A. Voltage-Gated Ion Channels Underlie Voltage-Dependent Membrane Conductances
In the past two decades, improvements in recording methodologies, pioneered by the group of Sakmann and Neher, as well as an explosion of knowledge in the field of molecular biology have demonstrated directly that membrane protein assemblies called ion channels underlie voltage-gated conductances in neurons and other excitable cells. The main (a) subunit of voltage-gated Na+ channels (Fig. 7a) is a membrane protein approximately 2000 amino acids in length and has a molecular weight >200,000. This protein includes four domains, each of which consists of six putative transmembrane segments. A smaller b subunit is not necessary to form the channel but is crucial for regulating aspects of channel function such as the speed of inactivation. The main subunit of the K + channel has a very similar structure, except that the each protein codes for only one domain. Thus, four a subunits are necessary to form a K+ channel.
Recordings from single channels (Fig. 7b) typically reveal two conductance states: ''open'' and ''closed.'' Switching between open and closed states appears random, but the probability that the channel is in the open state varies with membrane potential. These probabilities correspond approximately to the values of gating variables in the Hodgkin-Huxley formulation. Sums of repeated recordings from an individual ion channel show behavior that is very similar to the macroscopic behavior of the channel population (Fig. 7b). Sophisticated analyses of single-channel recordings yield probabilistic models that can account for both microscopic and macroscopic behavior. These
Figure 7 Na+ channels underlie the voltage-gated Na+ conductance. (a) Putative structure of the a and b subunits of the rat brain Na + channel (IIA). Roman numerals indicate the domains of the a subunit, each of which includes six putative transmembrane segments. Indicated residues are implicated in binding the channel blocker tetrodotoxin (E387) and in forming the inactivation gate (IFM 1488-1490) (adapted from Ashcroft (2000)). (b) The 10 middle traces show simulated single-channel recordings from a Na+ channel under voltage clamp. The top trace shows the voltage-clamp command. The bottom trace shows the sum of 625 single-channel records.
models are similar in structure to Hodgkin-Huxley-type models but different in some details. For example, careful analysis of recordings from single Na+ channels shows that their inactivation state is not controlled by an activation-independent process like the h gate but, rather, that Na+ channels must activate before they can inactivate.
Experiments with channels that have been subjected to site-directed mutations have revealed close connections between particular loci on the protein and specific aspects of channel behavior. Among the properties that have been tied to specific loci on the a subunit are those of pore formation, ionic selectivity, voltage dependence, inactivation, and blockage by specific toxins (Fig. 7a).
B. Diversity of Mechanisms Contributing to Neuronal Excitability
In the approximately 50 years since the development of the Hodgkin-Huxley model, researchers have discovered many ion channel-based mechanisms for generating and controlling electrical activity in neurons. Often, these mechanisms rely on Na + , Ca2 + , and K + channels. Sodium channels are relatively consistent in their properties from case to case but do show some variety. In particular, some Na+ channels do not exhibit fast inactivation; it is not clear whether these noninactivating Na+ channels are a separate population from the typical, fast-inactivating Na+ channels or a subset of the fast-inactivating Na+ channels that have slipped into a different "mode" of gating. Calcium and potassium channels show more diversity than Na+ channels. In particular, different classes of Ca2+ and K+ channels show widely diverse properties with regard to the presence and speed of inactivation, pharmacological properties, and voltage ranges of activation. Some K+ channels are sensitive to both membrane potential and the local intracellular concentration of Ca2+, giving rise to interesting interactions between these two systems.
Ion channel expression profiles and neuromodula-tory states can have profound consequences for neuronal function. A striking example of this point derives from thalamic relay neurons (Fig. 8). Depending on the level of depolarization or neuromodulatory state, these cells have two distinct firing modes. When relay neurons are hyperpolarized, they exhibit rhythmic bursting (Fig. 8a). The long interburst interval is determined by interaction of the low-threshold Ca2+ current and slowly activating, inwardly rectifying cation current. Superimposed on each slow Ca2+ spike are many fast action potentials, mediated by Na+ and K+ channels. When relay neurons are depolarized, either by electrical current or any of a number of neuromodulators, the low-threshold Ca2+ channels and inwardly rectifying cation channels are unimportant and the neurons fire in a tonic pattern much more reminiscent of the Hodgkin-Huxley model (Fig. 8b).
The properties of voltage-gated ion channels are not static. Many neuromodulators have been shown to alter ion channel function and the properties of action potentials by phosphorylating or dephosphorylating one or more sites on the channel protein. A host of neuronal firing properties, including spike width, average firing rate, and refractory period, are subject to metabolic control.
Although much about neuronal excitability can be learned by simply tracking changes in gating variables of the Hodgkin-Huxley-style model, computational neuroscientists and applied mathematicians have used mathematically based techniques to gain more general (and thus deeper) insights. Mathematical approaches a a mMMMm m/ml
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