Topic #3: Cooperative Binding Calculations
Model reaction: PA2
<=> P + 2 A
Dissociation constant: Kd = [P][A]nH/[PA2]
(and nH < 2)
Fractional occupancy: Y = [A]nH/Kd
+ [A]nH
[Note: P and A are used on this page (instead of the more
general, M and L) to indicate a particular binding reaction
under study. Any symbols can be (and are) used to represent the macromolecule
and ligand, respectively.]
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The Hill equation is derived from the expressions for Kd and
Y. In logarithmic form:
log(Y/1-Y) = nHlogA - logKd
,
where
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nH = the Hill coefficient (maximum slope of the Hill
plot);
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A = [A]free;
-
Kd = the dissociation constant.
We have a 0.4 mg/ml solution of a protein (Mr = 40,000 Da).
The stoichiometry of A binding is 2.0. When bound, the UV absorption of
the ligand changes. Thus, we can determine [A]bound directly.
We want to determine Kd and the Hill coefficient, nH.
This is done in three steps. (Each calculated [A]bound value has
a small "experimental error" added to it.
Tabbing out of the volume entry slot or clicking anywhere on the page
will also calculate [L]free.)
3. Record the values of [A]bound you obtain. Then, calculate
[A]free, Y, and (Y/1-Y). Finally, graph the values on a Hill
plot to determine Kd and nH. You should get enough
data so as to have 3 or 4 values of Y, both above and below the Kd
value.
(Hint: Graph the values you obtain as they are calculated; then
as the shape of the curve becomes apparent, choose values for [A]total
that fall into the appropriate range.)
Answers to this problem.
A sample Answer Sheet for a similar
problem shows the format of the results and the graph required. |
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