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.

• MasterPlex EX Tutorial Series
• MasterPlex QT Tutorial Series
• MasterPlex ReaderFit Tutorial Series

Each series guides the user through the entire analysis workflow.

It has been a long awaited item on our todo list and we hope MasterPlex users will find this content useful. Please let us know if you have any requests for “how-to’s” that you would like to see.

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

Current users of the above mentioned versions will be able to continue to use these products and existing support documents and content will continue to be available on the MiraiBio Group website.

Hitachi Software is retiring support for these products because they are outdated and do not offer our customers the experience and reliability of our newer versions of these products. We recommend that customers who are still running MasterPlex QT v2.5, MasterPlex QT v2.0, MasterPlex QT v1.2, or MasterPlex QT v1.0 upgrade to MasterPlex QT 2010.

We have created promotional pricing in order to encourage our users of these older versions to upgrade to MasterPlex QT 2010. Please contact info@miraibio.com if you would like to learn more about upgrading.

-The MiraiBio Team

Here is a list of what’s new in QT 2010:

• Acquire Results with One Click
  Templates can now store curve fitting parameters along with all your plate layout information. With a push of a button, your entire plate layout is loaded (along with your standard information) and your results will be automatically calculated for you.
• Quality Control Manager with new Upper Limit of Detection (ULOD)
  The Quality Control Manager is now included in every copy of MasterPlex QT 2010. In addition, we have now added the ULOD to help further refine your results.

  

• Added Compatibility for the Meso Scale Discovery (MSD) Platform
  MasterPlex QT 2010 is now fully compatible with data files from MSD’s MULTI-ARRAY® instruments.
• More Flexible Data Table
  Results for replicate samples can now be merged together for a cleaner look with a push of the Merge Cells By Group button.

  

• EC50/IC50 Field Available in the Data Table
  The EC50/IC50 values are now available (from 4PL & 5PL curve fits) in the Data Table for report generation via the Columns Selector.

  

• EC(anything) or IC(anything) Calculation
  Need to calculate the EC90 value? The new EC(anything) feature can calculate and report any value you need.

  

• More Flexible Standard Curve Chart
  You can now customize standard curve chart titles and X&Y axes.

  

Try the Free 14-Day Trial of MasterPlex QT 2010!

Are you planning to upgrade from an earlier version of MasterPlex QT?

Here is a list of features from previous versions:

• MasterPlex QT v4.1
  • Quality Control Manager (optional in v4.1 but it is built into v5)
  • Step-by-step video tutorials to guide the full analysis workflow
  • Copy and paste Group Names
  • Get at-a-glance views of all points on the standard curve by simply hovering over with your mouse
• MasterPlex QT v4.0
  • New user-friendly interface
  • Added new options for BestFit to optimize for Root Mean Square Error (RMSE) and Least Deviation from %Recovery
  • Plot unknown wells on the standard curve chart
  • Copy and paste Sample Names
  • Compatible with 384-well data.
  • Compatible with xPONENT 3.1 and 4.0
  • Improved Bio-Plex data file compatibility
  • Added 21 CFR Part 11/GxP (GCP, GLP, GMP) compliance module (optional)
  • Added AssayCheX module for easy analysis of the AssayCheX Process Control Panel
• MasterPlex QT v3.0
  • Normalized data can be viewed in Charts and Reports
  • Analyte names can be edited from the plate panel
  • Double-click to enter edit-mode for data that is editable such as sample name or dilution factor
  • Added HTML viewer to view custom reports
  • Compatible with xPONENT 2.x
• MasterPlex QT v2.5
  • Full support for Gene Expression data analysis
  • Customizable reports
  • Concurrent network licensing
  • Average, Standard Deviation, and %CV for MFI group replicates can be viewed in the Plate tab
  • Added error bars to bar graphs for replicate groups
  • Automatic outlier detection based on standard deviation
  • Ability to increase plex of the Virtual Plate feature by adding any analyte as a new analyte to an existing Virtual Plate
  • Support for Luminex 100/200 based systems such as IS 2.3
• MasterPlex QT v2.0
  • Added weighting options for more accurate curve fits
  • Added more reporting options including export to Excel
  • Added intensity map
  • Optimized curve fitting algorithms
  • Errors bars added for replicate standards in the standard curve chart
  • Virtual Plate feature implemented
  • Residual and % Recovery statistics added to the Standard Curve tab

This latest version of ReaderFit focuses on making data analysis even easier and more streamlined EC50/IC50 analysis.

Here is a list of what’s new in ReaderFit 2010:

• Easier Data Import
  You can now copy & paste your raw values (e.g. OD, absorbance, fluorescence intensities, etc.) instead of having to use the File Import Wizard.
  
• EC50/IC50 Field Available in Results tab
  The EC50/IC50 values are now available (from 4PL & 5PL curve fits) in the Results for report generation via the Columns Selector.

  

• EC(anything) or IC(anything) Calculation
  Need to calculate the EC90 or IC90 value? The new EC/IC(anything) feature can calculate and report any value you need.

  

• Quality Control Manager with new Upper Limit of Detection (ULOD)
  The Quality Control Manager is now included in every copy of MasterPlex ReaderFit. In addition, we have now added the ULOD to help further refine your results.

