Download 1 Problem set 3 Due dates: Official date is 12 Dec. However I will

1
Problem set 3
Due dates: Official date is 12 Dec. However I will accept problem sets for full
grades through Dec. 16 in recognition of the time it took me to finish providing
problems. (Note also that the problems for Chapters 14 and 15 are shorter.)
Chapter 16 will not be covered, for Chapter 17, please work the problems at the back fo
the chapter for practice.
Problem sets turned in on 12 Dec. will be graded by the morning of 18 Dec.
Chapter 12
1
The library
A genomic library of human is to be constructed in a plasmid that can accommodate 4
kbp inserts. How many individual clones must be in the library in order to have a 99 %
chance that one carries a fragment of interest ?
What if the library is constructed in a cosmid that can accommodate 40 kbp inserts ?
What if the library is constructed in a YAC that can accommodate 2 Mbp inserts ?
Write two primers, each 18 bases long that would enable you to PCR-amplify the gene
for phenylalanyl tRNA, assuming for now that the nucleotide sequence in Fig.11.33 is
encoded by the DNA.
2
Cloning
You are trying to clone up the gene for a protein. You already purified a little of
the protein. It took you three weeks working in the cold room and your yield was 0.2 mg
from 10 kg of liver tissue. However that was enough to allow N-terminal sequencing and
C-terminal sequencing (recall chapter 5). You now know that the protein begins with
Met-Gln-Ala-Arg-Pro-Trp- and ends with -Met-Leu-Val-Gly-Asp-Asn. You never want
to do that purification again, so you plan to use the amino acid sequence information to
design primers and use the primers to amplify the gene for your protein by PCR.
Use the genetic code provided in Table 30.1 to calculate: how many different primers
will be needed to be sure to have a complement to the beginning of the coding region of
the gene.
How many different primer sequences will be needed to be sure to have a complement to
the end of the coding region of the gene.
mRNA is copied off the 'template strand' of DNA, NOT the 'coding strand' (Under this
nomenclature, the coding DNA strand has the same sequence as the mRNA but with T
replacing U). Figure out what the DNA template strand will have to be for the beginning
of your gene, using the following codes to accommodate cases where the identity of the
base can be more than one thing: R=purine, Y=pyrimidine, N anything. This will be part
of one of your primers.
Do the same for the end of your gene. Then write down the sequence of the primer you
will use for this end of the gene.
In addition to targeting the correct gene, you will want your product to have restriction
endonuclease sites that will facilitate directional cloning. At the start end of the gene,
2
you can take advantage of the fact that the NcoI enzyme recognizes CCATGG, which
contains the codon for Met. However it also requires that the next codon begin with G.
Will this cause a change in the amino acid sequence ? If so, discuss the possible
significance of the change for protein structure, solubility and stability (two sentences
max). How many base mis-matches can the Nco1 site introduce into the base pairing you
expect between your primer and the DNA ?
Look up the cleavage site for Nde1, think of the considerations as we entertained for
Nco1 and discuss the advantages and disadvantages of building on an Nde1 site instead
of Nco1. Now write you extended your primer sequence, incorporating a cleavage site as
well as the code for the first six amino acids (possibly mutated).
Note that you would normally use slightly longer primers, but the logic is the same.
Also, computer programs would do the back-translation you have just done. All the user
does is type in amino acid codes. Finally the oligonucleotide synthesizing machine will
even use mixtures of pyrimidines, purines or all nucleotides, wherever the customer
requests Y, R or N. Also note that a few mismatched bases can be tolerated early in the
PCR, and moreover can be compensated for with adjustments to the melting and
annealing temperatures and times used.
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3
Primers
A successful PCR experiment often depends on
designing the correct primers (above). Inn particular,
the Tm for each primer should be approximately the
same.
What is the Tm ?
Why should the two primers' Tms be approximately the
same ?
4
Diagnosis of a problem
A number of people were found not to be able to
clear a certain drug from their bloodstream. This was
found to be related to their version of gene M, which
encodes enzyme m. Six people were tested for gene M
integrity using molecular biological methods. 'A' is the
positive control (clears the drug fine). 'B' is
asymptomatic but has children who cannot clear the
drug. Persons 'C' through 'F' cannot clear the drug.
Tissue samples were obtained from each person. DNA
was digested with restriction endonuclease HindIII in
preparation for Southern analysis. Northern analysis on
the mRNA was also performed, as was a Western
analysis employing antibody to enzyme m.
Based on the results shown to the right, say why person
'B' has no symptoms. Say why some of person 'B's
children do have symptoms.
