48
measured apparent dissociation constant. The magnitude of this
reduction may be estimated approximately by using the solution to the
rate equation to monitor the relaxation of to the new, low-but-
nonzero value of P (equilibrium value of B^) in the following way.
First, assume for kd the (underestimated) value that has been measured
experimentally; call this value ^(apparent). A previously estimated
value of k or K.. must also be assumed; if a value of k is assumed,
a ql a
then KdL is taken to be kd(apparent)/ka. Measured values of SL, Bq, and
(B^)q are also available. Now equation (2-12) is used with these values
of the independent variables to calculate B^ for the same values of t at
which actual measurements of BL have been made. These calculated values
of B^(t) are then used to derive, from the slope of a plot of t vs. In
[calculated BL(t)/(BL)g], another underestimated dissociation rate
I I
constant, called k^. Next assume simply that the amount by which kd
underestimates kd(apparent) is equal to the amount by which kd(apparent)
underestimates the "true" value of kd that is sought. Thus
I
"true" kd kd(apparent) ^ kd(apparent) kd, (2-26)
and finally
"true" kd jv 2 kd(apparent) kd. (2-27)
This rough estimate of the correction is reasonable when is small.
The solution to the rate equation may also be used to predict the
error in a determination of derived from a "nonequilibrium" isotherm
generated by measurements performed before equilibrium has been attained
in the incubation vessels containing the lower concentrations of S^.