78
FC50 ClKdC^FL^O/KdL ~ KdC^1+^FL VKdlJ (3-32)
thus indicating clearly that Fg^g (and, of course, ED^g) is quite
different from the desired parameter K^g, which must be determined by an
additional calculation. Although the above approximation that leads to
linearization of the logit-log Fg plot (i.e., Fg ^ (Fg)g) is derived
from the initial occupancy condition (Bg)g << Sg, the approximate
linearity of the plot is fairly robust over a broad spectrum of
experimental conditions and depends only on the initial conditions
relating to the labeled ligand L. Specifically, the approximate
linearity of the logit-log Fg plot does not depend on the relative
affinity of the two ligands, (Kdc/KdL)* The Plot containing
log Sg as abscissa (the "ED^q" logit-log Sg plot), however, departs
significantly from linearity because the approximation Fg Sg is a poor
one at low values of Sg. If K^g >> K^g then the large values of Sg
required to achieve ligand displacement will also make this formula
approximately valid and thus lead to linearization of the simpler ED^g
plot. The calculation of Fg for the construction of the logit-log Fg
plot from the measured data has been described above (equation 3-12
combined with the relation Fg = Sg Bg), and the initial binding (Bg)g
may either be measured directly or calculated from the values of K^g and
Bg (in combination with the known Sg) measured previously. In the
specific example under consideration simple linear regressions of the
theoretical logit-log data of fig. 3-4 yield the following results:
[ED50 (lin. regress.)/"true" EDgg] = 1.12 (13% error), and [Fg5Q (lin.
regress.)/"true" Fg^g] = 0.999 (0.1% error). (The "true" values of
ED^g and Fg¡-g are, respectively, 4.80 and 3.20 nM.)