Electrotonic potential

The membrane length constant measures how far it takes for an electrotonic potential to fall to 1/e or 37% of its amplitude at the place where it began.

It is important to contrast this with the all-or-none law propagation of the action potential down the axon of the neuron.

This difference in information rates can be up to almost an order of magnitude greater for electrotonic potentials.

[6] In 1855, Lord Kelvin devised this theory as a way to describe electrical properties of transatlantic telegraph cables.

[7] Almost a century later in 1946, Hodgkin and Rushton discovered cable theory could be applied to neurons as well.

[8] This theory has the neuron approximated as a cable whose radius does not change, and allows it to be represented with the partial differential equation[6][9] where V(x, t) is the voltage across the membrane at a time t and a position x along the length of the neuron, and where λ and τ are the characteristic length and time scales on which those voltages decay in response to a stimulus.

Referring to the circuit diagram on the right, these scales can be determined from the resistances and capacitances per unit length.

This organelle can hold thousands of synaptic vesicles close to the presynaptic membrane, enabling neurotransmitter release that can quickly react to a wide range of changes in the membrane potential.

Examples of electrotonic potentials
A diagram showing the resistance and capacitance across the cell membrane of an axon. The cell membrane is divided into adjacent regions, each having its own resistance and capacitance between the cytosol and extracellular fluid across the membrane. Each of these regions is in turn connected by an intracellular circuit with a resistance.
Equivalent circuit of a neuron constructed with the assumptions of simple cable theory.