NAME:_________________________________
GRADED EXERCISE 1, CHEMISTRY 156, SPRING, 2002
Answers to the following set of problems are due in class on Friday, 15 March. Your answers should show how the final results were obtained. Include printouts of all work done on the computer. In completing the problems, you may refer to your notes or any texts but you must work independently on the problems. Direct all questions on the problems to the instructor.
1) The extent of denaturation of a protein may be determined from CD spectroscopy, a technique that will be studied later. The fraction of native or folded protein, f, is given by the expression f = 1/(1 + K) where K is the equilibrium constant for the conversion of folded to denatured protein, i.e. for the reaction F ® D.
a) Using the denaturation data for the toxin ___________________, calculate K as a function of temperature. (The data are given below.)
b) Calculate values of D H° and D S° for the denaturation of the protein. Use the method of least squares in fitting the data. Include the graph of your fit with your answers.
2) p-Nitrophenyl a -D-mannoside binds to the protein concanavalin A. The free ligand absorbs light maximally at 305 nm but the spectrum shifts when the ligand is bound to the protein. The difference in the extinction coefficient, D e = e (bound ligand) - e (free ligand), is greatest at 317 nm. Furthermore, D A, the change in absorbance at 317 nm upon binding, is directly proportional to the concentration of bound ligand, i.e. D A = l [L]B where l , an unknown constant, equals lD e and l is the cell length.
In one experiment, the total protein concentration, [P]0, was 0.038 mM. The following values of D A were measured as a function of the concentration of free ligand, [L]F.
[L]F (mM) D A at 317 nm
0.025 0.025
0.050 0.038
0.075 0.047
0.100 0.053
0.125 0.056
0.150 0.060
One additional datum was obtained. When a large excess of ligand was used, D A was found to be 0.085. Under these saturating conditions, all of the n binding sites of the protein are occupied so that D A(max) = 0.085 = l [L]B,max = l n[P]0.
a) If there is no cooperativity between the n binding sites on the protein, binding is described by the following equation discussed in class:
n = nK[L]F/(1 + K[L]F)
Assume for the moment that the binding sites are non-interacting and obtain the following result:
D A/D A(max) = q = n /n = K[L]F/(1 + K[L]F)
b) Generate a Scatchard plot. Obtain a value of K and test the hypothesis that the binding sites are independent.
c) Confirm the conclusion reached in part (b) with a Hill plot.
3) An aqueous buffer was prepared with the following net composition:
acid concentration:______________________________________________
conjugate base concentration:____________________________________
counterion concentration:________________________________________
a) Calculate the equilibrium constant at 30.0° C for the ionization of your acid. Use D. D. Wagman et al., The NBS Tables of Chemical Thermodynamic Properties as the source of the thermodynamic data.
b) Calculate the pH = -log10(aH) and the equilibrium concentrations of all species at 30.0° C. These values must be calculated well enough that the buffer could be used to standardize a pH meter. Use Maple to obtain a numerical solution to the problem. Include all ions in the charge balance.
c) Suppose that the solution whose pH you have just calculated is the electrolyte in a cell in which one electrode is the classical hydrogen electrode and the other is a silver/silver chloride electrode. Calculate the potential of the cell at 30.0° C.
4) Consider a system in which two solutions are separated by a semi-permeable membrane. An aqueous solution of a salt is on the right side of the membrane and an aqueous solution of the same salt and a charged protein is on the left side.
a) Using the following information, solve for the concentration of permeable cation and anion on both sides of the membrane. In setting up your charge balances, ignore the hydronium and hydroxide ions as their relative concentration is very low. Assume that the ratio of activity coefficients is one.
b) Calculate the difference in pH across the membrane as well as the electrical potential at 25.0° C across the membrane.
USEFUL INFORMATION
identity of the salt:____________________________________
charge on the protein:___________________________________
concentration of the protein:____________________________
concentration of the metal cation on the right:__________________
DENATURATION DATA FOR PROBLEM ONE
1) protein: Gamma toxin from Tityus serrulatus
conditions: 0.4 millimolar at pH 2.46
Temperature Fraction of
(° C) Folded Protein
26.7 0.893
28.0 0.864
30.0 0.757
31.9 0.746
32.8 0.723
34.7 0.692
36.0 0.643
37.4 0.561
40.0 0.405
42.0 0.328
44.5 0.261
46.0 0.180
48.0 0.117
49.7 0.085
51.2 0.079
52.0 0.057
2) protein: Cardiotoxin CM2E from Naja haje annulifera
conditions: 0.4 millimolar at pH 3.02
Temperature Fraction of
(° C) Folded Protein
46.0 0.910
48.0 0.891
50.0 0.856
52.0 0.841
53.0 0.825
54.0 0.793
56.0 0.715
58.0 0.679
60.0 0.635
62.0 0.566
63.5 0.568
64.0 0.525
66.0 0.449
68.0 0.359
70.6 0.285
72.0 0.237
74.0 0.160
76.0 0.106
78.0 0.065
3) protein: Cardiotoxin CM10 from Naja haje annulifera
conditions: 0.4 millimolar in 20% ethanol at pH 2.0
Temperature Fraction of
(° C) Folded Protein
50.0 0.956
53.0 0.912
53.9 0.916
56.0 0.882
58.0 0.819
60.0 0.749
62.0 0.678
63.5 0.599
66.0 0.466
68.0 0.461
70.0 0.263
72.2 0.131
74.0 0.088
76.0 0.026
EX1_2002.htm, 14 Feb. 2002