# Excitable Cells

Explain the basic electro-physiology of neural tissue, including conduction of nerve impulses and synaptic function.

## Membrane Potential

At rest, membranes are:

• Permeable to potassium
• Impermeable to other ions

Generation of membrane potential:

• Intracellular potassium concentration is much higher than extracellular potassium concentration
Due to the action of the Na+-K+ pump.
• As the membrane is permeable to potassium, potassium will attempt to diffuse down this gradient, generating a negative intracellular charge which opposes further diffusion
• At some point, an electrochemical equilibrium is reached between:
• The concentration gradient dragging potassium out of the cell
• Negative electrical charge pulling it in
• This equilibrium is the resting membrane potential
• RMP is determined by:
• Permebility of the membrane to different ions
• Relative ionic concentrations on either side of the membrane
• Impermeable ions do not contribute to the resting membrane potential
Altering membrane permeability causes a flow of ions and a change in voltage.

### Nernst Equation

The potential difference generated by a permeable ion in electrochemical equilibrium when there are different concentrations on either side of the cell can be calculated via the Nernst Equation:

$$E \ (mV) = {R.T \over z.F}ln{[ion]{outside} \over [ion]{inside}}$$, where:

• $$E$$ is the equilibrium potential for the ion
• $$R$$ is the gas constant (8.314 J.deg-1.mol-1)
• $$T$$ is the temperature in Kelvin
• $$F$$ is Faraday's Constant
• $$z$$ is the ionic valency (e.g. +2 for Mg+2, -1 for Cl-)

### Goldman-Hodgkin-Katz Equation

The Nernst equation describes the equilibrium potential for a single ion, and assumes that the membrane is completely permeable to that ion.

However, calculation of membrane potential requires examining the effects of many different ions with different permeability. This can be performed with the Goldman-Hodgkin-Katz equation:

$$E \ (mV) = {R.T \over F }ln{PK[K^+]_o \ + \ P{Na}[Na^+]o \ + \ P{Cl}[Cl^-]i \over P_K[K^+]_i + \ P{Na}[Na^+]i \ + \ P{Cl}[Cl^-]_o}$$, where:

• $$P_x$$ is the permeability constant for the ion, $$x$$
If the membrane is impermeable to $$x$$, then $$P_x = 0$$.

Note that:

• This model does not consider valency
• The concentrations of negative ions are reversed relative to positive ions

## Action Potential

Excitable cells can respond to a stimulus by a changing their membrane potential. This may be mediated:

• Chemically
e.g. ACh receptors causing Na+ channels to open.
• Physically
Pressure receptors physically deforming and opening Na+ channels.
• Stimulating an excitable cell increases Na+ permeability
This increases (i.e. makes less negative) membrane potential
• If several stimuli, or a large enough stimuli raises the membrane potential above the threshold potential, then an action potential will be generated
• This is due to fast Na+ channels
• Also known as voltage-gated Na+ channels
• Open when membrane potential exceeds threshold potential
Threshold potential is typically -55mV.
• Fast sodium channels generate the all-or-nothing response:
• Stimuli below the threshold potential do not generate an action potential
• Stimuli above threshold potential generate an action potential
The size of the stimulus does not affect the magnitude of the action potential, as this is determined by the fast sodium channels.

### Key Players in the Action Potential

Fast Na+ channels are responsible for depolarisation. They exist in three states:

• Closed
Impermeable to Na+.
• Open
Permeable to Na+. Occurs when the membrane potential reaches threshold potential.
• Different voltage-gated channels may have slightly different opening (threshold) potentials
• Inactivated
Impermeble to Na+. Occurs shortly after the open state, and lasts until the membrane potential falls below -50mV.

Voltage-gated K+ channels:

• Are vital for repolarisation
• Open slowly with depolarisation
This increases potassium permeability and reduces membrane potential.

### Phases of the Action Potential

This describes the peripheral nerve action potential. The heart is covered under the cardiac action potential.

1. Rising Phase
A stimulus which rises above the threshold potential opens fast Na+ channels, increasing Na+ influx.
• Additional Na+ has a positive feedback effect, causing additional Na+ channels to open and further depolarisation
• This drives the membrane potential towards the Nernst equilibrium for Na+
2. Peak Phase
Inactivation of fast-channels and delayed activation of K+ channels slows depolarisation.
• Membrane potential peaks at 30mV
3. Falling Phase
As potassium exits the cell, membrane potential continues to fall.
• Voltage-gated K+ channels start to close at -50mV
• Inactivation of fast sodium channels defines the absolute refractory period
No Na+ can be conducted, regardless of the intensity of the stimulus, and so an action potential cannot be generated
• The absolute refractory perioid lasts ~1ms
4. Hyperpolarisation
As potassium channels close slowly, the membrane potential slightly undershoots resting potential, causing slight hyperpolarisation of the cell.
• This is the relative refractory period
A large enough stimulus may overcome the additional hyperpolarisation and generate a second action potential.
• The relative refractory period lasts 10-15ms
5. Resting
Cell is stable at resting membrane potential.

### Propagation of the Action Potential

• An increase in Na+ in one region will diffuse down the cell, raising the membrane potential above the resting potential in the adjacent membrane
• This causes local fast Na+ channels to open, and the cell depolarises
• This results in a propagating wave of depolarisation and repolarisation
• Regions of a nerve cell covered by a myelin sheath do not have ion channels
• In these cells, propagation is saltatory
This describes the "jumping" of the action potential between gaps in the myelin sheath.
• These gaps are known as nodes of Ranvier
Ion channels generate an action potential at the nodes in the usual manner.
• Between nodes, conduction is via local electrical currents
• Myelination:
• Increases conducting velocity
• Reduces energy expenditure
Via reduction in total ion flux.

### Classification of Nerve Fibres

Classified on their diameter and conduction velocity:

• Type A
Myelinated, 12-20μm in diameter, conduct at 70-120m.s-1. Subdivided into:

• Motor fibres.

• Touch fibres.

• Intrafusal (proprioceptive) muscle fibre.

• Pain fibres.
• Type B
Myelinated, < 3μm, conduct at 4-30m.s-1. Innervate pre-ganglionic neurons.
• Type C
Unmyelinated, 1μm, conduct at 0.5-2m.s-1. Pain fibres.

## References

1. Kam P, Power I. Principles of Physiology for the Anaesthetist. 3rd Ed. Hodder Education. 2012.
2. Chambers D, Huang C, Matthews G. Basic Physiology for Anaesthetists. Cambridge University Press. 2015.
Last updated 2017-09-17