

On Tue, 10 Jan 1995, Ellen R. Laird wrote:

...  <  several lines cut-off >
> 
> 	If this ratio equivalence has not been demonstrated (i.e., K_n have not
> 	been measured in a comparable assay), is there a general relationship
> 	that can be drawn between IC50 and Kd?

A  general relationship cannot be developed for drug  -  membrane  receptor
interactions.  When  assumptions are made about  the nature of the drug
(i.e.  agonist, partial agonist,  antagonist) and the properties  of
the receptor (i.e. type  of transduction mechanism)  you can develop
a relationship  between the IC50 and the Kd. See a reference below.
Unfortunately,  many  times this requires more knowledge of the
receptor system that actually be available.

> 
> 	I have read a straightforward treatment of this *for enzymes* by Cheng
> 	and Prusoff (Biochemical Pharmacology, 1973, 22, 3099 - thanks to Dr.
> 	James Blake of Pfizer Central Research for supplying this reference);
> 	according to their analysis, Kd for an inhibitor is equal to the IC50
> 	only when noncompetitive or uncompetitive kinetics apply.  

Noncompetitive or uncompetitive?  I would have expected it from
competitive kinetics, but I have  not read their paper!

> 	Unfortunately, I am dealing with binding to non-catalytic 
> 	protein domains; it is not clear to me how one could extend
> 	the Cheng and Prusoff arguments to compounds that simply inhibit
> 	receptor-ligand interactions.

I would suggest that you  read articles in pharmacodynamics.
A book by T. Kenakin (I'll get back to you with the full  reference) is
very useful and has a good set of references.

> 
> 	On a related issue - it is evident from the literature that the
> 	majority of researchers in medicinal chemistry use a direct comparison
> 	of IC50 values as sufficient for determining the relative efficacy
> 	among a set of inhibitors; other than a desire to validate ddG
> 	computed by via sophisticated simulations, do computational chemists
> 	involved in pharmaceutical research even care to consider IC50 
> 	data in terms of free energy relationships?
> 

IC50 are used for convenience and  basically necessity. In many
instances medicinal chemists deal with membrane bound receptors coupled
to a transducer system that complicates the  kinetics of binding. Many
times,  the molecular nature of the  membrane bound receptor
is simply unknown. Are you dealing with the simple protein, or the
protein coupled to its transducer, another protein.  For example,
in the case of  membrane receptors coupled to the G-proteins, the Kd of
the agonist is dependent on the presence of GTP because in the presence
of the agonist the  receptor binds the transducer which exists in two
states, a GDP bound form and a GTP bound form, each with different  Kd's.
In the case of antagonists
the binding of the receptor to the transducer protein does not occur
and the kinetics are simpler. In this case the IC50 reflects the Kd.

Finally,  in pharmacology  you must make the difference between a
binding site interrogated using a binding experiment where IC50's are
reported, and a dose -response curve that interrogates a receptor where
EC50's are reported. A binding site is not necessarily a receptor and is
necessary to show that a given  binding experiment does interrogate
a receptor defined on the basis of a dose - response curve. It is not
enough to simply use the same pharmaceuticals in both experiments. The
same complications that occur with associating  IC50 to Kd's occur
with associating EC50 to Kd's (may be worse due to issues of receptor
reserve etc.)

These complications have led pharmacologists to report  EC50 and IC50
rather than Kd's. You may wonder why not define the kinetics through
suitable kinetic  experiments. Unfortunately, for membrane receptors
kinetic experiments  are difficult because the rate limiting step
may be the diffusion of the drug into the membrane. If you  are curious
about this topic, I would suggest that you  get  in touch with Dr.
Roman Osman (Mount Sinai School of Medicine, NY, NY. Dept. of Physiology
and Biophysics and of Pharmacology).  Several years ago, one of his
students (Robert  Cory) wrote a thesis on the kinetics of  either
an adrenergic  or serotonergic receptor. They  worked  out the details
necessary to show that the observations were not a reflection of the
diffusion across membranes.

In spite of these limitations, EC50's are many  times taken  as a
reflection of Kd's by computational chemists. The  assumption is that
the rank order of the EC50's will reflect the rank order of the Kd's.

Good Luck!

G. A. Mercier, Jr.
[email-masked]

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