Action potential 156998 move=sysop 225602474 2008-07-14T14:37:15Z DOI bot 6652755 Citation maintenance. Formatted: doi, journal, title. Initiated by [[User:Nishkid64|Nishkid64]]. You can [[WP:DOI|use this bot]] yourself! Please [[User:DOI_bot/bugs|report any bugs]]. [[Image:Action potential vert.png|thumb|300px|Figure 1. '''A.''' Schematic view of an idealized action potential illustrates its various phases as the action potential passes a point on a [[cell membrane]]. '''B.''' Actual recordings of action potentials are often distorted compared to the schematic view because of variations in [[electrophysiology|electrophysiological]] techniques used to make the recording.]] In [[neurophysiology]], an '''action potential''' (also known as a '''nerve impulse''' or '''spike''') is a pulse-like wave of [[voltage]] that travels along several types of [[cell membrane]]s. The best-understood example is generated on the membrane of the [[axon]] of a [[neuron]], but also appears in other types of excitable [[cell]]s, such as [[cardiac muscle]] cells, and even [[plant]] cells. The [[membrane potential|resting voltage]] across the axonal membrane is typically &minus;70&nbsp;[[volt|millivolts]] (mV), with the inside being more negative than the outside. As an action potential passes through a point, this voltage rises to roughly +40&nbsp;mV in one millisecond, then returns to &minus;70&nbsp;mV. The action potential moves rapidly down the axon, with a [[conduction velocity]] as high as 100&nbsp;meters/second (224 miles per hour). Because they are able to transmit information so fast, the flow of action potentials is a very efficient form of data transmission, considering that each neuron the signal passes through can be up to a meter in length.<ref name="eukaryotic_cell_size" group=note>For comparison, ordinary eukaryotic cells are typically 100,000 times smaller than the longest neurons, having a size of roughly 10 μm. The extraordinary length of neurons may be responsible for some diseases specific to them. For example, defects in the long-distance transport system used to shuttle proteins and organelles from the nucleus to the peripheral synapses and back again may lead to their accumulation and aggregation and, eventually, to cell death by [[apoptosis]].</ref> An action potential is provoked on a patch of membrane when the membrane is depolarized sufficiently, i.e., when the voltage of the cell's interior relative to the cell's exterior is raised above a threshold. Such a depolarization opens voltage-sensitive channels, which allows current into the axon, further depolarizing the membrane. This will cause the membrane to "fire", initiating a [[positive feedback]] loop that suddenly and rapidly causes the voltage inside the axon to become more positive. After this rapid rise, the membrane voltage is restored to its resting value by a combination of effects: the channels responsible for the initial inward current are inactivated, while the raised voltage opens other voltage-sensitive channels that allow a compensating outward current. Because of the positive feedback, an action potential is ''all-or-none''; there are no partial action potentials. In neurons, a typical action potential lasts for just a few thousandths of a second at any given point along their length. The passage of an action potential can leave the [[ion channel]]s in a non-equilibrium state, making them more difficult to open, and thus inhibiting another action potential at the same spot: such an axon is said to be ''refractory''. The principal ions involved in an action potential are [[sodium]] and [[potassium]] [[cation]]s; sodium ions enter the cell, and potassium ions leave, restoring equilibrium. Relatively few ions need to cross the membrane for the membrane voltage to change drastically. The ions exchanged during an action potential, therefore, make a negligible change in the interior and exterior ionic concentrations. The few ions that do cross are pumped out again by the continual action of the [[Na+/K+-ATPase|sodium–potassium pump]], which, with other [[ion transporter]]s, maintains the normal ratio of ion concentrations across the membrane. [[Calcium]] [[cation]]s and [[chloride]] [[anion]]s are involved in a few types of action potentials, such as the [[cardiac action potential]] and the action potential in the single-celled [[algae|alga]] ''[[Acetabularia]]'', respectively. The action potential "travels" along the axon without fading out because the signal is regenerated at each patch of membrane. This happens because an action potential at one patch raises the voltage at nearby patches, depolarizing them and provoking a new action potential there. In [[myelin|unmyelinated]] neurons, the patches are adjacent, but in myelinated neurons, the action potential [[saltatory conduction|"hops"]] between distant patches, making the process both faster and more efficient. The axons of neurons generally branch, and an action potential often travels along both forks from a [[branch point]]. The action potential stops at the end of these branches, but usually causes the secretion of [[neurotransmitter]]s at the [[chemical synapse|synapses]] that are found there. These neurotransmitters bind to receptors on adjacent cells. These receptors are themselves ion channels, although—in contrast to the axonal channels—they are generally opened by the presence of a neurotransmitter, rather than by changes in voltage. The opening of these receptor channels can help to depolarize the membrane of the new cell (an [[Excitatory postsynaptic potential|excitatory channel]]) or work against its depolarization (an [[Inhibitory postsynaptic potential|inhibitory channel]]). If these depolarizations are sufficiently strong, they can provoke another action potential in the new cell. {{TOClimit}} ==Biophysical and cellular context== ===Ions and the forces driving their motion=== {{main|Ion|Diffusion|Electrochemical gradient|Electrophoretic mobility}} [[Image:Diffusion.en.jpg|thumb|right|250px|Ions (pink circles) will flow across a membrane from the high concentration to the low concentration, causing a current. However, this creates a voltage across the membrane that opposes the ions' motion. When this voltage reaches the equilibrium value, the flow of ions stops.]] Electrical signals within biological organisms are generally by [[ion]]s, which may be either positively charged [[cation]]s or negatively charged [[anion]]s.<ref>Johnston and Wu, p. 9.</ref> The most important cations for the action potential are [[sodium]] (Na<sup>+</sup>) and [[potassium]] (K<sup>+</sup>),<ref name="bullock_140_141">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 140–41.</ref> which are both ''monovalent'' cations that carry a single positive charge. Action potentials can also involve [[calcium]] (Ca<sup>2+</sup>),<ref>[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 153–54.</ref> which is a ''divalent'' cation that carries a double positive charge. The [[chloride]] anion (Cl<sup>&minus;</sup>) plays a major role in the action potentials of some [[algae]],<ref name="mummert_1991">{{cite journal | author = Mummert H, Gradmann D | date = 1991 | title = Action potentials in Acetabularia: measurement and simulation of voltage-gated fluxes | journal = Journal of Membrane Biology | volume = 124 | pages = 265–73 | pmid = 1664861}}</ref> but plays a negligible role in the action potentials of most animals.<ref>[[Knut Schmidt-Nielsen|Schmidt-Nielsen]], p. 483.</ref> Ions cross the cell membrane under two influences: [[diffusion]] and [[electric field]]s.<ref>Johnston and Wu, pp. 10&ndash;13.</ref> Diffusion allows net flow of ions from regions where the ions are highly [[concentration|concentrated]] into regions of low concentration. Ions also move in response to an [[electric field]]. By definition, the [[integral]] of the electric field across a patch of membrane equals the [[membrane potential|voltage]] ''V''<sub>''m''</sub> across that patch.<ref group=note>Here, a ''patch of membrane'' is defined as a segment of the membrane small enough that the transmembrane voltage does not vary significantly over its surface.</ref> Likewise by definition, the flows of different ions through that patch are the [[electric current|ionic currents]] at that patch; the total current is the sum of all the individual ionic currents. Using these definitions of voltage and current, such a membrane patch can be modeled by an [[equivalent circuit|equivalent electronic circuit]].<ref>Johnston and Wu, pp. 39&ndash;51.