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Biochemistry - Problem set 2
August 31, 2016
Problem Set 2 - Key
1. (4 pts, 10 min) A Venn diagram that organizes the amino acids by the
properties of their sidechains is shown on the right. Glycine is Charged
Pro
Leu
Lys
Non-polar
omitted since its sidechain is just a hydrogen atom. As the diagram
Asp
Arg
Met
Val
suggests, a sidechain can be non-polar, charged (pH between 0 and
Glu
Cys
10), or polar. Some amino acids belong to more than one set, e.g. all
Ala Ile
Asn
Trp
His
charged residues are also polar.
Phe
Gln
a) Explain, with reference to its sidechain atoms, where you would
Thr
place Tyrosine (Tyr) on this chart (2 pts).
Ser
Tyrosine is both polar, due to the –OH group, and non-polar,
Polar
due to the aromatic ring. You could also place tyrosine in Venn diagram grouping of Amino Acids based on Sidechain Properties.
the charged set too, since its pKa is 10 and would be 50% deprotonated at that pH. Since this is at
the edge of the normal range of pH values, tyrosine is typically not considered to be charged.
b) One amino acid is very clearly in the wrong set. Which one is it and where should it be placed? Briefly justify your
answer (2 pts).
There are two acceptable answers:
Asn – never ionizies (best answer)
Lys – also has a non-polar functionality (C-C-C-C)
Everyone else is pretty much in the right spot – Met straddles non-polar/polar because its sulfur is
slightly polar.
Fraction Protonated
pH Titration
% Activity
2. (10 pts, 15 min) An enzyme contains a single Histidine (His) residue that must be
deprotonated for the enzyme to be active. NMR was used to measure the
fraction of this histidine that is protonated as a function of pH. The dry-lab
associated with this problem set will allow you to measure the fraction protonated
versus pH.
a) Determine the pKa of this histidine (2 pts). To determine the pKa we need to
find the pH where the histidine residue is ½ protonated. Based on the plot of
fraction protonated versus pH (right), its pKa is about 5.2.
b) The pKa for this His residue is different than free His. Based on the shift in
pKa, what type of environment surrounds this His residue in the protein? (3
pts) This His is a stronger acid. Since the protonated state is the
state that is charged we only need to consider its interaction with
its surroundings. It must be in a positively charged environment
because that would destabilize (raise the energy of) the
protonated state, making it more favorable to deprotonate.
c) Sketch the curve of activity versus pH (5 pts). It is proportional to the
fraction deprotonated (fA), plotted on the right.
1
0.8
0.6
0.4
0.2
0
2
3
4
5
pH
6
7
8
3
4
5
pH
6
7
8
100
90
80
70
60
50
40
30
20
10
0
3. (5 pts, 10 min) The chemical structure of the naproxen, a common pain reliever, is
shown on the right. When this drug was first synthesized it was shown to cause
pain relief and liver damage. The current formulation of this drug does not cause
liver damage (of course). What do you think is the difference between the initial
2
batches of the drug and what you currently buy in the drug store? [Hint: Both the
early and current formulations give the same chemical analysis, e.g. carbon
composition, IR spectra, etc.], however the first formulation does not rotate linearly polarized
light. Naproxen has a chiral center (circled) and can exist in two enantiomers. The
first formulation, which causes liver damage, was a racemic mixture of both
enantiomers. One enantiomer caused liver damage. The current drug is a pure
enantiomer, and an effective at pain relief.
4. (8 points, 25 min) You are required to make a 250 ml solution of 0.05 M phosphate to use as a buffer to perform a
biochemical experiment at pH 6.8. You only have the fully deprotonated form of this acid (e.g. Na3PO4) in the lab, plus 1M
solutions of HCl and NaOH. Assume that the pKa values for phosphate at 2.8, 7.2, and 12.8. [Hint, it will be useful to sketch
a titration curve for phosphoric acid prior to doing this problem.]
Biochemistry - Problem set 2
August 31, 2016
a) How many moles of sodium phosphate would you need for your buffer solution? Why does this not depend on the pH
of the solution? (2 pts)
This would require AT x V moles of the weak acid, or .25 L x .05 moles/L = 0.0125 moles. This is
independent of pH – pH will affect the relative ratio of the different species, but the overall
concentration is fixed at the specified value = 0.05 M
b) Would you use HCl or NaOH to adjust the pH of the phosphate solution? Why? [Yes, this is simple](1 pt). HCl, since
the acid is fully deprotonated.
c) Calculate the number of equivalents of HCl or NaOH that you would need to adjust the pH of the sodium phosphate
solution. How many moles of HCl or NaOH will be required to make this buffer (5 pts).
First step = identify the buffer region, since the pH is close to the 2 nd pKa, we will use that in our
calculations.
Second step = calculate fHA and fA for this buffer region:
R=10pH-pKa = 106.8-7.2 = 0.398. fHA = 1/(1+R) = 0.715. This looks right because the pH of the solution is lower
than the pKa, so more than ½ will be protonated. There is no need to calculate f A-, but it would be 0.28.
The number of equivalents of HCl is 1.715, the first equivalent is required to cross the right most buffer
regions (fully converting PO4 to HPO4) and the 0.715 converts just the right amount of HPO4 to H2PO4
to give a pH=6.8 (H2PO4 = “HA”, HPO4=”A” for the second pKa).
5. (20 points, 25 min) View the Jmol structure associated with your recitation section and answer the following questions.
Please indicate your recitation section on your homework. For groups, pick the one that corresponds to the person in
your group whose last name is closest to A. I suggest that all members of groups actually do this problem to get
practice drawing peptides and identifying important features.
a) Write the correct sequence of your peptide. You will need to look at the sidechain groups to determine the identity of
each residue; the labels provided by Jmol are erroneous (2 pt).
b) Sketch the titration curve for your peptide, using the pKa values provided in the lecture notes. Use equivalents for the
x-axis. Indicate the buffer regions on your plot (5 pts).
c) Draw the chemical structure of this peptide, assuming pH = 8.0. You do not need to draw any hydrogens attached to
carbons, but you should clearly indicate the correct charge on all ionizable groups (5 pts).
d) Draw a dotted line that completely encloses all of the mainchain atoms of this peptide (2 pt).
e) Which pair of labeled atoms (A-F) on the Jmol structure represent the peptide bond, indicate this bond on your sketch
(2 pts).
f) Which labeled atom can act as a hydrogen bond acceptor? Indicate this atom on your sketch and draw a water
molecule forming a hydrogen bond with this atom (2 pts).
g) Which labeled atom (or pairs of atoms) on the Jmol structure can act as a hydrogen bond donor? Indicate this atom on
your sketch and draw a water molecule forming a hydrogen bond with this atom (2 pts).
a
b
c
Ala-Glu-Leu
Plot should show:
i) x-axis scale from 0 to 3
ii)
Three
buffer
regions,
pKa=2,4,9 @ x= 0.5, 1.5, 2.5.
iii) Three equivalence points
@ x=1, 2, 3.
peptide
bonds
H
O
H-bond
acceptor
H3C
H
CH3
H3N
N
+
O
N
H
H O
O
O
CH3
O
H
O
H
O
H-bond
donor
Biochemistry - Problem set 2
d
e
f
g
Note: The amino term is 90%
protonated at pH 8, fHA=+0.9.
Both carboxylates are fully
deprotonated.
See diagram.
Peptide bond: B-D
H-bond acceptor: C
H-bond donor: D & E
August 31, 2016