 51 9

5 40 52 8

5 40 53 7

5 40 49 11

5 40 48 12

5 40 47 13

4 42 48 10

4 45 46 9

4 50 42 8

4 30 58 12

4 10 75 15

2. Using equations 8 and 9, perform a sensitivity study of the classical nucleation rate expression. Specifically, prepare plots of (J/Ao) versus T, s, and S. Let T vary between 0 and 100ºC, let s vary between 1 and 15 erg/cm2, and let S vary between 1 and 5. You may use a value of 500 cubic angstroms for W.

3. Calculate the number of cholesterol molecules contained within a single lecithin-cholesterol vesicle for each of the following conditions:

Vesicle Diameter Cholesterol Mole Fraction

50 0.10

50 0.20

50 0.30

50 0.33

50 0.40

50 0.50

50 0.55

50 0.60

50 0.65

40 0.33

45 0.33

55 0.33

60 0.33

80 0.33

100 0.33

150 0.33

1000 0.33

4. Explain why multi-lamellar sheets ‘wrap up’ or ‘fold’ in water to yield multi-lamellar liposomes.

5. Which of the following bile salts do you expect will dissolve cholesterol to the greatest extent and why? Cholate, Deoxycholate, Ursodeoxycholate, Lithocholate

6. The CMC of a particular bile salt is 7.5 mM, and the actual concentration of the bile salt in an aqueous solution is 14.2 mM. What percentage of the bile salt exists as free monomer and what percentage is contained within micelles? If the aggregation number of the bile salt is 50, how many micelles are present? What do you think will happen as the solution is diluted with water?

7. An individual has an extremely high concentration of pro-nucleating enzymes in his/her bile. After mixing of vesicles and bile salts in this individual’s gallbladder, the vesicles contain a cholesterol loading of 46.3 mole%. How likely is this person to develop gallstones?

8. It was claimed in the lecture that gallstone disease and atherosclerosis are strikingly similar. However, most people with coronary artery disease do not develop gallstones, and most people with gallstones do not also have heart disease. Is this a contradiction? Why or why not?