Subject: Kd vs IC50

From: [email-masked] (Ellen R. Laird)
Date: Tue, 10 Jan 95 13:13:28 EST

Greetings:

	It is well known that for two compounds competing for binding
	to the same protein with equilibrium dissociation constants Kd_1 and 
	Kd_2, the difference in the Gibbs free energy of binding is given by

			ddG(2-1) = -RT ln(Kd_2/Kd_1)
	
	It is common in the pharmaceutical industry to have assays that
	generate IC50 values rather than equilibrium constants.  Clearly, if
	the ratio IC50_2/IC50_1 = Kd_2/Kd_1 then the IC50 ratio may be used in
	the above equation.

	I am requesting opinions and references on the following:

	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?

	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.  

	Their analysis assumes simple Michaelis-Menten behavior, 
	and begins from that equation:  

		        V_max [S]
                V_0 =    -------
                        K_m + [S]    i.e., rates of catalysis are involved
	                                   in the derivation

	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.

	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?

	I'll post a summary of responses, and thanks in advance

	- Ellen

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   ~~~~~~
  ~~~~~~~~  					 Ellen R. Laird
 ~~~~~~~~~~					 [email-masked]
 ~~~~~~~~~~
  ~~~~~~~~
   ~~~~~~ARIAD Pharmaceuticals, Inc.             26 Landsdowne St.
                                                 Cambridge MA  02139
                                                 (617) 494-0400, ext 234
                                                 fax:  494-8144
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From: Gustavo Mercier <[email-masked]>
Date: Tue, 10 Jan 1995 17:50:06 -0500 (EST)

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

...  <  several lines cut-off >
> 	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.

> 	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!

> 	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.

> 	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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From: Gustavo Mercier <[email-masked]>
Date: Tue, 10 Jan 1995 19:31:50 -0500 (EST)

Hi!

Here is the reference I promised with a few more added:

1)Pharmacologic Analysis of Drug - Receptor Interaction
T. P. Kenakin
Raven Press, New York
1987

This book is limited to the analysis of dose - response curves, but
response is related occupation through the "stimulus function". 
It also includes some kinetics of dose -response curves and a chapter
on the diffusion of drugs across membranes in a tissue preparation.

2)Protein Interactions
G. Weber
Chapman and Hall, New York
1992

A rather advanced treatment of protein - small ligand and protein - protein
binding. Together with (1) you can appreciate the complexity of relating
an IC50 or EC50 to a Kd value in the absence of information on the 
chemical nature of the receptor.

Below are some papers relevant to the topic:

An accurate method for determination of receptor - ligand and enzyme -
inhibitor dissociation constants from displacement curves.
A. Horowitz and A. Levitzki, Proc. Natl. Acad. Sci, USA v. 84, pp. 6654-6658
1987.

  This is a generalization of the binding equations by eliminating some
  of the usual assumptions about the concentrations of the ligand vs
  the concentration of the "receptor".

Estimation of the Affinities of Allosteric Ligands Using Radioligand
Binding and Pharmacological Null Methods.
F. J. Ehlert, Molecular Pharmacology 33: 187-184, 1988.

  This paper addresses the extraction of affinity constants from
  dose - response curves in the case when a receptor exhibits
  allosteric binding. The hard thing is realizing that your receptor
  does exhibit allosteric binding when the ligand affecting the
  binding of the drug is a molecule available in the in vivo
  state. In this case, the method of tissue preparation would affect
  both the binding curves and the dose - response curve if the methods
  differ in their ability to retain the native molecule responsible for the
  allosteric binding.

The Binding Capacity is a Probability Density Function.
E. Di Cera and Z.-Q. Chen, Biophysical Journal. v. 65 pp. 164-170 (1993)

  A paper of more interest to computational chemist who attempt
  to relate binding data to thermodynamic (MC,MD,BD) simulations.
  By way of reference 2 above you could link this paper to reference 1,
  but this is only speculation on my part and I cannot give you the
  steps to do so! Any takers on this one!

Good Luck!

Gustavo A. Mercier, Jr.