Download Problem Set 1

Problem Set 1
1.
Covers Lectures 2-5
The ε-NH2 group of lysine has a pKa= 10.5.
a) What fraction of these groups will be protonated at pH= 9.5 ?
b) At pH 11?
c) Explain why the pKa of the ε-NH2 group is higher than that of the α-NH2 group.
2.
Draw the four possible ionization states of glycine.
a) Which state predominates at pH 7?
b) What is a dipolar ion?
3.
Using a library of peptides to probe the active site specificity of protein kinases, it is
found that v-Src has a preference for Ile-Tyr-Gly-Glu-Phe (IYGEF).
Write the structure of this peptide.
4.
i) The hydrogen bond between two H2O molecules in isolation is about 10 times
stronger energetically (∆H) than a van der Waals contact between two xenon atoms. Compared
to the number of xenon dimers, the number of H2O dimers in the gas phase is :
a) about the same
b) 10 x greater
c) 10 x smaller
ii) The carbonyl and amide groups of the protein backbone are hydrophilic and form
hydrogen bonds with water; they can also hydrogen bond to each other. The free energy of
formation of a hydrogen bond between the atoms of the peptide group in the interior of a protein
is :
a) more favorable than it is in water.
b) less favorable than it is in water.
c) unaffected by its location and the same as in water.
iii) The pKa of the imidazolium group of a histidine residue at the NH2-terminus of an
α-helix, compared to that of one at the COOH-terminus, is likely to be:
a) increased
b) decreased
c) similar to each other, but not to the free amino acid
d) similar to the free amino acid
5.
A common motif in protein structure is β strand-turn-α helix. Consider such a motif
through the center of a globular protein of 40,000 daltons with a diameter of 5 nm.
a) What is the distance between adjacent amino acids in an α helix.
b) What is the distance between adjacent amino acids in a β strand.
c) What is the minimum number of residues required for a turn.
d) Calculate the total number of residues required to make this motif
(β strand-turn-α helix) in this protein.
6.
Hemoglobin dissociates into dimers in the following way :
β1
α1
α2
β2
α1
β1
+
β2
α2
In deoxyhemoglobin there are six salt bridges between the α1β1 and the α2β2 dimers
which are absent in oxyhemoglobin. There are two bridges between α and β chains and four
between α chains, as is shown in the diagram:
-
+
β1
+
α1
α2
α1
β2
+
- +
+ - +
α2
-
The dissociation constant for oxyhemoglobin is 10-6 M, and that for deoxyhemoglobin is
10-12 M.
What is the average standard free energy change for the formation of a salt bond?
7.
2,3-Bisphosphoglycerate (BPG) binds preferentially to deoxy-hemoglobin, as compared
to oxy-hemoglobin, in the cavity between the β chains; eight cationic groups
(four per β chain) of three different types interact with BPG via electrostatic interactions.
O
O-
O- P O
O
O
O
O-
P
O- O
a) Name four potential cationic groups of the protein that could be involved in these electrostatic
interactions.
b) Draw Hill plots for the binding of O2 to hemoglobin in the presence and absence of BPG. Put
both curves on one diagram, label the axes, and state the values of the Hill coefficients for the
binding of O2 in the presence and absence of BPG.
c) Fetal Hb has the composition α2γ2, as compared to α2β2 for adult hemoglobin. In the
gamma chain, one of the cationic groups is replaced by serine. Draw relative O2 dissociation
curves (saturation curves) for maternal and fetal blood. Label the axes, and indicate on your
graph the relative positions of the KD for each type of Hb.
8.
The Pompeii worm lives on the sides of underwater volcanoes at temperatures of up to 81°
C. The blood of these worms contains a hemoglobin of 3780 kDa. Each molecule of this
hemoglobin is comprised of 120 globin chains (each chain of 16.5 kDa and with one heme group)
surrounding a core of 72 linker chains (each of 25 kDa).
The P50 of the Pompeii worm Hb (Hbp) is 0.4 torr and the Hill coefficient, n, is 2.8. The
P50 for human Hb (Hbh) is 26 torr and the P50 of human myoglobin (Mbh) is 4 torr.
a) How many molecule(s) of oxygen per molecule of Hbh protein are released when the O2
concentration is changed from 100 torr to 26 torr?
.
b) How many molecule(s) of oxygen per molecule of Mbh protein are released when the O2
concentration is changed from 100 torr to 4 torr?
.
c) How many molecule(s) of oxygen per molecule of Hbp protein are released when the O2
concentration is changed from 100 torr to 0.4 torr?
.