Terlau et al. (1999) showed that in
Shaker channels the recovery from N-type inactivation and the rebinding of
κ-PVIIA could be simply unfolded by assuming their independence, supporting the view that the toxin does not distinguish between different nonconducting states of the channels if the closed gate is on the intracellular side. Such assumption is clearly not tenable in the case of M448K channels: as shown by Fig. 3
E, the apparent rebinding estimated by normalizing the early
P2 responses under toxin to those of control would show a fairly large and unaccountable delay. The double-exponential relaxation of Fig. 3
D can instead be accounted for by a simple kinetic scheme in which toxin binding is incompatible with inactivation and that comprises only three statistically significant states (see Scheme 3 in Appendix): an inactivated state, an unblocked state (activatable for conductance), and a toxin-liganded state (activatable, but unavailable for conductance). If we denote with
λI the rate characterizing the single exponential recovery of activatable currents in toxin-free conditions, and with
λR=
off +
on the rate of toxin binding relaxations, such scheme predicts that during repolarizations the fraction
U(
t) of channels available for conduction follows a double-exponential time course with decaying rates
λI and
λR, approaching asymptotically a resting value
UC =
off/(
off +
on). Even more stringently, for initial conditions in which the channels are all inactivated, it predicts that all four parameters that characterize the expression of
U(
t) are determined by the sole
off and
on binding rates according to (see Appendix) (2)

with

Confirming the above predictions, the smooth line in Fig. 3
D was obtained as the best fit of the data with Eq. 2 fixing
λI to the value of control and allowing only
on and
off as free parameters, estimated as
off = 0.3 s
−1 and
on = 0.42 s
−1.