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==动作电位的传播==

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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~~" name=":1~~">{{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 }} * {{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>

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轴丘产生的动作电位像波一样沿轴突传播。动作电位的膜内向电流会沿着轴突扩散，并使邻近的细胞膜去极化。足够强的去极化则会引起邻近的膜片发放类似的动作电位。Alan Lloyd Hodgkin 在 1937 年证明了这种基本的机制。他发现挤压（crushing）或冷却（cooling）神经节段，从而阻断动作电位，而传至阻断部位一侧的动作电位可以引发另一侧的动作电位，只要阻断的节段足够短。<ref name=":1" 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 }} * {{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>

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轴丘产生的动作电位沿轴突传播。当动作电位沿轴突扩散时，电流在轴突上的某一点向内流动，并使其膜的相邻部分去极化。如果足够强的话，这种去极化会在相邻的膜片上激发类似的动作电位。这一基本机制在1937年由艾伦·劳埃德·霍奇金 Alan Lloyd Hodgkin 证明。在挤压或冷却神经节段，从而阻断动作电位后，他表明，动作电位到达阻滞的一侧可以激发另一侧的动作电位，只要阻滞的节段足够短。<ref name=":1" group="lower-alpha" />

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.

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一旦膜片上的一个动作电位发生了，膜片需要时间恢复才能再次激活。在分子水平上，这个绝对不应期相当于电压激活的钠离子通道从失活状态恢复到关闭状态所需的时间。神经元中存在多种类型的电压激活钾通道。其中一些快速失活（A 型电流），一些慢速失活或根本不失活；这种变异性保证了总有可用的电流来源复极化，即使一些钾离子通道由于先前的去极化作用而失活。另一方面，在强去极化过程中，所有神经元电压激活钠通道在几毫秒内失活，从而使去极化不可能发生，直到相当一部分的钠通道恢复到它们的关闭状态。虽然它限制了放电的频率，但绝对不应期电位确保了动作电位沿轴突只向一个方向移动。由于动作电位的作用，电流沿轴突向两个方向扩散。然而，只有轴突未激活的部分才能作出动作电位的反应；刚刚激活的部分是没有反应的，直到动作电位安全地超出范围，不能再次激活该部分。在通常的正向传导中，动作电位从轴丘向突触扣结（轴突终端）传导，向相反方向传导的现象非常罕见。然而，如果一个实验室的轴突在它的中间被刺激，两半的轴突都是“新鲜的”，也就是说，没有被刺激，那么两个动作电位就会产生，一个朝向轴突小丘，另一个朝向突触扣结。

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膜片上一旦发生动作电位，膜片需要时间恢复才能再次激活。在分子水平上，这个绝对不应期相当于电压激活的钠离子通道从失活状态恢复到关闭状态所需的时间。神经元中存在多种类型的电压激活钾通道。其中一些迅速失活（A 型电流），一些缓慢失活或根本不失活；这种变异性保证了总有可用的电流来源复极化，即使一些钾离子通道由于先前的去极化作用而失活。另一方面，在强去极化过程中，所有神经元电压激活钠通道在几毫秒内失活，从而使去极化不可能发生，直到相当一部分的钠通道恢复到它们的关闭状态。虽然它限制了放电的频率，但绝对不应期电位确保了动作电位沿轴突只向一个方向移动。由于动作电位的作用，电流沿轴突向两个方向扩散。然而，只有轴突未激活的部分才能作出动作电位的反应；刚刚激活的部分是没有反应的，直到动作电位安全地超出范围，不能再次激活该部分。在通常的正向传导中，动作电位从轴丘向突触扣结（轴突终端）传导，向相反方向传导的现象非常罕见。然而，如果一个实验室的轴突在它的中间被刺激，两半的轴突都是“新鲜的”，也就是说，没有被刺激，那么两个动作电位就会产生，一个朝向轴突小丘，另一个朝向突触扣结。

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===~~髓鞘和跳跃式传导Myelin and saltatory conduction~~===

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===髓鞘和跳跃式传导===

In order 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 journal | vauthors = Zalc B | title = 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" name=":2">{{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" name=":3">{{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 | 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.

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为了在神经系统中快速有效地传递电信号，某些神经元的轴突上覆盖着髓鞘。髓鞘是一种多层膜，它将轴突包裹在一段段中，这段段间隔被称为郎飞结。它是由专门的细胞产生的：施万细胞专门在周围神经系统，少突胶质细胞专门在中枢神经系统。髓鞘减少膜电容和增加膜电阻在节间间隔，从而允许快速，跳跃性的动作电位从一个节点到另一个节点。<ref name="Zalc" group="lower-alpha" /><ref name="S. Poliak & E. Peles" group="lower-alpha" /><ref name=":2" group="lower-alpha" /> ~~髓鞘形成主要存在于脊椎动物中，但是在一些无脊椎动物中也发现了类似的系统，比如某些种类的虾。~~<ref name=":3" group="lower-alpha" /> ~~脊椎动物中并不是所有的神经元都是有髓神经元；例如，组成自主神经系统的神经元的轴突一般都不是有髓神经元。~~

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为了在神经系统中快速高效地传递电信号，某些神经元的轴突上覆有髓鞘（myelin sheath）。髓鞘是多层膜，它将轴突逐段包裹起来，段的间隔被称为郎飞结。它是由特化专门的细胞产生的：周围神经系统是施万细胞，中央神经系统中是少突胶质细胞。髓鞘减少了膜电容和增加结间段的膜电阻，从而让动作电位在郎飞结之间快速、跳跃式的运动。<ref name="Zalc" group="lower-alpha" /><ref name="S. Poliak & E. Peles" group="lower-alpha" /><ref name=":2" group="lower-alpha" /> 髓鞘形成（myelination）主要存在于脊椎动物中，但是在一些无脊椎动物中也发现了类似的系统，比如某些种类的虾。<ref name=":3" group="lower-alpha" /> 脊椎动物中并不是所有的神经元都是有髓鞘；例如，组成自主神经系统的神经元的轴突一般都没有髓鞘。

髓鞘阻止了离子从髓鞘包裹的轴突部位出入。一般地，髓鞘增加了动作电位的传导速度，使其能效更高。不管是否跳跃，动作电位的平均传导速度范围从 1 米每秒（m/s）到 100 m/s 以上，一般而言，随轴突直径的增大而增大。<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>

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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" name=":4">{{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 }} * {{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 name=":12">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 }} * {{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.

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动作电位不能在有髓鞘的轴突段的膜上传播。不过，电流由细胞质携带的，这足以使后面一两个郎飞结去极化。相反，一个郎飞结的动作电位产生的离子电流在下一个郎飞结引起另一个动作电位；这种从一个结点到另一个结点的动作电位的看似“跳跃”被称为跳跃式传导。虽然跳跃式传导的机制在 1925 年由 Ralph Lillie 提出，<ref name=":4" group="lower-alpha" /> ~~但是参见第一个关于跳跃式传导的实验证据来自~~ Ichiji Tasaki <ref name="tasaki_1939" group="lower-alpha" /> 和 Taiji Takeuchi <ref name="tasaki_1941_1942_1959" group="lower-alpha" /><ref name=":12" /> 以及 Andrew Huxley 和 Robert Stämpflii。<ref name="huxley_staempfli_1949_1951" group="lower-alpha" /> ~~相比之下，在无髓鞘的轴突中，动作电位在紧邻的膜上激发了另一个动作电位，并像波一样不断地沿着轴突移动。~~

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动作电位不能在有髓鞘的轴突段的膜上传播。不过，电流经细胞质传输，足以使后面的一两个郎飞结去极化。就是说，一个郎飞结的动作电位产生的离子电流在下一个郎飞结引起另一个动作电位；动作电位的这种在郎飞结之间看似“跳跃”被称为跳跃式传导。跳跃式传导的机制在 1925 年由 Ralph Lillie 提出，<ref name=":4" group="lower-alpha" /> 但是跳跃式传导的首个实验证据来自 Ichiji Tasaki <ref name="tasaki_1939" group="lower-alpha" /> 和 Taiji Takeuchi <ref name="tasaki_1941_1942_1959" group="lower-alpha" /><ref name=":12" /> 以及 Andrew Huxley 和 Robert Stämpflii。<ref name="huxley_staempfli_1949_1951" group="lower-alpha" /> 相比之下，在无髓鞘的轴突，动作电位在紧邻的膜上激发了另一个动作电位，并像波一样不断地沿着轴突移动。

[[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.

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~~比较猫中髓鞘和无髓鞘轴突s的传导速度。模板：Sfn 髓鞘神经元的传导速度~~ v 与轴突直径 ~~d（即~~ v ∝ ~~d）大致呈线性变化，[~~lower-alpha ~~1] 而无髓鞘神经元的速度大致与平方根（v ∝模板：Radic）一样变化。[下阿尔法2]红色和蓝色曲线是实验数据的拟合，而虚线是它们的理论推断。~~|链接=Special:FilePath/Conduction_velocity_and_myelination.png]]

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猫的有髓鞘和无髓鞘轴突的传导速度的比较。有髓鞘神经元的传导速度 ''v'' 与轴突直径 ''d'' 大致呈线性变化（即 ''v'' ∝ ''d''），<ref name="hursh_1939" group="lower-alpha" /> 而无髓鞘神经元的速度大致与平方根呈线性变化（''v'' ∝{{radic|''d''}}）。<ref name="rushton_1951" group="lower-alpha" /> 红色和蓝色曲线是实验数据的拟合，而虚线是其理论外推。|链接=Special:FilePath/Conduction_velocity_and_myelination.png]]

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 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 }}</ref>

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髓鞘具有两个重要的优点：传导速度快和能量效率高。对于大于最小直径（大约1微米）的轴突，髓鞘形成增加了动作电位的传导速度，通常是原来的十倍.<ref name="hartline_2007" group="lower-alpha" /> ~~Co。相反，相同的传导速度，有髓纤维比无髓纤维小。例如，在有髓青蛙轴突和无髓青蛙轴突中，动作电位的移动速度大致相同（25米~~/~~秒），但是青蛙轴突的直径要小30倍，横截面积要小~~ 1000 倍。此外，离子电流仅限于郎飞结，跨膜“泄漏”的离子要少得多，从而节省了新陈代谢能量。这种节省是一个重大的选择优势，考虑到人类神经系统消耗大约 20% ~~的身体代谢能量。~~<ref name="hartline_2007" group="lower-alpha" />

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髓鞘具有两个重要的优势：传导速度快和能效高。粗于一个最小直径（大约 1 微米）的轴突，髓鞘通常能让动作电位的传导速度增加十倍。<ref name="hartline_2007" group="lower-alpha" /> 反之，相同的传导速度，有髓鞘的神经纤维比无髓的更细。例如，有髓鞘的蛙轴突和无髓鞘的乌贼巨轴突（squid giant axon）的动作电位传导速度大致相同（25 米/秒），但是青蛙的轴突直径要小 30 倍，横截面积要小 1000 倍。此外，因为离子电流被局限于郎飞结，离子的跨膜“泄漏”要少得多，节省了新陈代谢能量。考虑到人类神经系统消耗大约 20% 的身体代谢能量，这种节省有显著的选择优势。<ref name="hartline_2007" group="lower-alpha" />

