Very wide concentration range titration of small molecule vs protein ligand.

If anyone tried to do titration of a compound in very wide range of concentrations against a protein ligand, and than determine the KD at each of used concentrations? If yes, what people do with non-specific binding that starts at high concentrations? I attached one graph I got with Dasatinib titrated against Abl kinase where I see a lot of non-specific binding at concentrations higher than 1 uM.

Hi and welcome,

I have first some questions because in the graph it says ka = 4.12E+05 and kd = 7.46E-2. When I calculate KD this is 1.8E-7 and not 5.9E-8. In addition, Emax is 44 RU and the curves are clearly going above 800 RU. My observation is that there is no saturation yet at 10 uM what is surpising.
But the fitting looks Ok.
Questions: 1) can you explain the KD difference? 2) what does you say that there is non-specific binding? 3) why does the fitting report a Emax of 44 and not something close to 800?

Kind regards
Arnoud

Dear Arnoud, Thank You for getting back to me!
Here I try to answer your questions, not exactly in chronological order.
First question: The values KD, kon and koff are medians of these corresponding values derived from each of the curves that are in blue color. In this situation the koff/kon not always give the KD because of median, and not average was used. I used median and not average because median is resistant to outliers.
Third question: I calculated the maximum possible Emax from the MW of the protein, MW of the compound, loading of the ligand RU and refraction index increments of both ligand and the compound. This appeared to be 120.7 RU.
The Emax 44 on the graph is also a median value from fitting of all of the blue curves. I probably should remove these confusing medians from the figure, especially the Emax, and indicate only the biggest one.
Second question: I decided that the curves that are in gray color represent non-specific binding because the signal in them is way above the 120.7 RU. And I excluded the gray curves fitting values from further analysis as concentration is too high and signal is way bigger then maximum possible RU 120.7.
Does any of these make sense?
Sincerely Yours, Alexey

Dear Alexey,

Just to make sure I understand: the Rmax calculation is done by formula on www.sprpages.nl/immobilization/strategy

I used median and not average [of the kinetic values] because median is resistant to outliers. --> The Rmax/Emax should be the same for all curves.

When fitting individual curves and the interaction is 1:1 the results should be comparable between nalayte concentrations.
Taking the median of the results is not the right way to do it.

It is better practice to do the global fitting over all (blue) curves. This will average the kinetic parameters and makes your outcome more robust.
See global fitting at www.sprpages.nl/data-fitting/kinetic-models

In the event that the global fitting does not work you know immediately that the interaction was not 1:1 due to possibly:
- non-specific binding
- mass transfer limitation
- an non 1:1 interaction (an antibody-> 2:1)
- concentration errors
- ?

There is no way to model non-specific binding without measuring it.

Can you try the global fitting of the lower curves?

Arnoud

Dear Arnoud,
I incorporated my responses below. Thank You for Your help!

Just to make sure I understand: the Rmax calculation is done by formula on www.sprpages.nl/immobilization/strategy

-->Not exactly. I used formula 1.3 on page 10 of the book "Surface Plasmon Resonance and Biomolecular Interaction Analysis, Theory and Practice" I got. This one taking into consideration the Refractive Index Increments.

I used median and not average [of the kinetic values] because median is resistant to outliers. --> The Rmax/Emax should be the same for all curves.

-->Yes. And on that graph I put the median of maximal signal for each curve and wrongfully called it Emax. I will delete this.

When fitting individual curves and the interaction is 1:1 the results should be comparable between nalayte concentrations.
Taking the median of the results is not the right way to do it.

It is better practice to do the global fitting over all (blue) curves. This will average the kinetic parameters and makes your outcome more robust.
See global fitting at www.sprpages.nl/data-fitting/kinetic-models

-->Yes. I also did the global fitting for the blue curves only. The result is similar to that of median, but more robust, and the KD=koff/kon.

In the event that the global fitting does not work you know immediately that the interaction was not 1:1 due to possibly:
- non-specific binding
- mass transfer limitation
- an non 1:1 interaction (an antibody-> 2:1)
- concentration errors
- ?
--> If I to include these gray curves with very high, much bigger than theoretical Rmax responses, than global fitting does not work well for 1:1. It will work only if I introduce more flexibility by letting the model be 1:2.

There is no way to model non-specific binding without measuring it.

Can you try the global fitting of the lower curves?