### Cooperative Binding: Answer Sheet Example

Example Problem:
You are given a 0.4 mg/ml solution of a protein (Mr = 40,000 Da). The binding stoichiometry is two ligands/protein.
You do a binding experiment at several concentrations of Atotal and determine Abound.
a) Determine Kd and the Hill Coefficient, nH.
b) Submit your calculations and a graph of log(Y/1-Y) = nHlogA - logKd (i.e. a Hill Plot).
What we know from the problem:
1) Concentration of the protein = 0.4 mg/ml.
2) Protein Mr = 40,000 Da
3) Stoichiometry = 2 A molecules/protein.
What we found in the experiment:
[A]total
(mM)
[A]bound
(mM)
[A]free
(mM)
Y

logA

log(Y/1-Y)

``` 0.010
0.020
0.050
0.075
0.100
0.150
0.200
0.400
0.700
1.000
```
``` 0.32
1.04
4.50
7.50
9.90
13.50
15.50
18.50
19.40
19.70
```
```0.010
0.019
0.046
0.068
0.090
0.137
0.185
0.382
0.681
0.980
```
```0.02
0.05
0.23
0.38
0.50
0.68
0.78
0.93
0.97
0.99
```
```-2.01
-1.72
-1.34
-1.17
-1.05
-0.86
-0.73
-0.42
-0.17
-0.01
```
```-1.79
-1.26
-0.54
-0.22
-0.01
0.32
0.54
1.09
1.51
1.82
```
The protein concentration = (0.4 mg/ml)/(40,000 g/mol) = 10 mM.
The last four columns were calculated using equations from the Cooperative Binding page.

Graph of the calculated results: The Kd = 0.10 mM.
The Hill Coefficient, nH = 1.8.

Compare the above graph to the Hill plot for non-cooperative binding with the same Kd. Coop.xls is the Excel spreadsheet used to calculate and graph these results; it can be copied to your disk.

8.20.03