The binding affinity between the protein and the fluroscent ligand derived from fluorescence experiments was in the millimolar range 0.18 mM ( 180 Micro molar). Unfortunately we did not get the saturation while titrating the protein to the lignad. I used the Benesi Hildebrand relation 1/(I-Io) = 1/(I1-Io) + 1/(I1-Io) K [protein] to fit the linear curve fitting in case of weak binding. I would like to know the concentration of the protein to saturate the Ligand approximately from the Kd . How can I calculate concentration of the protein to saturate the ligand from Kd if it is kd is 0.18 mM?
(please see figures : UV absorption of ligand at 318 nm (1A), Increase of fluorescence intensity while titration of protein to lignad (1B) . Curve fitting using Benesi Hildebrand relation (1C).
If the stoichiometry of the protein-ligand interaction is 1:1, the saturation fraction or fraction bound Fb for the ligand at a certain protein concentration P is given by:
Fb = P / (Kd + P)
where Kd is the dissociation constant of the protein-ligand complex.
If you solve for P, you get the expression for the concentration of protein P required in order to achieve a certain saturation fraction Fb for the ligand:
P = Kd x Fb / (1 - Fb)
From this, in order to get 90% saturation (Fb = 0.9) of the ligand you would need P = 9 x Kd; in order to get 95% saturation (Fb = 0.95) of the ligand you would need P = 19 x Kd; and in order to get 99% saturation (Fb = 0.99) of the ligand you would need P = 99 x Kd. For example, in your case, you would need 3.42 mM protein in order to get 95% ligand saturation; this corresponds to more than 85 mg/mL for a 25 kDa protein.
As you can see, after the equivalence point of the titration (P > Kd), large increments in protein concentration lead to marginal increments in ligand saturation. In addition, the Kd is rather high (low affinity interaction). You must decide where to draw the line and decide...
Dear Adrian Velazquez-Campoy,
Thanks for your reply , If possible, could you please provide any reference for above formula ! Thanking you for your great help !
Well, there is no need for any reference. You just need basic concepts.
The fraction of ligand bound to protein is given by:
Fb = [PL] / [L]t = [PL] / ([L] + [PL])
[PL] is the concentration of protein-ligand complex
[L]t is the total concentration of ligand
[L] is the concentration of free ligand
If the chemical equilibrium is introduced through the dissociation constant of the complex:
Kd = [P] [L] / [PL]
after some easy rearrangements you arrive to:
Fb = [P] / (Kd + [P])
Important remark: I forgot to say that the concentration of protein P required to get a certain saturation fraction in the ligand calculated in that way is the concentration of free protein [P] required, not the total concentration of protein required. In general, the total concentration of protein required would be [P]t = [P] + [PL]. In many situations [L]t
Dear Adrian Velazquez-Campoy, Thanking you for your detailed reply and your time !
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