1. It is best not to assume that 5PL equations are necessarily better than 4PL equations. 5PL equations require more calibrators to generate a meaningful curve, including points describing both the top and bottom plateaus; if you have these points and the 5PL fitting is advantageous because you see a lack of symmetry when reaching the plateaus, 5PL is the way to go. However, simpler equations are generally prefered if they fit the data, so 4PL equations are still widely used.

Contradicoary note: in my experience, 5PL have also been useful in fitting curves for ECL counts where there is often no hint of a top plateau. Anchor points are however often needed.

2. Some softwares include automatic weighting and can consider many curves generated with the same assay to determine the best weighting scheme. But to keep things simple, the weighting that that has generally given me the best results for immunoassays is 1/y^2 as it normalizes the importance given to the points at the top of the curve compared to the bottom of the curve. However, if you have an assay with a very small dynamic range (ODs of 0.2 to 0.5 for example), weighting will probably not help. And remember, choosing a simpler model is always preferable when possible.

3. In conclusion, I prone testing curve fitting every time. A tool I now used to compare 4PL vs 5PL is the "F" test which balances the importance of the simpler model and minimising the sum of squares of the curve fit. There is a free tool on the web from GraphPad which can perform the F test and gives oodles of helpful information: http://www.graphpad.com/quickcalcs/aic1/. The tool is more complete if you have the software, but the free tool gives you a good idea. Choosing the best curve fit will lead to accurate back-calculations of the most data points on your curve (especially near the top and bottom plateaus), so it is not something to be taken lightly.

Cheers,

André

1. It is best not to assume that 5PL equations are necessarily better than 4PL equations. 5PL equations require more calibrators to generate a meaningful curve, including points describing both the top and bottom plateaus; if you have these points and the 5PL fitting is advantageous because you see a lack of symmetry when reaching the plateaus, 5PL is the way to go. However, simpler equations are generally prefered if they fit the data, so 4PL equations are still widely used.

Contradicoary note: in my experience, 5PL have also been useful in fitting curves for ECL counts where there is often no hint of a top plateau. Anchor points are however often needed.

2. Some softwares include automatic weighting and can consider many curves generated with the same assay to determine the best weighting scheme. But to keep things simple, the weighting that that has generally given me the best results for immunoassays is 1/y^2 as it normalizes the importance given to the points at the top of the curve compared to the bottom of the curve. However, if you have an assay with a very small dynamic range (ODs of 0.2 to 0.5 for example), weighting will probably not help. And remember, choosing a simpler model is always preferable when possible.

3. In conclusion, I prone testing curve fitting every time. A tool I now used to compare 4PL vs 5PL is the "F" test which balances the importance of the simpler model and minimising the sum of squares of the curve fit. There is a free tool on the web from GraphPad which can perform the F test and gives oodles of helpful information: http://www.graphpad.com/quickcalcs/aic1/. The tool is more complete if you have the software, but the free tool gives you a good idea. Choosing the best curve fit will lead to accurate back-calculations of the most data points on your curve (especially near the top and bottom plateaus), so it is not something to be taken lightly.

Cheers,

André

Dear sir

Now there are many software to automatic weighting

We use Dplot for fitting ELISA data. See Bioconjugate Chemistry 23:485 (2012).

Merry Sherman

Andre,

thank you very much for the answer and link to calculator which can be very useful tool...

I have two questions:

1. I’m not sure if I understand it correctly, but “Number of data points (N)” in case of curve consist of 7 duplicate standards N will be 14?

2. in this calculator I can compare 4-PL fit to 5-PL fit, but it is not possible to compare 5-PL to 5-PL with 1/Y^2, right?

And general question:

Is there an easy way to recognize which sigmoidal curve is symmetrical and which is not? or the only way is to do 4-PL and then 5-PL fitting and check which is better?

(I'm using WorkOut 2.5 software)

Hanna,

1. the number of data points to use is indeed 14 in your case

2. I don't think you can compare two weightings of the same model (same number of parameters) using these comparison tests (Akaike and F-test).

Hello Hanna,

Olivier and you are correct, the N you want to be using is 14. And Olivier is correct again is stating that the F and AIC tests can't be used to compared weighting versus no weighting...

As for recognizing a symmetrical curve versus an asymmetrical curve, you need to look at how the curve reaches the top and bottom plateaus (shape of the curve). If the shape in both cases is a mirror image, you are dealing with a symmetrical curve. But in cases where, as in the attached example, the curve leaves the bottom plateau very gradually but reaches the top plateau very abruptly, it is an asymmetrical curve. As mentioned before, this is why meaningful 5PL curve fitting often requires more points as you need to clearly define how the curve reaches both plateaus. In summary, a visual inspection of a good data set can often give you a pretty good idea if you should be using 4PL or 5PL.

Hope this helps,

André

In general, the curve fitting model should fit to the chemical background, the law of mass action. Thats necessary to exclude by statistical methods points from the calibration curve which doesn't fit. The example above is a good one. Which of the three upper points is the wrong one?

