Encyclopedia of Computational Neuroscience

Living Edition
| Editors: Dieter Jaeger, Ranu Jung

Sodium Channels

  • Dominique EngelEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-1-4614-7320-6_134-1

Keywords

Sodium Channel Closed State Conformational State Excitable Cell Nonexcitable Cell 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Synonyms

Definition

Sodium channels are proteins enchased in the cell membrane of both excitable and nonexcitable cells. They are in general composed of two different types of proteins, termed subunits, an alpha (α) and two beta (β) subunits. The arrangement of the α subunit across the cell’s membrane enables the formation of an aqueous tunnel termed channel linking the cells interior and the extracellular space. Changes in the transmembrane voltage govern channel gating. When the channel is open, almost exclusively sodium (Na+) ions flow through the channel (Fig. 1a). The Na+ ion flow through the channel can be blocked by tetrodotoxin (TTX), a specific and widely used puffer fish toxin.
Fig. 1

Structure and function of sodium channels. (a) Schematic representation of a sodium channel enchased in the plasmic membrane of a cell. When the membrane potential is close to rest, Na+ ions are flowing inside the cell due to the driving force of Na+ (Vm – ENa). (b) Conductance model for sodium channels. ENa is the equilibrium potential for Na+ represented by the battery and gNa is the variable conductance of Na+ channels which dependents on time and potential represented by the arrow. Cm is the capacitance of the membrane. (c) Transmembrane organization of the α and β subunits of the sodium channel. Modified from Catterall W (2001) with permission

Functional properties of sodium channels can be translated into an electrical conductance model consisting of a battery in series with a resistor and an arrow indicating a time- and voltage-dependent conductance (Johnston and Wu 1995; Hille 2001; Fig. 1b).

Detailed Description

Structure and Function of Sodium Channels

Sodium channels are proteins enchased in the cell membrane of different excitable cell types including neurons of the central and peripheral nervous system and muscle cells including skeletal, smooth, and cardiac muscle cells but also in various nonexcitable cells (Black and Waxman 2013). They are composed of a principal alpha subunit responsible for the formation of the pore and beta auxiliary subunits implicated in the regulation of channel function (Johnston and Wu 1995; Hammond 2001; Catterall 2012; Fig. 1c). The alpha subunit exists in distinct isoforms (Table 1) and consists of a long chain of about 2000 amino acids arranged in four repetitions of a specific sequence of amino acids termed homologous domain (I, II, III, and IV). Within each domain, the sequence forms six transmembrane segments (S1–S6). The four homologous domains are presumably arranged across the membrane to form a central pore bordered by S6 segments. S4 segments are important for the gating as they are composed by positively charged amino acids and thereby are believed to represent the voltage sensor of the channel (Johnston and Wu 1995; Hammond 2001; Hille 2001; Catterall 2012). In neurons, sodium channels are present generally in each subcellular compartment (soma, axon, and dendrites). But a nonhomogeneous distribution of the channels may exist in the different neuronal compartments (Magee 2008; Vacher et al. 2008). The function of Na+ channels in excitable cells is to permit an entry of positive charges into the cell in order to depolarize the membrane and to generate action potentials (APs). Na+ channel permeability is essential for the initiation and the propagation of APs in excitable cells, and their open probability increases largely during the upstroke of APs. Na+ channels mentioned above and in the two following paragraphs have fast activation and inactivation and are therefore termed transient Na+ channels. Two additional Na+ currents may be expressed by excitable cells, termed “resurgent” and “persistent,” passing current during membrane potential repolarization after brief depolarizations (Cruz et al. 2011) and passing noninactivating current, respectively (Kiss 2008). Dysfunctions of sodium channels (sodium “channelopathies”) cause a variety of diseases among which are epileptic syndromes and muscle diseases (Waxman 2001; Savio-Galimberti et al. 2012).
Table 1

Mammalian sodium channel properties

Conventional

name

Original name

Corresponding

gene

TTX

sensitivity

Predominant

location

Nav1.1

Type I, rat I,

Scn1a

SCN1A

Yes

CNS, PNS

Nav1.2

Type II, rat II,

SCN2A

Yes

CNS

Nav1.3

Type III, rat III

SCN3A

Yes

Embryonic CNS

Nav1.4

SkM, μ1

SCN4A

Yes

skeletal muscle

Nav1.5

SkM2, rH1, H1

SCN5A

No

Heart muscle

Nav1.6

Type IV, NaCh6,

Na6, Scn8a

SCN8A

Yes

CNS, PNS, axons

Nav1.7

PN1, hNE, Nas

SCN9A

Yes

PNS, Schwann cells

Nav1.8

SNS, PN3, NaNG

SCN10A

No

PNS, sensory

neurons

Nav1.9

SNS2, NaN, SCN12A

SCN11A

No

PNS

Nax

Nav2.1, Nav2.2

SCN6A

No

Heart, uterus, glia

Nav2.3, SCL11, NaG

SCN7A

No

PNS smooth muscle

CNS: central nervous system, PNS: peripheral nervous system, TTX: tetrodotoxin (specific blocker of sodium channels. A more detailed description of the diversity of Na+ channels is reviewed in (Goldin, 2002). A detailed analysis of the localization of Na+ channels is reviewed in (Vacher et al. 2008).

