42
exp [kat(P-Q)] = [Bl-P][(Bl)0-Q]/[(Bl)0-P][Bl-Q].
(2-11)
Solving for BL, we eventually find that
Bl = [P(d/e) Q exp (-ft)]/[(d/e) exp (-ft)],
(2-12)
where d = Q (B^)q, e = P (B^)q, and f = kQ(Q-P). If the initial
binding is zero (a common application), then equation (2-12) simplifies
to
Bl = [l-exp(-ft)]SLBQ/[Q-P exp(-ft)],
(2-13)
since QP = S^Bq. (This form of the solution is computationally
convenient because it avoids the generation of large exponentials as t
becomes large.)
The relative error or fractional deviation from equilibrium is
defined as
e = absolute value of [(BL~P)/P], (2-14)
and is easily calculated. If equation (2-12) and (2-14) are solved for
t (e.g., Vassent, 1974), then an expression giving the time required for
an arbitrary degree of approach to equilibrium is obtained:
t (e) = [l/ka(Q-P)] In ([QP(1-E)]/ P[l+(Q-P)/e]).
(2-15)