# Exercise – Receptor binding and the Hill plot

```Tobin/Aronsson HT 2010
Exercise – Receptor binding and the Hill plot
The aims of this exercise are to teach and familiarize you with a number of pharmacological
terms and expressions.
Also the exercise will point out some important features in Microsoft Excel (2003/2007).
The data needed to complete this exercise can be found in the provided Excel-file.
Important terms and expressions
Concentration – Response curve
Logarithmic (log) scales and log plots
Mean values and standard deviation (SD)
EC50 - value
Hill plot / Hill slope
Cooperativity
Homogeneous receptor population
Heterogeneous receptor population
1)
Calculate the logarithmic values of the concentrations administered
(hint: use the command “=LOG(concentration)” in excel)
This will help you to be able to construct log plots later on.
2)
Calculate the mean % Response
(hint: use the command “=MEDEL(first response:last response)” or
“=AVERAGE(first response:last response)”in excel)
3)
Calculate the standard deviation for the % Responses A-C.
(hint: use the command “=STDAV(first response:last response)” or
“=STDEV(first response:last response)”in excel)
4)
Construct a Concentration – Response plot (with “mean % response” on the y-axis and
“log(concentration)” on the x-axis). For all graphs in this exercise, use the XY-scatter option.
Insert SD error bars
 In Excel 2003; (Right click on a data point  Format data series  Y error bars. Then
chose the double error bar and select custom input. Use your obtained SD values as
the source for the error bars).
1
Tobin/Aronsson HT 2010

In Excel 2007; (Mark a data point  Layout  Error Bars  More Error Bars Options
 Mark “Error Amount”; Custom and click “Specify Value”. Select your obtained SD
values as the source for the error bars).
Describe in your own words what the graph looks like.
2
Tobin/Aronsson HT 2010
5)
Graphically obtain the EC50-value. This is the concentration when you get 50% of the
maximal response. Remember that you have a logarithmic x-axis!
6)
Now make a Hill plot. This is a plot with
“log(MeanValue%Response/100- MeanValue%Response)” on the y-axis and
“log(concentration)” on the x-axis.
This should give you an almost straight line.
7)
The slope of the Hill plot tells you something about the ligand binding to the receptors.
The Hill slope equals 1 when a ligand binds with no cooperativity to one site.
When the slope is greater than 1 the receptor or ligand has multiple binding sites with
positive cooperativity.
The Hill slope is less than 1 when there are multiple binding sites with different affinities for
ligand or when there is negative cooperativity.
(hint: to get a straight trendline in your Hill plot, right click on a data point, chose add
trendline, chose a linear trendline.
To get the slope of the trendline, right click on the trendline and chose format trendline 
options  display equation on chart.
This equation is the standard straight line equation Y=kX+m; k being the slope.)
How would you interpret the data in this case?
3
```
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