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Chem 352 - Fall 2014 - Exam II
Some potentially useful information:
pKa values for ionizable groups in proteins: (α-carboxyl, 2.9; α-amino, 8.3; Asp side chain, 3.9, Glu
side chains, 4.2; His side chain, 6.8; Cys side chain, 9.2; Tyr side chain, 10.1; Lys side chain, 10.7;
Arg side chain, 12.3)
Ideal gas law constant (R) = 8.314 J/(mol•K) = 0.08206 (L•atm)/(mol•K)
Faraday’s constant (F ) = 9.646 x 104 J/(mol•V)
1. One of the steps in the citric acid cycle is the conversion of L-malate to oxaloacetate, a reaction that
is catalyzed by the enzyme malate dehydrogenase:
30/30
In an experiment carried out at 20°C in the presence of 2.0 nM malate dehydrogenase to observe the
kinetics of this reaction with varying concentrations of L-malate, the catalytic rate constant was
observed to be 49/s and the KM was observed to be 251 µM.
a. What was the observed Vmax for this reaction under these conditions? ___________
98.0 nM/s (Show your calculations.)
Vmax = k2 ⎡⎣E ⎤⎦ = kcat ⎡⎣E ⎤⎦ , where kcat is the catalytic rate constant.
tot
tot
Vmax = kcat ⎡⎣E ⎤⎦
(
tot
)(
)
= 49/s 2.0 nM = 98.0 nM/s
b. What is the turnover number for malate dehydrogenase under these conditions? _______________
49/s
(Show your calculations.)
The turnover number is another name for the catalytic rate constant.
Oxidoreductase
c. What class of enzyme does malate dehydrogenase belong to? ______________________
d. Under the conditions described above, does malate dehydrogenase display “catalytic perfection”
(Show your calculations.)
This is determined by calculating the catalytic efficiency, kcat/KM, in units of 1/M•s and
comparing this number to the theoretical maximum of ~108/M•s.
This value is considerably less than 108 and therefore, this
k cat
49/s
49/s
5
=
=
= 1.95 x 10 /M•s enzyme has a ways to go before it could be considered
K M 251 µM 251 x 10 −6 M
catalytically perfect.
e. When an enzyme displays “catalytic perfection”, what physical constraint has been placed on the
enzyme’s ability to further increase the rate of the reaction.
It means that the reaction has become diffusion rate-limited, which means that the rate
of the reaction is limited only by the frequency with which the substrate(s) diffuse into
the active site of the enzyme. This is something that is beyond the control of enzyme
and therefore there is no furthering tinkering to the enzyme that can be done to speed
up the rate of the reaction.
!1
Chem 352
Exam II
Fall, 2014
f. Using the axes drawn below, sketch the expected Lineweaver-Burke for this experiment. (Be sure
to label your axes, including units)
y-intercept =
1
1
=
Vmax 98.0 nM/s
If the inhibition is uncompetitive, then both Vmax and KM will be
decreased to the same extent; if Vmax is decreased by ½, then
KM is decreased by ½ as well. This will double the value of the
two intercepts and leave the slope the same.
80
⎛ 10 3 nM ⎞
= 0.0102 s/nM ⎜
⎟ = 10.2 s/µM
⎝ 1 µM ⎠
70
60
x-intercept =
−1
1
=
K M 251 µM
50
⎛ 10 µM ⎞
= 0.00398/µM ⎜
⎟ = 3.98 /mM
⎝ 1 mM ⎠
-3
3
x10
40
30
20
10
-10
•
-8
-6
•
-4
-2
•
•
0
2
4
6
8
10
12
14
g. Adenosine diphosphate ribose is an uncompetitive inhibitor of malate dehydrogenase. In the
presence of a 1.0 mM concentration of this inhibitor, the Vmax was cut in half. On the graph above,
sketch the observed results.
h. Explain where on the enzyme, relative to the substrate, is this inhibitor likely binding to?
