## Ion Diffusion Through Biologic Channels

To this point, we have considered the diffusion of ions across barriers without specifying the nature of the pathway(s) traversed. Because all of the reasoning was based on thermodynamic principles, the conclusions arrived at in that chapter are valid regardless of the nature of the barrier; that is, it could be a sintered glass disk, a sheet of cellophane, a sheet of filter paper, a lipid bilayerâ€”whatever! Turning now to biologic membranes, it has long been recognized that because ions are scarcely soluble in lipids, they can only cross those barriers by reversibly combining with some mobile component of the membrane and/or by diffusion through aqueous channels. There is now undeniable evidence for both types of mechanisms, and in this section we focus on the latter.

Let us start by inquiring how rapidly ions might be expected to traverse a lipid bilayer through an aqueous pathway assuming that the diffusion coefficient is the same as that in free aqueous solution. Let us assume that the ion has a ''naked'' or crystal radius, ri = 0.15 nm, and that its diffusion coefficient (D) = 2 x 10"5 cm2/sec; these are close to the values for K+. Let us further assume that the channel has a radius (rp) of only 0.2 nm, that the bilayer has thickness Ax = 5 nm, and that the concentration difference across the channel (AQ) = 100 mmol/L. From Eq. 1, it follows that:

J =(jrr2DiAQ/Ax) = 4 x 10"18mol/sec and, multiplying by Avogadro's number, J = 2.5 x 106 ions/sec. If the ion is monovalent, then, because the electronic charge is e = 1.6 x 10"19 C, the current attributable to this flux of ions is 0.4 10"12 C/sec, or 0.4 pA. The important point of this exercise is that ballpark estimates are consistent with the notion that more than a million ions can diffuse per second across a lipid bilayer through a very snug pore; this is sufficient to generate a current that can be readily measured using available amplifiers.

Since the mid-1970s, measurements of bursts of ionic currents across biologic membranes have proven to be entirely consistent with the above estimate and, together with other evidence, leave little doubt that these bursts are the results of ion movements through pores or channels that are integral membrane proteins. During the past two decades, many such channels have been identified, cloned, sequenced, expressed, and subjected to extensive study of structure-function relations.

The two methods that are employed to measure single-channel activities of ion channels are illustrated in Fig. 8. The first (Fig. 8A) was introduced in 1976 and is referred to as the patch-clamp technique. Briefly, a polished glass micropipette tip having a diameter of approximately 1 mm is pressed against a patch of cell membrane, forming a seal that is essentially leakproof to ions (seal resistance is greater than 1 billion ohms). Thus, if there happens to be an ion channel in the membrane patch, ionic currents into or out of the cell will be entirely constrained within the pipette and the connected circuitry. One may also mechanically rip (excise) the patch of membrane together with the channel off the cell and examine single-channel properties under artificial but well-defined and easily controlled conditions.

The other technique involves reconstituting or incorporating membrane vesicles containing channels, or purified channel proteins, into planar artificial lipid bilayers separating two easily accessible and controlled solutions (Fig. 8B).

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