Download Assignments 3 Problem 1 Below is the protein melting data for a pair

Assignments 3
Problem 1
Below is the protein melting data for a pair of wild-type and mutant proteins.
WT:
Temp: deg C
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
Mutant:
Temp: deg C
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
Fluorescence Int.
1.71
1.73
1.77
1.84
1.96
2.14
2.32
2.49
2.61
2.69
2.74
2.76
2.78
2.78
2.79
2.79
2.79
2.80
2.80
Fluorescence Int.
1.77
1.78
1.82
1.88
1.96
2.08
2.21
2.33
2.42
2.49
2.53
2.56
2.57
2.58
2.59
2.59
2.59
2.60
2.60
Determine the following pieces of information. Note: While you are doing the plots and
the calculations, make sure that you convert the temperatures from Celsius to Kelvin.
a) Plot the melting curves (Fluorescence intensity vs. temp) for both the mutant and the
wild-type protein.
b) Determine your signal for the fully folded and the fully unfolded form (both mutant
and WT).
c) Plot the melting curves as the fraction of folded protein vs. temp.
d) What are the melting temperatures for the two proteins?
e) Pick the appropriate plots to determine ΔH and ΔS of unfolding for both proteins.
f) What is the ΔΔG between the two proteins at 25 deg C.
g) What fraction of the molecules of the mutant is folded at 20 deg C.
h) If you want exactly 0.1 % of the wild-type protein to be folded, what temperature do
you have to choose?
Problem 2
Your lab is investigating a receptor molecule and wants to use your new physical
chemistry skills to answer some new questions. Here is the state of the project when you
come in:
- The lab has designed a mutant of the receptor, which converts an Asp in a
flexible, solvent-exposed loop on the protein surface into a Phe.
- They determined the structures of both the mutant and the wild-type protein and
except for the side-chain change the two structures look identical.
- Protein stability experiments on the wild-type protein gave: ΔHunfold=32kcal
ΔSunfold=90cal
You get the following data from a protein melting experiment of the mutant
Temp in deg C
25
40
55
70
85
rel. fluorescence intensity
0.5
0.61
1.15
1.80
2.0
a) Determine the Tm, ΔHunfold, ΔSunfold, ΔGunfold (at 20 deg.C) of the mutant and the
ΔΔHunfold, ΔΔSunfold, ΔΔGunfold (at 20 deg C) relative to the wild-type protein.
b) Somebody in your lab wonders if the unfolded form of the mutant protein may be
populated enough to play a biological role in the signaling reaction. To help out,
calculate the fraction of unfolded molecules at 20 degrees C. Why would it be
hard to measure the fraction of unfolded mutant protein at 20 deg. C
experimentally?
c) Now it is head scratching time! Do the results from the mutant surprise you?
What effect, if any, would you have expected to see for the mutation? How could
you rationalize the result? Two hints: i) remember that ΔG is defined by two
states of the protein. Which of the two states may be responsible for the effect of
the mutant. ii) Remember what you learned about the molecular nature of the
hydrophobic effect?
Problem 3
Below is the picture of a section through a protein interior that contains two methionine
residues. (The rest of the protein is shown as a solid mass. Assume that this interior is
entirely hydrophobic).
You want to use this protein to test how much energy it costs form a salt bridge in the
interior of a protein.
a) Which two amino acids would be best suited to substitute for the two methionines for
your mutants and why?
b) Calculate the expected energetic cost of burying this salt-bridge. (You did this in your
previous assignments)
c) Assume your wild-type protein has a ΔH of 52kcal and ΔS 160 cal. What would be the
Tm of the wild-type protein and what would be the Tm of your mutant.
d) Given what you learned in class, what should you do besides measuring ΔΔG of the
mutant, to convince yourself that your experiment is really working? What sort of things
could go “wrong” with your design?
Problem 4
You are working on a protein-engineering project. Your goal is to generate a more stable
version of protein X. You finally expressed and purified both the wild-type form of X and
the mutant you designed. Now want to know if the mutant is indeed more stable than the
wild-type protein.
To answer this question, you do two experiments: 1st you use fluorescence spectroscopy
to measure the fraction of unfolded protein at 37 deg. C. Second you use CD
spectroscopy to determine the unfolding temperature.
You are a bit puzzled by your results:
At 37 deg. C the wild-type sample contains less unfolded protein than the sample of the
mutant (i.e. wt is more stable). However, in your second experiment the mutant has the
higher temperature of unfolding (i.e. mutant is more stable).
First you think that either the CD or the Fluorescence spectrometer may be broken, or
that you switched your samples, but after checking everything twice you are sure that
your instruments seems to be working fine. So finally you go back and measure complete
melting curves for both wild-type and mutant protein.
Here is the data:
Wild-type
deg. C
10
20
30
40
50
60
70
80
90
signal
0.50177714
0.50703773
0.52477872
0.5745794
0.67674709
0.80715497
0.9067036
0.95924841
0.98254687
Mutant
deg. C
10
20
30
40
50
60
70
80
90
signal
0.50690435
0.51772131
0.54148579
0.58688752
0.6584774
0.74699714
0.83146568
0.89600718
0.93834395
Assume that a fully unfolded protein would give you a signal of 1 and a fully folded
protein gives you a signal of 0.5.
a) Determine ΔHunfold and ΔSunfold for both the mutant and the wild-type protein.
b) Do the values you get for ΔHunfold and ΔSunfold explain your previous observations?
Calculate the fraction of unfolded protein at 37 deg. C for both the wt and the
mutant protein. Also calculate the melting temperature (Tm) for both proteins.
c) Based on these results, does it really make sense to talk about one protein being
more stable than another one? Please comment.