<br />* {{cite journal | author = Finkelstein A, Mauro A | date = 1963 | title = Equivalent circuits as related to ionic systems | journal = Biophysical Journal | volume = 3 | pages = 215–37}}</ref> In particular, for each type of ion the patch will have a [[capacitance]] ''C'' and a [[electrical conductance|conductance]] ''g''; according to [[Ohm's law]], the current ''I'' of each ion type is related to the transmembrane voltage ''V''<sub>''m''</sub> by the equation ''I'' = g ''V''<sub>''m''</sub>. For a given set of ionic conductances, there is an equilibrium voltage ''E'' at which the total current across the membrane is zero; the natural flow of ions generally causes the membrane voltage ''V''<sub>''m''</sub> to approach ''E''.<ref name="junge_33_37">Junge, pp. 33–37.</ref> [[Image:CellMembraneDrawing.jpg|thumb|left|The hydrophobic [[cell membrane]] prevents charged molecules from easily diffusing through it, permitting a [[transmembrane potential|potential difference]] to exist across the membrane.]] ===Cell membrane=== Because the [[cell membrane|membrane]] surrounding [[cell (biology)|cells]] is nearly impermeable to [[ion]]s,<ref name="lieb_1986">{{cite book | author= Lieb WR, Stein WD | date = 1986 | chapter = Chapter 2. Simple Diffusion across the Membrane Barrier | title = Transport and Diffusion across Cell Membranes | publisher = Academic Press | location = San Diego | isbn = 0-12-664661-9 | pages = 69–112}}</ref> cells have evolved systems for transporting ions across the membrane. These systems can be divided into two classes: pores ("channels") that allow [[passive transport]] of ions, and [[ion transporter|ion pumps]] that use [[adenosine triphosphate]] for [[active transport]] of ions. The ion pumps tend to work continuously, as long as there are ions to be pumped. By contrast, the ion channels open and close in response to signals from their environment. The two classes play complementary roles; the ion pumps generate the differences in ion [[concentration]]s across the membrane, which the ion channels exploit to carry out electrical signaling. As an analogy, ion pumps play the role of the battery that allows a radio circuit (the ion channels) to transmit a signal.<ref>{{cite book | author = D Purves, GJ Augustine, D Fitzpatrick, WC Hall, A-S LaMantia, JO McNamara, LE White | title = [http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=neurosci.chapter.227 Neuroscience] | edition = 4th Edition | publisher = Sinauer Associates | location = Sunderland, MA | isbn = 978-0-87893-697-7}}</ref> [[Image:Action potential ion sizes.svg|thumb|left|Despite the small differences in their radii,<ref>''CRC Handbook of Chemistry and Physics'', 83rd edition, ISBN 0-8493-0483-0, pp. 12–14 to 12–16.</ref> ions rarely go through the "wrong" channel. For example, sodium or calcium ions rarely pass through a potassium channel.]] ===Ion channels=== {{main|Ion channel|Passive transport}} [[Ion channel]]s are [[integral membrane protein]]s through which ions can cross the membrane. Most channels are specific for one ion; whereas that ion passes through relatively quickly, other similar ions pass through very infrequently.<ref name="eisenman_theory">{{cite book | author = Eisenman G | date = 1961 | chapter = On the elementary atomic origin of equilibrium ionic specificity | title = Symposium on Membrane Transport and Metabolism | editors = A Kleinzeller, A Kotyk, eds. | publisher = Academic Press | location = New York | pages = 163&ndash;79}}<br />* {{cite book | author = Eisenman G | date = 1965 | chapter = Some elementary factors involved in specific ion permeation | title = Proc. 23rd Int. Congr. Physiol. Sci., Tokyo | publisher = Excerta Med. Found. | location = Amsterdam | pages = 489&ndash;506}}<br />* {{cite journal | author = Diamond JM, Wright EM | date = 1969 | title = Biological membranes: the physical basis of ion and nonekectrolyte selectivity | journal = Annual Review of Physiology | volume = 31 | pages = 581&ndash;646 | doi = 10.1146/annurev.ph.31.030169.003053}}</ref> For example, although potassium and sodium ions have the same charge and differ only slightly in their radius, potassium channels allow few sodium ions through, and vice versa. The pore through which the ion passes is typically so small that ions must pass through it alone and single-file.<ref name="doyle_1998" /> Channels are either fully open or fully closed. When the channel is open, ions flow through it by [[passive transport]], i.e., at a rate determined by the membrane voltage ''V''<sub>''m''</sub> and concentration difference across the membrane.<ref name="junge_33_37" /> The action potential is a manifestation of different ion channels opening and closing at different times.<ref name="bullock_132">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 132.</ref> [[Image:Potassium channel1.png|thumb|right|All-atom figure of the open potassium channel, with the potassium ion shown in purple in the middle. When the channel is closed, the passage is blocked.]] A channel may have several different states (corresponding to different [[protein structure|conformations]] of the protein), but each such state is either open or closed. In general, closed states correspond either to a contraction of the pore—making it impassable to the ion—or to a separate part of the protein stoppering the pore. For example, the voltage-dependent sodium channel undergoes ''inactivation'', in which a portion of the protein swings into the pore, sealing it.<ref>{{cite journal |author=Cai SQ, Li W, Sesti F |title=Multiple modes of a-type potassium current regulation |journal=Curr. Pharm. Des. |volume=13 |issue=31 |pages=3178–84 |year=2007 |pmid=18045167 |doi=10.2174/138161207782341286}}</ref> This inactivation shuts off the sodium current and plays a critical role in the action potential. Ion channels can be classified by how they respond to their environment.<ref name="goldin_2007">{{cite book | author = Goldin AL | date = 2007 | chapter = Neuronal Channels and Receptors | title = Molecular Neurology | editor = Waxman SG | publisher = Elsevier Academic Press | location = Burlington, MA | isbn = 978-0-12-369509-3 | pages = 43&ndash;58}}</ref> For example, the ion channels involved in the action potential are ''voltage-sensitive channels''; they open and close in response to the voltage across the membrane. ''Ligand-gated channels'' form another important class; these ion channels open and close in response to the binding of a [[ligand (biochemistry)|ligand molecule]], such as a [[neurotransmitter]]. Other ion channels open and close with mechanical forces. Still other ion channels—such as those of [[sensory neuron]]s—open and close in response to other stimuli, such as light, temperature or pressure. ===Ion pumps=== {{main|Ion transporter|Active transport}} The ionic currents of the action potential flow in response to [[concentration]] differences of the ions across the [[cell membrane]]. These concentration differences are established by [[ion transporter]]s, which are [[integral membrane protein]]s that carry out [[active transport]], i.e., use cellular energy (ATP) to "pump" the ions against their concentration gradient.<ref name="hodgkin_1955">{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Richard Keynes|Keynes RD]] | date = 1955 | title = Active transport of cations in giant axons from ''Sepia'' and ''Loligo'' | journal = J. Physiol. | volume = 128 | pages = 28–60}}</ref> Such ion pumps take in ions from one side of the membrane (decreasing its concentration there) and release them on the other side (increasing its concentration there). The ion pump most relevant to the action potential is the [[Na+/K+-ATPase|sodium–potassium pump]], which transports three sodium ions out of the cell and two potassium ions in.<ref name="caldwell_1960">{{cite journal | author = Caldwell PC, [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Richard Keynes|Keynes RD]], Shaw TI | date = 1960 | title = The effects of injecting energy-rich phosphate compounds on the active transport of ions in the giant axons of ''Loligo'' | journal = J. Physiol. | volume = 152 | pages = 561–90}}</ref> Consequently, the concentration of [[potassium]] ions K<sup>+</sup> inside the neuron is roughly 20-fold larger than the outside concentration, whereas the sodium concentration outside is roughly ninefold larger than inside.<ref name="steinbach_1943">{{cite journal | author = Steinbach HB, Spiegelman S | date = 1943 | title = The sodium and potassium balance in squid nerve axoplasm | journal = J. Cell. Comp. Physiol. | volume = 22 | pages = 187–96 | doi = 10.1002/jcp.1030220209}}</ref><ref name="hodgkin_1951">{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]] | date = 1951 | title = The ionic basis of electrical activity in nerve and muscle | journal = Biol. Rev. | volume = 26 | pages = 339–409 | doi = 10.1111/j.1469-185X.1951.tb01204.x}}</ref> Similarly, other ions have different concentrations inside and outside the neuron, such as [[calcium]], [[chloride]] and [[magnesium]].