The h and m gating variables in sodium channels represent inactivation and activation kinetics respectively.
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Standard neurophysiological references confirm that in Hodgkin-Huxley type models of sodium channels, the h variable represents inactivation kinetics and the m variable represents activation kinetics.
voltage-sensitive sodium channel was modeled to have three similar gates of probability m and a fourth gate, associated with inactivation, of probability h; thus
In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the Loligo squid exemplifies such models. Although qualitatively correct, the H-H model
where INa, IK, and IL are currents conveyed through the local sodium channels, potassium channels, and "leakage" channels (a catch-all), respectively. The initial term Iext represents the current arriving from external sources, such as excitatory postsynaptic potentials from the dendrites or a scientist's electrode.
The model further assumes that a given ion channel is either fully open or closed; if closed, its conductance is zero, whereas if open, its conductance is some constant value g. Hence, the net current through an ion channel depends on two variables: the probability popen of the channel being open, and the difference in voltage from that ion's equilibrium voltage, V − Veq. For example, the current through the potassium channel may be written as
which is equivalent to Ohm's law. By definition, no net current flows (IK = 0) when the transmembrane voltage equals the equilibrium voltage of that ion (when V = EK).
To fit their data accurately, Hodgkin and Huxley assumed that each type of ion channel had multiple "gates", so that the channel was open only if all the gates were open and closed otherwise. They also assumed that the probability of a gate being open was independent of the other gates being open; this assumption was later validated for the inactivation gate. Hodgkin and Huxley modeled the voltage-sensitive potassium channel as having four gates; letting pn denote the probability of a single such gate being open, the probability of the whole channel being open is the product of four such probabilities, i.e., popen, K = n4. Similarly, the probability of the voltage-sensitive sodium channel was modeled to have three similar gates of probability m and a fourth gate, associated with inactivation, of probability h; thus, popen, Na = m3h. The probabilities for each gate are assumed to obey first-order kinetics
where both the equilibrium value meq and the relaxation time…
# meaning of abbreviations h and m in Na channels
Tags: neuroscience
- Score: 5
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- Answers: 1
- Answered: yes
- Asked by: nvja (1160 rep)
- Asked: 2016-12-19
- Site: biology
## Question
In a voltage-gated sodium channel, there are two gates, one for activation and one for inactivation. They are also known as h- and m- gate. What are these letters standing for?
## Answers
### Answer by user24284 (score: 6 [ACCEPTED])
Those initials were proposed by Hodgkin and Huxley in their original paper modeling the action potential in nerve cells: https://en.wikipedia.org/wiki/Hodgkin%E2%80%93Huxley_model
They are not names for subunits, domains or motifs in the sodium channel, as your question may imply. Instead,
n, m, and h are dimensionless quantities between 0 and 1 that are associated with potassium channel activation, sodium channel activation, and sodium channel inactivation, respectively.
However, there is no indication of what those initials mean (if anything), apparently being just letters they chose to name the variables in their equations.
Derivation of Hodgkin-Huxley equations for a Na^{+} channel from a master equation for coupled activation and inactivation - PubMed
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## Abstract
The Na^{+} current in nerve and muscle membranes may be described in terms of the activation variable m(t) and the inactivation variable h(t), which are dependent on the transitions of S4 sensors of each of the Na^{+} channel domains DI to DIV. The time-dependence of the Na^{+} current and the rate equations satisfied by m(t) and h(t) may be derived from the solution to a master equation that describes the coupling between two or three activation sensors regulating the Na^{+} channel conductance and a two-stage inactivation process. If the inactivation rate from the closed or open states increases as the S4 sensors activate, a more general form of the Hodgkin-Huxley expression for the open-state probability may be derived where m(t) is dependent on both activation and inactivation processes. The voltage dependence of the rate functions for inactivation and recovery from inactivation are consistent with the empirically determined expressions and exhibit saturation for both depola
the conductance, or inverse resistance, which can be expanded in terms of its maximal conductance ḡ and the activation and inactivation fractions m and
Biological neuron models, also known as spiking neuron models, are mathematical descriptions of the conduction of electrical signals in neurons. Neurons (or nerve cells) are electrically excitable cells within the nervous system, able to fire electric signals, called action potentials, across a neural network. These mathematical models describe the role of the biophysical and geometrical characte
where g(t,V) is the conductance, or inverse resistance, which can be expanded in terms of its maximal conductance ḡ and the activation and inactivation fractions m and h, respectively, that determine how many ions can flow through available membrane channels. This expansion is given by
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