50
Thus, if a time and receptor concentration Bq are chosen such that
equation (2-29) is reduced to an acceptable level, then very low values
of may be used to generate an isotherm. (More rigorously, one may
find by setting equal to 0 the partial derivative of equation (2-28)
with respect to S^, the exact nonzero value of that maximizes e; then
a time may be chosen that reduces this maximum relative error to an
acceptable level.)
Predicting the effect of the addition of a competing, cold ligand
(C) on the rate of approach to equilibrium of is a more complex
problem; this calculation requires the numerical integration of the two
simultaneous rate equations
dBL/dt = ka (B0-Bl-Bc)(Sl-Bl) kdBL (2-30)
and
dBc/dt kaC (Bq-Bl-Bc)(Sc-Bc) kdcBc, (2-31)
where the subscript C refers to the competing ligand. Several
qualitative inferences can be drawn, however, from the fact that the
only effect of the competitor C is to decrease the free receptor
concentration in equation (2-30). Consider now the relative error e as
a function of Bq rather than of S^; since and Bq appear symmetrically
in equation (2-28), the left inset to fig. 4-10 also portrays the shape
of the plot of e considered as a function of Bq (with now held
fixed). If is sufficiently large, then the position of Bq will be to
the left of the maximum value of e on the plot; if is small enough,