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}}

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轴突有髓神经节段的长度对跳跃式传导的成功至关重要。它们应该尽可能长，以最大限度地提高传导速度，但不能太长，以至于到达的信号太弱，无法在郎飞结的下一个节点激发动作电位。在自然界中，有髓节段通常足够长，使传播的被动信号传播至少两个节点，同时保持足够的振幅，在第二或第三节点激发动作电位。因此，跳跃式传导的安全系数很高，在受伤的情况下可以通过旁路传播。然而，动作电位可能在安全系数较低的某些地方过早终止，甚至在无髓神经元中也是如此；一个常见的例子是轴突的分支点，在那里它分裂成两个轴突。

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髓鞘包裹的轴突节段的长度对跳跃式传导的成功至关重要。它们应该尽可能长，以最大限度地提高传导速度，但不能太长，以至于传过去的信号太弱，无法在下一个郎飞结触发动作电位。在自然界中，有髓鞘节段通常足够长，使信号被动传播至少两个节点而仍有足够的强度在第二或第三节点触发动作电位。因此，跳跃式传导的安全系数很高，可以绕过损伤的郎飞结继续传播。然而，动作电位可能在安全系数较低的某些地方过早终止，甚至在无髓神经元中也是如此；一个常见的例子是轴突分裂成两个轴突的分支点。

Some diseases degrade myelin and impair saltatory conduction, reducing the conduction velocity of action potentials.<ref group="lower-alpha" name=":5">{{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 name=":13">Waxman, SG in {{harvnb|Waxman|2007|loc=''Multiple Sclerosis as a Neurodegenerative Disease'', pp. 333–346.}}</ref>

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~~有些疾病会降低髓磷脂，损害跳跃式传导，降低动作电位的传导速度.~~<ref name=":5" group="lower-alpha" /> ~~。其中最著名的是多发性硬化症，髓磷脂的破裂妨碍了协调运动t.~~<ref name=":13" />

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有些疾病会降解髓鞘，损害跳跃式传导，降低动作电位的传导速度。<ref name=":5" group="lower-alpha" /> 其中最被人所知的是多发性硬化症（multiple sclerosis），髓鞘的降解削弱协调运动。<ref name=":13" />

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===电缆学说 ~~Cable theory~~===

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===电缆学说===

[[File:Cable theory Neuron RC circuit v3.svg|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 ''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.

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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" />

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轴突内电流的流动可以用电缆理论（cable theory）<ref name="rall_1989" /> ~~及其细致化，如房室模型来定量描述。.~~<ref name="segev_1989" /> ~~电缆理论是在1855年由开尔文勋爵发展起来用来跨大西洋电报电缆的建模~~ <ref name="kelvin_1855" group="lower-alpha" />，并在1946年被 Hodgkin 和 Rushton 证明与神经元很有价值。<ref name="hodgkin_1946" group="lower-alpha" /> 在简单的电缆理论中，神经元被看作是一根完美的电无源圆柱形传输电缆，可以用偏微分方程来描述<ref name="rall_1989" />

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轴突内电流的流动可以用电缆理论（cable theory）<ref name="rall_1989" /> 及其细化理论，如房室模型（compartmental model）来定量描述。<ref name="segev_1989" /> 电缆理论是 1855 年由 Lord Kelvin 发展起来用来对跨大西洋电报电缆进行建模 <ref name="kelvin_1855" group="lower-alpha" />，并在1946年被 Hodgkin 和 Rushton 证明与神经元很有价值。<ref name="hodgkin_1946" group="lower-alpha" /> 在简单的电缆理论中，神经元被看作是一根完美的电无源圆柱形传输电缆，可以用偏微分方程来描述<ref name="rall_1989" />

:<math>

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

</math>

−

~~\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.{{sfn|Purves|Augustine|Fitzpatrick|Hall|2008|pp=52–53}}

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其中 ~~v （x，t）是跨膜电压在时间~~ t 和沿神经元长度的位置 ~~x，其中~~ λ 和 τ ~~是特征性的长度和时间尺度，对刺激的反应电位的衰减。参考右边的电路图，这些比例可以通过单位长度的电阻和电容来确定。~~

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其中 ''V(x'', ''t)'' 是时间 ''t'' 和沿神经元长度的位置 ''x'' 的跨膜电压，其中 λ 和 τ 是特征长度和时间尺度，对刺激的反应电位的衰减。参考右边的电路图，这些比例可以通过单位长度的电阻和电容来确定。

:<math>

\tau =\ r_m c_m \,

</math>

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~~\tau =\ r_m c_m \,~~

:<math>

\lambda = \sqrt \frac{r_m}{r_\ell}

</math>

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~~\lambda = \sqrt \frac{r_m}{r_\ell}~~

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这些时间尺度和长度尺度可以用来理解传导速度与无髓纤维神经元直径的关系。例如，时间尺度 τ 随着膜电阻 rm 和膜电容 cm 的增大而增大。随着电容的增加，必须转移更多的电荷才能产生给定的跨膜电压（用 q = CV 方程式）；随着电阻的增加，每单位时间转移的电荷越少，越慢恢复平衡。同样，如果一个轴突的单位长度 ri 内阻低于另一个轴突（例如，因为前者的半径较大），空间衰减长度 λ 变长，动作电位的传导速度应该增加。如果跨膜电阻 rm 增大，则降低了跨膜平均“泄漏”电流，同样导致 λ 变长，增加了传导速度。

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==Termination 终止==

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==Termination 动作电位的终止==

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===~~Chemical synapses化学突触~~===

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===化学突触===

In general, action potentials that reach the synaptic knobs cause a [[neurotransmitter]] to be released into the synaptic cleft.<ref group="lower-alpha" name=":6">{{cite book | vauthors = Süudhof TC | title = Pharmacology of Neurotransmitter Release | chapter = Neurotransmitter release | volume = 184 | issue = 184 | pages = 1–21 | year = 2008 | pmid = 18064409 | doi = 10.1007/978-3-540-74805-2_1 | isbn = 978-3-540-74804-5 | series = Handbook of Experimental Pharmacology }}</ref> Neurotransmitters are small molecules that may open ion channels in the postsynaptic cell; most axons have the same neurotransmitter at all of their termini. The arrival of the action potential opens voltage-sensitive calcium channels in the presynaptic membrane; the influx of calcium causes [[synaptic vesicle|vesicles]] filled with neurotransmitter to migrate to the cell's surface and [[exocytosis|release their contents]] into the [[synaptic cleft]].<ref group="lower-alpha" name=":7">{{cite journal | vauthors = Rusakov DA | title = Ca2+-dependent mechanisms of presynaptic control at central synapses | journal = The Neuroscientist | volume = 12 | issue = 4 | pages = 317–26 | date = August 2006 | pmid = 16840708 | pmc = 2684670 | doi = 10.1177/1073858405284672 }}</ref> This complex process is inhibited by the [[neurotoxin]]s [[tetanospasmin]] and [[botulinum toxin]], which are responsible for [[tetanus]] and [[botulism]], respectively.<ref group="lower-alpha" name=":8">{{cite journal | vauthors = Humeau Y, Doussau F, Grant NJ, Poulain B | title = How botulinum and tetanus neurotoxins block neurotransmitter release | journal = Biochimie | volume = 82 | issue = 5 | pages = 427–46 | date = May 2000 | pmid = 10865130 | doi = 10.1016/S0300-9084(00)00216-9 }}</ref>

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一般来说，到达突触扣结（synaptic ~~knobs）突触节点的动作电位会使神经递质释放到突触间隙。~~<ref name=":6" group="lower-alpha" /> 神经递质是可以打开突触后细胞离子通道的小分子；大多数轴突在所有末端都有相同的神经递质。动作电位的到来打开了突触前膜上的电压敏感性钙通道，钙的内流导致充满神经递质的囊泡（vesicle）迁移到细胞表面，并将其内容物释放到突触间隙。<ref name=":7" group="lower-alpha" /> ~~破伤风和肉毒杆菌毒素分别引起神经毒素破伤风和肉毒杆菌毒素抑制这一复杂的过程。~~<ref name=":8" group="lower-alpha" />

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一般来说，到达突触扣结（synaptic knobs）的动作电位会使神经递质释放到突触间隙。<ref name=":6" group="lower-alpha" /> 神经递质是可以打开突触后细胞离子通道的小分子；大多数轴突在所有末梢都有同样的神经递质。传至的动作电位打开了突触前膜上的电压敏感性钙通道，钙的内流导致充满神经递质的囊泡（vesicle）迁移到细胞表面，并将其内容物释放到突触间隙。<ref name=":7" group="lower-alpha" /> 引起破伤风（[[tetanus]]）的破伤风痉挛毒素（tetanospasmin）和引起肉毒中毒（ [[botulism]]）的肉毒杆菌毒素（botulinum toxin）等神经毒素会抑制这一复杂的过程。<ref name=":8" group="lower-alpha" />

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~~[[Image:Gap cell junction-en.svg|thumb|right|[[Electrical synapse]]s between excitable cells allow ions to pass directly from one cell to another, and are much faster than [[chemical synapse]]s.~~

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~~兴奋性细胞之间的电突触让离子直接从一个神经元到另一个细胞流动，比化学突触快得多。~~|链接=Special:FilePath/Gap_cell_junction-en.svg]]

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[[Image:Gap cell junction-en.svg|thumb|right|兴奋性细胞之间的电突触让离子从一个细胞直接流到另一个细胞，比化学突触快得多。|链接=Special:FilePath/Gap_cell_junction-en.svg]]

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===~~电突触Electrical synapses~~===

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===电突触===

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~~Some synapses dispense with the~~ "~~middleman~~" ~~of the neurotransmitter, and connect the presynaptic and postsynaptic cells together.<ref~~ group="lower-alpha~~" name=":9~~">{{cite journal | vauthors = Zoidl G, Dermietzel R | title = On the search for the electrical synapse: a glimpse at the future | journal = Cell and Tissue Research | volume = 310 | issue = 2 | pages = 137–42 | date = November 2002 | pmid = 12397368 | doi = 10.1007/s00441-002-0632-x | s2cid = 22414506 }}</ref> When an action potential reaches such a synapse, the ionic currents flowing into the presynaptic cell can cross the barrier of the two cell membranes and enter the postsynaptic cell through pores known as [[connexon]]s.<ref group="lower-alpha~~" name=":10~~">{{cite journal | vauthors = Brink PR, Cronin K, Ramanan SV | title = Gap junctions in excitable cells | journal = Journal of Bioenergetics and Biomembranes | volume = 28 | issue = 4 | pages = 351–8 | date = August 1996 | pmid = 8844332 | doi = 10.1007/BF02110111 | s2cid = 46371790 }}</ref> Thus, the ionic currents of the presynaptic action potential can directly stimulate the postsynaptic cell. Electrical synapses allow for faster transmission because they do not require the slow diffusion of [[neurotransmitter]]s across the synaptic cleft. Hence, electrical synapses are used whenever fast response and coordination of timing are crucial, as in [[escape reflex]]es, the [[retina]] of [[vertebrate]]s, and the [[heart]].