<ref name="hodgkin_1951" /> Ion pumps influence the action potential only by establishing the relative ratio of intracellular and extracellular ion concentrations. The action potential mainly involves the opening and closing of ion channels, not ion pumps. If the ion pumps are turned off by removing their energy source, or by adding an inhibitor such as [[ouabain]], the axon can still fire hundreds of thousands of action potentials before their amplitudes begin to decay significantly.<ref name="hodgkin_1955" /> In particular, ion pumps play no significant role in the repolarization of the membrane after an action potential.<ref name="bullock_140_141" /> ===Resting potential=== {{main|Resting potential|Membrane potential|Reversal potential}} Each type of ion has a [[reversal potential]] ''E''—also called its ''equilibrium voltage'' or ''equilibrium potential''—at which the net current of that ion across the membrane is zero; the ionic current due to the electric field exactly cancels the current due to the differences in concentration across the membrane. That equilibrium voltage is given by the [[Nernst equation]]<ref name="nernst">Purves ''et al.'', pp. 28&ndash;32; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 133&ndash;134; Schmidt-Nielsen, pp. 478&ndash;480, 596&ndash;597; Junge, pp. 33&ndash;35</ref><ref name="bernstein_1902_1912" /> :<math> E = \frac{RT}{nF} \ln{ \left( \frac{\mathrm{outside\ ion\ concentration}}{\mathrm{inside\ ion\ concentration}} \right) }. </math> The constants in this equation are the [[electric charge|charge]] [[valence (chemistry)|valence]] ''n'' of the ion (e.g., +1 for K<sup>+</sup>, +2 for Ca<sup>2+</sup> and &minus;1 for Cl<sup>&minus;</sup>), the [[temperature]] ''T'' (in [[Kelvin]]s), the molar [[gas constant]] ''R'', and the [[Faraday]] ''F'', which is the total charge of a [[Mole (unit)|mole]] of [[electron]]s. For illustration, at a typical physiological ratio of concentrations, the potassium equilibrium voltage ''E''<sub>K</sub> is &minus;75 mV, whereas the sodium equilibrium voltage ''E''<sub>Na</sub> is +55mV. Since these disagree, there is no voltage at which the currents of potassium and sodium ions are both zero.<ref group=note>Membrane voltages are defined relative to the exterior of the cell; thus, a potential of &minus;70 mV implies that the interior of the cell is negative relative to the exterior.</ref> However, there is a voltage ''E''<sub>''m''</sub> at which the ''net'' current of all ions across the membrane is zero; this voltage is given by the [[Goldman equation]]<ref name="Goldman">Purves ''et al.'', pp. 32&ndash;33; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 138&ndash;140; Schmidt-Nielsen, pp. 480; Junge, pp. 35&ndash;37</ref><ref name="goldman_1943" /> :<math> E_{m} = \frac{RT}{F} \ln{ \left( \frac{ P_{\mathrm{K}}[\mathrm{K}^{+}]_\mathrm{out} + P_{\mathrm{Na}}[\mathrm{Na}^{+}]_\mathrm{out} + P_{\mathrm{Cl}^{-}}[\mathrm{Cl}^{-}]_\mathrm{in}}{ P_{\mathrm{K}}[\mathrm{K}^{+}]_\mathrm{in} + P_{\mathrm{Na}}[\mathrm{Na}^{+}]_\mathrm{in} + P_{\mathrm{Cl}}[\mathrm{Cl}^{-}]_\mathrm{out}} \right) } </math> for the three monovalent ions most important to action potentials: potassium (K<sup>+</sup>), sodium (Na<sup>+</sup>), and chloride (Cl<sup>&minus;</sup>). Being an anion, the chloride terms are treated differently than the cation terms; the inside concentration is in the numerator, and the outside concentration is in the denominator, which is reversed from the cation terms. ''P''<sub>i</sub> stands for the [[permeability]] of the ion type i. If calcium ions are also considered, the formula for the equilibrium voltage becomes more complicated.<ref name="goldman_calcium">{{cite journal | author = Spangler SG | date = 1972 | title = Expansion of the constant field equation to include both divalent and monovalent ions | journal = Ala J Med Sci | volume = 9 | pages = 218–23|pmid=5045041 }}</ref> The membrane voltage ''V''<sub>m</sub> need not equal its equilibrium value ''E''<sub>m</sub>. However, since ''V''<sub>m</sub> can change drastically when only a few ions cross the membrane,<ref group=note>This follows from the capacitance equation, Δq = C ΔV, where ΔV is the change in voltage that results from the transfer of a charge Δq to a capacitor. To obtain the given ΔV ≈ 100&nbsp;mV of an action potential, the charge Δq transferred per area of membrane is small (≈0.1&nbsp;μ[[Coulomb|C]] per cm<sup>2</sup>) because the [[capacitance]] ''C'' per area of the membrane is likewise small (≈1&nbsp;μ[[farad|F]] per cm<sup>2</sup>; see [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 135).</ref> ''V''<sub>m</sub> tracks ''E''<sub>m</sub> closely, so that the two are effectively equivalent. In a typical action potential, where ''V''<sub>m</sub> changes by roughly 100&nbsp;mV, the ionic concentrations inside the axon change only by roughly 1 part in 10 million;<ref>[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 135–36.</ref> hence, hundreds of thousands of action potentials can be fired before the ion pumps are needed to restore the standard ratio of ionic concentrations.<ref name="hodgkin_1955" /> The equilibrium voltage ''E''<sub>''m''</sub> under normal, unstimulated conditions is called the [[resting potential]] ''V''<sub>rest</sub>, typically &minus;70&nbsp;mV.<ref>Purves ''et al.'', pp. 33&ndash;36; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 131.</ref> (The word "potential" or "potential difference" is sometimes a synonym for [[voltage]].) Under those conditions, the membrane is much more permeable to potassium than to any other ion; thus, consistent with the Goldman equation, the resting potential is close to the potassium equilibrium potential ''E''<sub>K</sub>.<ref name="resting_potential">Purves ''et al.'', p. 34; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 134; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 478&ndash;480.</ref><ref name="hodgkin_1949" /> In the middle of the action potential, however, the sodium permeability dominates, so that ''E''<sub>''m''</sub> is +45&nbsp;mV, close to the sodium equilibrium voltage ''E''<sub>Na</sub>.<ref name="E_Na_peak">Purves ''et al.'', p. 37; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 135; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 480&ndash;481.</ref><ref name="hodgkin_1949" /> [[Image:Neurons big1.jpg|thumb|left|250px|Action potentials arriving at the synapses of the upper right neuron stimulate currents in its [[dendrite]]s; these currents depolarize the membrane at its [[axon hillock]], provoking an action potential that propagates down the axon to its synaptic knobs, releasing [[neurotransmitter]] and stimulating the post-synaptic neuron (lower left).]] ===Anatomy of a neuron=== Several types of cells support an action potential, such as plant cells, muscle cells, and the specialized cells of the heart (in which occurs the [[cardiac action potential]]). However, the main excitable cell is the [[neuron]], which also has the simplest mechanism for the action potential. Most neurons have numerous branched tendrils called [[neurite]]s,<ref name="bullock_p11">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 11.</ref> which are divided into two main types, [[dendrite]]s and [[axon]]s. Most neurons have only one axon but numerous dendrites;<ref name="bullock_p14">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 14.</ref> the beginning of the axon is called the [[axon hillock]].<ref name="bullock_axon_hillock">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 19, 25.</ref> Action potentials almost always begin at the axon hillock, and travel down the axon; it is very rare for an action potential to occur in the dendrites.<ref name="bullock_p11" /> A typical axon has a few branch points, forming a tree-like shape; the tips of this tree (the axonal termini) are generally called the ''synaptic knobs''. These knobs are usually adjacent to the dendrites of another neuron or, more generally, to another excitable cell; the contact between them is called the [[synapse]].<ref name="bullock_synapses">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 29–49.</ref> {{Neuron map|Neuron}}<!-- This is causing text squeeze, reducing text to a one word between images on my browser --> In some animals (mostly vertebrates), segments of the axon are sheathed in [[myelin]],<ref name="bullock_p58_61">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 58–61.</ref> which generally increases the [[conduction velocity]] at which action potentials travel down the axon.<ref name="bullock_p157_164">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 157–64.</ref> Myelin is composed of [[Schwann cells]] that wrap themselves multiple times around the axonal segment, forming a thick fatty layer that prevents ions from entering or escaping the axon. Ions can flow into and out of the axon only at the [[node of Ranvier|nodes of Ranvier]], which are the gaps between the Schwann cells, the "chinks" in the myelin armor.<ref name="bullock_p58_61" /> Therefore, the action potential "hops" from one node of Ranvier to the next (the process of [[saltatory conduction]]); it does not move continuously down the axon, as it does in unmyelinated axons.<ref name="stevens_conduction">Stevens, pp. 25–31.</ref> ==Phases== The course of the action potential is determined by two coupled effects.<ref name="coupling">Stevens, pp. 127&ndash;128.</ref> First, voltage-sensitive ion channels open and close in response to changes in the [[membrane potential|membrane voltage]] ''V''<sub>''m''</sub>, thus changing the membrane's permeability to those ions.<ref name="permeability_channels" >Purves ''et al.'', pp. 61&ndash;65.</ref> However, by the [[Goldman equation]], changes in the ionic permeabilities causes changes in the equilibrium potential ''E''<sub>''m''</sub>, and, thus, the membrane voltage ''V''<sub>''m''</sub>.<ref name="goldman_1943" /> This two-way interaction between ''V''<sub>''m''</sub> and the ion channels sets up the possibility for [[positive feedback]], which is a key part of the rising phase of the action potential.<ref name="positive_feedback">Purves ''et al.'', pp. 48&ndash;49; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 141, 150&ndash;151; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], p. 483; Junge, p. 89; Stevens, p. 127</ref> A complicating factor is that a single ion channel may have multiple internal "gates" that respond to changes in ''V''<sub>''m''</sub> in opposite ways, or at different rates.<ref name="multiple_gates">Purves ''et al.'', pp. 64&ndash;74; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 149&ndash;150; Junge, pp. 84&ndash;85; Stevens, pp. 152&ndash;158.</ref><ref name="hodgkin_1952" /> For example, although raising ''V''<sub>''m''</sub> ''opens'' most gates in the voltage-sensitive sodium channel, it also ''closes'' the channel's "inactivation gate", albeit more slowly.<ref name="sodium inactivation">''Purves ''et al.'', pp. 47, 65; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 147&ndash;148; Stevens, p. 128.</ref> Hence, when ''V''<sub>''m''</sub> is raised suddenly, the sodium channels open initially, but then close due to the slower inactivation. The course of the action potential can be divided into four parts: the rising phase, the falling phase, the undershoot phase, and the refractory period. The initial membrane permeability to potassium is low, but much higher than that of other ions, making the resting potential close to ''E''<sub>K</sub>.<ref name="resting_potential" /> A sufficiently strong depolarization (increase in ''V''<sub>''m''</sub>) causes the voltage-sensitive sodium channels to open; the increasing permeability to sodium drives ''V''<sub>''m''</sub> closer to the sodium equilibrium voltage ''E''<sub>Na</sub>≈ +55&nbsp;mV. The increasing voltage in turn causes even more sodium channels to open, which pushes ''V''<sub>''m''</sub> still further towards ''E''<sub>Na</sub>. This positive feedback continues until the sodium channels are fully open and ''V''<sub>''m''</sub> is close to ''E''<sub>Na</sub>.<ref name="rising phase">Purves ''et al.'', pp. 49&ndash;50; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 140&ndash;141, 150&ndash;151; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 480&ndash;481, 483&ndash;484; Junge, pp. 89&ndash;90.</ref> This is the ''rising phase''.<ref name="phase_nomenclature" >Purves ''et al.'', p. 38.</ref> At this point, the sodium channels begin to inactivate, lowering the membrane's permeability to sodium and driving ''V''<sub>''m''</sub> back down toward the original resting potential.<ref name="sodium inactivation" /> Meanwhile, the potassium channels open more fully; the increased permeability to potassium likewise helps to drive the membrane voltage back down towards ''E''<sub>K</sub>, the potassium equilibrium voltage.<ref name="repolarization">Purves ''et al.'', p. 49; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 147&ndash;149, 152; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 483&ndash;484; Stevens, pp. 126&ndash;127.</ref> This is the ''falling phase''.<ref name="phase_nomenclature" /> The potassium conductance remains unusually high, causing the membrane voltage to dip below even the resting potential; this is the ''undershoot phase''.<ref name="phase_nomenclature" /> Finally, the time during which a subsequent action potential is impossible or difficult to fire is called the ''refractory period'', which may overlap with the other phases.<ref name="phase_nomenclature" /> The voltages and currents of the action potential in all of its phases were modeled accurately by [[Alan Lloyd Hodgkin]] and [[Andrew Huxley]] in 1952,<ref name="hodgkin_1952" /> for which they were awarded the [[Nobel Prize in Physiology or Medicine]] in 1963.<ref name="Nobel_1963">[http://nobelprize.org/medicine/laureates/1997/index.html The Nobel Prize in Physiology or Medicine 1963.]</ref> However, their model considers only two types of voltage-sensitive ion channels, and makes several assumptions about them, e.g., that their internal gates open and close independently of one another. In reality, there are many types of ion channels,<ref name="goldin_2007" /> and they do not always open and close independently.<ref>{{cite journal|author = Naundorf B, Wolf F, Volgushev M | url=http://www.nature.com/nature/journal/v440/n7087/abs/nature04610.html|title=Unique features of action potential initiation in cortical neurons|journal=Nature |volume=440|pages=1060–1063 |year=2006|month=Apr | format = Letter | accessdate=2008-03-27| doi= 10.1038/nature04610}} </ref> ===Stimulation and rising phase=== A typical action potential begins at the [[axon hillock]]<ref name="axon_hillock_origin">Stevens, p. 49.</ref> with a sufficiently strong depolarization, e.g., a stimulus that increases ''V''<sub>''m''</sub>. This depolarization is often caused by the injection of extra sodium [[cation]]s into the cell; these cations can come from a wide variety of sources, such as [[chemical synapse]]s, [[sensory neuron]]s or [[pacemaker potential]]s. The depolarization opens both the sodium and potassium channels in the membrane, allowing the ions to flow into and out of the axon, respectively. If the depolarization is small (say, increasing ''V''<sub>''m''</sub> from &minus;70&nbsp;mV to &minus;60&nbsp;mV), the outward potassium current overwhelms the inward sodium current and the membrane repolarizes back to its normal resting potential around &minus;70&nbsp;mV.<ref name="failed_initiations" /> The "failed initiations" shown in Figure 1 illustrate this response. However, if the depolarization is large enough, the inward sodium current increases more than the outward potassium current and a runaway condition ([[positive feedback]]) results: the more inward current flows, the more ''V''<sub>''m''</sub> increases, which in turn further increases the inward current.<ref name="positive_feedback" /> The sharp rise in ''V''<sub>''m''</sub> and sodium permeability correspond to the ''rising phase'' of the action potential.<ref name="rising_phase" /> The critical threshold voltage for this runaway condition is usually around &minus;45&nbsp;mV, but it depends on the recent activity of the axon. A membrane that has just fired an action potential cannot fire another one immediately, since the ion channels have not returned to their usual state. The period during which no new action potential can be fired is called the ''absolute [[refractory period]]''.<ref name="refractory" /> At longer times, after some but not all of the ion channels have recovered, the axon can be stimulated to produce another action potential, but only with a much stronger depolarization, e.g., &minus;30&nbsp;mV. The period during which action potentials are unusually difficult to provoke is called the ''relative refractory period''.<ref name="refractory" /> ===Peak and falling phase=== The positive feedback of the rising phase slows and comes to a halt as the sodium ion channels become maximally open. At the peak of the action potential, the sodium permeability is maximized and the membrane voltage ''V''<sub>''m''</sub> is nearly equal to the sodium equilibrium voltage ''E''<sub>Na</sub>. However, the same raised voltage that opened the sodium channels initially also slowly shuts them off, by stoppering their pores; the sodium channels become ''inactivated''.<ref name="sodium inactivation" /> This lowers the membrane's permeability to sodium, driving the membrane voltage back down. At the same time, the raised voltage opens voltage-sensitive potassium channels; the increase in the membrane's potassium permeability drives ''V''<sub>''m''</sub> towards ''E''<sub>K</sub>. Combined, these changes in sodium and potassium permeability cause ''V''<sub>''m''</sub> to drop quickly, repolarizing the membrane and producing the "falling phase" of the action potential.<ref name="repolarization" /> ===Hyperpolarization ("undershoot")=== The raised voltage opened many more potassium channels than usual, and these do not close right away when the membrane returns to its normal resting voltage. The potassium permeability of the membrane is transiently unusually high, driving the membrane voltage ''V''<sub>''m''</sub> even closer to the potassium equilibrium voltage ''E''<sub>K</sub>. Hence, there is an undershoot, a ''hyperpolarization'' in technical language, that persists until the membrane potassium permeability returns to its usual value.<ref name="hyperpolarization">Purves ''et al.'', p. 37; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 152.</ref> ===Refractory period=== The opening and closing of the sodium and potassium channels during an action potential may leave some of them in a "refractory" state, in which they are unable to open again until they have recovered.<ref name="refractory">Purves ''et al.'', p. 49; [[Theodore Holmes Bullock|Bullock]], Orkand, Grinell, p. 151; Stevens, pp. 19&ndash;20; Junge, pp. 4&ndash;5.</ref> In the ''absolute refractory period'', so many ion channels are refractory that no new action potential can be fired. Significant recovery (de-inactivation) requires that the membrane potential remain hyperpolarized for a certain length of time. In the ''relative refractory period'', enough channels have recovered that an action potential can be provoked, but only with a stimulus much stronger than usual. These [[refractory period]]s ensure that the action potential travels in only one direction along the axon.<ref name="unidirectional" >Purves ''et al.'', p. 56.</ref> ==Initiation, propagation and termination== A typical action potential is initiated at the axon hillock when the membrane is depolarized sufficiently, i.e., when its voltage is increased sufficiently. As the membrane voltage is increased, both the sodium and potassium ion channels begin to open up, increasing both the inward sodium current and the balancing outward potassium current. For small voltage increases, the potassium current triumphs over the sodium current and the voltage returns to its normal resting value, typically −70&nbsp;mV.<ref name="failed_initiations">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 150&ndash;151; Junge, pp. 89&ndash;90; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], p. 484.</ref> However, if the voltage increases past a critical threshold, typically 15&nbsp;mV higher than the resting value, the sodium current dominates and a runaway condition results; the cell "fires", producing an action potential.<ref name="positive_feedback" /> Once started, the action potential propagates down the axon without diminishing;<ref name="no_decrement">[[Knut Schmidt-Nielsen|Schmidt-Nielsen]], p. 484.</ref> the inwards current of an action potential at one patch of membrane depolarizes nearby membrane patches, sparking another action potential there. In effect, the action potential is created afresh at each patch of membrane; its energy derives from the local differences in ionic concentrations, not from the depolarization that triggered it. The axon may branch along its length, and there the inward current may not quite suffice to trigger a new action potential in one or both of its branches; the action potential may stop.<ref name="axon_branch_points">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 209.</ref> Action potentials that do reach the ends of the axon generally cause the release of a [[neurotransmitter]] into the [[chemical synapse|synapse]], which may combine with other inputs to provoke a new action potential in the post-synaptic neuron or muscle cell. ===Initiation=== Before considering the propagation of action potentials along [[axon]]s and their termination at the synaptic knobs, it is helpful to consider the methods by which action potentials can be initiated at the [[axon hillock]]. The basic requirement is that the membrane voltage at the hillock be raised above the threshold for firing;<ref name="rising_phase" /> there are several ways in which this depolarization can occur. [[Image:Synapse Illustration2 tweaked.svg|thumb|left|300px|When an action potential arrives at the end of the pre-synaptic axon (yellow), it causes the release of [[neurotransmitter]] molecules that open ion channels in the post-synaptic neuron (green). The combined [[excitatory postsynaptic potential|excitatory]] and [[inhibitory postsynaptic potential]]s of such inputs can begin a new action potential in the post-synaptic neuron.]] ====Neurotransmission==== {{main|Neurotransmission}} Action potentials are most commonly initiated by [[excitatory postsynaptic potential]]s from a presynaptic neuron.<ref name="neurotransmission">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 177&ndash;240; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 490&ndash;499; Stevens, pp. 47&ndash;68.</ref> Typically, [[neurotransmitter]] molecules are released by the [[synapse|presynaptic]] [[neuron]] bound to receptors on the postsynaptic cell. This binding opens various types of [[ion channel]]s, changing the local permeability of the [[cell membrane]] and thereby altering the membrane potential. If the binding increases the voltage (depolarizes the membrane), the synapse is excitatory; if the binding decreases the voltage (hyperpolarizes the membrane), it is inhibitory. Whether the voltage is decreased or increased, the change propagates passively to nearby regions of the membrane, as described by the [[cable equation]] and its refinements; typically, the voltage stimulus decays exponentially with the distance from the synapse and with time from the binding of the neurotransmitter. Some fraction of an excitatory voltage may reach the [[axon hillock]] and may (in rare cases) depolarize the membrane enough to provoke a new action potential. More typically, the excitatory potentials from several synapses must [[spatial summation|work together]] [[temporal summation|at nearly the same time]] to provoke a new action potential. Their joint efforts can be thwarted, however, by the counter-acting [[inhibitory postsynaptic potential]]s. Neurotransmission can also occur through [[electrical synapse]]s.<ref name="electrical_synapses">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 178&ndash;180; [[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 490&ndash;491.</ref> Due to the direct connection between the excitable cells in such cases, an action potential can well be transmitted directly from one cell to the next. Rectifying channels ensure that action potentials only move in one direction through an electrical synapse. ====Sensory neurons==== {{main|Sensory neuron}} In [[sensory neurons]], an external signal such as pressure, temperature, light, or sound is coupled with the opening and closing of [[ion channels]], which in turn alter the ionic permeabilities of the membrane and its voltage.<ref name="sensory_neurons">[[Knut Schmidt-Nielsen|Schmidt-Nielsen]], pp. 535&ndash;580; [[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 49&ndash;56, 76&ndash;93, 247&ndash;255; Stevens, 69&ndash;79</ref> These voltage changes can again be excitatory (depolarizing) or inhibitory (hyperpolarizing) and, in some sensory neurons, their combined effects can depolarize the axon hillock enough to provoke action potentials. Examples in humans include the [[olfactory receptor neuron]] and [[Meissner's corpuscle]], which are critical for the sense of [[olfaction|smell]] and [[somatosensory system|touch]], respectively. However, not all sensory neurons convert their external signals into action potentials; some do not even have an axon!<ref name="amacrine_cells">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 53, 122&ndash;124.</ref> Instead, they may convert the signal into the release of a [[neurotransmitter]], or into continuous [[receptor potential|graded potentials]], either of which may stimulate subsequent neuron(s) into firing an action potential. For illustration, in the human [[ear]], [[hair cell]]s convert the incoming sound into the opening and closing of [[stretch-activated ion channel|mechanically gated ion channels]], which may cause [[neurotransmitter]] molecules to be released. Similarly, in the human [[retina]], the initial [[photoreceptor cell]]s and the next two layers of cells ([[bipolar cell]]s and [[amacrine cell]]s) do not produce action potentials; only the third layer, the [[ganglion cell]]s, produce action potentials, which then travel up the [[optic nerve]]. ====Pacemaker potentials==== {{main|Pacemaker potential}} [[Image:Pacemaker potential.svg|thumb|right|In [[pacemaker potential]]s, the cell spontaneously depolarizes (straight line with upward slope) until it fires an action potential.]] In the cases of neurotransmission and sensory neurons, action potentials result from an external stimulus. However, some excitable cells require no such stimulus to fire: they spontaneously depolarize their axon hillock and fire action potentials at a regular rate, like an internal clock.<ref name="pacemakers">Junge, pp. 115&ndash;132</ref> The voltage traces of such cells are known as [[pacemaker potential]]s.<ref name="pacemaker_potentials">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 152&ndash;153.</ref> The [[cardiac pacemaker]] cells of the [[sinoatrial node]] in the [[heart]] provide a good example.<ref name="noble_1960">{{cite journal | author = Noble D | date=1960 | title = Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations | journal = Nature | volume = 188 | pages = 495&ndash;497 | doi = 10.1038/188495b0}}</ref> Although such pacemaker potentials have a natural rhythm, it can be adjusted by external stimuli; for instance, [[heart rate]] can be altered by pharmaceuticals as well as signals from the [[sympathetic nervous system|sympathetic]] and [[parasympathetic nervous system|parasympathetic]] nerves.<ref name="parasympathetic">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 444&ndash;445.</ref> The external stimuli do not cause the cell's repetitive firing, but merely alter its timing.<ref name="pacemaker_potentials" /> In some cases, the regulation of frequency can be more complex, leading to patterns of action potentials, such as [[bursting]]. ===Propagation=== {{main|Conduction velocity}} The action potential propagates as a wave along the axon.<ref>Bullock, Orkland, and Grinnell, pp. 160–64.</ref> 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>{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]] | date = 1937 | title = Evidence for electrical transmission in nerve, Part I | journal = Journal of Physiology | volume = 90 | pages = 183–210}}<br />* {{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]] | date = 1937 | title = Evidence for electrical transmission in nerve, Part II | journal = Journal of Physiology | volume = 90 | pages = 211–32}}</ref> Once an action potential has occurred at a patch of membrane, the membrane patch needs time to recover before it can fire again. At the molecular level, this ''absolute refractory period'' corresponds to the time required for its ion channels to return to their normal open or closed states.<ref>Stevens, pp. 19&ndash;20.</ref> Although it limits the frequency of firing,<ref frequency_coding">Stevens, pp. 21&ndash;23.</ref> the absolute refractory period ensures that the action potential moves in only one direction along an axon.<ref name="unidirectional" /> The currents flowing in due to an action potential spread out in both directions along the axon.<ref name="internal_currents">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, pp. 161&ndash;164.</ref> 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.<ref name="orthodromic">[[Theodore Holmes Bullock|Bullock]], Orkand, and Grinnell, p. 509.</ref> 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. [[Image:Neuron1.jpg|thumb|left|In [[saltatory conduction]], an action potential at one [[node of Ranvier]] causes inwards currents that depolarize the membrane at the next node, provoking a new action potential there; the action potential "hops" from node to node.]] ====Myelin and saltatory conduction==== {{main|Myelination|Saltatory conduction}} The axons of some neurons are ensheathed in [[myelin]], a fatty (ie, [[lipid]]-rich) insulating material that increases the speed and energy efficiency of action potential conduction.<ref name=Zalc>{{cite journal |author=Zalc B |title=The acquisition of myelin: a success story |journal=Novartis Found. Symp. |volume=276 |issue= |pages=15–21; discussion 21–5, 54–7, 275–81 |year=2006 |pmid=16805421 |doi=10.1002/9780470032244.ch3}}</ref> Axons are myelinated by specialized cells, [[Schwann cell]]s and [[oligodendrocyte]]s, that wrap themselves multiple times around segments of axon.<ref>{{cite journal |author=Simons M, Trotter J |title=Wrapping it up: the cell biology of myelination |journal=Curr. Opin. Neurobiol. |volume=17 |issue=5 |pages=533–40 |year=2007 |month=October |pmid=17923405 |doi=10.1016/j.conb.2007.08.003}}</ref> The gaps between these segments are known as the [[node of Ranvier|nodes of Ranvier]]. Myelin prevents ions from entering or leaving the axon along myelinated segments. 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>{{cite journal |author=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=J. Exp. Biol. |volume=202 |issue=Pt 15 |pages=1979–89 |year=1999 |month=August |pmid=10395528 |url=http://jeb.biologists.org/cgi/pmidlookup?view=long&pmid=10395528}}</ref> As a general rule, myelination increases the [[conduction velocity]] of action potentials and makes them more energy-efficient. However, not all neurons in vertebrates are myelinated. Whether saltatory or not, the mean [[conduction velocity]] of an action potential ranges from 1&nbsp;m/s to over 100&nbsp;m/s, and generally increases with axonal diameter.<ref name="hursh_1939">{{cite journal | author = Hursh JB | date = 1939 | title = Conduction velocity and diameter of nerve fibers | journal = American Journal of Physiology | volume = 127 | pages = 131–39}}</ref> Action potentials cannot propagate through the myelinated segments of the axon, since no ions can flow across the membrane there. Instead, the ionic current from an action potential at one [[node of Ranvier]] provokes another action potential at the next node; this "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>{{cite journal | author = Lillie RS | date = 1925 | title = Factors affecting transmission and recovery in passive iron nerve model | journal = J. Gen. Physiol. | volume = 7 | pages = 473–507 | doi = 10.1085/jgp.7.4.473}} See also Keynes and Aidley, p. 78.</ref> the first experimental evidence for saltatory conduction came from [[Ichiji Tasaki]]<ref name="tasaki_1939">{{cite journal | author = Tasaki I | date = 1939 | title = Electro-saltatory transmission of nerve impulse and effect of narcosis upon nerve fiber | journal = Amer. J. Physiol. | volume = 127 | pages = 211–27}}</ref> and Taiji Takeuchi<ref name="tasaki_1941_1942_1959">{{cite journal | author = Tasaki I, Takeuchi T | date = 1941 | title = Der am Ranvierschen Knoten entstehende Aktionsstrom und seine Bedeutung für die Erregungsleitung | journal = Pflüger's Arch. Ges. Physiol. | volume = 244 | pages = 696–711 | doi = 10.1007/BF01755414}}<br />* {{cite journal | author = Tasaki I, Takeuchi T | date = 1942 | title = Weitere Studien über den Aktionsstrom der markhaltigen Nervenfaser und über die elektrosaltatorische Übertragung des nervenimpulses | journal = Pflüger's Arch. Ges. Physiol. | volume = 245 | pages = 764–82 | doi = 10.1007/BF01755237}}<br />* {{cite book | author = Tasaki I | date = 1959 | title = Conduction of the nerve impulse | title = Handbook of Physiology: Neurophysiology | edition = (sect. 1, vol. 1) | editor = J Field, HW Magoun, VC Hall | publisher = American Physiological Society | location = Washington, D.C. | pages = pp. 75–121}}</ref> and from [[Alan Lloyd Hodgkin|Alan Hodgkin]] and Robert Stämpfli.<ref name="huxley_staempfli_1949_1951">{{cite journal | author = [[Andrew Huxley|Huxley A]], Stämpfli R | date = 1949 | title = Evidence for saltatory conduction in peripheral myelinated nerve-fibers | journal = Journal of Physiology | volume = 108 | pages = 315–39}}<br />* {{cite journal | author = [[Andrew Huxley|Huxley A]], Stämpfli R | date = 1949 | title = Direct determination of membrane resting potential and action potential in single myelinated nerve fibers | journal = Journal of Physiology | volume = 112 | pages = 476–95}}</ref> By contrast, in unmyelinated axons, the action potential provokes another in the membrane immediately adjacent, and moves continuously down the axon like a wave. [[Image:Conduction velocity and myelination.png|thumb|right|300px|Comparison of the [[conduction velocity|conduction velocities]] of myelinated and unmyelinated [[axon]]s in the [[cat]].<ref>Schmidt-Nielsen, Figure 12.13.</ref> The conduction velocity ''v'' of myelinated neurons varies roughly linearly with axon diameter ''d'' (that is, ''v'' &prop; ''d''),<ref name="hursh_1939" /> whereas the speed of unmyelinated neurons varies roughly as the square root (''v'' &prop;&radic; ''d'').