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).

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

• 5PL nonlinear regression model
• Tips for ELISA analysis
• The importance of weighting with the 4PL and 5PL
• Dose response analysis and EC₅₀/IC₅₀ determination

Here are some curve-fitting tips for ELISA data analysis:
Read the rest of this entry »

Quick Demo of MasterPlex ReaderFit (1:43 min.)

The microplate analysis demo includes the following simple steps:

1. Importing an Excel file with the RLU values
2. Marking the background, standard, and unknown samples
3. Filling in the standard concentrations with the AutoFill Feature
4. Pressing the Best Fit button
5. Reviewing standard curve, concentrations, and charts

Save time, stop copying & pasting, and download the FREE MasterPlex ReaderFit trial and see for yourself how easy it can be!

The Hitachi Software MiraiBio group has just released a new build for MasterPlex ReaderFit, the quantitative analysis and curve-fitting data analysis software for microplate readers. New features and improvements include:

• File Import Wizard – Although MasterPlex ReaderFit can automatically import some of the known file formats from common plate readers that are out there in the market, it does not handle all 100% of them. Unknown file formats can now be handled by the File Import Wizard in 1 of 2 ways:
  1. Plate Format

     

  2. List

     

  More details on using the File Import Wizard for MasterPlex ReaderFit

• Best Fit Options – The Best Fit feature now offers 3 parameters for which you can optimize for to determine the best curve fit:
  1. Root Mean Square Error (RMSE) – RMSE is a good measure of accuracy or goodness of fit which aggregates the individual differences or residuals between your expected and calculated values into a single measure of predictive power. This is the default option as it is the one that is recommended.
  2. Standard Deviation of % Recovery – This option will provide the model equation and weighting algorithm combination with the lowest standard deviation of percent recovery. The percent recovery is basically the calculated concentration – the expected concentration * 100.
  3. R-squared – This option is the only Best Fit option in previous builds of MasterPlex ReaderFit. It is not as sensitive to the goodness of fit as the RMSE option.

  

• Competitive Binding and Inhibition Assays – This build provides improved support for competitive binding or inhibition assays.

  

• More Intuitive Auto Fill – The Auto Fill feature helps to automate the entry of the standard concentration values for serial dilutions. This feature has been simplified with more intuitive dilution direction buttons and being able to preview the standard values.

  

Try it out and download the free trial now!