Multioccupancy models for single filing ionic channels: Theoretical behavior of a four-site channel with three barriers separating the sites

Abstract

A procedure is developed for dealing with multioccupancy in single-filing channels having any number of sites internal to the barriers at the channel ends but having the outermost sites in equilibrium with the bathing solutions. Using this procedure, a general theory is developed for a single-filing channel having three barriers and four sites, the outermost of which are in equilibrium with the bathing solutions. By introducing a vectorial representation, it is shown that the four-site model can be reduced to an equivalent two-site model with respect to the number of possible transitions, thereby simplifying the algebraic steps required to solve transport equations for the system. The transport coefficients are derived and expressed in terms of the energy levels of the peaks and the wells for the different occupancy configurations. An explicit solution to the transport equations is given in a comprised form for a single permeable species. The solution allows some important properties for the system to be deduced, specifically with regard to the conductance at zero current, the correlation factor between electrical conductance and tracer flux, and the current-voltage relationship. Examples are given for the use of the present results in a physical interpretation of the data from the gramicidin A channel.

Molecular dynamics simulation of cation motion in water-filled gramicidinlike pores

“…At both saddle points and local energy minima inside the channel, the waters line up with the negative end of the dipoles pointing toward the cation, as has been seen previously only near local minima (15). At the outer minimum, which we identify with the exterior binding site suggested by Eisenman (32,33), the channel water molecules maintain the linear arrangement while the exterior water molecules appear similar to bulk water of solvation. The motions of the ions with water in the channel are found to be single file, which is in agreement with the experiment of Rosenberg and Finkelstein (5) and the calculations of Mackay et al (15).…”

“…Thus in moving from the exterior minimum to the channel interior, the ion has to shed one of its nearest neighbor water molecules. The exterior site is thus qualitatively different from any of the sites, K = 0 to 6; it might possibly be identified with an exterior binding site such as that proposed by Eisenman on kinetic grounds (32,33).…”

Ionic selectivity revisited: The role of kinetic and equilibrium processes in ion permeation through channels

“…To answer these questions it now becomes desirable to carry out current-voltage studies for each ion over a sufficiently wide concentration range to characterize the I-V behavior for the empty channel, as well as for the highest occupancy state experimentally accessable; for such measurements give information on the levels and locations of the energy wells and the barriers (cf [35]). Measurements of the flux ratio exponent, on the other hand, provide independent, and sometimes crucial, information about the peaks alone [41,112]. Since measurements of selectivity by reversal potentials require the simultaneous presence of more than one permeant species, it may, moreover, be necessary to extend the I-V studies to ionic mixtures.…”

Evaluation of surface tension and ion occupancy effects on gramicidin A channel lifetime

“…From these measurements it was concluded that each half of the channel has a site located -0.25 nm from the channel opening with a barrier for channel entry at each end and a central barrier arising partially due to the low dielectric constant of the membrane. Also, there is evidence for the existence of an external site ( 11) at each end of the channel, extending into the solutions. This paper examines the factors governing the lifetime properties of gramicidin A channels, an issue that has not been as extensively dealt with as have the permeability properties of the channel, mainly due to the inconvenience of the larger samples required to characterize the lifetime distribution (18) and earlier problems with the reproducibility of the measurements for certain experimental conditions (19,20).…”

“…Theoretical modeling of channel permeability has focused on the Eyring rate-theory analysis (10)(11)(12) of the channel in terms of multiple barrier-site models. Recent theoretical advances using molecular dynamics (13)(14)(15) and quantum mechanical ab initio (16) calculations for simple gramicidin-like channels are consistent with the results of fitting the barrier models to experimental data.…”