Uncompetitive inhibition means that the inhibitor must bind to the enzyme before the substrate (Lmalate in this case) binds. It is likely binding to the NAD+ binding site and that this enzyme has a
sequential substrate binding order, with the NAD+ first followed by the L-malate
2. Draw the structure of the phospholipid phosphotidylcholine containing a palmityl (16:0) acyl group at
the C1 position a linoleyl (18:2, cis-Δ9,12 ) acyl group at the C2 position.
13/13
a. In a couple of sentences, describe the structure that forms spontaneously when
phosphotidylcholine is mixed with water. Include in this description a mention of the
intermolecular interactions that lead to the formation of this structure.
Phospholipids, such as phosphotidylcholine, are highly amphipathic, meaning they contain a
moiety that is very hydrophobic, along with a moiety that is at the same time very
hydrophilic. When placed in water these molecules will aggregate in away that satisfies both
of these characteristics. Phospholipids form lipid bilayers, in which the surfaces of the
bilayer expose the hydrophilic moieties to water, while also burying the hydrophobic
moieties on the inside of the bilayer and away from exposure to water. Once formed, the
micelle structure is then stabilized by the favorable hydrogen bonding interactions between
2
the exposed choline head group and the water, and the vander Waals interactions between
the fatty acid acyl side chains.
Chem 352
Exam II
Fall, 2014
3. Below is a figure illustrating the active site of an enzyme found in the glycolytic pathway. The
enzyme catalyzes the following reaction,
15/15
1
2
3
a. What class of biological molecule, e.g., amino acid, carbohydrate, lipid, etc. does the product of
sugar derivative (phosphosugar)
this reaction belong to? ________________________
dihydroxyacetone phosphate
b. What is the name of the substrate in this reaction? _________________________
isomerase
c. What class does this enzyme belong to? _______________________________
acid/base catalyst (as an acid)
d. What catalytic mode does His 95 play in step 1 of this reaction? ___________________
acid/base catalyst (as a base)
e. What catalytic role does Glu 165 play in step 1 of this reaction? ______________________
4. Why are some sugars considered reducing sugars while others are not?
12/12
Reducing sugars are carbohydrates that are capable of reducing Cu2+ to Cu+. To do this, the sugar
molecule needs to be able to expose either an aldehyde (aldoses) or α-hydroxyketone (ketoses).
The pyranose and furanose ring forms of monosaccharides can also be reducing sugars if they still
have an anomeric carbon that is either a hemiacetal of hemiketal. Sugars become non-reducing
when they form glycosidic bonds and convert their hemiacetal or hemiketal to an acetal or ketal.
a. Draw and label the structure of a disaccharide that is not a reducing sugar.
Sucrose (α-D-glucopyranosyl-(1→2)-β-D-fructofuranose
3
Chem 352
Exam II
Fall, 2014
5. Lactose permease is an integral membrane
protein that transports lactose across
bacterial cell membranes along with
hydrogen ions. The transport cycle is shown
in the diagram to the right.
30/30
symport
a. Is this transport uniport, symport or antiport? ________________________
b. Given the membrane potential ΔΨ (Ψin - Ψout) is -55 mV, is the transport of lactose into the cell
favorable at 37°C if the pH is 6.2 and the concentration of lactose is 0.040 mM on the outside of
the cell, when the pH is 7.3 and the concentration of lactose is 0.90 mM on the inside of the cell? _
Explain and show your calculations: In this transport system the transport of lactose into the cell is coupled to the simultaneous
transport of hydrogen ions into the cell. The overall free energy change (ΔG) therefore is represented by the sum of the free energy changes for both.
