From ellen -A_T- nautilus.ariad.com  Tue Jan 10 13:46:41 1995
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From: ellen |-at-| nautilus.ariad.com (Ellen R. Laird)
Message-Id: <9501101813.AA20852(+ at +)nautilus.ariad.com>
Subject: Kd vs IC50
To: chemistry&$at$&ccl.net
Date: Tue, 10 Jan 95 13:13:28 EST
Reply-To: <ellen-: at :-ariad.com>
Organization: ARIAD Pharmaceuticals, Inc.
X-Mailer: ELM [version 2.3 PL11]



	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
 ~~~~~~~~~~					 ellen \\at// ariad.com
 ~~~~~~~~~~
  ~~~~~~~~
   ~~~~~~ARIAD Pharmaceuticals, Inc.             26 Landsdowne St.
                                                 Cambridge MA  02139
                                                 (617) 494-0400, ext 234
                                                 fax:  494-8144
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