Calculating the EC10 or IC90 values for a dose response curve is not as simple as the EC50 or IC50 values when using the 4PL or 5PL model equations.

The equation for calculating any EC value given a 4PL curve fit is the following:

EC_F = (F/(100-F))^(1/H) * EC₅₀

0 < F < 100 (This is the EC value you are interested in. For example, F=10 for EC₁₀.)
H = Hill Slope for the 4PL curve fit

Luckily, our latest release of MasterPlex ReaderFit 2010 makes this easy. Yes, even with the 5PL curve-fit!

Here’s how:

1. Copy & paste your data into ReaderFit

   Copy your response values from the source and paste it into ReaderFit via CTRL+V -> Paste Response Values.

2. Mark data as Sample Curve type (part 1)

   Select all of the data points that will be used to fit one entire dose response curve including all replicates. In the example given below, there are 7 groups each done in duplicate.
   

3. Mark data as Sample Curve type (part 2)

   Click on the blue Mark Sample Curve button. (The Auto Fill dialog may pop up. Click the Close button if you see it.)
   

4. Indicate known dose concentration values (part 1)

   Select Independent Values(X-axis) from the data pull-down menu. This will show the corresponding data in the plate view. By default, all of the Independent Values(X-axis) will be 0.
   

5. Indicate known dose concentration values (part 2)

   Select the sample of interest and double-click the lower-cell to enter edit mode. Once in edit mode, type in the concentration value. Make sure all values have the same unit. We will edit that later.
   

6. Fitting the curve (part 1)

   Select the Fit Curves tab.
   

7. Fitting the curve (part 2)

   Select either the Four Parameter Logistic (4PL) or Five Parameter Logistic (5PL) from the Curve Fitting section and press the Calculate button.
   

8. Edit dose response curve axes

   Right-click on the dose response curve chart and edit the x and y axes. You also have the option to add a chart title.
   

9. Calculate EC or IC(Anything) value (part 1)

   Press the Statistics Toolbar button.

10. Calculate EC or IC(Anything) value (part 2)

    By default the EC50 and the log EC50 values are calculated for you. If you have an inhibition curve, press the ICxx radio button to switch to IC50 and log IC50 values.
    

11. Calculate EC or IC(Anything) value (part 3)

    If you have an inhibition curve and you are interested in the IC90 calculation, simply select the ICxx radio button and enter “90” into the Percentages section and press the Add button.
    

If you have not done so yet, I would like to invite you to try the free 14-day trial of MasterPlex ReaderFit.

The 4 Parameter Logistic or 4PL nonlinear regression model is commonly used for curve-fitting analysis in bioassays or immunoassays such as ELISAs or dose-response curves.

The following is the 4PL model equation where x is the concentration (in the case of ELISA analysis) or the independent value and F(x) would be the response value (e.g. absorbance, OD, response value) or dependent value.

F(x) = ((A-D)/(1+((x/C)^B))) + D

Not surprisingly, the 4PL model equation comprises of 4 parameters:

4 Parameter Logistic Nonlinear Regression Model

1. A = minimum asymptote
   
   In an ELISA assay where you have a standard curve, this can be thought of as the response value at 0 standard concentration.
2. B = Hill slope
   
   The Hill Slope or slope factor refers to the steepness of the curve. It could either be positive or negative. As the absolute value of the Hill slope increases, so does the steepness of the curve.
3. C = inflection point
   
   The inflection point is defined as the point on the curve where the curvature changes direction or signs. This can be better explained if you can imagine the concavity of a sigmoidal curve. The inflection point is where the curve changes from being concave upwards to concave downwards (see picture below).
   

   Inflection point and change in curvature or concavity

4. D = maximum asymptote
   
   In an ELISA assay where you have a standard curve, this can be thought of as the response value for infinite standard concentration.

The following are some key characteristics of the 4PL curve-fit model:

• Symmetry – There is perfect symmetry for the sigmoidal curve around the inflection point for 4PL curve fits.
  
  

  Symmetry around inflection point for 4PL

• Monotonic – A monotonic function is either always increasing or decreasing for all values of x.
  
  

  An example of a monotonic increasing function

  

  An example of a monotonic decreasing function

• Assumptions made by the 4PL model equation
  • It assumes that the standard deviation of the scatter is the same for all values of x (homoscedastic data). In the example of a standard curve, this is saying that the standard deviation for all the replicates of a low standard is equal to the standard deviation of the replicates for your high standard (see example curve below).
    
    

    Homoscedastic Data

    Of course, this is rarely the case when dealing with bioassays or immunoassays (ELISAs) where the data is heteroscedastic. We normally see something like this where the standard deviation increases as x increases:

    

    Heteroscedastic Data

    Applying weighting algorithms for 4PL and 5PL curve fitting is something that can be done to offset the assumption that data is homoscedastic.

  • The 4PL model equation also assumes that the scatters a normal (or Gaussian) distribution.

If you are looking for a curve-fitting software with the 4PL model equation and also does weighting, then try out the Free 14-Day Trial of MasterPlex ReaderFit (fully-functional) or our online free version at ReaderFit.com (light version).

You may also be interested in reading our blog post on:

• Dummies Guide to Curve-Fitting for Quantitative Analysis
• 5PL nonlinear regression model
• Tips for ELISA analysis
• The importance of weighting with the 4PL and 5PL
• Dose response analysis and EC₅₀/IC₅₀ determination

We recently had a customer that was interested in MasterPlex QT because his current analysis software for his Bio-Plex instrument was reporting a lot of “OOR < ” or out of range concentration values (below the lower asymptote in this case) for points on the lower end of curve. This is what you would normally expect to see for values that fall below the minimum asymptote BUT the software did not have the capability to use weighting in calculating the lower asymptote which can greatly affect points on the lower part of the curve.
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