⎛
⎞
⎛ ⎡⎣H+ ⎤⎦ ⎞
⎛
⎞
⎛ [lac ]in ⎞
ΔG = ⎜ RT ln ⎜
+ ⎜ RT ln ⎜ + in ⎟ + zF ΔΨ ⎟
⎟ + zF ΔΨ ⎟
⎝ [lac ]out ⎠
⎝
⎠ lactose ⎜⎝
⎝ ⎡⎣H ⎤⎦ out ⎠
⎠⎟ H+
⎛⎛
⎞
⎛⎛
⎞
⎛ 0.090 x 10-3 M ⎞
⎛ 10 −7.3 M ⎞
J ⎞
J ⎞
J ⎞
J ⎞
⎛
⎛
4
= ⎜ ⎜ 8.314
+ ( 0 ) ⎜ 9.646 x 10 4
+ ⎜ 8.314
⎟ ( 310 K ) ln ⎜
⎟ ( −0.055 V )⎟
⎟ ( 310 K ) ln ⎜ −6.2 ⎟ + ( +1) ⎜⎝ 9.646 x 10
⎟ ( −0.055 V )⎟
⎝
mol•K ⎠
mol•V ⎠
mol•K ⎠
M⎠
mol•V ⎠
⎝ 0.040 x 10 −3 M ⎠⎟
⎝ 10
⎝⎝
⎠ lactose ⎝⎜ ⎝
⎠ lactose
J
J ⎞
J
J ⎞
J ⎞
J ⎞
J
⎛
⎛
⎛
⎛
= ⎜ 8,025
+0
+ ⎜ −6,528
− 5,305
+ ⎜ −11,833
⎟
⎟ = ⎜ 8,025
⎟
⎟ = −3,809
⎝
mol
mol ⎠ lactose ⎝
mol
mol ⎠ H+ ⎝
mol ⎠ lactose ⎝
mol ⎠ H+
mol
(The transport of lactose is favorable.)
active
c. If the transport of lactose into the cell is favorable, is the transport active or passive? ___________
Explain The transport of lactose is active. On its own the transport is unfavorable (ΔGlactose =
8,025 J/mol. By coupling its transport to the favorable transport of H+ across the membrane, the
overall transport is now favorable. (ΔGlactose = 8,025 J/mol + ΔGH+ = -11,833 J/mol)
d. If the membrane potential were 0 mV instead of -55 mV, with everything else being the same,
would the transport of lactose into the cell be favorable? _____________________
No
Explain and show your calculations.
⎛
⎞
⎛ ⎡⎣H+ ⎤⎦ ⎞
⎛
⎞
⎛ [lac ]in ⎞
ΔG = ⎜ RT ln ⎜
+ ⎜ RT ln ⎜ + in ⎟ + zF ΔΨ ⎟
⎟ + zF ΔΨ ⎟
⎝ [lac ]out ⎠
⎝
⎠ lactose ⎜⎝
⎝ ⎡⎣H ⎤⎦ out ⎠
⎠⎟ H+
⎛⎛
⎞
⎛⎛
⎞
⎛ 0.090 x 10-3 M ⎞
⎛ 10 −7.3 M ⎞
J ⎞
J ⎞
J ⎞
J ⎞
⎛
⎛
4
= ⎜ ⎜ 8.314
+ ( 0 ) ⎜ 9.646 x 10 4
+ ⎜ 8.314
⎟ ( 310 K ) ln ⎜
⎟ ( −0.055 V )⎟
⎟ ( 310 K ) ln ⎜ −6.2 ⎟ + ( 0 ) ⎜⎝ 9.646 x 10
⎟ ( −0.055 V )⎟
⎝
mol•K ⎠
mol•V ⎠
mol•K ⎠
M⎠
mol•V ⎠
⎝ 0.040 x 10 −3 M ⎠⎟
⎝ 10
⎝⎝
⎠ lactose ⎝⎜ ⎝
⎠ lactose
J
J ⎞
J
J ⎞
J
⎛
⎛
= ⎜ 8,025
+0
+ ⎜ −6,528
+0
⎟
⎟ = 1,497
⎝
mol
mol ⎠ lactose ⎝
mol
mol ⎠ H+
mol
e. What class of biological molecule, e.g., amino acid, carbohydrate, lipid, etc. does lactose belong
carbohydrate
to? ____________________
f. Draw the chemical structure for α-lactose.
g. What two monosaccharides comprise lactose?
____________________________________
β-D-galactose
D-glucose
____________________________________
h. How many chiral carbons does lactose possess? _______________
10
β(1→4)
i. What type of glycosidic bond connects the two monosaccharides? _______________________
4