A variety of mechanisms were considered possible. These included permeation in a homogeneous membrane, binding and migration along charged sites, passage on carriers, and flow through pores...The pathways might be formed from phospholipid or from protein, or even from nucleic acid. Each of these ideas was seriously advanced and rationalized in published articles.
Between the early 1960s and 1976 (in 1976 Neher and Sakmann published the first single channel patch recording), the mystery of the currents was essentially solved. First, in the 1960s toxins were found that could selectively block Ina (TTX and STX) or Ik (TEA) while the other current remained unaltered (Figure 3.2). This, in addition to the results of HH's ion substitution experiments, was taken as evidence that there were two separate ion pathways, or channels, one for K and one for Na.
The discovery of neurotoxins has been a boon for neuroscience. In addition to letting us turn individual currents on and off at will, they have helped us count individual channels (channel density is an important parameter in realistic neuronal models), and have suggested structural models of channels.
The action of TEA, TTX, and STX is well-described by a simple model in which a single molecule of the toxin T binds reversibly to a single receptor site R in an individual channel. This model is represented in Equation 3.1. The strength of binding is given by the equilibrium dissociation constant Kd. Kd is the toxin concentration at which half of the available receptors are occupied by the toxin. The model allows for a relatively simple algebraic derivation of the proportion of bound receptors, denoted with the variable y (see equation 3.2 and Figure 3.3).
If the above is unfamiliar, I highly recommend reading this site for a good introduction to the kinetics of such ligand-receptor interactions, which includes a discussion of Kd. As usual, Hille is leaving out lots of details in his exposition, but his terse summaries are very accurate.
The simple model of toxin-receptor interactions described above allows us to directly estimate the number of receptor sites, Bmax in a preparation. This is typically done with radioactively labeled toxins denoted radioligands. After marinating the preparation with radioligand, the preparation is thoroughly washed out to remove all the radioligand that is not bound to the receptor. Often it is washed out with a specific competitor such as a nonradioactive form of the toxin. If the radioligand only bound to the receptor, then estimating Bmax, the number of receptors in the tissue, would be relatively simple. We could apply different concentrations of radioligand and fit the data to the equation Bmaxy, where y is the proportion of bound receptors as a function of toxin concentration (Equation 3.2), and Bmax is the number of radioligand molecules at saturation. Note that Bmaxy is the first term in Equation 3.4.
Unfortunately, reality isn't quite so simple: we are never able to wash out all of the radioligand that isn't bound to receptor. It binds "nonspecifically" to other molecules in the preparation. Indeed, there is evidence that certain drugs bind to the plastic out of which test tubes are made! Luckily, this general, nonspecific binding typically has very different properties than the toxin-receptor binding: it is a linear nonsaturating function (i.e., the radioligand remaining after washout continues to increase linearly without bound as the concentration of radioligand is increased). Because of such nonspecific binding, a second linear term must be added to the saturating function, as represented by the right-hand term a[T] in Equation 3.4. [T] is the toxin concentration and a is a free parameter that represents the slope of the linear relationship.
Figure 3.4 shows the various curves we have discussed in the context of a clever experiment. The amount of radiolabeled STX was measured at different concentrations before and after wash with a high concentration of TTX, which has a higher affinity for the Na-channel receptor than STX. The remaining radiolableed STX was due to nonspecific binding, and exhibits the expected linear relationship with STX concentration. The difference between the linear curve and the overall saturating curve observed before TTX wash reveals the amount of radioligand remaining due to specific binding of STX to the Na-receptor. Such data has shown us that the Na-channel density on membrane is about 100-400 channels per square micron of unmyelenated axon.
Initial channel models
In addition to helping us count receptors, toxins have helped generate predictions about channel structure. For instance, a model of K channels was suggested by the effects of intracellular TEA on Ik. Namely, intracellular TEA blocks Ik only in open channels (a phenomenon known as open channel block (Figure 3.5). This suggested that the channel is a pore with a wide cytoplasmic opening (large enough for a big toxin like TEA to block it), an opening which is typically blocked by a gate that moves out of the way when the channel opens, thus allowing TEA to enter and close the channel. Because the toxin does not simply flow out of the extracellular pore, the model also assumes that the pore narrows toward the extracellular side. A cartoon of this model of the voltage-gated channel is shown in Figure 3.6. I