For each of people 'C', 'D', 'E' and 'F' suggest a reason
why they may not be able to clear the drug.
Data for Problem 4
Chapter 13 (back to number answers !)
1
Antibiotic resistance:
Some bacteria are resistant to penicillin because they export an enzyme that degrades
penicillin by hydrolyzing it. One such enzyme is !-lactamase. The molecular weight of
Staphylococcus aureus' !"lactamase is 29.6 kDa. Researchers measured the amount of
penicillin hydrolyzed per minute in a 10 ml solution containing 10-9 g of pure !lactamase, for various concentrations of penicillin. The resulting initial velocities are
provided below
[Penicillin]
Amount hydrolyzed per unit of time (eg. minute)
(µM)
(nmoles)
1
0.11
3
0.25
5
0.34
4
10
30
50
0.45
0.58
0.61
a
Plot vo vs. [S] and also plot 1/vo vs. 1/[S] for the above data. Does this !lactamase obey Michaelis-Menten kinetics ?
If yes, what is the KM ?
b
What is the value of Vmax ?
c
What is the enzyme's turnover number under the conditions used ? (assume one
active site per 29.6 kDa molecule.
d
What is the catalytic efficiency of this enzyme ? Does this enzyme display
catalytic perfection ?
2
Enzyme inhibition
The kinetics of an enzyme are measured as a function of substrate concentration in the
presence and in the absence of an inhibitor I ([I] = 2 mM).
[S]
(µ#)
3
5
10
30
90
vo (µM/min)
no inhibitor 2 mM inhibitor
10.4
4.1
14.5
6.4
22.5
11.3
33.8
22.6
40.5
33.8
a
What are the values of Vmax and KM in the absence of inhibitor ?
b
What are the values of Vmax and KM in the presence of inhibitor ?
c
What type of inhibition is this ?
d
What is the dissociation constant KI for this inhibitor ?
e
If [S] = 10 µM and [I] = 2 mM, what fraction of the enzyme molecules have a
bound substrate ? a bound inhibitor ?
f
If [S] = 30 µM and [I] = 2 mM, what fraction of the enzyme molecules have a
bound substrate ? a bound inhibitor ?
Compare this ratio with the ratio of the reaction velocities under the same conditions.
5
3
Uncompetitive Inhibition
Assume that an inhibitor I can bind reversibly to an ES complex (but not to E alone).
The resulting IES complex does not go forward to produce product (see scheme).
Use same the logic as
S
we did in deriving the
Michaelis-Menten
E
ES
equations to derive
mathematical equations
for the apparent Vmax'
I
and KM' applicable in
this case. Vmax' is the
maximum reaction
velocity and Km' is the
IES
concentration of
substrate producing halfmaximal velocity, at a
given inhibitor
concentration. You should get the results listed in Table 13.6
E+P
K’I
These expressions will make reference to the dissociation constant for [IES], KI'.
4
Linear relationships
Recast the Michaelis - Menten equation in order to describe a plot of vo vs. vo/[S].
This is called an Eadie-Hofstee plot. Use excell or equivalent software to generate a data
set and an Eadie-Hofstee plot of it. Along with vo, for each substrate concentration, also
plot a point using that substrate concentration and 1.05x vo and another using the
substrate concentration and 0.95x vo. These latter two point will demonstrate the effect
of a 5% error in measuring Vo.
Comment on the merits or cautions associated with using an Eadie-Hofstee analysis.
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Chapter 14
1
Mutational analysis
In a Ser protease, researchers found that mutating the active site His to Ala decreased the
kcat by a factor of 105 (kca,mut = .00001 kcat). Mutation of the active site Ser to Ala causes
kcat to decrease by a factor of 106. . Would you expect a doubly mutated protein to display
10-11 times the normal activity ?
Explain the basis for your answer.
2
Designer enzyme
If you had the gene for trypsin, but a mutation changed the codon for Asp 189 to a codon
for Lys, what change might this produce in substrate specificity ? Would you expect
your mutant trypsin to be as good a protease catalyst as the normal ("wild-type") trypsin ?
(i.e. would it be as good at accelerating peptide bond cleavage ?)