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有些突触不用“中间人”——神经递质，而将突触前细胞和突触后细胞连接起来。<ref name=":9" group="lower-alpha">{{cite journal | vauthors = Zoidl G, Dermietzel R | title = On the search for the electrical synapse: a glimpse at the future | journal = Cell and Tissue Research | volume = 310 | issue = 2 | pages = 137–42 | date = November 2002 | pmid = 12397368 | doi = 10.1007/s00441-002-0632-x | s2cid = 22414506 }}</ref> 当动作电位达到这样的突触时，流入突触前细胞的离子电流可以穿过两个细胞膜的屏障，通过称为连接子（connexon）的孔进入突触后细胞。<ref name=":10" group="lower-alpha">{{cite journal | vauthors = Brink PR, Cronin K, Ramanan SV | title = Gap junctions in excitable cells | journal = Journal of Bioenergetics and Biomembranes | volume = 28 | issue = 4 | pages = 351–8 | date = August 1996 | pmid = 8844332 | doi = 10.1007/BF02110111 | s2cid = 46371790 }}</ref> 因此，突触前动作电位的离子电流可以直接刺激突触后细胞。电突触允许更快的传递，因为它们不需要神经递质在突触间隙中的缓慢扩散。因此，当快速反应和同步性协调非常重要的地方，就会使用电突触，例如在逃跑反射、脊椎动物的视网膜和心脏中。

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有些突触免除了神经递质的“中间人”，而将突触前细胞和突触后细胞连接在一起。<ref name=":9" group="lower-alpha" /> 当一个动作电位达到这样的突触时，流入突触前细胞的离子电流可以穿过两个细胞膜的屏障，通过称为连接子的孔进入突触后细胞。<ref name=":10" group="lower-alpha" /> 因此，突触前动作电位的离子电流可以直接刺激突触后细胞。电突触允许更快的传递，因为它们不需要神经递质在突触间隙中的缓慢扩散。因此，只要快速反应和协调时间是至关重要的，就会使用电突触，例如在逃跑反射、脊椎动物的视网膜和心脏中。

===神经肌肉接头===

A special case of a chemical synapse is the [[neuromuscular junction]], in which the [[axon]] of a [[motor neuron]] terminates on a [[muscle fiber]].<ref group="lower-alpha" name=":11">{{cite journal | vauthors = Hirsch NP | title = Neuromuscular junction in health and disease | journal = British Journal of Anaesthesia | volume = 99 | issue = 1 | pages = 132–8 | date = July 2007 | pmid = 17573397 | doi = 10.1093/bja/aem144 | df = dmy-all | doi-access = free }}</ref> In such cases, the released neurotransmitter is [[acetylcholine]], which binds to the acetylcholine receptor, an integral membrane protein in the membrane （the ''[[sarcolemma]]''） of the muscle fiber.<ref group="lower-alpha" name=":12">{{cite journal | vauthors = Hughes BW, Kusner LL, Kaminski HJ | title = Molecular architecture of the neuromuscular junction | journal = Muscle & Nerve | volume = 33 | issue = 4 | pages = 445–61 | date = April 2006 | pmid = 16228970 | doi = 10.1002/mus.20440 | s2cid = 1888352 }}</ref> However, the acetylcholine does not remain bound; rather, it dissociates and is [[hydrolysis|hydrolyzed]] by the enzyme, [[acetylcholinesterase]], located in the synapse. This enzyme quickly reduces the stimulus to the muscle, which allows the degree and timing of muscular contraction to be regulated delicately. Some poisons inactivate acetylcholinesterase to prevent this control, such as the [[nerve agent]]s [[sarin]] and [[tabun (nerve agent)|tabun]],<ref name=Newmark group=lower-alpha>{{cite journal | vauthors = Newmark J | title = Nerve agents | journal = The Neurologist | volume = 13 | issue = 1 | pages = 20–32 | date = January 2007 | pmid = 17215724 | doi = 10.1097/01.nrl.0000252923.04894.53 | s2cid = 211234081 }}</ref> and the insecticides [[diazinon]] and [[malathion]].<ref group="lower-alpha" name=":13">{{cite journal | vauthors = Costa LG | title = Current issues in organophosphate toxicology | journal = Clinica Chimica Acta; International Journal of Clinical Chemistry | volume = 366 | issue = 1–2 | pages = 1–13 | date = April 2006 | pmid = 16337171 | doi = 10.1016/j.cca.2005.10.008 }}</ref>

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~~突触间隙的一个特例是神经肌肉接点（neuromuscular junction），运动神经元的轴突终止于肌纤维上。~~<ref name=":11" group="lower-alpha" /> ~~在这种情况下，释放出来的神经递质是乙酰胆碱，它结合在肌肉纤维膜（肌膜）上的内在膜蛋白乙酰胆碱受体。~~<ref name=":12" group="lower-alpha" /> 然而，乙酰胆碱并不保持结合状态，而是解离并被位于突触中的乙酰胆碱酯酶水解。这种酶能迅速减少对肌肉的刺激，从而使肌肉收缩的程度和时间得到精细的调节。一些毒药使乙酰胆碱酯酶失活，以阻断这种控制，如神经毒剂沙林（[[sarin]]）和塔崩（tabun），<ref name="Newmark" group="lower-alpha" /> 以及杀虫剂二嗪农（[[diazinon]]）和马拉硫磷（[[malathion]]）。<ref name=":13" group="lower-alpha" />

+

化学突触有个特例，就是运动神经元轴突末梢与肌纤维形成的神经肌肉接点（neuromuscular junction）。<ref name=":11" group="lower-alpha" /> 运动神经元释放神经递质乙酰胆碱（acetylcholine），结合到肌膜（''[[sarcolemma]]''）上的内在膜蛋白乙酰胆碱受体（acetylcholine receptor）。<ref name=":12" group="lower-alpha" /> 不过，乙酰胆碱不会结合状态，而很快解离并被位于突触中的乙酰胆碱酯酶（[[acetylcholinesterase]]）水解。这种酶能迅速减少对肌肉的刺激，从而使肌肉收缩的程度和时间得到精细的调节。一些毒药使乙酰胆碱酯酶失活，以阻断这种控制，如神经毒剂沙林（[[sarin]]）和塔崩（tabun），<ref name="Newmark" group="lower-alpha" /> 以及杀虫剂二嗪农（[[diazinon]]）和马拉硫磷（[[malathion]]）。<ref name=":13" group="lower-alpha" />

==其他细胞类型==

第218行：第208行：

===植物动作电位===

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~~[[Plant cells|Plant]] and [[fungi|fungal cells]]~~<ref name="Slayman_1976" group=lower-alpha>{{cite journal | vauthors = Slayman CL, Long WS, Gradmann D | title = "Action potentials" in Neurospora crassa, a mycelial fungus | journal = Biochimica et Biophysica Acta (BBA) - Biomembranes | volume = 426 | issue = 4 | pages = 732–44 | date = April 1976 | pmid = 130926 | doi = 10.1016/0005-2736(76)90138-3 }}</ref> are also electrically excitable. The fundamental difference from animal action potentials is that the depolarization in plant cells is not accomplished by an uptake of positive sodium ions, but by release of negative ''chloride'' ions.<ref name = "Mummert_1991" group=lower-alpha>{{cite journal | vauthors = Mummert H, Gradmann D | title = Action potentials in Acetabularia: measurement and simulation of voltage-gated fluxes | journal = The Journal of Membrane Biology | volume = 124 | issue = 3 | pages = 265–73 | date = December 1991 | pmid = 1664861 | doi = 10.1007/BF01994359 | s2cid = 22063907 }}</ref><ref name = "Gradmann_2001" group=lower-alpha>{{cite journal | vauthors = Gradmann D | year = 2001 | title = Models for oscillations in plants | journal = Aust. J. Plant Physiol. | volume = 28 | issue = 7 | pages = 577–590 | doi = 10.1071/pp01017}}</ref><ref name="Beilby_2007" group="lower-alpha">{{cite book | vauthors = Beilby MJ | title = Action potential in charophytes | volume = 257 | pages = 43–82 | year = 2007 | pmid = 17280895 | doi = 10.1016/S0074-7696(07)57002-6 | isbn = 978-0-12-373701-4 | series = International Review of Cytology }}</ref> In 1906~~, J~~. C. Bose ~~published the first measurements of action potentials in plants, which had previously been discovered by~~ Burdon-Sanderson ~~and~~ Darwin.<ref name=":14">{{Cite journal|last=Tandon|first=Prakash N|date=2019-07-01|title=Jagdish Chandra Bose and Plant Neurobiology: Part I|url=http://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol54_2_2019__Art05.pdf|journal=Indian Journal of History of Science|volume=54|issue=2|doi=10.16943/ijhs/2019/v54i2/49660|issn=0019-5235|doi-access=free}}</ref> An increase in cytoplasmic calcium ions may be the cause of anion release into the cell. This makes calcium a precursor to ion movements, such as the influx of negative chloride ions and efflux of positive potassium ions, as seen in barley leaves.<ref name=":15">{{cite journal | vauthors = Felle HH, Zimmermann MR | title = Systemic signalling in barley through action potentials | journal = Planta | volume = 226 | issue = 1 | pages = 203–14 | date = June 2007 | pmid = 17226028 | doi = 10.1007/s00425-006-0458-y | s2cid = 5059716 }}</ref>

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植物和真菌细胞<ref name="Slayman_1976" group="lower-alpha">{{cite journal | vauthors = Slayman CL, Long WS, Gradmann D | title = "Action potentials" in Neurospora crassa, a mycelial fungus | journal = Biochimica et Biophysica Acta (BBA) - Biomembranes | volume = 426 | issue = 4 | pages = 732–44 | date = April 1976 | pmid = 130926 | doi = 10.1016/0005-2736(76)90138-3 }}</ref> 也是电兴奋性的。与动物动作电位的根本区别在于，植物细胞的去极化不是通过摄入带正电的钠离子，而是通过释放带负电的氯离子来完成的。<ref name="Mummert_1991" group="lower-alpha">{{cite journal | vauthors = Mummert H, Gradmann D | title = Action potentials in Acetabularia: measurement and simulation of voltage-gated fluxes | journal = The Journal of Membrane Biology | volume = 124 | issue = 3 | pages = 265–73 | date = December 1991 | pmid = 1664861 | doi = 10.1007/BF01994359 | s2cid = 22063907 }}</ref><ref name="Gradmann_2001" group="lower-alpha">{{cite journal | vauthors = Gradmann D | year = 2001 | title = Models for oscillations in plants | journal = Aust. J. Plant Physiol. | volume = 28 | issue = 7 | pages = 577–590 | doi = 10.1071/pp01017}}</ref> 1906 年，J. C. Bose 发表了对先前由 Burdon-Sanderson 和 Darwin 发现的植物动作电位 <ref name=":14">{{Cite journal|last=Tandon|first=Prakash N|date=2019-07-01|title=Jagdish Chandra Bose and Plant Neurobiology: Part I|url=http://insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol54_2_2019__Art05.pdf|journal=Indian Journal of History of Science|volume=54|issue=2|doi=10.16943/ijhs/2019/v54i2/49660|issn=0019-5235|doi-access=free}}</ref> 进行首次测量的结果。细胞质中钙离子的增加可能是阴离子释放进入细胞中的原因。因此，钙是离子移动的前体，比如大麦（barley）叶中负氯离子的内流和正钾离子的外流时。<ref name=":15">{{cite journal | vauthors = Felle HH, Zimmermann MR | title = Systemic signalling in barley through action potentials | journal = Planta | volume = 226 | issue = 1 | pages = 203–14 | date = June 2007 | pmid = 17226028 | doi = 10.1007/s00425-006-0458-y | s2cid = 5059716 }}</ref>

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植物和真菌细胞<ref name="Slayman_1976" group="lower-alpha" /> 也是电兴奋性的。与动物动作电位的根本区别在于，植物细胞的去极化不是通过摄入带正电的钠离子，而是通过释放带负电的氯离子来完成的。<ref name="Mummert_1991" group="lower-alpha" /><ref name="Gradmann_2001" group="lower-alpha" /> 1906 年，J. C. Bose 发表了对先前由 Burdon-Sanderson 和 Darwin 发现的植物动作电位 <ref name=":14" /> 进行了首次测量的结果。细胞质中钙离子的增加可能是阴离子释放进入细胞中的原因。因此，钙可以预测离子运动，比如大麦叶中的负氯离子的内流和正钾离子的外流。<ref name=":15" />

The initial influx of calcium ions also poses a small cellular depolarization, causing the voltage-gated ion channels to open and allowing full depolarization to be propagated by chloride ions.

