Say you have an inhibitor who's binding is either dependent on or enhanced by a metal cation binding to either an allosteric site, or by forming part of the binding site of the inhibitor. So as you increase cation, IC50 drops in a hyperbolic manner until plateauing when the enzyme is saturated with cation. GraphPad claims the inflection point of this IC50 (or could get Ki via Cheng prusoff equation) vs. Mg curve is the Kd of the modulator, but I've been told by someone this is not an appropriate way to determine binding constants of the modulator.
The IC50 help you in estimating the Kd. However, the Cheng-Prusoff equation is not the only element to be considered.
The Cheng-Prusoff equation is used to remove the influence of the competitive binding of substrate or other competitive/noncompetitive ligand employed in the experimental assay on the apparent Kd or Ki.
If you search on Google or RG, you may find several posts related to the issue you are interested in.
There are two mixxed issues on your questions: 1) If you have IC50 vs. ligand concentration data for an effector ligand, would you be able to get the dissociation constant for the effector ligand interacting with the enzyme?; and 2) Would the IC50 data correspond to the inihibition constant, Ki, of the inhibitor on the enzyme at different ligand effector concentration?
The answer to the first question is YES, but not always.
The answer to the second question is NO.
The apparent IC50 for your inhibitor at a certain ligand effector concentration would be equal to:
IC50 = Kiapp + [E]T/2
where [E]T is the total concentration of enzyme.
according to the definition of:
Kiapp: free concentration of inhibitor to get 50% enzyme inhibition.
IC50: total concentration of inhibitor to get 50% enzyme inhibition.
If the inhibitor potency is affected by the presence of an effector ligand, then, the apparent Ki will be dependent on the effector ligand L:
Kiapp = Ki (1 + [L]/Kd,L) for an inactivator ligand
Kiapp = Ki / (1 + [L]/Kd,L) for an activator ligand
where Kd,L is the dissociation constant for the enzyme-ligand interaction.
Therefore, if you have IC50 data at different effector ligand concentration, and your case is that of an activator ligand:
IC50 = Ki / (1 + [L]/Kd,L) + [E]T/2
Then, it looks that, in principle, IC50 vs. [L] data would allow you to estimate Kd,L.
However, remember that [L] is the free concentration of effector ligand, and it cannot be approximated by the total concentration of effector ligand [L]T unless the total concentration of effector ligand is much larger than that of the enzyme. Still, considering that approximation the incorrect Kd,L would represent an upper bound for the real Kd,L value.
I forgot to say that when I wrote:
Kiapp = Ki (1 + [L]/Kd,L) for an inactivator ligand
Kiapp = Ki / (1 + [L]/Kd,L) for an activator ligand
I did not include explicitly an additional factor taking into account the influence of the substrate concentration, which in the case of a competitive substrate would be:
(1 + [S]/Km)
appearing as a multiplying factor for Ki in the two previous expressions.
However, for estimating Kd,L that factor is not required to be explicitly considered. It can be taken implicitly within Ki.
Thanks so much Adrian! This was a really helpful answer.
In my case [L] = [L]T as the estimated Kd of this interaction is over .1 mM, whereas the enzyme concentration in the assay is
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