Editing Action potential (section)

==Propagation==
{{Main|Nerve conduction velocity}} <!-- note: factually not a main article, but a stub in need of expansion; perhaps the material below should simply be moved there and a summary left in its place -->

The action potential generated at the axon hillock propagates as a wave along the axon.{{sfn|Bullock|Orkand|Grinnell|1977|pp=160–164}} The currents flowing inwards at a point on the axon during an action potential spread out along the axon, and depolarize the adjacent sections of its membrane. If sufficiently strong, this depolarization provokes a similar action potential at the neighboring membrane patches. This basic mechanism was demonstrated by [[Alan Lloyd Hodgkin]] in 1937. After crushing or cooling nerve segments and thus blocking the action potentials, he showed that an action potential arriving on one side of the block could provoke another action potential on the other, provided that the blocked segment was sufficiently short.<ref group=lower-alpha>{{cite journal | vauthors = Hodgkin AL | title = Evidence for electrical transmission in nerve: Part I | journal = The Journal of Physiology | volume = 90 | issue = 2 | pages = 183–210 | date = July 1937 | pmid = 16994885 | pmc = 1395060 | doi = 10.1113/jphysiol.1937.sp003507 | author-link = Alan Lloyd Hodgkin }}<br />* {{cite journal | vauthors = Hodgkin AL | title = Evidence for electrical transmission in nerve: Part II | journal = The Journal of Physiology | volume = 90 | issue = 2 | pages = 211–32 | date = July 1937 | pmid = 16994886 | pmc = 1395062 | doi = 10.1113/jphysiol.1937.sp003508 | author-link = Alan Lloyd Hodgkin }}</ref>

Once an action potential has occurred at a patch of membrane, the membrane patch needs time to recover before it can fire again. At the molecular level, this ''absolute refractory period'' corresponds to the time required for the voltage-activated sodium channels to recover from inactivation, i.e., to return to their closed state.{{sfn|Stevens|1966|pp=19–20}} There are many types of voltage-activated potassium channels in neurons. Some of them inactivate fast (A-type currents) and some of them inactivate slowly or not inactivate at all; this variability guarantees that there will be always an available source of current for repolarization, even if some of the potassium channels are inactivated because of preceding depolarization. On the other hand, all neuronal voltage-activated sodium channels inactivate within several milliseconds during strong depolarization, thus making following depolarization impossible until a substantial fraction of sodium channels have returned to their closed state. Although it limits the frequency of firing,{{sfn|Stevens|1966|pp=21–23}} the absolute refractory period ensures that the action potential moves in only one direction along an axon.{{sfn|Purves|Augustine|Fitzpatrick|Hall|2008|p=56}} The currents flowing in due to an action potential spread out in both directions along the axon.{{sfn|Bullock|Orkand|Grinnell|1977|pp=161–164}} However, only the unfired part of the axon can respond with an action potential; the part that has just fired is unresponsive until the action potential is safely out of range and cannot restimulate that part. In the usual [[orthodromic conduction]], the action potential propagates from the axon hillock towards the synaptic knobs (the axonal termini); propagation in the opposite direction—known as [[antidromic conduction]]—is very rare.{{sfn|Bullock|Orkand|Grinnell|1977|p=509}} However, if a laboratory axon is stimulated in its middle, both halves of the axon are "fresh", i.e., unfired; then two action potentials will be generated, one traveling towards the axon hillock and the other traveling towards the synaptic knobs.

===Myelin and saltatory conduction===
{{Main|Myelination|Saltatory conduction}}
[[Image:Neuron1.jpg|thumb|In [[saltatory conduction]], an action potential at one [[node of Ranvier]] causes inwards currents that depolarize the membrane at the next node, provoking a new action potential there; the action potential appears to "hop" from node to node.|alt=Axons of neurons are wrapped by several myelin sheaths, which shield the axon from extracellular fluid. There are short gaps between the myelin sheaths known as ''nodes of Ranvier'' where the axon is directly exposed to the surrounding extracellular fluid.]]
To enable fast and efficient transduction of electrical signals in the nervous system, certain neuronal axons are covered with [[myelin]] sheaths. Myelin is a multilamellar membrane that enwraps the axon in segments separated by intervals known as [[nodes of Ranvier]]. It is produced by specialized cells: [[Schwann cell]]s exclusively in the [[peripheral nervous system]], and [[oligodendrocyte]]s exclusively in the [[central nervous system]]. Myelin sheath reduces membrane capacitance and increases membrane resistance in the inter-node intervals, thus allowing a fast, saltatory movement of action potentials from node to node.<ref name=Zalc group=lower-alpha>{{cite book | vauthors = Zalc B | title = Purinergic Signalling in Neuron–Glia Interactions | chapter = The Acquisition of Myelin: A Success Story | journal = Novartis Foundation Symposium | volume = 276 | pages = 15–21; discussion 21–5, 54–7, 275–81 | year = 2006 | pmid = 16805421 | doi = 10.1002/9780470032244.ch3 | isbn = 978-0-470-03224-4 | series = Novartis Foundation Symposia }}</ref><ref name="S. Poliak & E. Peles" group=lower-alpha>{{cite journal | vauthors = Poliak S, Peles E | title = The local differentiation of myelinated axons at nodes of Ranvier | journal = Nature Reviews. Neuroscience | volume = 4 | issue = 12 | pages = 968–80 | date = December 2003 | pmid = 14682359 | doi = 10.1038/nrn1253 | s2cid = 14720760 }}</ref><ref group=lower-alpha>{{cite journal | vauthors = Simons M, Trotter J | title = Wrapping it up: the cell biology of myelination | journal = Current Opinion in Neurobiology | volume = 17 | issue = 5 | pages = 533–40 | date = October 2007 | pmid = 17923405 | doi = 10.1016/j.conb.2007.08.003 | s2cid = 45470194 }}</ref> Myelination is found mainly in [[vertebrate]]s, but an analogous system has been discovered in a few invertebrates, such as some species of [[shrimp]].<ref group=lower-alpha>{{cite journal | vauthors = Xu K, Terakawa S | title = Fenestration nodes and the wide submyelinic space form the basis for the unusually fast impulse conduction of shrimp myelinated axons | journal = The Journal of Experimental Biology | volume = 202 | issue = Pt 15 | pages = 1979–89 | date = August 1999 | doi = 10.1242/jeb.202.15.1979 | pmid = 10395528 | bibcode = 1999JExpB.202.1979X | url = http://jeb.biologists.org/cgi/pmidlookup?view=long&pmid=10395528 }}</ref> Not all neurons in vertebrates are myelinated; for example, axons of the neurons comprising the autonomous nervous system are not, in general, myelinated.

Myelin prevents ions from entering or leaving the axon along myelinated segments. As a general rule, myelination increases the [[conduction velocity]] of action potentials and makes them more energy-efficient. Whether saltatory or not, the mean conduction velocity of an action potential ranges from 1&nbsp;[[Metre per second|meter per second]] (m/s) to over 100&nbsp;m/s, and, in general, increases with axonal diameter.<ref name="hursh_1939" group=lower-alpha>{{cite journal | vauthors = Hursh JB | year = 1939 | title = Conduction velocity and diameter of nerve fibers | journal = American Journal of Physiology | volume = 127 | pages = 131–39| doi = 10.1152/ajplegacy.1939.127.1.131 }}</ref>

Action potentials cannot propagate through the membrane in myelinated segments of the axon. However, the current is carried by the cytoplasm, which is sufficient to depolarize the first or second subsequent [[node of Ranvier]]. Instead, the ionic current from an action potential at one [[node of Ranvier]] provokes another action potential at the next node; this apparent "hopping" of the action potential from node to node is known as [[saltatory conduction]]. Although the mechanism of saltatory conduction was suggested in 1925 by Ralph Lillie,<ref group=lower-alpha>{{cite journal | vauthors = Lillie RS | title = Factors Affecting Transmission and Recovery in the Passive Iron Nerve Model | journal = The Journal of General Physiology | volume = 7 | issue = 4 | pages = 473–507 | date = March 1925 | pmid = 19872151 | pmc = 2140733 | doi = 10.1085/jgp.7.4.473 }} See also {{harvnb|Keynes|Aidley|1991|p=78}}</ref> the first experimental evidence for saltatory conduction came from [[Ichiji Tasaki]]<ref name="tasaki_1939" group=lower-alpha>{{cite journal | vauthors = Tasaki I | year = 1939 | title = Electro-saltatory transmission of nerve impulse and effect of narcosis upon nerve fiber | journal = Am. J. Physiol. | volume = 127 | pages = 211–27| doi = 10.1152/ajplegacy.1939.127.2.211 }}</ref> and Taiji Takeuchi<ref name="tasaki_1941_1942_1959" group=lower-alpha>{{cite journal | vauthors = Tasaki I, Takeuchi T | year = 1941 | title = Der am Ranvierschen Knoten entstehende Aktionsstrom und seine Bedeutung für die Erregungsleitung | journal = Pflügers Archiv für die gesamte Physiologie | volume = 244 | pages = 696–711 | doi = 10.1007/BF01755414 | issue = 6 | s2cid = 8628858 }}<br />* {{cite journal | vauthors = Tasaki I, Takeuchi T | year = 1942 | title = Weitere Studien über den Aktionsstrom der markhaltigen Nervenfaser und über die elektrosaltatorische Übertragung des nervenimpulses | journal = Pflügers Archiv für die gesamte Physiologie | volume = 245 | pages = 764–82 | doi = 10.1007/BF01755237 | issue = 5 | s2cid = 44315437 }}</ref><ref>Tasaki, I in {{harvnb|Field|1959|pp=75–121}}</ref> and from [[Andrew Huxley]] and Robert Stämpfli.<ref name="huxley_staempfli_1949_1951" group=lower-alpha>{{cite journal | vauthors = Huxley AF, Stämpfli R | title = Evidence for saltatory conduction in peripheral myelinated nerve fibres | journal = The Journal of Physiology | volume = 108 | issue = 3 | pages = 315–39 | date = May 1949 | pmid = 16991863 | pmc = 1392492 | doi = 10.1113/jphysiol.1949.sp004335 | author-link1 = Andrew Huxley }}<br />* {{cite journal | vauthors = Huxley AF, Stampfli R | title = Direct determination of membrane resting potential and action potential in single myelinated nerve fibers | journal = The Journal of Physiology | volume = 112 | issue = 3–4 | pages = 476–95 | date = February 1951 | pmid = 14825228 | pmc = 1393015 | doi = 10.1113/jphysiol.1951.sp004545 | author-link1 = Andrew Huxley }}</ref> By contrast, in unmyelinated axons, the action potential provokes another in the membrane immediately adjacent, and moves continuously down the axon like a wave.

[[Image:Conduction velocity and myelination.png|thumb|right|300px|Comparison of the [[conduction velocity|conduction velocities]] of myelinated and unmyelinated [[axon]]s in the [[cat]].{{sfn|Schmidt-Nielsen|1997|loc=Figure 12.13}} The conduction velocity ''v'' of myelinated neurons varies roughly linearly with axon diameter ''d'' (that is, ''v'' ∝ ''d''),<ref name="hursh_1939" group=lower-alpha /> whereas the speed of unmyelinated neurons varies roughly as the square root (''v'' ∝{{radic|''d''}}).<ref name="rushton_1951" group=lower-alpha>{{cite journal | vauthors = Rushton WA | title = A theory of the effects of fibre size in medullated nerve | journal = The Journal of Physiology | volume = 115 | issue = 1 | pages = 101–22 | date = September 1951 | pmid = 14889433 | pmc = 1392008 | doi = 10.1113/jphysiol.1951.sp004655 | author-link = W. A. H. Rushton }}</ref> The red and blue curves are fits of experimental data, whereas the dotted lines are their theoretical extrapolations.|alt=A log-log plot of conduction velocity (m/s) vs axon diameter (μm).]]

Myelin has two important advantages: fast conduction speed and energy efficiency. For axons larger than a minimum diameter (roughly 1 [[micrometre]]), myelination increases the [[conduction velocity]] of an action potential, typically tenfold.<ref name="hartline_2007" group=lower-alpha /> Conversely, for a given conduction velocity, myelinated fibers are smaller than their unmyelinated counterparts. For example, action potentials move at roughly the same speed (25&nbsp;m/s) in a myelinated frog axon and an unmyelinated [[squid giant axon]], but the frog axon has a roughly 30-fold smaller diameter and 1000-fold smaller cross-sectional area. Also, since the ionic currents are confined to the nodes of Ranvier, far fewer ions "leak" across the membrane, saving metabolic energy. This saving is a significant [[natural selection|selective advantage]], since the human nervous system uses approximately 20% of the body's metabolic energy.<ref name="hartline_2007" group=lower-alpha>{{cite journal | vauthors = Hartline DK, Colman DR | title = Rapid conduction and the evolution of giant axons and myelinated fibers | journal = Current Biology | volume = 17 | issue = 1 | pages = R29-35 | date = January 2007 | pmid = 17208176 | doi = 10.1016/j.cub.2006.11.042 | s2cid = 10033356 | doi-access = free | bibcode = 2007CBio...17R..29H }}</ref>

The length of axons' myelinated segments is important to the success of saltatory conduction. They should be as long as possible to maximize the speed of conduction, but not so long that the arriving signal is too weak to provoke an action potential at the next node of Ranvier. In nature, myelinated segments are generally long enough for the passively propagated signal to travel for at least two nodes while retaining enough amplitude to fire an action potential at the second or third node. Thus, the [[safety factor]] of saltatory conduction is high, allowing transmission to bypass nodes in case of injury. However, action potentials may end prematurely in certain places where the safety factor is low, even in unmyelinated neurons; a common example is the branch point of an axon, where it divides into two axons.{{sfn|Bullock|Orkand|Grinnell|1977|p=163}}

Some diseases degrade myelin and impair saltatory conduction, reducing the conduction velocity of action potentials.<ref group=lower-alpha>{{cite journal | vauthors = Miller RH, Mi S | title = Dissecting demyelination | journal = Nature Neuroscience | volume = 10 | issue = 11 | pages = 1351–4 | date = November 2007 | pmid = 17965654 | doi = 10.1038/nn1995 | s2cid = 12441377 }}</ref> The most well-known of these is [[multiple sclerosis]], in which the breakdown of myelin impairs coordinated movement.<ref>Waxman, SG in {{harvnb|Waxman|2007|loc=''Multiple Sclerosis as a Neurodegenerative Disease'', pp. 333–346.}}</ref>

===Cable theory===
{{Main|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|Cable theory's simplified view of a neuronal fiber. The connected [[RC circuit]]s correspond to adjacent segments of a passive [[neurite]]. The extracellular resistances ''r<sub>e</sub>'' (the counterparts of the intracellular resistances ''r<sub>i</sub>'') 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]]<ref name="rall_1989">[[Wilfrid Rall|Rall, W]] in {{harvnb|Koch|Segev|1989|loc=''Cable Theory for Dendritic Neurons'', pp. 9–62.}}</ref> and its elaborations, such as the compartmental model.<ref name="segev_1989">{{cite book | vauthors = Segev I, Fleshman JW, Burke RE | chapter = Compartmental Models of Complex Neurons | title = Methods in Neuronal Modeling: From Synapses to Networks. | veditors = Koch C, Segev I  | editor1-link = Christof Koch | date = 1989 | pages = 63–96 | publisher = The MIT Press | location = Cambridge, Massachusetts | isbn = 978-0-262-11133-1 | lccn = 88008279 | oclc = 18384545 }}</ref> Cable theory was developed in 1855 by [[William Thomson, 1st Baron Kelvin|Lord Kelvin]] to model the transatlantic telegraph cable<ref name="kelvin_1855" group=lower-alpha>{{cite journal | vauthors = Kelvin WT | year = 1855 | title = On the theory of the electric telegraph | journal = Proceedings of the Royal Society | volume = 7 | pages = 382–99 | doi = 10.1098/rspl.1854.0093| s2cid = 178547827 | author-link = William Thomson, 1st Baron Kelvin }}</ref> and was shown to be relevant to neurons by [[Alan Lloyd Hodgkin|Hodgkin]] and [[W. A. H. Rushton|Rushton]] in 1946.<ref name="hodgkin_1946" group=lower-alpha>{{cite journal | vauthors = Hodgkin AL, Rushton WA | title = The electrical constants of a crustacean nerve fibre | journal = Proceedings of the Royal Society of Medicine | volume = 134 | issue = 873 | pages = 444–79 | date = December 1946 | pmid = 20281590 | doi = 10.1098/rspb.1946.0024 | author-link1 = Alan Lloyd Hodgkin | bibcode = 1946RSPSB.133..444H | doi-access = free }}</ref> 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]]<ref name="rall_1989" />

:<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.{{sfn|Purves|Augustine|Fitzpatrick|Hall|2008|pp=52–53}}

:<math>
\tau =\ r_m c_m \,
</math>

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

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 ''r<sub>m</sub>'' and capacitance ''c<sub>m</sub>''. As the capacitance increases, more charge must be transferred to produce a given transmembrane voltage (by [[capacitance|the equation ''Q''&nbsp;=&nbsp;''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 ''r<sub>i</sub>'' 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 ''r<sub>m</sub>'' is increased, that lowers the average "leakage" current across the membrane, likewise causing ''λ'' to become longer, increasing the conduction velocity.