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~~钙离子的初始注入也产生了一个小的细胞去极化，导致电压门控离子通道打开并允许氯离子传播完全去极化。~~

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钙离子的初始注入也使细胞些许去极化，导致电压门控离子通道打开并让氯离子流动产生完全的去极化。

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~~Some plants （e.g.~~ ''[[Dionaea ~~muscipula]]~~''~~） use sodium-gated channels to operate movements and essentially "count". ''Dionaea muscipula'', also known as the Venus flytrap, is found in subtropical wetlands in North and South Carolina.~~<ref name=":16">{{Cite journal|last=Luken|first=James O. | name-list-style = vanc |date= December 2005 |title=Habitats of Dionaea muscipula (Venus' Fly Trap), Droseraceae, Associated with Carolina Bays|journal=Southeastern Naturalist|language=en|volume=4|issue=4|pages=573–584|doi=10.1656/1528-7092(2005)004[0573:HODMVF]2.0.CO;2|issn=1528-7092}}</ref> ~~When there are poor soil nutrients, the flytrap relies on a diet of insects and animals.~~<ref name=":1">{{cite journal | vauthors = Böhm J, Scherzer S, Krol E, Kreuzer I, von Meyer K, Lorey C, Mueller TD, Shabala L, Monte I, Solano R, Al-Rasheid KA, Rennenberg H, Shabala S, Neher E, Hedrich R | display-authors = 6 | title = The Venus Flytrap Dionaea muscipula Counts Prey-Induced Action Potentials to Induce Sodium Uptake | journal = Current Biology | volume = 26 | issue = 3 | pages = 286–95 | date = February 2016 | pmid = 26804557 | pmc = 4751343 | doi = 10.1016/j.cub.2015.11.057 }}</ref> ~~Despite research on the plant, there lacks an understanding behind the molecular basis to the Venus flytraps, and carnivore plants in general.~~<ref name=":2">{{cite journal | vauthors = Hedrich R, Neher E | title = Venus Flytrap: How an Excitable, Carnivorous Plant Works | journal = Trends in Plant Science | volume = 23 | issue = 3 | pages = 220–234 | date = March 2018 | pmid = 29336976 | doi = 10.1016/j.tplants.2017.12.004 }}</ref>

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一些植物（例如捕蝇草（''Dionaea muscipula，也叫 Venus flytrap''））使用钠门控的通道操作运动，本质上是“计数”。捕蝇草可以在北卡罗来纳州和南卡罗来纳州的亚热带湿地见到。<ref name=":16">{{Cite journal|last=Luken|first=James O. | name-list-style = vanc |date= December 2005 |title=Habitats of Dionaea muscipula (Venus' Fly Trap), Droseraceae, Associated with Carolina Bays|journal=Southeastern Naturalist|language=en|volume=4|issue=4|pages=573–584|doi=10.1656/1528-7092(2005)004[0573:HODMVF]2.0.CO;2|issn=1528-7092}}</ref> 当土壤养分不足时，捕蝇草依靠昆虫和动物为食。<ref name=":1">{{cite journal | vauthors = Böhm J, Scherzer S, Krol E, Kreuzer I, von Meyer K, Lorey C, Mueller TD, Shabala L, Monte I, Solano R, Al-Rasheid KA, Rennenberg H, Shabala S, Neher E, Hedrich R | display-authors = 6 | title = The Venus Flytrap Dionaea muscipula Counts Prey-Induced Action Potentials to Induce Sodium Uptake | journal = Current Biology | volume = 26 | issue = 3 | pages = 286–95 | date = February 2016 | pmid = 26804557 | pmc = 4751343 | doi = 10.1016/j.cub.2015.11.057 }}</ref> 尽管对这种植物进行了研究，但对于捕蝇草以及一般的食肉植物的分子机制还缺乏了解。<ref name=":2">{{cite journal | vauthors = Hedrich R, Neher E | title = Venus Flytrap: How an Excitable, Carnivorous Plant Works | journal = Trends in Plant Science | volume = 23 | issue = 3 | pages = 220–234 | date = March 2018 | pmid = 29336976 | doi = 10.1016/j.tplants.2017.12.004 }}</ref>

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一些植物（例如:。捕蝇草）使用钠门控通道操作运动，本质上是“计数”。捕蝇草，也被称为捕蝇草，发现于北卡罗来纳州和南卡罗来纳州的亚热带湿地。<ref name=":16" /> 当土壤养分不足时，捕蝇草依靠昆虫和动物为食。<ref name=":1" />。尽管对这种植物进行了研究，但对于金星捕蝇草和一般的食肉植物的分子基础还缺乏了解。<ref name=":2" />

+

不过，已经有很多关于捕蝇草的动作电位及其对捕蝇草的运动和机械原理的作用研究。首先，捕蝇草的静息膜电位（-120 mV）低于动物细胞（通常为 -90 mV 至 -40 mV）。<ref name=":2" /><ref name=":17">Purves D, Augustine GJ, Fitzpatrick D, et al., editors. Neuroscience. 2nd edition. Sunderland (MA): Sinauer Associates; 2001. Electrical Potentials Across Nerve Cell Membranes.Available from: <nowiki>https://www.ncbi.nlm.nih.gov/books/NBK11069/</nowiki></ref> 更低的静息电位使得动作电位更容易激发。因此，当一只昆虫落在植物的陷阱上时，它就会触发一个毛发样的机械感受器。<ref name=":2" /> 这个受体激活一个持续约 1.5 毫秒的动作电位。<ref name=":18">{{cite journal | vauthors = Volkov AG, Adesina T, Jovanov E | title = Closing of venus flytrap by electrical stimulation of motor cells | journal = Plant Signaling & Behavior | volume = 2 | issue = 3 | pages = 139–45 | date = May 2007 | pmid = 19516982 | pmc = 2634039 | doi = 10.4161/psb.2.3.4217 }}</ref> 最终，这会导致钙离子进入细胞，使细胞稍微去极化。

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~~However, plenty of research has been done on action potentials and how they affect movement and clockwork within the Venus flytrap. To start, the resting membrane potential of the Venus flytrap （~~-~~120mV） is lower than animal cells （usually~~ -~~90mV to~~ -~~40mV）.~~<ref name=":2" /><ref name=":17">Purves D, Augustine GJ, Fitzpatrick D, et al., editors. Neuroscience. 2nd edition. Sunderland (MA): Sinauer Associates; 2001. Electrical Potentials Across Nerve Cell Membranes.Available from: <nowiki>https://www.ncbi.nlm.nih.gov/books/NBK11069/</nowiki></ref> ~~The lower resting potential makes it easier to activate an action potential. Thus, when an insect lands on the trap of the plant, it triggers a hair-like mechanoreceptor.~~<ref name=":2" /> ~~This receptor then activates an action potential which lasts around~~ 1.5 ~~ms.~~<ref name=":18">{{cite journal | vauthors = Volkov AG, Adesina T, Jovanov E | title = Closing of venus flytrap by electrical stimulation of motor cells | journal = Plant Signaling & Behavior | volume = 2 | issue = 3 | pages = 139–45 | date = May 2007 | pmid = 19516982 | pmc = 2634039 | doi = 10.4161/psb.2.3.4217 }}</ref~~> Ultimately, this causes an increase of positive Calcium ions into the cell, slightly depolarizing it.~~

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然而，已经有很多关于动作电位以及它们如何影响捕蝇草内的运动和钟表的研究。首先，捕蝇草的静息膜电位（- 120mV）低于动物细胞（通常为-90mv 至-40mv）。<ref name=":2" /><ref name=":17" /> 神经细胞膜上的电位。的静息电位可以更容易地激活动作电位。因此，当一只昆虫落在植物的陷阱上时，它就会触发一个毛发样的机械感受器。.<ref name=":2" /> 低这个受体激活一个持续约1.5毫秒的动作电位。<ref name=":18" /> 最终，这会导致钙离子进入细胞，使细胞稍微去极化。

However, the flytrap doesn't close after one trigger. Instead, it requires the activation of 2 or more hairs.<ref name=":1" /><ref name=":2" /> If only one hair is triggered, it throws the activation as a false positive. Further, the second hair must be activated within a certain time interval （0.75 s - 40 s） for it to register with the first activation.<ref name=":2" /> Thus, a buildup of calcium starts and slowly falls from the first trigger. When the second action potential is fired within the time interval, it reaches the Calcium threshold to depolarize the cell, closing the trap on the prey within a fraction of a second.<ref name=":2" />

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~~然而，捕蝇器不会在一次触发后关闭。相反，它需要激活2根或更多的毛发。~~<ref name=":1" /><ref name=":2" /> ~~如果只有一根头发被触发，它就会将这个激活作为一个假阳性而抛出。此外，第二根头发必须在一定的时间间隔（0~~.75 s-40 ~~s）内被激活，才能在第一次激活中注册。~~<ref name=":2" /> 因此，钙的积累开始并且从第一个触发点开始慢慢下降。当第二个动作电位在时间间隔内被激发时，它达到钙阈值使细胞去极化，在几分之一秒内关闭捕获物的陷阱。<ref name=":2" />

+

然而，捕蝇器不会在一次触发后闭合。而是需要激活 2 根或更多的毛。<ref name=":1" /><ref name=":2" /> 如果只有一根毛被触发，这个激活会被视为假阳性。进而，第二根毛必须在一定的时间间隔（0.75 s - 40 s）内被激活，才能将其与第一次激活一起记录。<ref name=":2" /> 因此，钙的积累从第一个触发开始并且然后慢慢下降。当第二个动作电位在时间间隔内被激发时，它达到钙阈值使细胞去极化，在几分之一秒内关闭捕获物的陷阱。<ref name=":2" />

Together with the subsequent release of positive potassium ions the action potential in plants involves an [[osmotic]] loss of salt （KCl）. Whereas, the animal action potential is osmotically neutral because equal amounts of entering sodium and leaving potassium cancel each other osmotically. The interaction of electrical and osmotic relations in plant cells<ref name="Gradmann_1998" group="lower-alpha">{{cite journal | vauthors = Gradmann D, Hoffstadt J | title = Electrocoupling of ion transporters in plants: interaction with internal ion concentrations | journal = The Journal of Membrane Biology | volume = 166 | issue = 1 | pages = 51–9 | date = November 1998 | pmid = 9784585 | doi = 10.1007/s002329900446 | s2cid = 24190001 }}</ref> appears to have arisen from an osmotic function of electrical excitability in a common unicellular ancestors of plants and animals under changing salinity conditions. Further, the present function of rapid signal transmission is seen as a newer accomplishment of [[metazoan]] cells in a more stable osmotic environment.<ref name="Gradmann_1980">

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不同于上升相和峰值，下降相和后超极化似乎主要依赖于不是钙的阳离子。为了启动复极化，细胞需要钾离子通过细胞膜上的被动运输离开细胞。事实上，为了完全再极化，植物细胞需要能量以 ATP 的形式帮助细胞释放氢-利用一种通常被称为 H+-ATPase 酶的转运蛋白。<ref name="Opritov" /><ref name=":2" />

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==~~Taxonomic distribution and evolutionary advantages~~ 分类学分布和进化优势==

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==分类学分布和进化优势==

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~~Action potentials are found throughout [[multicellular organism]]s, including [[plant]]s, [[invertebrate]]s such as [[insect]]s, and [[vertebrate]]s such as [[reptile]]s and [[mammal]]s.~~<ref name="Fromm" group="lower-alpha">{{cite journal | vauthors = Fromm J, Lautner S | title = Electrical signals and their physiological significance in plants | journal = Plant, Cell & Environment | volume = 30 | issue = 3 | pages = 249–257 | date = March 2007 | pmid = 17263772 | doi = 10.1111/j.1365-3040.2006.01614.x }}</ref> [[Sponge]]s seem to be the main [[phylum]] of multicellular [[eukaryote]]s that does not transmit action potentials, although some studies have suggested that these organisms have a form of electrical signaling, too.<ref group="lower-alpha~~" name=":15~~">{{cite journal | vauthors = Leys SP, Mackie GO, Meech RW | title = Impulse conduction in a sponge | journal = The Journal of Experimental Biology | volume = 202 (Pt 9) | issue = 9 | pages = 1139–50 | date = May 1999 | doi = 10.1242/jeb.202.9.1139 | pmid = 10101111 | url = http://jeb.biologists.org/cgi/pmidlookup?view=long&pmid=10101111 }}</ref> The resting potential, as well as the size and duration of the action potential, have not varied much with evolution, although the [[conduction velocity]] does vary dramatically with axonal diameter and myelination.

