

Dear Dr. Laird:

     I am replying to your post today discussing several matters related to the question of
equivalence of IC50 values and Ki values.  I am a chemist who has worked in matters related
to pharmacology for some time, and the following points might be useful to consider:

     In general your reservations about the Cheng-Prusoff treatment are correct.  However,
consider that the determination of an IC50 value involves (generally) the incubation of a
radioligand with a receptor preparation of some sort.  The binding isotherm must thus be
saturable and the binding must in principle be to a single site.  These are the basic assumptions
of the Scatchard isotherm which are de facto the assumptions involved in determining an IC50. 
Rather more correctly, one could state that while one could certainly measure an IC50 value if
the assumptions of the Scatchard isotherm were violated it would not be valid to compare relative
avlues of IC50 the way people normally do.

     Thus, the point which I am trying to make here is that the whole idea of attempting to
equate IC50 values to a delta,delta G is fine in a system where the assumptions of equilibrium
binding are not violated, that is:

1. All the sites are identical and have identical affinity
     
2. All of the sites do not interact with one another as a function of fractional occupancy (e.g.,
no allosteric interaction).

     But in ANY other situation, the comparison isn't correct.  How incorrect is a good
question which has not been frequently addressed.

     In fact, if you read Scatchard's old papers he was mostly interested in binding of charged
ions to serum albumin, in which allosteric interaction wasn't the problem but simple charge
interaction was.  I would refer you to C. Tanford's old Biophysical Chemistry text for the
derivation of these equations.  Tanford discusses some quite elegant extensions of free energy
calculations for binding situations in which multiple ions can bind and interact on a protein
surface using analytical (before computers!!!) solutions of the Poisson-Boltzmann equation.

     Thus, the bottom line would seem to me to be that if you can describe a model for the
interaction of you multiple binding sites, even if it is a very simplistic one, then you can readily
fit bidning and competetion data to it. Of course, if you have no idea what the interaction is, you
could still probably model it by fitting to a sum of multiple Kis.  The problem that you will
immediately face is that the quality of the binding data will not allow you to distinguish between
multiple models.

     Ultimately, this is the problem that we faced in our systems; that binding data generally
just are not of a quality to enable more that the usual semi-quantitative comparisons.  Even
running fifty-point displacements (and we sometimes do!!) barely will give you the precision you
need to distinguish models.  

     Thus my advice would be to measure IC50 values, convert them to Ki values, and not
worry too much about it provided that you are well aware of the assumptions involved.  Perhaps
if you really have a cloned, purified receptor and can do microcalorimetry on it then you can get
reliable themrmodynamic data on it.

     Other references;  Molinoff and cowhokers wrote a couple of papers about ten (12?) 
years ago in which they calculated thermodynamic data from binding data for a series of drugs
which bound the the beta-adrenoceptor (I think beta-1).  If you're interested I can find the ref.
in my files or someplace here.  As far as I know, this is the only decent attempt to do this for
a real receptor.  He made some interesting conclusions which were a little simplistic but thought-
provoking about " entropic" versus "enthalpic" contributions.

     We are extremely interested in general in the questions that you raise and would welcome
more discussion of them amongst pharmacologists.

best regards
Randy murphy

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Randall B. Murphy, Ph.D.       [email-masked]  or [email-masked]
Associate Professor of Chemistry and Neural Sciences
New York University, Washington Square, New York, NY 10003 USA
Tel. 914-591-7573; 212-998-8433;  FAX 212-260-7905
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