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第116行： − 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。+ − 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.+ − 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>+ − 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 }}<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 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 }}<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.+ − 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. − − 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> − − 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}} − − 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> − − 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" /> + − + − − 电缆理论的神经原纤维的简化视野。连接的RC电路对应于被动的神经突相邻的分节。|链接=Special:FilePath/Cable_theory_Neuron_RC_circuit_v3.svg]] − + 第157行：
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第153行： − 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。+ − + − 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>+ − − 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" /> 第184行：
第165行： − 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>+ − − 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" /> − + − − 心肌动作电位的阶段。电压的急剧上升（“0”）对应于钠离子的流入，而两个衰变（分别为“1”和“3”）对应于钠通道失活和钾离子的再极化流。特征性平台（“2”）是由电压敏感钙通道的打开引起的。|链接=Special:FilePath/Ventricular_myocyte_action_potential.svg.png]] − − The cardiac action potential differs from the neuronal action potential by having an extended plateau, in which the membrane is held at a high voltage for a few hundred milliseconds prior to being repolarized by the potassium current as usual.<ref name=Kleber group=lower-alpha /> This plateau is due to the action of slower [[calcium]] channels opening and holding the membrane voltage near their equilibrium potential even after the sodium channels have inactivated. − − 心肌动作电位与神经元动作电位的不同之处在于，心肌动作电位有一个延长的平台期，在这个平台期间，膜在被钾电流复极化之前以高电位保持几百毫秒。<ref name="Kleber" group="lower-alpha" /> 这个平台是由于慢速钙通道打开的作用，即使在钠通道失去活性之后，仍然保持膜电位接近其平衡电位。 − − The cardiac action potential plays an important role in coordinating the contraction of the heart.<ref name=Kleber group=lower-alpha>{{cite journal | vauthors = Kléber AG, Rudy Y | title = Basic mechanisms of cardiac impulse propagation and associated arrhythmias | journal = Physiological Reviews | volume = 84 | issue = 2 | pages = 431–88 | date = April 2004 | pmid = 15044680 | doi = 10.1152/physrev.00025.2003 | s2cid = 21823003 }}</ref> The cardiac cells of the [[sinoatrial node]] provide the [[pacemaker potential]] that synchronizes the heart. The action potentials of those cells propagate to and through the [[atrioventricular node]] （AV node）, which is normally the only conduction pathway between the [[atrium (heart)|atria]] and the [[ventricle (heart)|ventricles]]. Action potentials from the AV node travel through the [[bundle of His]] and thence to the [[Purkinje fiber]]s.<ref group="note" name=":0">Note that these [[Purkinje fiber]]s are muscle fibers and not related to the [[Purkinje cell]]s, which are [[neuron]]s found in the [[cerebellum]].</ref> Conversely, anomalies in the cardiac action potential—whether due to a congenital mutation or injury—can lead to human pathologies, especially [[Heart arrhythmia|arrhythmia]]s.<ref name=Kleber group=lower-alpha /> Several anti-arrhythmia drugs act on the cardiac action potential, such as [[quinidine]], [[lidocaine]], [[beta blocker]]s, and [[verapamil]].<ref group="lower-alpha" name=":14">{{cite journal | vauthors = Tamargo J, Caballero R, Delpón E | title = Pharmacological approaches in the treatment of atrial fibrillation | journal = Current Medicinal Chemistry | volume = 11 | issue = 1 | pages = 13–28 | date = January 2004 | pmid = 14754423 | doi = 10.2174/0929867043456241 }}</ref> − 心肌动作电位在协调心脏收缩中起着重要作用。窦房结的心脏细胞提供了同步心脏的起搏器电位。<ref name="Kleber" group="lower-alpha" /> 这些细胞的动作电位传导到并通过房室结，这通常是心房和心室之间唯一的传导通路。房室结的动作电位通过 His 束传递到浦肯野纤维。请注意，这些浦肯野纤维是肌纤维，与小脑中的神经元浦肯野细胞无关。<ref name=":0" group="note" /> 相反，心肌动作电位的异常ーー无论是由于先天性突变还是损伤ーー都可能导致人类疾病，尤其是心律失常。<ref name="Kleber" group="lower-alpha" /> 几种抗心律失常药物作用于心肌动作电位，如奎尼丁、利多卡因、 β 受体阻滞剂和维拉帕米。<ref name=":14" group="lower-alpha" />+ − + − The action potential in a normal skeletal muscle cell is similar to the action potential in neurons.{{sfn|Ganong|1991|pp=59–60}} Action potentials result from the depolarization of the cell membrane （the [[sarcolemma]]）, which opens voltage-sensitive sodium channels; these become inactivated and the membrane is repolarized through the outward current of potassium ions. The resting potential prior to the action potential is typically −90mV, somewhat more negative than typical neurons. The muscle action potential lasts roughly 2–4 ms, the absolute refractory period is roughly 1–3 ms, and the conduction velocity along the muscle is roughly 5 m/s. The action potential releases [[calcium]] ions that free up the [[tropomyosin]] and allow the muscle to contract. Muscle action potentials are provoked by the arrival of a pre-synaptic neuronal action potential at the [[neuromuscular junction]], which is a common target for [[neurotoxin]]s.<ref name=Newmark group=lower-alpha /> − 正常骨骼肌细胞的动作电位与神经元的动作电位相似。动作电位是细胞膜（肌膜）去极化的结果，这种去极化开启了电压敏感的钠通道，这些电压敏感的钠通道失活，膜通过钾离子的外向电流再次极化。动作电位之前的静息电位通常是 -90mV，比典型的神经元稍微负。肌肉动作电位持续时间约为2-4ms，绝对不应期约为1-3ms，肌肉传导速度约为5 m/s。动作电位释放钙离子，释放原肌球蛋白，使肌肉收缩。肌肉动作电位是由突触前神经元动作电位传至神经肌肉接点引起的，这是神经毒素的一个共同靶点。<ref name="Newmark" group="lower-alpha" />+ + 第220行：
第191行： − 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" />+ 第274行：
第245行： − 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。+ 第335行：
第306行： − 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== − <references group="note" /> − +
无编辑摘要
===起搏电位===
===起搏电位===
[[文件:Pacemaker potential.svg.png|替代=|缩略图|在起搏电位中，细胞自发地去极化（斜向上的直线），直到它发放动作电位。]]
[[文件:Pacemaker potential.svg.png|替代=|缩略图|在起搏电位中，细胞自发地去极化（斜向上的直线），直到它发放动作电位。]]
感觉神经元中，动作电位是由外部刺激引起的。然而，一些兴奋性细胞不需要这样的刺激就可以发放动作电位：它们自发地使轴丘去极化，以特定的速率发放动作电位，像内部时钟一样。这种细胞的电位变化称为起搏电位（pacemaker potentials）。心脏窦房结（ sinoatrial node）的心脏起搏细胞（cardiac pacemaker cells）就是一个很好的例子。<ref name="noble_1960" group="lower-alpha">{{cite journal | vauthors = Noble D | title = Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations | journal = Nature | volume = 188 | issue = 4749 | pages = 495–7 | date = November 1960 | pmid = 13729365 | doi = 10.1038/188495b0 | bibcode = 1960Natur.188..495N | s2cid = 4147174 }}</ref> 虽然这种起搏电位有其自然节奏，但可以通过外部刺激进行调节；例如，药物以及交感神经和副交感神经发出的信号可以改变心率。外部刺激不是引起细胞动作电位的连续性发放，仅是改变其节奏。某些情况下，存在对发放频率更为复杂的调节，引起特定的动作电位模式，比如爆发（bursting）。
感觉神经元中，动作电位是由外部刺激引起的。然而，一些兴奋性细胞不需要这样的刺激就可以发放动作电位：它们自发地使轴丘去极化，以特定的速率发放动作电位，像内部时钟一样。这种细胞的电位变化称为起搏电位（pacemaker potentials）。心脏窦房结（ sinoatrial node）的心肌起搏细胞（cardiac pacemaker cells）就是一个很好的例子。<ref name="noble_1960" group="lower-alpha">{{cite journal | vauthors = Noble D | title = Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations | journal = Nature | volume = 188 | issue = 4749 | pages = 495–7 | date = November 1960 | pmid = 13729365 | doi = 10.1038/188495b0 | bibcode = 1960Natur.188..495N | s2cid = 4147174 }}</ref> 虽然这种起搏电位有其自然节奏，但可以通过外部刺激进行调节；例如，药物以及交感神经和副交感神经发出的信号可以改变心率。外部刺激不是引起细胞动作电位的连续性发放，仅是改变其节奏。某些情况下，存在对发放频率更为复杂的调节，引起特定的动作电位模式，比如爆发（bursting）。
==动作电位的相位==
==动作电位的相位==
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.
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.
细胞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，这个绝对不应期对应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），一些缓慢失活或从不失活；这种变异性保证了，即使一些钾离子通道因去极化而失活，总有电流来源使膜复极化。另一方面，去极化较强时，神经元所有的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关闭状态。绝对不应期虽然限制了发放频率，但确保了动作电位沿轴突单向传播。动作电位产生的电流会沿轴突双向扩布。然而，只有未发放的轴突部位才能作出动作电位的反应；刚刚发放过的部位是没有反应的，直到动作电位移到安全范围，不能再刺激该部位。在通常的正向传导（[[orthodromic conduction]]）中，动作电位从轴丘向突触扣结（轴突末梢）传导，向相反方向传导的反向传导（[[antidromic conduction]]）现象非常罕见。不过，如果实验中从中间刺激轴突，两边的轴突都是“新鲜的”，即未被刺激，那么就会产生两个动作电位，一个传向轴丘，另一个传向突触扣结。
===髓鞘和跳跃式传导===
===髓鞘和跳跃式传导===
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，将轴突逐段包裹起来，段的间隔被称为郎飞结。它由专门的细胞产生：周围神经系统中是施万细胞（[[Schwann cell]]s），中央神经系统中是少突胶质细胞（[[oligodendrocyte]]s）。髓鞘减少了膜电容，并增加结间段的膜电阻，从而让动作电位在郎飞结之间快速、跳跃式的移动。<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 name=":2" 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> 髓鞘形成（myelination）主要存在于脊椎动物，不过一些无脊椎动物也有类似的系统，比如某些种类的虾。<ref name=":3" 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 | url = http://jeb.biologists.org/cgi/pmidlookup?view=long&pmid=10395528 }}</ref> 脊椎动物中并不是所有的神经元都有髓鞘；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>
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；动作电位的这种看似在郎飞结之间“跳跃”被称为跳跃式传导。跳跃式传导的机制在 1925 年就由 Ralph Lillie 提出，<ref name=":4" 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> 但其首个实验证据来自 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> 和 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 name=":12">Tasaki, I in {{harvnb|Field|1959|pp=75–121}}</ref> 以及 Andrew Huxley 和 Robert Stämpflii。<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> 而在无髓鞘的轴突，动作电位在紧邻的膜上引起另一个动作电位，并像波一样沿着轴突不断地移动。
[[Image:Conduction velocity and myelination.png|thumb|right|300px|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'' ∝√''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> 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]]
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">{{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> 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（[[natural selection|selective advantage]]）。<ref name="hartline_2007" group="lower-alpha" />
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结点而仍有足够的强度在第二、三结点触发动作电位。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位置过早终止，即使在无髓神经元中也是如此；一个常见的例子是轴突分支成两个轴突的分支点。
有些疾病会降解髓鞘，破坏跳跃式传导，降低动作电位的传导速度。<ref name=":5" 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> 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">Waxman, SG in {{harvnb|Waxman|2007|loc=''Multiple Sclerosis as a Neurodegenerative Disease'', pp. 333–346.}}</ref>
===电缆学说===
===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 ''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.
