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The dissociation rate constant kd is determined by simply measuring
the bound ligand as a function of time following some manipulation
that prevents any further association (or reassociation) of labeled
ligand with the receptors. Ordinarily this is accomplished by adsorbing
the free labeled steroid onto activated charcoal, followed by either
dilution of the preparation to further reduce the concentration of free
steroid to a negligible level or by the addition of a high concentration
of unlabeled steroid to dilute the specific activity of any remaining
labeled free steriod (and to dilute the labeled steroid that is released
into the free pool during the course of dissociation). Thus, since the
association of labeled ligand is blocked, equation (2-1) becomes
dBL/dt = kdBL, (2-22)
where B^ now represents only labeled bound ligand. Upon integration we
obtain the familiar first order dissociation relations
ln[BL/(BL)0] = kdt (2-23)
and finally
Bl = (Bl)q exp (-kdt), (2-24)
where (B^)q is the initial bound concentration at the beginning of the
dissociation period. The rate constant kd is simply the slope of the
plot of 1 n[B^/(Bj^)q] as a function of t. The dissociation rate is also
frequently reported as the half-life (t^) of the bound complex: