Biochemistry I Fall Term

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.

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8.20.03