[[File:Cable theory Neuron RC circuit v3.svg|thumb|300x300px|电缆理论对神经元纤维的简化图。连接的 RC 电路对应于被动的神经突相邻的节段。（与胞内阻抗 ''r<sub>i</sub>'' 对应的）胞外阻抗 ''r<sub>e</sub>'' 未显示，因其通常小到可以忽略不计；细胞外液可以认为是处处电位相等。|链接=Special:FilePath/Cable_theory_Neuron_RC_circuit_v3.svg]]
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" />
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" />
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" />
轴突内电流的流动可以用电缆理论（cable theory）<ref name="rall_1989" /> 及其细化模型，如房室模型（compartmental model）来定量描述。<ref name="segev_1989" /> 电缆理论是 Lord Kelvin 在 1855 年提出的，用来对跨大西洋电报电缆进行建模 <ref name="kelvin_1855" group="lower-alpha" />，并于 1946 年被 Hodgkin 和 Rushton 证明描述神经元也很有用。<ref name="hodgkin_1946" group="lower-alpha" /> 简单的电缆理论中，神经元被看作是一个电被动的完美圆柱形的传输电缆，可用一个偏微分方程来描述<ref name="rall_1989" />
:<math>
:<math>
\tau \frac{\partial V}{\partial t} = \lambda^2 \frac{\partial^2 V}{\partial x^2} - V
\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}}
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}}
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。
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，对刺激的反应电位以这些尺度发生衰减。参考右边的电路图，这些尺度可以通过单位长度的电阻和电容来确定。
:<math>
:<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'' = ''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.
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'' = ''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.
这些时间尺度和长度尺度可以用来理解无髓鞘纤维中传导速度依赖于神经元直径。比如，时间尺度 τ 随着膜电阻 ''r<sub>m</sub>'' 和膜电容 ''c<sub>m</sub>'' 的增大而增大。随着电容的增加，（根据公式 [[capacitance|''Q'' = ''CV'']]）必须转移更多的电荷才能产生给定的跨膜电压；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 ''r<sub>i</sub>'' 低于另一个轴突（比如，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 ''r<sub>m</sub>'' 增大，降低平均跨膜“泄漏”电流，同样导致 λ 变长，增加了传导速度。
==Termination 动作电位的终止==
==动作电位的终止==
===化学突触===
===化学突触===
一般而言，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">{{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> 神经递质是可以打开突触后细胞离子通道的小分子；大多数轴突的所有末梢都有相同的神经递质。传来的动作电位打开了突触前膜上的电压敏感性钙通道，钙内流导致充满神经递质的突触囊泡（vesicle）迁移到细胞表面，并将其内容物释放到突触间隙（synaptic cleft）。<ref name=":7" group="lower-alpha">{{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> 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">{{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>
[[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]]
[[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]]
===神经肌肉接头===
===神经肌肉接头===
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头（neuromuscular junction）。<ref name=":11" group="lower-alpha">{{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> 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">{{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> 不过，乙酰胆碱结合后又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受到精细的调控。一些毒药，例如神经毒剂沙林（[[sarin]]）和塔崩（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> 以及杀虫剂二嗪农（[[diazinon]]）和马拉硫磷（[[malathion]]），会使乙酰胆碱酯酶失活，从而阻断这种控制。<ref name=":13" group="lower-alpha">{{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>
==其他细胞类型==
==其他细胞类型==
===心肌动作电位===
===心肌动作电位===
[[Image:Ventricular myocyte action potential.svg|thumb|220px|[[文件:Ventricular myocyte action potential.svg.png|缩略图]]Phases of a cardiac action potential. The sharp rise in voltage （"0"） corresponds to the influx of sodium ions, whereas the two decays （"1" and "3", respectively） correspond to the sodium-channel inactivation and the repolarizing eflux of potassium ions. The characteristic plateau （"2"） results from the opening of voltage-sensitive [[calcium]] channels.
