Model for the Binding of the Inactivation N−Terminal to the Ion Pore of Shaker Potassium Channel: Both Electrostatic Attraction and Covalent Linkage Are Required for Rapid Inactivation

Abstract

A model is presented for relating the binding of the inactivation N-terminal to the ion pore of the Shaker potassium channel (ShB) to the bimolecular binding of the N-terminal peptide with the deletion mutant ShB¢646. The binding site is modeled as a small patch on the surface of the channel protein, to which the N-terminal “inactivation ball” is tethered by a flexible linker. The potential energy due to electrostatic interactions between the channel and the N-terminal is ‚U(r) )- Qexp[-(r - a)/I]/(1 + a/I)r, where a is the closest approach distance and I is the screening length determined by the ionic strength. The probability density for the endto-end vector of the flexible linker (with L residues) is taken from a previous study [Zhou, J. Phys. Chem. B 2001, 105, 6763] as p(r) ) (3/4﷿lpbL) 3/2 exp(-3r 2 /4lpbL)(1-5lp/4bL + ...). The intramolecular binding rate constant kon in of the intact ShB is related to the bimolecular binding rate constant kon bi via kon in ) kon bi p(a)/ sexp[-‚U(r)]p(r)dV. The model rationalizes a number of important experimental observations. (1) The weaker ionic strength dependence of kon in is quantitatively reproduced by the relation between kon in and kon bi . (2) The linker length dependence of kon in (observed when the linker length is reduced by deletion and extended by insertion) is qualitatively predicted by the L dependence of p(r). (3) The fact that koff in ) koff bi and both are insensitive to the change in ionic strength is due to the stereospecificity of the binding site. If the binding of the activation N-terminal were to occur in a bimolecular fashion, the millisecond inactivation time would have required the presence of the N-terminal at a concentration of 0.2 mM, even after considering the binding rate enhancement by the electrostatic attraction of the channel pore. The difficult task of maintaining such a high concentration underscores the importance of covalently linking the inactivation peptide to the ion channel.