Patch-Clamp Recordings of Single-Channel and Macroscopic Sodium Currents

The development of the patch-clamp technique gave the opportunity to measure directly the unitary Na+ current flowing through a single sodium channel (Sakmann and Neher 1995). Unitary Na+ currents have a typical rectangular time course representing transitions between open and closed states of the channel. Unitary currents are therefore all-or-none events, and their peak amplitude is voltage-dependent according to Ohm’s law:
$$ {\mathrm{i}}_{\mathrm{Na}}={\gamma}_{\mathrm{Na}}\left({\mathrm{V}}_{\mathrm{m}}-{\mathrm{E}}_{\mathrm{Na}}\right) $$
where iNa is the unitary Na+ current, γ Na is the single-channel conductance, Vm is the membrane potential, and ENa is the reversal potential of Na+ ions.
The summation of a large number of unitary Na+ currents results in a macroscopic Na+ current which corresponds nearly to the “whole-cell” current recorded in a cell. Unitary and macroscopic Na+ currents are proportional and related by the following equation:
$$ {\mathrm{I}}_{\mathrm{Na}}=\mathrm{N}\kern0.36em {\mathrm{p}}_{\left(\mathrm{t}\right)}{\mathrm{i}}_{\mathrm{Na}} $$
where INa is the macroscopic current, N is the number of Na+ channels, and p(t) is the open probability at a time t. Mechanistically, the behavior of Na+ channels is characterized by transitions between three distinct states, an open state (O), a closed state (C), and an inactivated state (I). Transitions are illustrated by the scheme in Fig. 2.
Fig. 2

Conformational states in the Hodgkin Huxley formalism. Sequence of transitions of sodium channels through C, O and I states illustrated with the movement of the gating particles (m and h)

Typically, the sodium channel switches from C to O on depolarization and rapidly back from O to C with repolarization when the depolarization time is very short. On sustained depolarization, the sodium channel closes more slowly and switches from O to I. The latter transition is termed inactivation and corresponds to a refractory state of the channel characterized by a non-passing ion state (Ulbricht 2005; Catterall et al. 2012). The probability of the Na+ channels being open increases with depolarization and the duration of the open state varies around a mean value termed mean open time. To be able to reopen after inactivation, sodium channels need to transit through the C state for a certain period of time, and this is achieved with membrane hyperpolarization (Hammond 2001). With fundamental work published in 1952, Hodgkin and Huxley interpreted the transitions between the conformational states of sodium channels with the movement of activation (m) and inactivation (h) gates regulating the permeability of the channel (Fig. 2; Johnston and Wu 1995; Koch 1999). In the Hodgkin–Huxley (HH) formalism, permeability changes are described by ionic conductance which is voltage- and time-dependent:
$$ {\mathrm{g}}_{\mathrm{Na}}={\overline{\mathrm{g}}}_{\mathrm{Na}}{m}^3\;h $$
from which the right side of the equation can be implemented in the equation describing the macroscopic Na+ current:
$$ {\mathrm{I}}_{\mathrm{Na}}={\overline{\mathrm{g}}}_{\mathrm{Na}}{m}^3\;h\;\left({\mathrm{V}}_{\mathrm{m}}-{\mathrm{E}}_{\mathrm{Na}}\right) $$
where \( {\overline{\mathrm{g}}}_{\mathrm{Na}} \) (gNa “bar”) is the maximal value of the conductance and m, h represent the fraction of two distinct type of gating particles in the inside of the membrane.

Modeling Sodium Channel Conductance to Estimate Membrane Potential Changes

A detailed functional analysis of sodium channel properties is fundamental to understand the generation of APs in excitable cells. With their pioneer study, Hodgkin and Huxley proposed a quantitative model describing the permeability of sodium channels in terms of ionic conductance changes using experimental data. With this model, they could also predict the time course of APs. Without any knowledge about the structure of an ion channel, they predicted that sodium channels are gated by gating variables which are dependent on time and voltage and postulated that the transitions between open and closed states obey first-order kinetics (Johnston and Wu 1995; Destexhe and Huguenard 2001; Hille 2001; Koch 1999). While the HH formalism has still a large influence to describe channel functional properties and to predict AP time course, it is a macroscopic approximation (Catterall et al. 2012) and may have some limitations. For instance, the HH formalism is unable to describe the abrupt onset of APs of cortical neurons (Naundorf et al. 2006).

Alternatively, the gating of sodium channels in stochastic Markov models is described by transitions through a series of distinct conformational states. These models assume that the transitions between conformational states are memoryless and depend only on the current state (Destexhe and Huguenard 2001; Kispersky and White 2008). Markov models are thereby more precise to describe conformational changes of single channels (Destexhe and Huguenard 2001).

Cross-References

References

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Further Reading

  1. Carnevale N, Hines M (2005) The neuron book. Cambridge University Press, New YorkGoogle Scholar
  2. Jack J, Noble D, Tsien R (1983) Electric current flow in excitable cells. Oxford University Press, OxfordGoogle Scholar
  3. Scholarpedia. www.scholarpedia.org. (conductance-based models, gating currents, ion channels, electrical properties of cell membranes)

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.GIGA-NeurosciencesUniversity of LiegeLiegeBelgium