[[Image:Ventricular myocyte action potential.svg|thumb|220px|[[文件:Ventricular myocyte action potential.svg.png|缩略图]]心肌动作电位的阶段。电压的急剧上升（“0”）对应于钠离子的内流，而两个下降（分别为“1”和“3”）对应于钠通道失活和复极化的钾离子外流。特征性平台（“2”）是由电压敏感性钙通道的打开产生的。|链接=Special:FilePath/Ventricular_myocyte_action_potential.svg.png]]
心肌动作电位与神经元动作电位的不同之处在于，心肌动作电位有一个延长的平台期，即膜会保持几百毫秒高电位之后，才被钾电流复极化。<ref name="Kleber" group="lower-alpha">{{cite journal | vauthors = Kléber AG, Rudy Y | title = Basic mechanisms of cardiac impulse propagation and associated arrhythmias | journal = Physiological Reviews | volume = 84 | issue = 2 | pages = 431–88 | date = April 2004 | pmid = 15044680 | doi = 10.1152/physrev.00025.2003 | s2cid = 21823003 }}</ref> 这个平台是慢速钙通道打开的作用，使膜电位在钠通道失活之后，仍保持在其平衡电位附近。
===肌肉动作电位 Muscular action potentials===
心肌动作电位在协调心脏收缩中起着重要作用。窦房结的心肌细胞提供了同步心脏的起搏电位。<ref name="Kleber" group="lower-alpha" /> 这些细胞的动作电位传导到并通过房室结（atrioventricular node）——心房和心室之间唯一的传导通路。房室结的动作电位通过希斯氏束（bundle of His）传递到浦肯野纤维（Purkinje fibers）。相对的，心肌动作电位的异常ーー无论是由于先天性基因突变还是损伤ーー都可能导致人类疾病，尤其是心律失常。<ref name="Kleber" group="lower-alpha" /> 几种抗心律失常药物作用于心肌动作电位，如奎尼丁（[[quinidine]]）、利多卡因（[[lidocaine]]）、 β 受体阻滞剂（[[beta blocker]]s）和维拉帕米（[[verapamil]]）。<ref name=":14" group="lower-alpha">{{cite journal | vauthors = Tamargo J, Caballero R, Delpón E | title = Pharmacological approaches in the treatment of atrial fibrillation | journal = Current Medicinal Chemistry | volume = 11 | issue = 1 | pages = 13–28 | date = January 2004 | pmid = 14754423 | doi = 10.2174/0929867043456241 }}</ref>
===肌肉动作电位===
正常的骨骼肌细胞的动作电位与神经元的动作电位相似。动作电位是细胞膜（肌膜）去极化的结果，这种去极化开启了电压敏感的钠通道；这些电压敏感的钠通道失活，膜通过钾离子外向复极化。动作电位之前的静息电位通常是 -90mV，比典型的神经元稍微负。肌肉动作电位持续时间约为 2-4 ms，绝对不应期约为 1-3 ms，肌肉传导速率约为 5 m/s。动作电位释放钙离子，释放原肌球蛋白（tropomyosin），使肌肉收缩。肌肉动作电位是由突触前神经元动作电位传至神经肌肉接头引起的。神经肌肉接头是很多神经毒素的共同靶点。<ref name="Newmark" group="lower-alpha" />
===植物动作电位===
===植物动作电位===
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" />
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" />
然而，捕蝇草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。而且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，钙的积累从第一次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">
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">
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.
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.
动作电位的研究一直以来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.
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.
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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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}}<br />* {{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.}}<br />* FitzHugh, R in {{harvnb|Schwann|1969|loc=''Mathematical models of axcitation and propagation in nerve'', pp. 12–16.}}<br />* {{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 }}<br />* {{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.}}<br />* 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>
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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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 }}<br />* {{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}}<br />* {{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.}}<br />* FitzHugh, R in {{harvnb|Schwann|1969|loc=''Mathematical models of axcitation and propagation in nerve'', pp. 12–16.}}<br />* {{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 }}<br />* {{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.}}<br />* 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>
数学和计算模型对于理解动作电位是必不可少的，通过将模型产生的预测与实验数据进行比对，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" />
== References ==
==References==
===Footnotes===
===Footnotes===
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