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多细胞生物，包括植物、昆虫等无脊椎动物、爬行动物和哺乳动物等脊椎动物都存在动作电位。<ref name="Fromm" group="lower-alpha">{{cite journal | vauthors = Fromm J, Lautner S | title = Electrical signals and their physiological significance in plants | journal = Plant, Cell & Environment | volume = 30 | issue = 3 | pages = 249–257 | date = March 2007 | pmid = 17263772 | doi = 10.1111/j.1365-3040.2006.01614.x }}</ref> 海绵似乎是没有动作电位传递的主要多细胞真核生物门类，尽管一些研究表明这些生物也有一种电信号的形式。<ref name=":15" group="lower-alpha">{{cite journal | vauthors = Leys SP, Mackie GO, Meech RW | title = Impulse conduction in a sponge | journal = The Journal of Experimental Biology | volume = 202 (Pt 9) | issue = 9 | pages = 1139–50 | date = May 1999 | doi = 10.1242/jeb.202.9.1139 | pmid = 10101111 | url = http://jeb.biologists.org/cgi/pmidlookup?view=long&pmid=10101111 }}</ref> 尽管神经传导速率随轴突直径和髓鞘形成而发生显著变化，但静息电位、动作电位的大小和持续时间并没有随着进化而发生很大变化。

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在多细胞生物，包括植物、无脊椎动物如昆虫和脊椎动物如爬行动物和哺乳动物中发现了动作电位。<ref name="Fromm" group="lower-alpha" /> 海绵似乎是不传递动作电位的多细胞真核生物的主要门类，尽管一些研究表明这些生物也有一种电信号的形式。<ref name=":15" group="lower-alpha" /> 虽然神经传导速度随轴突直径和髓鞘形成而发生显著变化，但神经静息电位和动作电位的大小和持续时间并没有随着进化而发生很大变化。

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~~{| class="wikitable" id="action_potential_texonomic_comparison" border="2" cellpadding="5" cellspacing="1" align="center"~~

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~~|+Comparison of action potentials （APs） from a representative cross-section of animals{{sfn|Bullock|Horridge|1965}}~~

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~~! Animal !! Cell type !! Resting potential （mV） !! AP increase （mV） !! AP duration （ms） !! Conduction speed （m/s）~~

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|-

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~~| Squid （''Loligo''） || Giant axon || −60 || 120 || 0.75 || 35~~

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|-

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~~| Earthworm （''Lumbricus''） || Median giant fiber || −70 || 100 || 1.0 || 30~~

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|-

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~~| Cockroach （''Periplaneta''） || Giant fiber || −70 || 80–104 || 0.4 || 10~~

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|-

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~~| Frog （''Rana''） || Sciatic nerve axon || −60 to −80 || 110–130 || 1.0 || 7–30~~

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|-

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~~| Cat （''Felis''） || Spinal motor neuron || −55 to −80 || 80–110 || 1–1.5 || 30–120~~

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|}

{| class="wikitable" id="action_potential_texonomic_comparison" border="2" cellpadding="5" cellspacing="1" align="center"

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|+~~Comparison of action potentials （APs） from a representative cross-section of animals动物的代表性横切的动作电位的比较~~

+

|+代表性动物的动作电位（AP）的比较

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! ~~Animal~~ !! ~~Cell type~~ !! ~~Resting potential （mV）~~ !! AP ~~increase （mV）~~ !! AP ~~duration~~ （ms） !! ~~Conduction speed~~ （m/s）

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! 动物 !! 细胞类型 !! 静息电位（mV） !! AP 增量（mV） !! AP 持续时间（ms） !! 传导速率（m/s）

|-

−

| ~~Squid （Loligo）~~ || ~~Giant axon~~ || −60 || 120 || 0.75 || 35

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| 乌贼 || 巨大轴突 || −60 || 120 || 0.75 || 35

|-

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| ~~Earthworm （Lumbricus）~~ || ~~Median giant fiber~~ || −70 || 100 || 1.0 || 30

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| 蚯蚓 || 中间大神经纤维 || −70 || 100 || 1.0 || 30

|-

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| ~~Cockroach （Periplaneta）~~ || ~~Giant fiber~~ || −70 || 80–104 || 0.4 || 10

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| 蟑螂 || 大神经纤维 || −70 || 80–104 || 0.4 || 10

|-

−

| ~~Frog （Rana）~~ || ~~Sciatic nerve axon~~ || −60 to −80 || 110–130 || 1.0 || 7–30

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| 蛙 || 坐骨神经轴突 || −60 to −80 || 110–130 || 1.0 || 7–30

|-

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| ~~Cat （Felis）~~ || ~~Spinal motor neuron~~ || −55 to −80 || 80–110 || 1–1.5 || 30–120

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| 猫 || 脊髓运动神经元 || −55 to −80 || 80–110 || 1–1.5 || 30–120

|}

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Given its conservation throughout evolution, the action potential seems to confer evolutionary advantages. One function of action potentials is rapid, long-range signaling within the organism; the conduction velocity can exceed 110 m/s, which is one-third the [[speed of sound]]. For comparison, a hormone molecule carried in the bloodstream moves at roughly 8 m/s in large arteries. Part of this function is the tight coordination of mechanical events, such as the contraction of the heart. A second function is the computation associated with its generation. Being an all-or-none signal that does not decay with transmission distance, the action potential has similar advantages to [[digital electronics]]. The integration of various dendritic signals at the axon hillock and its thresholding to form a complex train of action potentials is another form of computation, one that has been exploited biologically to form [[central pattern generator]]s and mimicked in [[artificial neural network]]s.

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~~鉴于动作电位在整个进化过程中的保守性，它似乎赋予了进化优势。动作电位的一个功能是在生物体内快速的远程信号传导，传导速度可以超过110米~~/秒，这是声速的三分之一。相比之下，血液中携带的荷尔蒙分子在大动脉中的运动速度大约为每秒8米。这个功能的一部分是机械事件的紧密协调，例如心脏的收缩。第二个功能是与其生成相关的计算。动作电位作为一种全或无信号，不随传输距离衰减，与数字电子技术具有相似的优点。轴突小丘上各种树突信号的整合及其阈值化形成一系列复杂的动作电位是另一种形式的计算方法，这种方法已被生物学方法用来形成中心模式发生器，并在人工神经网络中进行模拟。

+

鉴于动作电位在整个进化过程中的保守性，它似乎赋予生物某些进化优势。动作电位的一个功能是在生物体内快速的远距离信号传导，传导速率可逾 110 米/秒，即声速的三分之一。相比之下，血液携带的激素分子在大动脉中的运动速度约为 8 米/秒。一个功能是对力学活动，例如心脏的收缩，进行严格的协调。第二个功能是产生动作电位相关的计算。动作电位作为一种全或无信号，不随传输距离衰减，与数字电子技术具有相似的优点。轴丘上各种树突信号的整合及其阈值化形成一系列复杂的动作电位是另一种形式的计算方法，在生物中用来形成中央模式发生器，并在人工神经网络中进行模拟。

The common prokaryotic/eukaryotic ancestor, which lived perhaps four billion years ago, is believed to have had voltage-gated channels. This functionality was likely, at some later point, cross-purposed to provide a communication mechanism. Even modern single-celled bacteria can utilize action potentials to communicate with other bacteria in the same biofilm.<ref name=":19">{{cite journal | vauthors = Kristan WB | title = Early evolution of neurons | journal = Current Biology | volume = 26 | issue = 20 | pages = R949–R954 | date = October 2016 | pmid = 27780067 | doi = 10.1016/j.cub.2016.05.030 | doi-access = free }}</ref>

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生活在大约 40 亿年前的原核/真核生物的共同祖先，被认为具有电压门控通道。在以后的某个时候，这个功能可能会被用来提供一个通信机制。即使是现代的单细胞细菌也可以利用动作电位与生物膜中的其他细菌进行交流。<ref name=":19" />

+

生活在大约 40 亿年前的原核/真核生物的共同祖先，被认为具有电压门控通道。在以后的某个时候，这个功能可能会被用来提供一个通信机制。即使是现代的单细胞细菌也可以利用动作电位与生物膜（biofilm）中的其他细菌进行交流。<ref name=":19" />

==实验方法==

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The study of action potentials has required the development of new experimental methods. The initial work, prior to 1955, was carried out primarily by [[Alan Lloyd Hodgkin]] and [[Andrew Fielding Huxley]], who were, along [[John Carew Eccles]], awarded the 1963 [[Nobel Prize in Physiology or Medicine]] for their contribution to the description of the ionic basis of nerve conduction. It focused on three goals: isolating signals from single neurons or axons, developing fast, sensitive electronics, and shrinking [[electrode]]s enough that the voltage inside a single cell could be recorded.

−

动作电位的研究需要开发新的实验方法。在 1955 ~~年之前，最初的工作主要是由艾伦·劳埃德·霍奇金和~~ Andrew Fielding Huxley ~~完成的，他们因为在描述神经传导的离子基础方面做出的贡献，和约翰·卡鲁·埃克尔斯一起被授予~~ 1963 年诺贝尔生理学或医学奖。它着重于三个目标：从单个神经元或轴突中分离出信号，发展快速、灵敏的电子设备，以及缩小电极，使单个细胞内的电压能够被记录下来。

+

动作电位的研究需要开发新的实验方法。在 1955 年之前最初的工作主要是由 [[Alan Lloyd Hodgkin]] 和 Andrew Fielding Huxley 完成的，他们因为在描述神经传导的离子基础方面做出的贡献，和 [[John Carew Eccles]] 一起被授予 1963 年诺贝尔生理学或医学奖。它聚焦于三个目标：从单个神经元或轴突中分离出信号，发展快速、灵敏的电子设备，以及缩小电极，使单个细胞内的电压能够被记录下来。

The first problem was solved by studying the [[Squid giant axon|giant axons]] found in the neurons of the [[squid]] （''[[Loligo forbesii]]'' and ''[[Doryteuthis pealeii]]'', at the time classified as ''Loligo pealeii''）.<ref name="keynes_1989" group="lower-alpha">{{cite journal | vauthors = Keynes RD | title = The role of giant axons in studies of the nerve impulse | journal = BioEssays | volume = 10 | issue = 2–3 | pages = 90–3 | year = 1989 | pmid = 2541698 | doi = 10.1002/bies.950100213 }}</ref> These axons are so large in diameter （roughly 1 mm, or 100-fold larger than a typical neuron） that they can be seen with the naked eye, making them easy to extract and manipulate.<ref name="hodgkin_1952" group="lower-alpha" /><ref name="Meunier" group="lower-alpha">{{cite journal | vauthors = Meunier C, Segev I | title = Playing the devil's advocate: is the Hodgkin-Huxley model useful? | journal = Trends in Neurosciences | volume = 25 | issue = 11 | pages = 558–63 | date = November 2002 | pmid = 12392930 | doi = 10.1016/S0166-2236(02)02278-6 | s2cid = 1355280 }}</ref> However, they are not representative of all excitable cells, and numerous other systems with action potentials have been studied.

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The second problem was addressed with the crucial development of the [[voltage clamp]],<ref name="cole_1949" group="lower-alpha">{{cite journal | vauthors = Cole KS | year = 1949 | title = Dynamic electrical characteristics of the squid axon membrane | journal = Arch. Sci. Physiol. | volume = 3 | pages = 253–8| author-link = Kenneth Stewart Cole }}</ref> which permitted experimenters to study the ionic currents underlying an action potential in isolation, and eliminated a key source of [[electronic noise]], the current ''IC'' associated with the [[capacitance]] ''C'' of the membrane.{{sfn|Junge|1981|pp=63–82}} Since the current equals ''C'' times the rate of change of the transmembrane voltage ''Vm'', the solution was to design a circuit that kept ''Vm'' fixed （zero rate of change） regardless of the currents flowing across the membrane. Thus, the current required to keep ''Vm'' at a fixed value is a direct reflection of the current flowing through the membrane. Other electronic advances included the use of [[Faraday cage]]s and electronics with high [[input impedance]], so that the measurement itself did not affect the voltage being measured.{{sfn|Kettenmann|Grantyn|1992}}

−

~~第二个问题是关于电压钳,~~<ref name="cole_1949" group="lower-alpha" /> ~~的关键发展，它允许实验者在分离的情况下研究作用于动作电位的离子电流，并消除了电子噪声的一个关键来源---- 与膜电容 c~~''C'' ~~相关的电流~~ ''IC'' ~~IC。由于电流等于~~''C'' c 乘以跨膜电压 ''Vm'' 的变化率，所以解决方案是设计一个电路，使 ''Vm'' 保持固定（零变化率），而不管跨膜电流的变化。因此，使 ''Vm'' Vm 保持在一个固定值所需的电流是流过薄膜的电流的直接反射。其他电子方面的进步包括使用法拉第笼和具有高输入阻抗的电子器件，这样测量本身就不会影响被测量的电压。

+

第二个问题由于电压钳<ref name="cole_1949" group="lower-alpha" /> 的重要发展解决，让实验人员可以研究单个实验者研究单独的动作电位的离子电流，并消除了电子噪声的主要根源——与膜电容 ''C'' 关联的电流 ''IC''。由于电流等于''C'' c 乘以跨膜电压 ''Vm'' 的变化率，所以解决方案是设计一个电路，使 ''Vm'' 保持固定（零变化率），而不管跨膜电流的变化。因此，使 ''Vm'' Vm 保持在一个固定值所需的电流是流过薄膜的电流的直接反射。其他电子方面的进步包括使用法拉第笼和具有高输入阻抗的电子器件，这样测量本身就不会影响被测量的电压。

The third problem, that of obtaining electrodes small enough to record voltages within a single axon without perturbing it, was solved in 1949 with the invention of the glass micropipette electrode,<ref name="ling_1949" group="lower-alpha">{{cite journal | vauthors = Ling G, Gerard RW | title = The normal membrane potential of frog sartorius fibers | journal = Journal of Cellular and Comparative Physiology | volume = 34 | issue = 3 | pages = 383–96 | date = December 1949 | pmid = 15410483 | doi = 10.1002/jcp.1030340304 }}</ref> which was quickly adopted by other researchers.<ref name="nastuk_1950" group="lower-alpha">{{cite journal | vauthors = Nastuk WL, Hodgkin A | year = 1950 | title = The electrical activity of single muscle fibers | journal = Journal of Cellular and Comparative Physiology | volume = 35 | pages = 39–73 | doi = 10.1002/jcp.1030350105 }}</ref><ref name="brock_1952" group="lower-alpha">{{cite journal | vauthors = Brock LG, Coombs JS, Eccles JC | title = The recording of potentials from motoneurones with an intracellular electrode | journal = The Journal of Physiology | volume = 117 | issue = 4 | pages = 431–60 | date = August 1952 | pmid = 12991232 | pmc = 1392415 | doi = 10.1113/jphysiol.1952.sp004759 }}</ref> Refinements of this method are able to produce electrode tips that are as fine as 100 [[Ångström|Å]] （10 [[nanometre|nm]]）, which also confers high input impedance.<ref name=":20">Snell, FM in {{harvnb|Lavallée|Schanne|Hébert|1969|loc=''Some Electrical Properties of Fine-Tipped Pipette Microelectrodes''.}}</ref> Action potentials may also be recorded with small metal electrodes placed just next to a neuron, with [[neurochip]]s containing [[EOSFET]]s, or optically with dyes that are [[Calcium imaging|sensitive to Ca2+]] or to voltage.<ref name="dyes" group="lower-alpha">{{cite journal | vauthors = Ross WN, Salzberg BM, Cohen LB, Davila HV | title = A large change in dye absorption during the action potential | journal = Biophysical Journal | volume = 14 | issue = 12 | pages = 983–6 | date = December 1974 | pmid = 4429774 | pmc = 1334592 | doi = 10.1016/S0006-3495(74)85963-1 | bibcode = 1974BpJ....14..983R }} * {{cite journal | vauthors = Grynkiewicz G, Poenie M, Tsien RY | title = A new generation of Ca2+ indicators with greatly improved fluorescence properties | journal = The Journal of Biological Chemistry | volume = 260 | issue = 6 | pages = 3440–50 | date = March 1985 | doi = 10.1016/S0021-9258(19)83641-4 | pmid = 3838314 | doi-access = free }}</ref>

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~~第三个问题是如何获得足够小的电极来记录单个轴突内的电压而不对其造成干扰，这个问题在1949年由于玻璃微移液管电极，~~<ref name="ling_1949" group="lower-alpha" /> 的发明而得到解决，并且很快被其他研究人员采用。<ref name="nastuk_1950" group="lower-alpha" /><ref name="brock_1952" group="lower-alpha" /> ~~这种方法的改进可以生产出100纳米的电极尖端，同时也提供了高的输入阻抗。~~<ref name=":20" /> ~~动作电位中的 Snell 和 FM 也可以用放置在神经元旁的小金属电极记录下来，用含有th [[neurochip]]s containing~~ [[EOSFET]]s ~~eosfet~~ 的神经芯片，或者用对 Ca2+ 或电压敏感的染料记录下来。<ref name="dyes" group="lower-alpha" />

+

第三个问题是如何获得足够小的电极来记录单个轴突内的电压而不对其造成干扰，这个问题在1949年由于玻璃微电极<ref name="ling_1949" group="lower-alpha" /> 的发明而得到解决，并且很快被其他研究人员采用。<ref name="nastuk_1950" group="lower-alpha" /><ref name="brock_1952" group="lower-alpha" /> 这种方法的改进可以生产出 [[Ångström|Å]] （10 [[nanometre|nm]]）100 纳米的电极尖端，同时也提供了高的输入阻抗。<ref name=":20" /> 动作电位也可以用放置在神经元旁的小金属电极记录下来，用含有 [[EOSFET]]s 的神经芯片，或者用对 Ca2+ 或电压敏感的染料记录下来。<ref name="dyes" group="lower-alpha" />

[[Image:Single channel.png|thumb|left|As revealed by a [[patch clamp]] electrode, an [[ion channel]] has two states: open （high conductance） and closed （low conductance）.

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==神经毒素==

−

[[Image:Puffer Fish DSC01257.JPG|thumb|right|~~[[Tetrodotoxin]] is a lethal toxin found in [[pufferfish]] that inhibits the [[voltage-gated ion channel|voltage-sensitive sodium channel]], halting action potentials.~~|链接=Special:FilePath/Puffer_Fish_DSC01257.JPG]]

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[[Image:Puffer Fish DSC01257.JPG|thumb|right|河豚中的河豚毒素是一种致命的毒素，其抑制电压敏感性钠通道，阻止动作电位|链接=Special:FilePath/Puffer_Fish_DSC01257.JPG]]

Several [[neurotoxin]]s, both natural and synthetic, are designed to block the action potential. [[Tetrodotoxin]] from the [[pufferfish]] and [[saxitoxin]] from the ''[[Gonyaulax]]'' （the [[dinoflagellate]] genus responsible for "[[Paralytic shellfish poisoning|red tide]]s"） block action potentials by inhibiting the voltage-sensitive sodium channel;<ref name="TTX_refs" group="lower-alpha">{{cite journal | vauthors = Milligan JV, Edwards C | title = Some factors affecting the time course of the recovery of contracture ability following a potassium contracture in frog striated muscle | journal = The Journal of General Physiology | volume = 48 | issue = 6 | pages = 975–83 | date = July 1965 | pmid = 5855511 | pmc = 2195447 | doi = 10.1085/jgp.48.6.975 }} * {{cite book | vauthors = Ritchie JM, Rogart RB | title = Reviews of Physiology, Biochemistry and Pharmacology, Volume 79 | chapter = The binding of saxitoxin and tetrodotoxin to excitable tissue | volume = 79 | pages = 1–50 | year = 1977 | pmid = 335473 | doi = 10.1007/BFb0037088 | isbn = 0-387-08326-X | series = Reviews of Physiology, Biochemistry and Pharmacology }} * {{cite journal | vauthors = Keynes RD, Ritchie JM | title = On the binding of labelled saxitoxin to the squid giant axon | journal = Proceedings of the Royal Society of London. Series B, Biological Sciences | volume = 222 | issue = 1227 | pages = 147–53 | date = August 1984 | pmid = 6148754 | doi = 10.1098/rspb.1984.0055 | bibcode = 1984RSPSB.222..147K | s2cid = 11465181 }}</ref> similarly, [[dendrotoxin]] from the [[mamba|black mamba]] snake inhibits the voltage-sensitive potassium channel. Such inhibitors of ion channels serve an important research purpose, by allowing scientists to "turn off" specific channels at will, thus isolating the other channels' contributions; they can also be useful in purifying ion channels by [[affinity chromatography]] or in assaying their concentration. However, such inhibitors also make effective neurotoxins, and have been considered for use as [[Chemical warfare|chemical weapon]]s. Neurotoxins aimed at the ion channels of insects have been effective [[insecticide]]s; one example is the synthetic [[permethrin]], which prolongs the activation of the sodium channels involved in action potentials. The ion channels of insects are sufficiently different from their human counterparts that there are few side effects in humans.

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[[Image:3b8e.png|thumb|right|[[Ribbon diagram]] of the sodium–potassium pump in its E2-Pi state. The estimated boundaries of the [[lipid bilayer]] are shown as blue （intracellular） and red （extracellular） planes.

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~~钠钾泵在其E2~~-~~Pi状态下的带状图。脂质双层的估计边界显示为蓝色（细胞内）和红色（细胞外）平面。~~|链接=Special:FilePath/3b8e.png]]

+

钠钾泵在其 E2-Pi 状态下的带状图（[[Ribbon diagram]]）。脂质双层的估计边界显示为蓝色（细胞内）和红色（细胞外）平面。|链接=Special:FilePath/3b8e.png]]

The 20th century was a significant era for electrophysiology. In 1902 and again in 1912, [[Julius Bernstein]] advanced the hypothesis that the action potential resulted from a change in the [[permeation|permeability]] of the axonal membrane to ions.<ref name="bernstein_1902_1912" group="lower-alpha">{{cite journal | vauthors = Bernstein J | year = 1902 | title = Untersuchungen zur Thermodynamik der bioelektrischen Ströme | journal = Pflügers Archiv für die gesamte Physiologie | volume = 92 | pages = 521–562 | doi = 10.1007/BF01790181 | issue = 10–12| s2cid = 33229139 | author-link = Julius Bernstein | url = https://zenodo.org/record/2192363 }}</ref>{{sfn|Bernstein|1912}} Bernstein's hypothesis was confirmed by [[Kenneth Stewart Cole|Ken Cole]] and Howard Curtis, who showed that membrane conductance increases during an action potential.<ref group="lower-alpha" name=":16">{{cite journal | vauthors = Cole KS, Curtis HJ | title = Electric Impedance of the Squid Giant Axon During Activity | journal = The Journal of General Physiology | volume = 22 | issue = 5 | pages = 649–70 | date = May 1939 | pmid = 19873125 | pmc = 2142006 | doi = 10.1085/jgp.22.5.649 | author-link1 = Kenneth Stewart Cole }}</ref> In 1907, [[Louis Lapicque]] suggested that the action potential was generated as a threshold was crossed,<ref group="lower-alpha" name=":17">{{cite journal | vauthors = Lapicque L | year = 1907 | title = Recherches quantitatives sur l'excitationelectrique des nerfs traitee comme une polarisation | journal = J. Physiol. Pathol. Gen | volume = 9| pages = 620–635 }}</ref> what would be later shown as a product of the [[dynamical system]]s of ionic conductances. In 1949, [[Alan Lloyd Hodgkin|Alan Hodgkin]] and [[Bernard Katz]] refined Bernstein's hypothesis by considering that the axonal membrane might have different permeabilities to different ions; in particular, they demonstrated the crucial role of the sodium permeability for the action potential.<ref name="hodgkin_1949" group="lower-alpha">{{cite journal | vauthors = Hodgkin AL, Katz B | title = The effect of sodium ions on the electrical activity of giant axon of the squid | journal = The Journal of Physiology | volume = 108 | issue = 1 | pages = 37–77 | date = March 1949 | pmid = 18128147 | pmc = 1392331 | doi = 10.1113/jphysiol.1949.sp004310 | author-link1 = Alan Lloyd Hodgkin | author-link2 = Bernard Katz }}</ref> They made the first actual recording of the electrical changes across the neuronal membrane that mediate the action potential.<ref group="lower-Greek" name=":0">{{cite journal |last=Warlow|first=Charles| name-list-style = vanc |title=The Recent Evolution of a Symbiotic Ion Channel in the Legume Family Altered Ion Conductance and Improved Functionality in Calcium Signaling|journal=Practical Neurology|volume=7|issue=3|pages=192–197|url=http://pn.bmj.com/content/7/3/192.full|publisher=BMJ Publishing Group|access-date=23 March 2013|url-status=live|archive-url=https://web.archive.org/web/20120314104408/http://pn.bmj.com/content/7/3/192.full|archive-date=14 March 2012|df=dmy-all|date=June 2007}}</ref> This line of research culminated in the five 1952 papers of Hodgkin, Katz and [[Andrew Huxley]], in which they applied the [[voltage clamp]] technique to determine the dependence of the axonal membrane's permeabilities to sodium and potassium ions on voltage and time, from which they were able to reconstruct the action potential quantitatively.<ref name="hodgkin_1952" group="lower-alpha" /> Hodgkin and Huxley correlated the properties of their mathematical model with discrete [[ion channel]]s that could exist in several different states, including "open", "closed", and "inactivated". Their hypotheses were confirmed in the mid-1970s and 1980s by [[Erwin Neher]] and [[Bert Sakmann]], who developed the technique of [[patch clamp]]ing to examine the conductance states of individual ion channels.<ref name="patch_clamp" group="lower-alpha">{{cite journal | vauthors = Neher E, Sakmann B | title = Single-channel currents recorded from membrane of denervated frog muscle fibres | journal = Nature | volume = 260 | issue = 5554 | pages = 799–802 | date = April 1976 | pmid = 1083489 | doi = 10.1038/260799a0 | author-link1 = Erwin Neher | bibcode = 1976Natur.260..799N | s2cid = 4204985 }} * {{cite journal | vauthors = Hamill OP, Marty A, Neher E, Sakmann B, Sigworth FJ | title = Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches | journal = Pflügers Archiv | volume = 391 | issue = 2 | pages = 85–100 | date = August 1981 | pmid = 6270629 | doi = 10.1007/BF00656997 | s2cid = 12014433 }} * {{cite journal | vauthors = Neher E, Sakmann B | title = The patch clamp technique | journal = Scientific American | volume = 266 | issue = 3 | pages = 44–51 | date = March 1992 | pmid = 1374932 | doi = 10.1038/scientificamerican0392-44 | author-link1 = Erwin Neher | bibcode = 1992SciAm.266c..44N }}</ref> In the 21st century, researchers are beginning to understand the structural basis for these conductance states and for the selectivity of channels for their species of ion,<ref name="yellen_2002" group="lower-alpha">{{cite journal | vauthors = Yellen G | title = The voltage-gated potassium channels and their relatives | journal = Nature | volume = 419 | issue = 6902 | pages = 35–42 | date = September 2002 | pmid = 12214225 | doi = 10.1038/nature00978 | bibcode = 2002Natur.419...35Y | s2cid = 4420877 }}</ref> through the atomic-resolution [[X-ray crystallography|crystal structures]],<ref name="doyle_1998" group="lower-alpha">{{cite journal | vauthors = Doyle DA, Morais Cabral J, Pfuetzner RA, Kuo A, Gulbis JM, Cohen SL, Chait BT, MacKinnon R | display-authors = 6 | title = The structure of the potassium channel: molecular basis of K+ conduction and selectivity | journal = Science | volume = 280 | issue = 5360 | pages = 69–77 | date = April 1998 | pmid = 9525859 | doi = 10.1126/science.280.5360.69 | bibcode = 1998Sci...280...69D }} * {{cite journal | vauthors = Zhou Y, Morais-Cabral JH, Kaufman A, MacKinnon R | title = Chemistry of ion coordination and hydration revealed by a K+ channel-Fab complex at 2.0 A resolution | journal = Nature | volume = 414 | issue = 6859 | pages = 43–8 | date = November 2001 | pmid = 11689936 | doi = 10.1038/35102009 | bibcode = 2001Natur.414...43Z | s2cid = 205022645 }} * {{cite journal | vauthors = Jiang Y, Lee A, Chen J, Ruta V, Cadene M, Chait BT, MacKinnon R | title = X-ray structure of a voltage-dependent K+ channel | journal = Nature | volume = 423 | issue = 6935 | pages = 33–41 | date = May 2003 | pmid = 12721618 | doi = 10.1038/nature01580 | bibcode = 2003Natur.423...33J | s2cid = 4347957 }}</ref> fluorescence distance measurements<ref name="FRET" group="lower-alpha">{{cite journal | vauthors = Cha A, Snyder GE, Selvin PR, Bezanilla F | title = Atomic scale movement of the voltage-sensing region in a potassium channel measured via spectroscopy | journal = Nature | volume = 402 | issue = 6763 | pages = 809–13 | date = December 1999 | pmid = 10617201 | doi = 10.1038/45552 | bibcode = 1999Natur.402..809C | s2cid = 4353978 }} * {{cite journal | vauthors = Glauner KS, Mannuzzu LM, Gandhi CS, Isacoff EY | title = Spectroscopic mapping of voltage sensor movement in the Shaker potassium channel | journal = Nature | volume = 402 | issue = 6763 | pages = 813–7 | date = December 1999 | pmid = 10617202 | doi = 10.1038/45561 | bibcode = 1999Natur.402..813G | s2cid = 4417476 }} * {{cite journal | vauthors = Bezanilla F | title = The voltage sensor in voltage-dependent ion channels | journal = Physiological Reviews | volume = 80 | issue = 2 | pages = 555–92 | date = April 2000 | pmid = 10747201 | doi = 10.1152/physrev.2000.80.2.555 }}</ref> and [[cryo-electron microscopy]] studies.<ref name="cryoEM" group="lower-alpha">{{cite journal | vauthors = Catterall WA | title = A 3D view of sodium channels | journal = Nature | volume = 409 | issue = 6823 | pages = 988–9, 991 | date = February 2001 | pmid = 11234048 | doi = 10.1038/35059188 | bibcode = 2001Natur.409..988C | s2cid = 4371677 | doi-access = free }} * {{cite journal | vauthors = Sato C, Ueno Y, Asai K, Takahashi K, Sato M, Engel A, Fujiyoshi Y | title = The voltage-sensitive sodium channel is a bell-shaped molecule with several cavities | journal = Nature | volume = 409 | issue = 6823 | pages = 1047–51 | date = February 2001 | pmid = 11234014 | doi = 10.1038/35059098 | bibcode = 2001Natur.409.1047S | s2cid = 4430165 }}</ref>

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[[Image:MembraneCircuit.svg|thumb|336px|right|Equivalent electrical circuit for the Hodgkin–Huxley model of the action potential. ''Im'' and ''Vm'' represent the current through, and the voltage across, a small patch of membrane, respectively. The ''Cm'' represents the capacitance of the membrane patch, whereas the four ''g'''s represent the [[electrical conductance|conductances]] of four types of ions. The two conductances on the left, for potassium （K） and sodium （Na）, are shown with arrows to indicate that they can vary with the applied voltage, corresponding to the [[voltage-gated ion channel|voltage-sensitive ion channels]]. The two conductances on the right help determine the [[resting membrane potential]].

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~~作用电位的霍奇金-赫胥黎模型的等效电路。~~''Im'' 和 ''Vm'' 分别表示通过一小块膜的电流和两端的电压。''Cm''~~代表膜贴片的电容，而四~~''g''代表四种离子的电导率。左边的两个电导，钾（K）和钠（Na），用箭头显示，表明它们可以随着施加的电压而变化，对应于电压敏感的离子通道。右侧的两个电导有助于确定静息膜电位。|链接=Special:FilePath/MembraneCircuit.svg]]

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动作电位的 Hodgkin–Huxley 模型的等效电路。''Im'' 和 ''Vm'' 分别表示通过一小块膜的电流和两端的电压。''Cm'' 代表膜片的电容，而四个 ''g'' 代表四种离子的电导率。带箭头的左边两个电导，钾（K）和钠（Na），表明它们可以随着施加的电压而变化，对应于电压敏感的离子通道。右侧的两个电导有助于确定静息膜电位。|链接=Special:FilePath/MembraneCircuit.svg]]

Mathematical and computational models are essential for understanding the action potential, and offer predictions that may be tested against experimental data, providing a stringent test of a theory. The most important and accurate of the early neural models is the [[Hodgkin–Huxley model]], which describes the action potential by a coupled set of four [[ordinary differential equation]]s （ODEs）.<ref name="hodgkin_1952" group="lower-alpha" /> Although the Hodgkin–Huxley model may be a simplification with few limitations<ref name=":23">{{cite journal | vauthors = Baranauskas G, Martina M | title = Sodium currents activate without a Hodgkin-and-Huxley-type delay in central mammalian neurons | journal = The Journal of Neuroscience | volume = 26 | issue = 2 | pages = 671–84 | date = January 2006 | pmid = 16407565 | pmc = 6674426 | doi = 10.1523/jneurosci.2283-05.2006 }}</ref> compared to the realistic nervous membrane as it exists in nature, its complexity has inspired several even-more-simplified models,{{sfn|Hoppensteadt|1986}}<ref group="lower-alpha" name=":20">*{{cite journal | vauthors = Fitzhugh R | title = Thresholds and plateaus in the Hodgkin-Huxley nerve equations | journal = The Journal of General Physiology | volume = 43 | issue = 5 | pages = 867–96 | date = May 1960 | pmid = 13823315 | pmc = 2195039 | doi = 10.1085/jgp.43.5.867 }} * {{cite journal | vauthors = Kepler TB, Abbott LF, Marder E | title = Reduction of conductance-based neuron models | journal = Biological Cybernetics | volume = 66 | issue = 5 | pages = 381–7 | year = 1992 | pmid = 1562643 | doi = 10.1007/BF00197717 | s2cid = 6789007 }}</ref> such as the [[Morris–Lecar model]]<ref name="morris_1981" group="lower-alpha">{{cite journal | vauthors = Morris C, Lecar H | title = Voltage oscillations in the barnacle giant muscle fiber | journal = Biophysical Journal | volume = 35 | issue = 1 | pages = 193–213 | date = July 1981 | pmid = 7260316 | pmc = 1327511 | doi = 10.1016/S0006-3495(81)84782-0 | bibcode = 1981BpJ....35..193M }}</ref> and the [[FitzHugh–Nagumo model]],<ref name="fitzhugh" group="lower-alpha">{{cite journal | vauthors = Fitzhugh R | title = Impulses and Physiological States in Theoretical Models of Nerve Membrane | journal = Biophysical Journal | volume = 1 | issue = 6 | pages = 445–66 | date = July 1961 | pmid = 19431309 | pmc = 1366333 | doi = 10.1016/S0006-3495(61)86902-6 | bibcode = 1961BpJ.....1..445F }} * {{cite journal | vauthors = Nagumo J, Arimoto S, Yoshizawa S | year = 1962 | title = An active pulse transmission line simulating nerve axon | journal = Proceedings of the IRE | volume = 50 | pages = 2061–2070 | doi = 10.1109/JRPROC.1962.288235 | issue = 10 | s2cid = 51648050 }}</ref> both of which have only two coupled ODEs. The properties of the Hodgkin–Huxley and FitzHugh–Nagumo models and their relatives, such as the Bonhoeffer–Van der Pol model,<ref name="bonhoeffer_vanderPol" group="lower-alpha">{{cite journal | vauthors = Bonhoeffer KF | title = Activation of passive iron as a model for the excitation of nerve | journal = The Journal of General Physiology | volume = 32 | issue = 1 | pages = 69–91 | date = September 1948 | pmid = 18885679 | pmc = 2213747 | doi = 10.1085/jgp.32.1.69 }} * {{cite journal | vauthors = Bonhoeffer KF | year = 1953 | title = Modelle der Nervenerregung | journal = Naturwissenschaften | volume = 40 | pages = 301–311 | doi = 10.1007/BF00632438|bibcode = 1953NW.....40..301B | issue = 11 | s2cid = 19149460 }} * {{cite journal | vauthors = Van der Pol B | year = 1926 | title = On relaxation-oscillations | journal = Philosophical Magazine | volume = 2 | pages = 977–992| author-link = Balthasar van der Pol }} * {{cite journal | year = 1928 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Philosophical Magazine | volume = 6 | pages = 763–775| vauthors = Van der Pol B, Van der Mark J| author-link1 = Balthasar van der Pol | doi=10.1080/14786441108564652}} * {{cite journal | year = 1929 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Arch. Neerl. Physiol. | volume = 14 | pages = 418–443| vauthors = Van der Pol B, van der Mark J| author-link1 = Balthasar van der Pol }}</ref> have been well-studied within mathematics,<ref name="math_studies">Sato, S; Fukai, H; Nomura, T; Doi, S in {{harvnb|Reeke|Poznanski|Sporns|Rosenberg|2005|loc=''Bifurcation Analysis of the Hodgkin-Huxley Equations'', pp. 459–478.}} * FitzHugh, R in {{harvnb|Schwann|1969|loc=''Mathematical models of axcitation and propagation in nerve'', pp. 12–16.}} * {{harvnb|Guckenheimer|Holmes|1986|pp=12–16}}</ref><ref group="lower-alpha" name=":21">{{cite journal | vauthors = Evans JW | year = 1972 | title = Nerve axon equations. I. Linear approximations | journal = Indiana Univ. Math. J. | volume = 21 | pages = 877–885 | doi = 10.1512/iumj.1972.21.21071 | issue = 9| doi-access = free }} * {{cite journal | vauthors = Evans JW, Feroe J | year = 1977 | title = Local stability theory of the nerve impulse | journal = Math. Biosci. | volume = 37 | pages = 23–50 | doi = 10.1016/0025-5564(77)90076-1 }}</ref> computation<ref name="computational_studies">Nelson, ME; Rinzel, J in {{harvnb|Bower|Beeman|1995|loc=''The Hodgkin-Huxley Model'', pp. 29–49.}} * Rinzel, J & Ermentrout, GB; in {{harvnb|Koch|Segev|1989|loc=''Analysis of Neural Excitability and Oscillations'', pp. 135–169.}}</ref> and electronics.<ref name="keener_1983" group="lower-alpha">{{cite journal | vauthors = Keener JP | year = 1983 | title = Analogue circuitry for the Van der Pol and FitzHugh-Nagumo equations | journal = IEEE Transactions on Systems, Man and Cybernetics | volume = 13 | issue = 5 | pages = 1010–1014 | doi = 10.1109/TSMC.1983.6313098 | s2cid = 20077648 }}</ref> However the simple models of generator potential and action potential fail to accurately reproduce the near threshold neural spike rate and spike shape, specifically for the [[mechanoreceptors]] like the [[Pacinian corpuscle]].<ref name=":24">{{cite journal | vauthors = Biswas A, Manivannan M, Srinivasan MA | title = Vibrotactile sensitivity threshold: nonlinear stochastic mechanotransduction model of the Pacinian Corpuscle | journal = IEEE Transactions on Haptics | volume = 8 | issue = 1 | pages = 102–13 | year = 2015 | pmid = 25398183 | doi = 10.1109/TOH.2014.2369422 | s2cid = 15326972 | url = https://zenodo.org/record/894772 }}</ref> More modern research has focused on larger and more integrated systems; by joining action-potential models with models of other parts of the nervous system （such as dendrites and synapses）, researchers can study [[neural computation]]{{sfnm|1a1=McCulloch|1y=1988|1pp=19–39, 46–66, 72–141|2a1=Anderson|2a2=Rosenfeld|2y=1988|2pp=15–41}} and simple [[reflex]]es, such as [[escape reflex]]es and others controlled by [[central pattern generator]]s.<ref name="cpg">Getting, PA in {{harvnb|Koch|Segev|1989|loc=''Reconstruction of Small Neural Networks'', pp. 171–194.}}</ref><ref name="pmid10713861" group="lower-alpha">{{cite journal | vauthors = Hooper SL | title = Central pattern generators | journal = Current Biology | volume = 10 | issue = 5 | pages = R176–R179 | date = March 2000 | pmid = 10713861 | doi = 10.1016/S0960-9822(00)00367-5 | citeseerx = 10.1.1.133.3378 | s2cid = 11388348 }}</ref>

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数学和计算模型对于理解动作电位是必不可少的，它们提供的预测可以与实验数据进行检验，从而为理论提供严格的检验。早期神经模型中最重要和最准确的是 Hodgkin-Huxley 模型，它通过一组四个常微分方程（ODEs）来描述动作电位。<ref name="hodgkin_1952" group="lower-alpha" /> 虽然 Hodgkin-Huxley 模型可能是一个带有限制的简化模型，<ref name=":20" group="lower-alpha" /> ~~s，但与实际存在的神经膜相比，它的局限性很小s~~<ref name=":23" />，其复杂性激发了几个更简化的模型，例如 Morris-Lecar 模型[[Morris–Lecar model|l]]<ref name="morris_1981" group="lower-alpha" /> a和 FitzHugh-Nagumo ~~模型,~~<ref name="fitzhugh" group="lower-alpha" />~~，这两个模型都只有两个耦合的常微分方程。Hodgkin~~-Huxley 模型和 FitzHugh-Nagumo 模型以及它们的近亲，如 Bonhoeffer-Van der Pol ~~模型l，~~<ref name="bonhoeffer_vanderPol" group="lower-alpha" />，已经在数学中得到了很好的研究，<ref name="math_studies" /><ref name=":21" group="lower-alpha" /> 计算，<ref name="computational_studies" /> 和电子学。<ref name="keener_1983" group="lower-alpha" /> 然而，简单的生成电位和动作电位模型并不能准确地再现近阈值神经元刺激速率和刺激形态，特别是对于机械性受体如帕西尼氏小体（Pacinian corpuscle）<ref name=":24" /> 。更多的现代研究侧重于更大、更完整的系统；通过将动作电位模型与神经系统其他部分的模型（如树突和突触）结合起来，研究人员可以研究神经计算和简单反射，如逃逸反射和其他由中枢模式发生器控制的反射。<ref name="cpg" /><ref name="pmid10713861" group="lower-alpha" />

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数学和计算模型对于理解动作电位是必不可少的，它们提供的预测可以与实验数据进行检验，从而为理论提供严格的检验。早期神经模型中最重要和最准确的是 Hodgkin-Huxley 模型，它通过一组四个常微分方程（ODEs）来描述动作电位。<ref name="hodgkin_1952" group="lower-alpha" /> 虽然 Hodgkin-Huxley 模型可能是一个带有限制的简化模型，<ref name=":20" group="lower-alpha" /> 但与实际存在的神经膜相比，它的局限性很小 <ref name=":23" />，其复杂性激发了几个更简化的模型，例如 Morris-Lecar 模型[[Morris–Lecar model|l]]<ref name="morris_1981" group="lower-alpha" /> a和 FitzHugh-Nagumo 模型，<ref name="fitzhugh" group="lower-alpha" /> 这两个模型都只有两个耦合的常微分方程。Hodgkin-Huxley 模型和 FitzHugh-Nagumo 模型以及它们的近亲，如 Bonhoeffer-Van der Pol 模型，<ref name="bonhoeffer_vanderPol" group="lower-alpha" /> 已经在数学中得到了很好的研究，<ref name="math_studies" /><ref name=":21" group="lower-alpha" /> 计算，<ref name="computational_studies" /> 和电子学。<ref name="keener_1983" group="lower-alpha" /> 然而，简单的生成电位和动作电位模型并不能准确地再现近阈值神经元刺激速率和刺激形态，特别是对于机械性受体如帕西尼氏小体（Pacinian corpuscle）<ref name=":24" /> 。更多的现代研究侧重于更大、更完整的系统；通过将动作电位模型与神经系统其他部分的模型（如树突和突触）结合起来，研究人员可以研究神经计算和简单反射，如逃逸反射和其他由中枢模式发生器控制的反射。<ref name="cpg" /><ref name="pmid10713861" group="lower-alpha" />

==Notes==

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