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We now examine some applications of the rate equation and its
solution. In the following discussions we shall assume that Bq remains
constant with time (unless a deliberate dilution or concentration is
performed). Many in vitro steroid receptor preparations do not,
however, possess this stability. For example, a frequent observation
has been the gradual inactivation or loss, with time, of unoccupied
(free) receptor binding sites (e.g., Luttge et al., 1982). If this is
the case, then the rate equation (2-1) must be supplemented with the
simultaneous inactivation equation
d(BQ-BL)/dt = -kin (Bq-Bl) dBL/dt,
(2-16)
where k^n is an empirical inactivation constant describing a process of
simple unimolecular decay of the normal binding site conformation.
(This assumption has, of course, no theoretical basis; it is merely a
statement of the observation that the relative early regions of slow
receptor inactivation curves may be approximately fit to simple
exponentials.) Equation (2-16) simplifies to
(2-17)
which may be solved simultaneously with the rate equation (2-1) by
standard computerized numerical integration methods (e.g., Yeakley et
al., 1980).