<ref name="rushton_1951">{{cite journal | author = [[W. A. H. Rushton|Rushton WAH]] | date = 1951 | title = A theory of the effects of fibre size in the medullated nerve | journal = Journal of Physiology | volume = 115 | pages = 101–22}}</ref> The red and blue curves are fits of experimental data, whereas the dotted lines are their theoretical extrapolations.]] Myelin has two important advantages: fast conduction speed and energy efficiency. For axons larger than a minimum diameter (roughly 1 [[micron]]), myelination increases the [[conduction velocity]] of an action potential, typically tenfold.<ref name="hartline_2007" /> 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 100-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">{{cite journal |author=Hartline DK, Colman DR |title=Rapid conduction and the evolution of giant axons and myelinated fibers |journal=Curr. Biol. |volume=17 |issue=1 |pages=R29–R35 |year=2007 |pmid=17208176 |doi=10.1016/j.cub.2006.11.042}}</ref> The length of axons' myelinated segments is important to the success of saltatory conduction. They should be as long as possible to maximize the speed of conduction, but not so long that the arriving signal is too weak to provoke an action potential at the next node of Ranvier. In nature, myelinated segments are generally long enough for the passively propagated signal to travel for at least two nodes while retaining enough amplitude to fire an action potential at the second or third node. Thus, the [[safety factor]] of saltatory conduction is high, allowing transmission to bypass nodes in case of injury. However, action potentials may end prematurely in certain places where the safety factor is low, even in unmyelinated neurons; a common example is the branch point of an axon, where it divides into two axons.<ref>Bullock, Orkland, and Grinnell, p. 163.</ref> Some diseases degrade myelin and impair saltatory conduction, reducing the conduction velocity of action potentials.<ref>{{cite journal |author=Miller RH, Mi S |title=Dissecting demyelination |journal=Nat. Neurosci. |volume=10 |issue=11 |pages=1351–54 |year=2007 |pmid=17965654 |doi=10.1038/nn1995}}</ref> The most well-known of these is [[multiple sclerosis]], in which the breakdown of myelin impairs coordinated movement.<ref>{{cite book | author = Waxman SG | date = 2007 | chapter = Multiple Sclerosis as a Neurodegenerative Disease | title=Molecular Neurology |editor = Waxman SG | publisher = Elsevier Academic Press | location = Burlington, MA | isbn = 978-0-12-369509-3 | pages = 333&ndash;46}}</ref> ====Cable theory==== {{main|Cable theory}} [[Image:NeuronResistanceCapacitanceRev.jpg|thumb|Schematic of resistance and capacitance in an abstract neuronal fiber|300px|right|Figure.1: Cable theory's simplified view of a neuronal fiber. The connected [[RC circuit]]s correspond to adjacent segments of a passive [[neurite]]. The extracellular resistances ''r''<sub>''e''</sub> (the counterparts of the intracellular resistances ''r''<sub>''i''</sub>) are not shown, since they are usually negligibly small; the extracellular medium may be assumed to have the same voltage everywhere.]] The flow of currents within an axon can be described quantitatively by [[cable theory]]<ref name="rall_1989">{{cite book | author = [[Wilfrid Rall|Rall W]] | date = 1989 | title = Methods in Neuronal Modeling: From Synapses to Networks | chapter = Cable Theory for Dendritic Neurons | editor = [[Christof Koch|C. Koch]] and I. Segev | publisher = Bradford Books, MIT Press | location = Cambridge MA | isbn = 0-262-11133-0 | pages = pp. 9–62}}</ref> and its elaborations, such as the compartmental model.<ref name="segev_1989">{{cite book | author = Segev I, Fleshman JW, Burke RE | date = 1989 | title = Methods in Neuronal Modeling: From Synapses to Networks | chapter = Compartmental Models of Complex Neurons | editor = [[Christof Koch|C. Koch]] and I. Segev | publisher = Bradford Books, MIT Press | location = Cambridge MA | isbn = 0-262-11133-0 | pages = pp. 63–96}}</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">{{cite journal | author = [[William Thomson, 1st Baron Kelvin|Kelvin WT]] | date = 1855 | title = On the theory of the electric telegraph | journal = Proceedings of the Royal Society | volume = 7 | pages = 382–99}}</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">{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[W. A. H. Rushton|Rushton WAH]] | date = 1946 | title = The electrical constants of a crustacean nerve fibre | journal = Proceedings of the Royal Society B | volume = 133 | pages = 444–79}}</ref> In simple cable theory, the neuron is treated as an electrically passive, perfectly cylindrical transmission cable, which can be described by a [[partial differential equation]]<ref name="rall_1989" /> :<math> \tau \frac{\partial V}{\partial t} = \lambda^{2} \frac{\partial^{2} V}{\partial x^{2}} - V </math> where ''V(x, t)'' is the voltage across the membrane at a time ''t'' and a position ''x'' along the length of the neuron, and where λ and τ are the characteristic length and time scales on which those voltages decay in response to a stimulus. Referring to the circuit diagram above, these scales can be determined from the resistances and capacitances per unit length<ref name="space_time_constants" >Purves ''et al.'', pp. 52&ndash;53.</ref> :<math> \tau =\ r_{m} c_{m} </math> :<math> \lambda = \sqrt \frac{r_m}{r_l} </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. Similarly, 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. ===Termination=== ====Chemical synapses==== {{main|Chemical synapse|Neurotransmitter|Excitatory postsynaptic potential|Inhibitory postsynaptic potential}} Action potentials that reach the synaptic knobs generally cause a [[neurotransmitter]] to be released into the synaptic cleft.<ref>{{cite journal |author=Süudhof TC |title=Neurotransmitter release |journal=Handb Exp Pharmacol |volume= 184|issue=184 |pages=1–21 |year=2008 |pmid=18064409 |doi=10.1007/978-3-540-74805-2_1}}</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>{{cite journal |author=Rusakov DA |title=Ca2+-dependent mechanisms of presynaptic control at central synapses |journal=Neuroscientist |volume=12 |issue=4 |pages=317–26 |year=2006 |month=August |pmid=16840708 |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>{{cite journal |author=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 |year=2000 |month=May |pmid=10865130 |doi=10.1016/S0300-9084(00)00216-9}}</ref> [[Image:Gap cell junction.svg|thumb|left|[[Electrical synapse]]s between excitable cells allow ions to pass directly from one cell to another, and are much faster than [[chemical synapse]]s.]] ====Electrical synapses==== {{main|Electrical synapse|Gap junction|Connexin}} Some synapses dispense with the "middleman" of the neurotransmitter, and connect the presynaptic and postsynaptic cells together.<ref>{{cite journal |author=Zoidl G, Dermietzel R |title=On the search for the electrical synapse: a glimpse at the future |journal=Cell Tissue Res. |volume=310 |issue=2 |pages=137–42 |year=2002 |pmid=12397368 |doi=10.1007/s00441-002-0632-x}}</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 [[connexin]]s.<ref>{{cite journal |author=Brink PR, Cronin K, Ramanan SV |title=Gap junctions in excitable cells |journal=J. Bioenerg. Biomembr. |volume=28 |issue=4 |pages=351–8 |year=1996 |pmid=8844332 |doi=10.1007/BF02110111}}</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]]. ====Neuromuscular junctions==== {{main|Neuromuscular junction|Acetylcholine receptor|Cholinesterase enzyme}} 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>{{cite journal |author=Hirsch NP |title=Neuromuscular junction in health and disease |journal=Br J Anaesth |volume=99 |issue=1 |pages=132–8 |year=2007 |month=July |pmid=17573397 |doi=10.1093/bja/aem144 |url=http://bja.oxfordjournals.org/cgi/pmidlookup?view=long&pmid=17573397}}</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>{{cite journal |author=Hughes BW, Kusner LL, Kaminski HJ |title=Molecular architecture of the neuromuscular junction |journal=Muscle Nerve |volume=33 |issue=4 |pages=445–61 |year=2006 |month=April |pmid=16228970 |doi=10.1002/mus.20440}}</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]],<ref name=Newmark>{{cite journal |author=Newmark J |title=Nerve agents |journal=Neurologist |volume=13 |issue=1 |pages=20–32 |year=2007 |pmid=17215724 |doi=10.1097/01.nrl.0000252923.04894.53}}</ref> and the insecticides [[diazinon]] and [[malathion]].<ref>{{cite journal |author=Costa LG |title=Current issues in organophosphate toxicology |journal=Clin. Chim. Acta |volume=366 |issue=1-2 |pages=1–13 |year=2006 |pmid=16337171 |doi=10.1016/j.cca.2005.10.008}}</ref> ==Other cell types== ===Cardiac action potentials=== {{main|Cardiac action potential|Electrical conduction system of the heart|Cardiac pacemaker|Arrhythmia}} [[Image:Action_potential.png|thumb|right|220px|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.]] 