User:23francesco/sandbox

However, all action potentials are begun by electrotonic potentials depolarizing the membrane above the threshold potential which converts the electrotonic potential into an action potential.

Electrotonic potentials have an amplitude that is usually 5-20 mV and they can last from 1 ms up to several seconds long.

In order to quantify the behavior of electrotonic potentials there are two constants that are commonly used: the membrane time constant λ, and the membrane length constant τ. The membrane time constant measures the amount of time for an electrotonic potential to passively fall to 1/e or 37% of its maximum. A typical value for neurons can be from 1 to 20 ms. 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. Common values for the length constant of dendrites are from .1 to 1 mm.

Because of the continuously varying nature of the electrotonic potential versus the binary response of the action potential, this creates implications for how much information can be encoded by each respective potential. Electrotonic potentials are able to transfer more information within a given time period than action potentials. This difference in information rates can be up to almost an order of magnitude greater for electrotonic potentials.

Examples of electrotonic potentials

Ribbon synapses

Ribbon synapses are a type of synapse often found in sensory neurons and are of a unique structure that specially equips them to respond dynamically to inputs from electrotonic potentials. They are so named for an organelle they contain, the synaptic ribbon. 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.

Cable theory

Equivalent circuit of a neuron constructed with the assumptions of simple cable theory.

Cable theory can be useful for understanding how currents flow through the axons of a neuron. In 1855 Lord Kelvin devised this theory as a way to describe electrical properties of transatlantic cables. Almost a century later in 1946, Hodgkin and Rushton discovered cable theory could be applied to neurons as well. 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

$\tau {\frac {\partial V}{\partial t}}=\lambda ^{2}{\frac {\partial ^{2}V}{\partial x^{2}}}-V$

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.

$\tau =\ r_{m}c_{m}\,$

$\lambda ={\sqrt {\frac {r_{m}}{r_{\ell }}}}$

From these equations one can understand how properties of a neuron affect the current passing through it. The length constant λ, increases as membrane resistance becomes larger and as the internal resistance becomes smaller, allowing current to travel farther down the neuron. The time constant τ, increases as resistance and capacitance of the membrane increase, which causes current to travel more slowly through the neuron.

Where are your references? DJW56 (talk) 20:22, 22 October 2018 (UTC)