3
Make your own mechanism
Based on the mechanism of Ser proteases, propose a mechanism for a Cys protease. For
your answer, draw a segment of the substrate peptide backbone in the presence of a Cys
side chain from the enzyme active site. Use R and R' for the amino acid side chains
adjacent to the peptide bond to be cleaved and don't bother drawing more distant portions
of the substrate peptide (eg. terminate the backbone with a squiggle to indicate that it
continues beyond the drawing). Then draw transition states and intermediates involving
the enzyme Cys side chain and the peptide in which you can sketch in features you would
expect a good enzyme active site to use to stabilize the transition states. A perfect answer
will show what the enzyme's Cys side chain probably does, what some other active site
residue could do to activate the Cys for that role, what the peptide transition state likely
looks like and what the active site likely does to stabilize it. Draw analogous structures
to indicate how the enzyme is restored to its starting state, and what is done by active site
residues to favour transition states along the way.
4
Fundamentals of catalysis
Based on the fundamental principles of catalysis, will an enzyme that accelerates the rate
of A $ B affect the rate of B $ A ?
What should its effect be ? (qualitative answer).
A quantitative example:
If Keq for A $ B is 10, (kcat/KM)A$B is 103 M-1 s-1, and knon,A$B is 1 s-1, calculate knon,B$A
and (kcat/KM)B$A For inspiration, you can reread the 'deeper look' on page 443. Also
recall that equilibrium constants can be expressed in terms of either concentrations or rate
constants.
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Chapter 15
1
A smart enzyme, by design.
If you wish to build into your designer enzyme the possibility of turning it off/on on a
timescale of microseconds, will you design in an allosteric site, sensitivity to covalent
modification, or amino acid sequences that cause the protein to be degraded within an
hour of biosynthesis in conjunction with regulatory sequences in the mRNA that favour
production of the protein when it is needed ?
What if you want the possibility of turning on or off your enzyme on a timescale of
minutes and keeping it on or off for minutes at a time ?
What if you want your enzyme to turn off an hour or so after it is administered to a
patient ?
2
Anticooperativity
In class, we looked at the effect of allosteric modulation of affinity for substrate.
The case in class was one of positive cooperativity, wherein binding of the effector 'A'
increased the protein's affinity for substrate 'B'. Indeed, KAB = 0.1 mM whereas KB = 1
mM in our excel example. Now, use the same equation (below) and KAB = 10 mM vs. KB
= 1 to model negative cooperativity (anticooperativity between A and B).
For KA = 0.7 mM, what is KBA ?
Generate an excel (or equivalent) spread sheet for concentrations of B ranging from 0 to
50 mM. Generate a plot of the fractional saturation of B-binding sites when [A] = 0.
[B] ! [A] $
1+ B &
K B #"
KA %
[PB] + [APB]
Fractional saturation with respect to B =
=
[P]Tot
[A] [B] ! [A] $
1+
+
1+ B &
K A K B #"
KA %
Do the same for [A] = 20 mM, [A] = 2 mM and [A] = 0.2 mM. How does the shape of
the curve change ? What is the span of B concentrations in which the fractional
saturation goes from approximately 10% to approximately 90% in each of the above four
cases ?
3
Allosteric modulation of Vmax
The above is an example of a K-system.
Now model a V-system by holding KAB = KB = 1 mM but VAmax = 100 s-1 whereas Vmax =
10 s-1. Is A a positive effector or a negative effector ?
Now that we are working on a V-system instead of a K-system, KAB = KB. What
consequence does this have for KBA vs. KA ? (Write a very short equation.)
Derive an equation for fractional saturation with respect to B. You can use the equation
above as a starting point.
Does this depend on [A] ? Should it ?
8
Use excel or equivalent means to plot vo as a function of [B] ([substrate]) for the simple
Michaelis-Menten case, [B] ranging from 0 to 10 mM and [A] = 0.
Now use KA = 0.4 mM, and [A]=0.2 mM, and calculate the fraction of the population
with A bound ([AP*]/[P*]tot) and the fraction of the population without A bound
([P*]/[P*]tot. Because binding of A is not coupled to binding of B in this case, we can
consider just binding of A alone, using the simple definition of the dissociation constant
as applied to a single binding site. (The use of an asterisk above indicates no constraints
on the contents of the B site (sum of all possibilities)). KA = [A][P*]/[AP*].
For the proteins with A bound, VAmax applies but for the proteins without A bound, VA
applies. Calculate the effective Vmax,eff by taking the appropriately weighted average of
the two Vmax values above.
Use Vmax,eff in the Michaelis-Menten spread sheet and plot the vo vs. [S] for [A]=0.2 mM.
Repeat the above and plot vo vs. [S] for [A]=0.4 mM, 0.6 mM, 0.8 mM 1.0 mM and 2
mM. Provide all seven plots in a single chart. You do not need to turn in separate charts
of [A] = 0 mM and 0.2 mM.