Remarks on the nature of ion-ion interactions in channels, as presented by Wu

Abstract

To explain the multi binding behavior of the potassium channel, Jin V. Wu argued in his paper: Dynamic ion-ion and water-ion interactions in ion channels ( 1), that the kinetic energy and the inertial mass in general is a major factor in the ion-ion displacements (knock-off's) at the channel binding site. This argument has, however, the severe flaw that the kinetic energy 1/2 mV2 even of a very heavy ion (M = 200) at the highest thinkable velocity within the membrane of 200 cm/s for a local electric field of 106 V/cm is three to four orders of magnitude smaller than kT. It is inappropriate to assume as done by Wu that the short range collision free speed is equal to the surface escape velocity V = (8 kT/rm)/2 when the mean free path in the free volume approaches zero. Moreover the Maxwellian velocity distribution implies that one molecule is kicked up to its velocity by collision with other molecules of comparable velocities. In the liquid states the long or short range velocities of all the molecules are determined by the hydrodynamic resistance or viscosity and the Maxwellian velocity distribution is centered around the velocity determined by the hydrodynamic properties ofthe solution. Is the implication of the mass really required in order to resolve the following paradoxes pointed out by Wu: Why is conductance ofK+ in a K+ channel higher than that of Tl in symmetrical solutions while in bionic solutions the permeability of Tl appears to be higher than that of K+ as determined by reversal potential? Does the higher binding affinity of ions of equal radii and higher masses mean that the inertial mass is involved or that the mass affects other properties, e.g., ionic polarizability (deviation of the charge from the ionic center)? The paradoxical phenomena ofthe higher permeability of K+ than that ofT1+ in pure salts and higher permeability ofT1+ in salt mixtures can be explained without invoking the ion masses or any fictitious kinetic energies. The qualitative description is as follows: Ionic association or ion pair formation is by and large a diffusion controlled process. An ion with a higher affinity to a site has, therefore, a slower dissociation rate. This dissociation rate is usually the rate controlling step in ion channel permeability and therefore the permeability in pure salts of the faster dissociating K+ is higher than of the slower dissociating TI. To the scheme on page 1319 of reference 1 for the case of a symmetrical pore: