Determinants of Channel Selectivity

One amazing property of many biological ion channels is their ability to sharply distinguish among ions of the same charge whose dimensions differ by less than 0.1 nm. For example, as we will consider in greater detail below, some channels in nerve and muscle membranes may be more than 1000 times more permeable to K+ than to Na+ in spite of the fact that the former has a crystal radius of 0.133 nm, and the latter is actually smaller, having a radius of 0.095 nm!

The best explanation for the exquisite ability of many channels to discriminate among ions with a high degree of selectivity is the closest fit theory advanced by Hille. It has long been recognized that because water is a polar molecule, ions float around in aqueous solution in association with a cloud or shell of water molecules; that is, ions in aqueous solution are hydrated. Furthermore, the electrostatic attractions between ions and water molecules are quite strong (recall that the heat of solution of salts can be quite large), so a considerable amount of energy is needed to dehydrate an already hydrated ion. Now, Hille argues, suppose the steric arrangement of fixed charged groups in the region of the channel that determines ionic selectivity is such that an ion traversing that region can be stripped of its water of hydration without its knowing it. In other words, if, as illustrated in Fig. 12 for the case of a cation, the water of hydration can be replaced by the negative poles, or dipoles, of amino acids that line the channel

Channel

"Free" solution

Channel

FIGURE 12 The left side shows a monovalent cation in free solution with the hydration shell of three water molecules. On the right, the same cation is in a cylindrical channel where the interaction with electronegative fixed charges in the wall of the pore exactly mimics the interactions with the water dipoles. The dashed circle represents a smaller cation that cannot fit in the channel while retaining its hydration shell but is energetically uncomfortable without it.

(e.g., carbonyl groups) in such a way that the cation is as energetically "comfortable" in the channel as it is in water, then the ion would not recognize the fact that it left its aqueous environment for that of the channel. (In the language of thermodynamics, the energy needed to partition into or out of the channel would be negligible so that, according to the Boltzman distribution, the probability of being in the channel is equal to the probability of being in the aqueous solution; this is analogous to an amphipathic molecule whose oil-water partition coefficient is unity so that it is just as comfortable in an aqueous solution as in a lipid solvent.) Clearly, if the radius of the dehydrated ion is too large to be accommodated by the channel, it will be excluded. But, if the radius of the dehydrated ion is too small to fit snugly (dashed circle in Fig. 12), it will be energetically disadvantaged compared to the ion with the closer fit; it will not be as willing to shed its comfortable coat of water molecules for the more foreign environment of the channel, and its partitioning into the channel will be energetically less favorable than that of the ion with the closer fit. An elegant discussion of the structure-function relations of a prototypical K+ channel may be found in the paper by Doyle et al. (1998).

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