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the solution to the rate equation has been used to examine the effect of
inadequate incubation time (during which equilibrium was not attained
under conditions of low ligand concentration) on measured "equilibrium"
dissociation constants (Aranyi, 1979; Yeakley, Balasubramanian and
Harrison, 1980). The solution to the rate equation can also provide
insight into several superficially paradoxical phenomena, such as the
observation that the degree of approach to equilibrium within a given
time is not always a monotonically increasing function of ligand
concentration (Vassent, 1974). We present a concise derivation of a
computationally convenient form of the solution and discuss several of
its applications. Methods for the determination of association and
dissociation rate constants (not requiring the complete solution to the
rate equation) are also discussed.
Theory
Equation (2-1) may be rewritten in the classical Ricatti form as
d6L/dt kaB2-ka(KdL+SL+Bfl)BL+kaSLB0, (2-2)
where k^ has been replaced by At equilibrium dB^/dt=0 and thus
(at equilibrium)
BL (KdL+SL+B0)BL+SLB0 = * (2-3)
This may be rewritten as
(bl-p)(bl-q) = 0,
(2-4)