NAME:_________________________________
GRADED EXERCISE 1, CHEMISTRY 156, SPRING, 2006
Answers to the following set of problems, which are designed to illustrate a range of
problems encountered in molecular biology and environmental science, are due in class
on Monday, 3 April. Your answers should clearly show how the final results were
obtained. Include printouts of all work done on the computer. You may wish to Email
any spreadsheets or computer-generated reports in electronic form to the instructor. 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.
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 H and 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. (A careful statistical analysis has shown that an accurate value of Cp
cannot be extracted from the data so assume that Cp  0.)
2) Professor Michael Rosen, Department of Biochemistry, University of Texas
Southwestern Medical Center, presented at a seminar his model for the allosterism of the
Wiskett-Aldrich Syndrome protein (WASP). WASP is involved in a chain of events that
leads to the production of new actin filaments. WASP exists in two conformations,
designated T and R following the notation of Monod. In its thermodynamically more
stable and folded T conformation, WASP does not initiate the formation of actin.
However, when WASP binds to a second protein, Cdc42 GTPase (designated here as A),
it undergoes a conformational change to a second unfolded form, R, which is capable of
initiating the formation of actin. The Cdc42 protein, A, therefore serves as a regulator.
In this exercise, you will numerically simulate Rosen's model and apply the results to
examine allosterism. The following equilibria are relevant for this exercise. Four species
are present: T, R, AT, and AR. The associated equilibrium constants are given in
parentheses. In Rosen's model the T form of WASP has a low binding affinity for A and
the R form, a high affinity. In this respect, WASP is similar to hemoglobin.
T  R (KRT << 1)
A + T  AT (KAT)
A + R  AR (KAR)
Your calculations will be based on the following data which Professor Rosen presents in
a forthcoming paper on his model:
a) [WASP]0 = 9 μM ([WASP]0 is the total concentration of WASP.)
b) KAT = (1.50.067) x 105 M-1
c) KAR = (4.40.71) x 107 M-1
d) In the absence of A (the Cdc42 GTPase), 0.4 mole-% of the WASP
protein is present in the kinetically active R form.
e) WASP is monomeric and has a single binding site for A.
In this exercise, perform the following steps:
a) Set up the mass balance and the three unique equilibrium expressions
that define the concentrations of all species. You will be able to calculate
a value of KRT from the information provided above.
b) Calculate using Maple or Mathematica the concentrations of all four
species as a function of the total concentration of the regulator A, i.e. [A]0.
Rosen does not provide explicit values for [A]0 but does note that its in
vivo value is low. As a first step in your simulation, vary [A]0 by orders of
magnitude, i.e. 1 fM, 10 fM, 100 fM, 1 nM, 10 nM, 100 nM, and 1 μM.
c) From the results of your trial calculations, calculate for each value of
[A]0 the fraction of sites bound, . , designated by f in Tinoco et al.,
equals ([A]0 - [A])/[WASP]0. Note that [A] refers to the concentration of
free A. Make a preliminary plot of  versus [A].
d) Perform further calculations of concentrations at additional values of
[A]0. The preliminary binding plot will indicate the range of [A]0 that will
yield information that will enable informative Scatchard and Hill plots.
There is no need to perform calculations for a large set of [A]0's but you
need sufficient information to define the binding curve.
e) Construct a Scatchard plot using the values of  and [A] generated in
the previous steps. Does the plot indicate cooperativity or noncooperativity? Briefly discuss your results.
f) Next construct a Hill plot, i.e. a plot of log10{/(1-)} versus log10([A]).
Does this plot indicate cooperativity or non-cooperativity? Briefly discuss
your results.
2) An aqueous buffer was prepared with the following net composition:
acid concentration:______________________________________________
conjugate base concentration:____________________________________
counterion concentration:________________________________________
concentration of spectator ions: [Na+] = 0.025 m, [Cl-] = 0.025 m
a) Accurately calculate the equilibrium constant at 37.0C (98.6F) for the
ionization of your acid. Some useful data may be found in D. D. Wagman et al.,
The NBS Tables of Chemical Thermodynamic Properties. A better source of
thermodynamic data related to acid-base equilibria may be found in the
comprehensive NIST review R. H. Goldberg, N. Kishore, and R. M. Lennen,
"Thermodynamic Quantities for the Ionization Reactions of Buffers", J. Phys.
Chem. Ref. Data, 31, 231-370 (2002. This review can be accessed via Honnold
Library's Webpage and its portal to electronic journals.
b) Calculate the pH = -log10(aH) and the equilibrium concentrations of all species
at 37.0C. These values must be calculated well enough that the buffer could be
used to standardize a pH meter. Maple and Mathematica have utilities that solve
the problem numerically. 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 37.0C and
with a partial pressure of H2 = 1.000 atm.
DENATURATION DATA FOR PROBLEM ONE
(collected in the laboratory of Kurt Wuethrich at the ETH by Wayne Steinmetz)
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
(C)
50.0
53.0
53.9
56.0
58.0
60.0
62.0
63.5
66.0
68.0
70.0
72.2
74.0
76.0
Fraction of
Folded Protein
0.956
0.912
0.916
0.882
0.819
0.749
0.678
0.599
0.466
0.461
0.263
0.131
0.088
0.026
c:\courses\chem156\ex1_2006.doc, WES, 1 March 2006