Question 1 - Brandeis University

Question 1

You have just cloned the gene for a new growth hormone receptor. You have
expressed and purified the protein and determined that in the presence of the hormone
the receptor’s kinase activity is stimulated. You want to learn more about the
molecular architecture of your receptor and performed a ligand-binding experiment.
Below is the graph and 3 data points from the graph:

relative kinase activity Kinase activity as function of free [X] rel. kinase act.
ligand
1.0 0.02
1 2.0 0.5
0.9 3.0 0.9
0.8
0.7 5
0.6
0.5
0.4
0.3
0.2
0.1

0
01234
[X]

a) Use the three data points to determine the Hill coefficient for this binding
curve.
Answer:

The Hill coefficient is 5.55.

b) The number you got for the Hill coefficient will probably not be an integer.
What is the relationship between the Hill coefficient and the likely number of
binding sites on the receptor?
Answer: The Hill coefficient gives the number of binding sites in the case of
absolutely perfect cooperativity. Such perfect cooperativity rarely exists in
any real molecule. Therefore the number of ligands that are required to bind
to one receptor to give a certain degree of cooperativity is always larger than
the Hill coefficient. In our case this means that at least 6 ligands have to bind
to our receptor.

Question 2

You have a new protein and you noticed that binding a certain ligand to it changes the
fluorescence signal. When you titrate in the ligand and then record the fluorescence
signal vs. free ligand, you get the curve below.

a) Do you think your protein shows binding cooperativity? Do the appropriate plot
to make sure your answer is correct.
Answer: The Langmuir plot is nice and linear.

b) Determine the apparent binding constant.
Answer: Based on the graph, the apparent binding constant is 1/y-intercept = 1.3
nM.

c) You want to know how many binding sites your protein has? Can you answer this
question with the data you have?
Answer: No, one could have multiple binding sites that are not cooperatively
linked. In this case one would get a perfect langmuir as a binding curve.

Free Ligand Fluorescence
(nM) 4.766666667
5 4.955445545
7 5.107142857
10 5.231707317
15 5.296296296
20

Question 3

You have a wild-type receptor, in which the binding of a ligand regulates the activity
of the receptor’s kinase domain. In the absence of a ligand, that kinase is inactive.
You have recorded the kinase activity of your receptor as a function of free ligand.
The data is shown below. Your hypothesis is that ligand binding allows a
conformational change to take place that activates the kinase and simultaneously traps
the ligand in the binding site.

a) Write down the binding scheme that describes the reaction according to this
hypothesis
Answer: I + L -> IL ->AL

b) Does the data for the wild-type protein (solid line) allow you to determine if your
model is correct? In particular does the data allow you to distinguish between
your model and an alternative model, in which the receptor exists in an active and
an inactive conformation and the ligand binds only to the active form of the
receptor?
Answer: No, both models would give simple Langmuir binding.

c) Assume you made mutations in a region of the receptor that links the ligand-
binding domain to the kinase domain. You test three mutants and record the data
shown in the dotted lines. Does this data support your model or the alternative
model? In other words does the data suggest your mutants affect a conformational
equilibrium in the ligand-free or in the ligand bound form?
Answer: The data suggests that the initial hypothesis is correct: The
conformational equilibrium appears to occur after ligand binding and the mutants
appear to specifically effect the equilibrium between the active and inactive form.
If the conformational equilibrium would occur prior to binding, we would expect
wt and mutant plots to all level off at the same relative kinase activity, but the
individual binding curves would all have different apparent binding constants.

Question 4

The MWC model can explain cooperativity in binding reactions.

a) Draw the reaction scheme for the MWC model.
b) Why is the MWC considered such a good model to explain cooperativity? What

makes it better than the Hill model?
c) Where does the cooperativity come from?
d) Do all cooperative proteins follow the MWC model? Explain.

Answer: Please see class notes for answers to question 4.