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	== Information Transfer ==		== 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.<ref>{{Cite journal\|last=Juusola\|first=Mikko\|date=July 1996\|title=Information processing by graded-potential transmission through tonically active synapses\|journal=Trends in Neurosciences\|volume=19\|issue=7\|pages=292–7\|doi=10.1016/S0166-2236(96)10028-X\|pmid=8799975\|s2cid=13180990}}</ref><ref>{{Cite journal\|last=Niven\|first=Jeremy Edward\|date=January 2014\|title=Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency\|journal=PLOS Computational Biology\|volume=10\|issue=1\|~~pages~~=e1003439\|doi=10.1371/journal.pcbi.1003439 \|pmid=24465197 \|pmc=3900385\|bibcode=2014PLSCB..10E3439S\|s2cid=15385561\|doi-access=free}}</ref>		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.<ref>{{Cite journal\|last=Juusola\|first=Mikko\|date=July 1996\|title=Information processing by graded-potential transmission through tonically active synapses\|journal=Trends in Neurosciences\|volume=19\|issue=7\|pages=292–7\|doi=10.1016/S0166-2236(96)10028-X\|pmid=8799975\|s2cid=13180990}}</ref><ref>{{Cite journal\|last=Niven\|first=Jeremy Edward\|date=January 2014\|title=Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency\|journal=PLOS Computational Biology\|volume=10\|issue=1\|article-number=e1003439\|doi=10.1371/journal.pcbi.1003439 \|pmid=24465197 \|pmc=3900385\|bibcode=2014PLSCB..10E3439S\|s2cid=15385561\|doi-access=free}}</ref>

	== Cable theory ==		== Cable theory ==

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[[File:1223 Graded Potentials-02.jpg|thumb|350px|Examples of electrotonic potentials]]

In [[physiology]], '''electrotonus''' refers to the passive spread of charge inside a [[neuron]] and between [[cardiac muscle cell]]s or [[smooth muscle]] cells. ''Passive'' means that voltage-dependent changes in membrane conductance do not contribute. Neurons and other excitable cells produce two types of electrical potential:
* ''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).
* ''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]].<ref>[http://medical-dictionary.thefreedictionary.com/electrotonic electrotonic - definition of electrotonic in the Medical dictionary - by the Free Online Medical Dictionary, Thesaurus and Encyclopedia]</ref> However, all action potentials are begun by electrotonic potentials [[Depolarization|depolarizing]] the membrane above the [[threshold potential]] which converts the electrotonic potential into an action potential.<ref name=":1" /> Neurons which are small in relation to their length, such as some neurons in the brain, have only electrotonic potentials ([[starburst amacrine cell]]s 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.<ref>{{Cite book|title=Clinical Neuroscience|last=Pauls|first=John|publisher=Churchill Livingstone|year=2014|isbn=978-0-443-10321-6|pages=71–80}}</ref> 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.<ref name=":1" /> Electrotonic potentials are conducted faster than action potentials, but attenuate rapidly so are unsuitable for long-distance signaling. The phenomenon was first discovered by [[Eduard Friedrich Wilhelm Pflüger|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.<ref name=":1" />

== EPSPs ==
Electrotonic potential can either increase the membrane potential with positive charge or decrease it with negative charge. Electrotonic potentials that increase the membrane potential are called [[excitatory postsynaptic potential]]s (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 [[Sodium|Na+]] or [[Calcium in biology|Ca2+]] coming into the cell.<ref name=":1">{{Cite book|title=Cell Physiology Source Book|last=Sperelakis|first=Nicholas|publisher=Academic Press|year=2011|isbn=978-0-12-387738-3|pages=563–578}}</ref>

== IPSPs ==
Electrotonic potentials which decrease the membrane potential are called [[inhibitory postsynaptic potential]]s (IPSPs). They [[Hyperpolarization (biology)|hyperpolarize]] the membrane and make it harder for a cell to have an action potential. IPSPs are associated with [[Chloride|Cl−]] entering the cell or [[Potassium in biology|K+]] leaving the cell. IPSPs can interact with EPSPs to "cancel out" their effect.<ref name=":1" />