Thats why the 3 parameter Rodbard model is one of the best. The more parameter a logistic regression have, the more is the curve fitting like a prostitute. This will fit to any point cloud.

see at: Rodbard D , Frazier GR . Statistical analysis of radioligand assay data.

Methods Enzymol . 1975 ; 37 : 3 - 22 .

There are some more parameters to be taken into account. There is LAMBERT-BEERS law. The absorbance (extinction) is the reciprocal value of the transmission. Many people forget, that therefore absorbances should not be higher than 2.0. The higher the concentration of the (oxidized) chromogenic substrate gets, the lower the differences in the absorbances will be. Many instruments market the product that they are ablte to measure absorbances up to 4. That's nonsence, they forget the reciprocal relationship. Thry to keep the absorances for the negative controls below 0.1 (better 0.01) and the absorbances of the positive controls between 1 and 1.5. So you have a P/N-Ratio (at least the slope) of 15 and higher. 

The other arguments about the curve fitting are mentioned above. 

Amended on 12 September 2017

Furthermore, I would like to express on the ELISA issue.

I must sadly repeat about the differences in determination value between HPLC-photometric method and ELISA method (please see files to compare; SEC fucoidan determination and ELISA fucoidan).

The determined value of fucoidan (Okinawa-fucan) is c.a. 2,000-fold higher in the HPLC-photometric analysis as compared to notorious ELISA method (our experience together with Dr. Takeaki Nagamine, M.D., Graduate School of Health Sciences, Gunma University, 3-39-15 Showa-machi, Maebashi, Gunma 371-8514, Japan).   Dr. Nagamine has sadly thrown away the fucoidan-assay kit of ELISA when he is retiring from the University (my unpublished observation or experience).

(1) Direct photometric assay without purification gives only 50% value as compared to HPLC-photometric assay due to violence to Lambert-Beer's law (please see Fig. 10 of file "SEC fucoidan determination" again). 

(2) Further, binding protein is not so specific; i.e., avidin binds biotin (vitamin H), lipoic acid (thioctic acid), and amino acids, and binding is stronger to lipoic acid than biotin (please see file; Thioctic acid determination) .   Then, biotin assay by using avidin is very difficult since serum has 10-fold higher concentration of lipoic acid than biotin; i.e., lipoic acid may interfere the biotin binding reaction of avidin.   Similarly, binding protein of IgG seems to have a broad binding specificity. 

(3) Furthermore, specificity of binding protein increases 10-fold by homo-dimerization(please see file; The Fascio Effect).   The specificity of IgG seems to be 100-fold lower than pentamer IgM due to the Fascio effect.

Then, 2 (1) x 10 (2) x 100 (3) = 2000-fold difference seems to be occurred between HPLC-photometric method and ELISA method.

ELISA is not quantitative since it has no linear calibraion line inserting to zero point, on the other hand HPLC-photometric assay uniquely has the linear calibraion line inserting to zero point.   Then, HPLC-photometric assay is uniquely the quantitative method (HPLC condition for high recovery analysis is necessary).

Therefore, ELISA is not quantitative and not sensitive; i.e., it gives only false value at ng/mL.

Further, I must sadly repeat about the differences in determination value of biotin between HPLC-photometric method and binding assay method; i.e., such a biotin assay as

"Anal Biochem. 1986 Apr;154(1):367-70.

A sensitive enzyme assay for biotin, avidin, and streptavidin

Edward A. Bayer, Haya Ben-Hur, Meir Wilchek

Department of Biophysics, The Weizmann Institute of Science, Rehovot 76100, Israel

Reciprocal enzyme assays are described for the vitamin biotin and for the biotin-binding proteins avidin and streptavidin. The assays are based on the following steps: (a) biotinylated bovine serum albumin is adsorbed onto microtiter plates; (b) streptavidin (or avidin) is bound to the biotincoated plates: (c) biotinylated enzyme (in this case alkaline phosphatase) is then interacted with the free biotin-binding sites on the immobilized protein. For biotin assay, competition between the free vitamin and the biotinylated enzyme is carried out between steps (b) and (c). The method takes advantage of the four biotin-binding sites which characterize both avidin and streptavidin. The method is extremely versatile and accurate over a concentration range exceeding three orders of magnitude. The lower limits of detection are approximately 2 pg/ml (0.2 pg/sample) for biotin and less than 100 ng/ml (10 ng/sample) for either avidin or streptavidin."

gives only a false value with detection limit as 0.2 pg of biotin.   This detection limit is not true since linear correlation line or linear regression line is not obtainable in the binding assay.  

True HPLC-biotin determination method is presented in the file (Netherlands biotin).   HPLC-method gives a true value with detection limit 17 pg of biotin.  

Hello, I was wondering if the dissociation constant can be calculated from the 4PL curve fitting of the ELISA? Thanks.