Ionic interactions and anion binding in the gramicidin channel. An electrostatic calculation

Abstract

An electrostatic calculation is performed in order to examine basic features of interactions between ions (including anions) within the gramicidin channel. The calculation focuses on the effect of image forces. The substitute charge method is used for the calculation of image-force energies. Good arrangements of fictitious charges and contour points are described. Errors of calculated image-force energies are estimated not to greatly exceed 0.1%. The cases assumed are (i) the effective radius r of the channel is between 2·5 and 3·5 Å, (ii) the binding site with the highest affinity is between 1 and 3·5 Å from the channel end ( outer site), and (iii) the dimple at the channel mouth is 0–5 Å in depth. The induced energy of an ion placed at the outer site increases (and hence the affinity of the outer site decreases) with the increase in the depth of dimples, whereas the barrier height for translocation between the outer sites decreases in the presence of deeper dimples. The interactional energy between two monovalent cations placed at the outer sites is relatively small in the absence of dimples. It is large, however, in the presence of deeper dimples if the outer sites are 2·5 or 3·5 Å from the ends; but, it is still relatively small even in the presence of dimples if the sites are 1 Å from the ends. The interactional energy is very unfavorable for simultaneous occupancy by three cations. It is suggested that an ion pair may be formed at the channel mouth. Deeper positions of the outer site, smaller values of r, and deeper dimples favor the formation of the ion pair. In the presence of 5 Å dimples, the binding constant of an anion (Cl −) for a cation (Na +) which has already been bound at an outer site (with no second cation at the opposite mouth) is estimated to be 0·4–8 molal −1 if local interactions between the bound anion and the channel wall is negligibly small. The anion binding constant increases in the presence of a cation (or an ion pair) at the opposite mouth. It decreases markedly in the absence of dimples. The interactional energy is considerably unfavorable for the binding of a third cation even if the presence of an ion pair is postulated. It is still large in the presence of an ion pair at each of the mouths.