== 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.<ref>{{Cite journal|last=Juusola|first=Mikko|date=July 1996|title=Information processing by graded-potential transmission through tonically active synapses|journal=Trends in Neurosciences|volume=19|issue=7|pages=292–7|doi=10.1016/S0166-2236(96)10028-X|pmid=8799975|s2cid=13180990}}</ref><ref>{{Cite journal|last=Niven|first=Jeremy Edward|date=January 2014|title=Consequences of Converting Graded to Action Potentials upon Neural Information Coding and Energy Efficiency|journal=PLOS Computational Biology|volume=10|issue=1|pages=e1003439|doi=10.1371/journal.pcbi.1003439 |pmid=24465197 |pmc=3900385|bibcode=2014PLSCB..10E3439S|s2cid=15385561|doi-access=free}}</ref>

== Cable theory ==
[[File:Cable_theory_Neuron_RC_circuit_v3.svg|alt=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.|thumb|300x300px|[[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.<ref name=":0">{{cite book |last=Rall |first=Wilfrid |author-link=Wilfrid Rall |chapter=Cable Theory for Dendritic Neurons |pages=9–62 |editor-last1=Koch |editor-first1=Christof |editor-last2=Segev |editor-first2=Idan |title=Methods in Neuronal Modeling: From Ions to Networks |date=1998 |publisher=MIT Press |isbn=978-0-262-11231-4 |url=https://books.google.com/books?id=5GMV2onekvsC |language=en}}</ref> In 1855, [[Lord Kelvin]] devised this theory as a way to describe electrical properties of transatlantic telegraph cables.<ref>[[William Thomson, 1st Baron Kelvin|Kelvin WT]] (1855). "On the theory of the electric telegraph". ''Proceedings of the Royal Society''. '''7''': 382–99.</ref> Almost a century later in 1946, [[Alan Lloyd Hodgkin|Hodgkin]] and [[W. A. H. Rushton|Rushton]] discovered cable theory could be applied to neurons as well.<ref>{{cite journal | last1 = Hodgkin | first1 = AL | author-link = Alan Lloyd Hodgkin | year = 1946 | title = The electrical constants of a crustacean nerve fibre | journal = Proceedings of the Royal Society B | volume = 133 | issue = 873| pages = 444–79 | doi = 10.1098/rspb.1946.0024 | pmid = 20281590 | bibcode = 1946RSPSB.133..444H | doi-access = }}</ref> 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]]<ref name=":0" /><ref>{{Cite book|title=Mathematics for Neuroscientists|last=Gabbiani|first=Fabrizio|publisher=Academic Press|year=2017|isbn=978-0-12-801895-8|pages=73–91}}</ref>

: <math>
\tau \frac{\partial V}{\partial t} = \lambda^2 \frac{\partial^2 V}{\partial x^2} - V
</math>

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.<ref>[[Action potential#CITEREFPurvesAugustineFitzpatrickHall2008|Purves et al. 2008]], pp. 52–53.</ref>

:<math>
\lambda = \sqrt \frac{r_m}{r_\ell}
</math>
:<math>
\tau =\ r_m c_m \,
</math>

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 the resistance and capacitance of the membrane increase, which causes current to travel more slowly through the neuron.<ref name=":1" />

== Ribbon synapses ==
[[Ribbon synapse]]s 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.<ref>{{Cite journal|last=Matthews|first=Gary|date=January 2005|title=Structure and function of ribbon synapses|journal=Trends in Neurosciences|volume=28|issue=1|pages=20–29|doi=10.1016/j.tins.2004.11.009|pmid=15626493|s2cid=16576501}}</ref><ref>{{Cite journal|last=Lagnado|first=Leon|date=August 2013|title=Spikes and ribbon synapses in early vision|journal=Trends in Neurosciences|volume=36|issue=8|pages=480–488|doi=10.1016/j.tins.2013.04.006|pmid=23706152|s2cid=28383128}}</ref>

==See also==
*[[Plateau potentials]]
*[[Cable theory]]
*[[Bioelectrochemistry]]
*[[Voltage-gated ion channel]]

==References==
{{Reflist|2}}

==External links==
*[https://www.khanacademy.org/science/biology/human-biology/neuron-nervous-system/v/electrotonic-action%20potential Khan Academy: Electrotonic and action potential] {{Webarchive|url=https://web.archive.org/web/20140702113034/http://www.khanacademy.org/science/biology/human-biology/neuron-nervous-system/v/electrotonic-action%20potential |date=2014-07-02 }}

[[Category:Neurophysiology]]
[[Category:Electrophysiology]]
[[Category:Membrane biology]]
[[Category:Graded potentials]]

Electrotonic potential - Revision history

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