  

• Acquire Results with One Click
  Templates can now store curve fitting parameters along with all your plate layout information. With a push of a button, your entire plate layout is loaded (along with your standard information) and your results will be automatically calculated for you.
• More Flexible Curve-Fitting Chart
  You can now customize curve-fitting chart titles and X&Y axes with a simple right-click.

  

Try the Free 14-Day Trial Today!

Are you planning to upgrade from an earlier version of MasterPlex ReaderFit?

Here is a list of features from previous versions:

• MasterPlex ReaderFit v1.1
  • Quality Control Manager (optional in v1.1 but it is built into v2)
  • Step-by-step video tutorials to guide the full analysis workflow
  • Copy and paste Group Names
  • Get at-a-glance views of all points on the standard curve by simply hovering over with your mouse
  • Added compatibility with .xlsx files

1. Sandye Adams
2. Marcus Carr
3. Hannah Cheung
4. Brook Danboise
5. Lijin Li
6. Jannifer Tyrrell
7. Timothy Van Meter
8. Masahito Yamagata

OriGene’s strength in multiplexed assays relies on its genome wide collection of high-quality full-length human cDNA clones, over 5000 human-cell produced proteins, and its growing collection of TrueMAB™ monoclonal antibodies. OriGene scientists have developed many research and diagnostic assays based on Luminex platform, including multiplexed assays for microRNA expression, transcription factors profiling, and genotyping.

As part of the agreement, Hitachi Software and OriGene will also present quarterly scientific webinars that provide an in-depth view into both OriGene’s assays and the key features of MasterPlex that enable researchers to analyze data in this increasingly complex research domain. The webinars will be available to registered participants at no charge.

“We are very excited to be partnering with OriGene Technologies,” said Robert Lynde, Director of Sales for Hitachi Software. “We believe that in combination with OriGene’s broad range of multiplex assays, the Hitachi Software MasterPlex Suite and custom reporting services are, without a doubt, the market-leading solution for xMAP® technology users. Going forward, OriGene and Hitachi Software plan to leverage our new partnership to bring an even broader range of research and analysis solutions to our current and future life sciences customers.”

Commenting on the agreement, James G. Lazar, Ph.D., VP of Assay Development at OriGene Technologies, Inc. said, “OriGene is extremely pleased to be working with Hitachi Software in providing a whole product solution to our assay customers. OriGene chose to work with Hitachi Software based on the quality and breadth of the MasterPlex offering and Hitachi Software’s commitment to the multiplexed assay market. We look forward to working together with Hitachi Software to bring improved assay solutions to market.”

SOURCE OriGene Technologies, Inc.

Sample A = 20 MFI – 10 MFI (background) = 10 MFI (50% reduction)
Sample B = 5000 MFI – 10 MFI (background) = 4990 MFI (0.2% reduction)

As can clearly be seen, slight MFI changes on the lower end of the curve can dramatically affect MFI values on the lower end where it barely makes a dent with points on the higher end of the curve. To make things worse, if Sample A were on the really flat part of the curve, this issue will be magnified as really small changes in MFI greatly affect the concentration values.

An MFI change on the lower part of the curve has greater weight

A change in MFI has greater weight on the lower end of the curve because values here have smaller variance. This is a natural situation that arises in almost all fields, including chemical- and immuno-assays, in which the variance of a dependent variable varies across the data. Simply using the 4PL or 5PL model equations without weighting will assume equal variance across the entire curve which is certainly not optimal.

Heteroscedasticity - Nonconstant Variance in Immunoassay Data

Ok…back to my story on the true case. We first wanted to compare apples to apples so we imported the data into MasterPlex QT and used the 5PL model equation with no weighting. The results were very similar where both analysis software had calculated the minimum asymptote to roughly about 8. This means that any sample with an MFI lower than 8 is considered out of range (for the lower part of the curve). Both analysis software reported out of range results since most of the samples were on the lower part of the curve. Not good.

We then applied 1/Y weighting to our 5PL model equation and the minimum asymptote was lowered to about -4. I know what you are thinking right about now; how it is possible to have a negative MFI value for the minimum asymptote? This is something that is certainly possible with background subtraction on background wells with higher MFI values than the actual samples. Anyway, with weighting applied, we were able to recover 95% of the out of range values =) It is also worthy to note that the majority of these points were interpolated rather than extrapolated so they were in fact within standard range. This is not to say to adding weighting will always push the minimum asymptote lower. What can be said with confidence is that the lower asymptote is more accurate with weighting than without weighting because it takes into account the natural heteroscedastic nature of bioassay data. In this particular case, having weighting was able to bring a large majority of the unknown samples into calculable range.

For more details regarding heteroscedasticity, please review point #2 of our 10 Tips for Luminex/Bio-Plex Data Analysis post.

You may also be interesting in reading our previous blog post on the 5PL nonlinear regression model equation.

This is sort of non-related but I just wanted to add that according to our most recent survey results, users who switch to MasterPlex QT from their old analysis software, save (on average) 83 minutes per analysis!

1. Daniel Standage
2. Chunfu Xu
3. Bernard Rajeev Srambical Wilfred
4. Sandye Adams
5. Jim Dunbar
6. Rakesh Reddy
7. Ajeeth Pingili
8. Yao Hu
9. Randy Weinberg
10. Deepti Terala

1. George Kamita
2. Jingjing Dong
3. Bernard Rajeev Srambical Wilfred
4. Ping Lou
5. Tonya Walser
6. Sandye Adams
7. Kevin Brick