Fig. 4-9. Simulated approach to equilibrium of specifically bound steroid (for a
representative set of incubations of ['3H]dexamethasone with glucocorticoid
receptors in perfused mouse brain cytosol) as a function of time and total
ligand concentration.
The fraction of the final equilibrium value attained is plotted on the ordinate as a
function of time after mixing, with total steroid concentration as the indicated parameter.
The simulation was performed by using the mean values of the measured steroid association
and dissociation rate constants (described in chapter VI) as inputs to equations (2-5) and
(2-13). The assumed binding site concentration (Bq) was 3.2 nM, the mean generated by
16 individual isotherms whose values of Bq ranged from 2.1 to 3.9 nM. The mean measured
values of the association and dissociation rate constants assumed for this simulation were
ka = 0.69 x 10^M"*min"* and = 3.4 x lO'^min-''' (see chapter VI). Left inset: Relative
deviation from equilibrium (e) of specific binding (B ) as a function of total
3
[ Hjdexamethasone concentration (abscissa), with incubation time as the indicated
parameter. The rate constants and receptor concentration listed above were input to
equation (2-28) to generate the relative error (e) curves; these curves have maxima in the
low nanomolar range and actually decrease to approach constant values as the steroid
concentration is reduced indefinitely. Right inset: The effect of inadequate incubation
times on the slopes of Scatchard plots derived from "equilibrium" binding isotherms. The
binding parameters (rate constants and receptor concentration) listed above were input to
equation (2-13) to generate the values of B^ for each indicated incubation time at the
seven different steroid concentrations (.5-50 nM). The lines were fit to the resulting
points by simple linear regression. The curvature in the simulated data is concentrated in
the region near the x-intercept and is not readily apparent upon visual inspection; it is
obvious that the apparent linearity of a Scatchard plot is not an adequate criterion for
the attainment of equilibrium.