# Electrotonic potential

Examples of electrotonic potentials

In physiology, electrotonus refers to the passive spread of charge inside a neuron. Passive means that voltage-dependent changes in membrane conductance do not contribute. Neurons and other excitable cells produce two types of electrical potential:

1. Electrotonic potential (or graded potential) a non-propagated local potential, resulting from a local change in ionic conductance (e.g. synaptic or sensory that engenders a local current). When it spreads along a stretch of membrane, it becomes exponentially smaller (decrement).
2. Action potential — a propagated impulse.

Electrotonic potentials represent changes to the neuron's membrane potential that do not lead to the generation of new current by action potentials.[1] 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.[2] Neurons which are small in relation to their length, such as some neurons in the brain, have only electrotonic potentials (starburst amacrine cells in the retina are believed to have these properties); longer neurons utilize electrotonic potentials to trigger the 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.[3] In order to quantify the behavior of electrotonic potentials there are two constants that are commonly used: the membrane time constant τ, and the membrane length constant λ. 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.[2]

Electrotonic potentials are conducted faster than action potentials, but attenuate rapidly so are unsuitable for long-distance signaling. The phenomenon was first discovered by the Eduard Pflüger.

## Summation

The electrotonic potential travels via electrotonic spread, which amounts to attraction of opposite- and repulsion of like-charged ions within the cell. Electrotonic potentials can sum spatially or temporally. Spatial summation is the combination of multiple sources of ion influx (multiple channels within a dendrite, or channels within multiple dendrites), whereas temporal summation is a gradual increase in overall charge due to repeated influxes in the same location. Because the ionic charge enters in one location and dissipates to others, losing intensity as it spreads, electrotonic spread is a graded response. It is important to contrast this with the all-or-none law propagation of the action potential down the axon of the neuron.[2]

## EPSPs

Electrotonic potential can either increase the membrane potential with positive charge or decrease it with negative charge. Electronic potentials that increase the membrane potential are called excitatory postsynaptic potentials (EPSPs). This is because they depolarize the membrane, increasing the likelihood of an action potential. As they sum together they can depolarize the membrane sufficiently to push it above the threshold potential, which will then cause an action potential to occur. EPSPs are often caused by either Na+ or Ca2+ coming into the cell.[2]

## IPSPs

Electrotonic potentials which decrease the membrane potential are called inhibitory postsynaptic potentials (IPSPs). They hyperpolarize the membrane and make it harder for a cell to have an action potential. IPSPs are associated with Cl entering the cell or K+ leaving the cell. IPSPs can interact with EPSPs to "cancel out" their effect.[2]

## Information Transfer

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.[4][5]

## Cable theory

Cable theory's simplified view of a neuronal fiber. The connected RC circuits correspond to adjacent segments of a passive neurite. The extracellular resistances re (the counterparts of the intracellular resistances ri) are not shown, since they are usually negligibly small; the extracellular medium may be assumed to have the same voltage everywhere.

The flow of currents within an axon can be described quantitatively by cable theory[6] and its elaborations, such as the compartmental model.[7] Cable theory was developed in 1855 by Lord Kelvin to model the transatlantic telegraph cable[8] and was shown to be relevant to neurons by Hodgkin and Rushton in 1946[9]. In simple cable theory, the neuron is treated as an electrically passive, perfectly cylindrical transmission cable, which can be described by a partial differential equation[6]

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

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.[10]

${\displaystyle \tau =\ r_{m}c_{m}\,}$
${\displaystyle \lambda ={\sqrt {\frac {r_{m}}{r_{\ell }}}}}$

These time and length-scales can be used to understand the dependence of the conduction velocity on the diameter of the neuron in unmyelinated fibers. For example, the time-scale τ increases with both the membrane resistance rm and capacitance cm. As the capacitance increases, more charge must be transferred to produce a given transmembrane voltage (by the equation Q = CV); as the resistance increases, less charge is transferred per unit time, making the equilibration slower. In a similar manner, if the internal resistance per unit length ri is lower in one axon than in another (e.g., because the radius of the former is larger), the spatial decay length λ becomes longer and the conduction velocity of an action potential should increase. If the transmembrane resistance rm is increased, that lowers the average "leakage" current across the membrane, likewise causing λ to become longer, increasing the conduction velocity.[11]

## 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.[12][13]

## References

1. ^ electrotonic - definition of electrotonic in the Medical dictionary - by the Free Online Medical Dictionary, Thesaurus and Encyclopedia
2. Sperelakis, Nicholas (2011). Cell Physiology Source Book. Academic Press. pp. 563–578. ISBN 978-0-12-387738-3.
3. ^ Pauls, John (2014). Clinical Neuroscience. Churchill Livingstone. pp. 71–80. ISBN 978-0-443-10321-6.
4. ^ Juusola, Mikko (July 1996). "Information processing by graded-potential transmission through tonically active synapses". Trends in Neurosciences. 19.
5. ^ Niven, Jeremy Edward (January 2014). "Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency". PLOS Computational Biology. 10.
6. ^ a b Rall, W in Koch & Segev 1989, Cable Theory for Dendritic Neurons, pp. 9–62.
7. ^ Segev, I; Fleshman, JW; Burke, RE in Koch & Segev 1989, Compartmental Models of Complex Neurons, pp. 63–96.
8. ^ Kelvin WT (1855). "On the theory of the electric telegraph". Proceedings of the Royal Society. 7.
9. ^ Hodgkin AL (1946). "The electrical constants of a crustacean nerve fibre". Proceedings of the Royal Society B. 133.
10. ^ Purves et al. 2008, pp. 52–53.
11. ^ Squire, Larry R. (2002). Fundamental Neuroscience. Academic Press. pp. 115–122. ISBN 978-0126603033.
12. ^ Matthews, Gary (January 2005). "Structure and function of ribbon synapses". Trends in Neurosciences. 28: 20–29.
13. ^ Lagnado, Leon (August 2013). "Spikes and ribbon synapses in early vision". Trends in Neurosciences. 36: 480–488.