51
however, the position of the same value of Bq will now be to the right
of the e maximum value. Thus, depending on the relations among S^, Bq
and K^, the effect of the reduction of free receptor concentration by
the competing ligand can be either to increase, decrease, or leave
essentially unchanged the value of e at a given time. Under the right
conditions a competitor may easily increase £ from near 0 to the maximum
value consistent with the given values of and t. (The rate constants
for ligand C and its concentration will, of course, affect £ by
determining how fast the competitor depletes the free receptor
concentration.) A very rough estimate of the effect of a high-affinity
competing ligand on the time required for B^ to approach equilibrium may
be obtained simply by assuming that the competitor is identical to the
labeled ligand. In this simple case becomes the sum of the labeled
and competing ligands, and equation (2-28) predicts £ for the total
bound ligand (B^ + Bq) for different times. Clearly this value of the
relative error also applies to B^, since for this special case
bL = SL (Bl+Bc)/(Sl+Sc). (2-32)
In order to facilitate estimation of the times required for the
approach to equilibrium under a variety of conditions, we present in
table 2-1 a short summary of solutions to the rate equation (2-1) for
several useful combinations of the variables Bq, S^, and (i.e.,
kj/ka) for the case of a single ligand and binding site. The initial
condition is simply (B^)q = 0, and the solution is presented as a table
of pairs of numbers representing the number of hours required for B^ to
attain 80% and 95%, respectively, of the equilibrium value. These