# 04.The Zoo of ion channels

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## The Zoo of ion channels

Hodgkin-Huxley model captures the essence of spike generation by sodium and potassium ion channels. But cortical neurons in vertebrates exhibit a much richer repertoire of electrophysiological properties than the squid axon studied by Hodgkin and Huxley. This is mostly due to a large variety of different ion channels.

#### Sodium channels

fast sodium ion channels $I_{Na}$

persistent or non inactivating sodium current described by an activation variable m only and does not have a separate inactivation variable h -> $I_{NaP}=\bar{g}{NaP}m(u-E{Na})$

#### Potassium channels

Thalamic relay neurons have two different types of potassium channels: a rapidly inactivating potassium current $I_{A}$ and a slowly inactivating potassium current $I_{K2}$.

$I_{A}$ -> $I_{A1}$ and $I_{A2}$

$I_{K2}$ -> $I_{K2a}$ and $I_{K2b}$

$I_{A}$ -> slowly firing neurons that slow down the firing of action potentials

type I: neurons with continuous gain function and delayed pulse generation

type II: neurons with discontinuous gain function

#### Low-threshold calcium current

Neurons of the deep cerebellar nuclei contain two different types of calcium channels: a high-threshold calcium current ($I_{L}$) and a low-threshold calcium current ($I_{T}$)

$I_{T}$ -> Postinhibitory rebound means that a hyperpolarizing current, which is suddenly switched off, results in an overshoot of the membrane potential or even in the triggering of one or more action potentials. Through this mechanism, action potentials can be triggered by inhibitory input.

What is similar to the fast sodium current of the Hodgkin-Huxley model: $I_{T}$ is inactivating

What is different: in the Hodgkin-Huxley model the sodium channels are not activated (m ≈ 0) whereas the T-type calcium current is inactivated (h ≈ 0)

#### High-threshold calcium current and calcium-activated potassium channels

some neurons contain $I_{T}$ current

the inactivation variable h is absent