79
Further analysis is, of course, required to calculate Kdc from the
estimates of either ED^q or Fq5q obtained from the logit-log plots
discussed above. If, in equation (3-32) above, Fq5Q is replaced by ED
50
and (Fl)0 by Sq, one obtains the Cheng-Prusoff (Cheng and Prusoff, 1973;
Munson and P.odbard, 1980) correction
KdC^ ED50/(1+SL/KdL)* (3-33)
This formula is derived from equations (3-2) and (3-3) above by using
the definition of ED5Q (i.e., that (Bl)q = 2B^ when Sq = ED5Q) and
applying the drastic approximation that both Fq Sq and Fq % S. As
the illustrative example will demonstrate, this does not provide a good
estimate of when the affinity of the competing ligand is too high.
We now show that this Cheng-Prusoff correction can be improved
substantially by including in the calculation the value of (Bq)q, which
easily can be measured experimentally or calculated from the values of
KdL and Bq measured previously. Combining the above equations (3-3),
(3-23) and (3-26) yields, upon elimination of Bq, the expression
^FL^0FC50^KdL + (FlJo-^FC50+iy FL/^Kdl_(1+FC/lW+FlJ *
(3-34)
which, when evaluated at the 50% displacement point, becomes
(FL)0/2[KdL+(FL)0] a, FL5o/tKdL^1+FC50/KdC^+FL50-''
(3-35)