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 /> 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. The cardiac action potential plays an important role in coordinating the contraction of the heart.<ref name=Kleber>{{cite journal |author=Kléber AG, Rudy Y |title=Basic mechanisms of cardiac impulse propagation and associated arrhythmias |journal=Physiol. Rev. |volume=84 |issue=2 |pages=431–88 |year=2004 |month=April |pmid=15044680 |doi=10.1152/physrev.00025.2003 |url=http://physrev.physiology.org/cgi/pmidlookup?view=long&pmid=15044680}}</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>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 [[arrhythmia]]s.<ref name=Kleber/> Several anti-arrhythmia drugs act on the cardiac action potential, such as [[quinidine]], [[lidocaine]], [[beta blocker]]s, and [[verapamil]].<ref>{{cite journal |author=Tamargo J, Caballero R, Delpón E |title=Pharmacological approaches in the treatment of atrial fibrillation |journal=Curr. Med. Chem. |volume=11 |issue=1 |pages=13–28 |year=2004 |month=January |pmid=14754423 |doi=10.2174/0929867043456241}}</ref> ===Muscular action potentials=== {{main|Neuromuscular junction|Muscle contraction}} The action potential in a normal skeletal muscle cell is similar to the action potential in neurons.<ref name="ganong_1991">{{cite book | author = Ganong W | date = 1991 | title = Review of Medical Physiology | edition = 15th edition | publisher = Appleton and Lange | location = Norwalk CT | isbn = 0-8385-8418-7 | pages = pp. 59–60}}</ref> Action potentials result from the depolarization of the cell membrane (the [[sarcolemma]]), which opens voltage-sensitive sodium channels; these becomes inactivated and the membrane is repolarized through the outward current of potassium ions. The resting potential prior to the action potential is typically &minus;90mV, somewhat more negative than typical neurons. The muscle action potential lasts roughly 2&ndash;4&nbsp;ms, the absolute refractory period is roughly 1&ndash;3&nbsp;ms, and the conduction velocity along the muscle is roughly 5&nbsp;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/> ===Plant action potentials=== Many plants also exhibit action potentials that travel via their [[phloem]] to coordinate activity. The physiology of these ion movements has been studied most in [[algae]] such as [[charophyte]]s.<ref>{{cite journal |author=Beilby MJ |title=Action potential in charophytes |journal=Int. Rev. Cytol. |volume=257 |issue= |pages=43–82 |year=2007 |pmid=17280895 |doi=10.1016/S0074-7696(07)57002-6}}</ref> The main difference between plant and animal action potentials is that plants primarily use [[potassium]] and [[calcium]] currents while animals typically use currents of [[potassium]] and [[sodium]]. These signals are used by plants to rapidly transmit information from environmental signals such as temperature, light, touch or wounding.<ref name=Fromm>{{cite journal |author=Fromm J, Lautner S |title=Electrical signals and their physiological significance in plants |journal=Plant Cell Environ. |volume=30 |issue=3 |pages=249&ndash;257 |year=2007 |pmid=17263772 |doi=10.1111/j.1365-3040.2006.01614.x}}</ref> ==Taxonomic distribution and evolutionary advantages== 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/> [[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>{{cite journal |author=Leys SP, Mackie GO, Meech RW |title=Impulse conduction in a sponge |journal=J. Exp. Biol. |volume=202 (Pt 9) |issue= |pages=1139–50 |year=1999 |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. <center> {| class="wikitable" id="action_potential_texonomic_comparison" border="2" cellpadding="5" cellspacing="1" align="center" |+ Comparison of action potentials (APs) from a representative cross-section of animals<ref name="bullock_1965">{{cite book | author = [[Theodore Holmes Bullock|Bullock TH]], Horridge GA | date = 1965 | title = Structure and Function in the Nervous Systems of Invertebrates | publisher = W. H. Freeman | location = San Francisco}}</ref> ! Animal !! Cell type !! Resting potential (mV) !! AP increase (mV) !! AP duration (ms) !! Conduction speed (m/s) |- | Squid (''Loligo'') || Giant axon || &minus;60 || 120 || 0.75 || 35 |- | Earthworm (''Lumbricus'') || Median giant fiber || &minus;70 || 100 || 1.0 || 30 |- | Cockroach (''Periplaneta'') || Giant fiber || &minus;70 || 80–104 || 0.4 || 10 |- | Frog (''Rana'') || sciatic nerve axon || &minus;60 to &minus;80 || 110–130 || 1.0 || 7–30 |- | Cat (''Felis'') || Spinal motor neuron || &minus;55 to &minus;80 || 80–110 || 1–1.5 || 30&ndash;120 |} </center> 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]]. No material object could convey a signal that rapidly throughout the body; 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. ==Experimental methods== {{seealso|Electrophysiology}} [[Image:Loligo vulgaris.jpg|thumb|right|250px|The giant axons of the European squid (''[[Loligo vulgaris]]'') were crucial for scientists to understand the action potential.]] The study of action potentials has required the development of new experimental methods. The initial work, prior to 1955, 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 first problem was solved by studying the giant axons found in the neurons of the [[squid]] genus ''[[Loligo]]''.<ref name="keynes_1989">{{cite journal | author = Keynes RD | date = 1989 | title = The role of giant axons in studies of the nerve impulse | journal = BioEssays | volume = 10 | pages = 90–93|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=Meunier><ref name="hodgkin_1952" />{{cite journal |author=Meunier C, Segev I |title=Playing the devil's advocate: is the Hodgkin-Huxley model useful? |journal=Trends Neurosci. |volume=25 |issue=11 |pages=558–63 |year=2002 |pmid=12392930 |doi=10.1016/S0166-2236(02)02278-6}}</ref> However, the ''Loligo'' axons are not representative of all excitable cells, and numerous other systems with action potentials have been studied. The second problem was addressed with the crucial development of the [[voltage clamp]],<ref name="cole_1949">{{cite journal | author = [[Kenneth Stewart Cole|Cole KS]] | date = 1949 | title = Dynamic electrical characteristics of the squid axon membrane | journal = Arch. Sci. Physiol. | volume = 3 | pages = 253&ndash;8}}</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 ''I''<sub>''C''</sub> associated with the [[capacitance]] ''C'' of the membrane.<ref name="junge_63_82">Junge, pp. 63&ndash;82.</ref> Since the current equals ''C'' times the rate of change of the transmembrane voltage ''V''<sub>''m''</sub>, the solution was to design a circuit that kept ''V''<sub>''m''</sub> fixed (zero rate of change) regardless of the currents flowing across the membrane. Thus, the current required to keep ''V''<sub>''m''</sub> 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.<ref name="kettenmann_1992">{{cite book | author = Kettenmann H, Grantyn R | date = 1992 | title = Practical Electrophysiological Methods | publisher = Wiley | location = New York | isbn = 978-0471562009}}</ref> 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">{{cite journal | author = Ling G, Gerard RW | date = 1949 | title = The normal membrane potential of frog sartorius fibers | journal = J. Cell. Comp. Physiol. | volume = 34 | pages = 383&ndash;396 |pmid=15410483 | doi = 10.1002/jcp.1030340304}}</ref> which was quickly adopted by other researchers.<ref name="nastuk_1950">{{cite journal | author = Nastuk WL, [[Alan Lloyd Hodgkin|Hodgkin AL]] | date = 1950 | title = The electrical activity of single muscle fibers | journal = J. Cell. Comp. Physiol. | volume = 35 | pages = 39&ndash;73 | doi = 10.1002/jcp.1030350105}}</ref><ref name="brock_1952">{{cite journal | author = Brock LG, Coombs JS, Eccles JC | date = 1952 | title = The recording of potentials from motoneurones with an intracellular electrode | journal = J. Physiol. (London) | volume = 117 | pages = 431&ndash;460}}</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>{{cite book | author = Snell FM | date = 1969 | chapter = Some Electrical Properties of Fine-Tipped Pipette Microelectrodes | title = Glass Microelectrodes | editor = M. Lavallée, OF Schanne, NC Hébert | publisher = John Wiley and Sons | location = New York | id = {{LCCN|68|00|9252}}}}</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 Ca<sup>2+</sup>]] or to voltage.<ref name="dyes">{{cite journal | author = Ross WN, Salzberg BM, Cohen LB, Davila HV | date = 1974 | title = A large change in dye absorption during the action potential | journal = Biophysical Journal | volume = 14 | pages = 983&ndash;986}}<br />* {{cite journal | author = Grynkiewicz G, Poenie M, Tsien RY | date = 1985 | title = A new generation of Ca<sup>2+</sup> indicators with greatly improved fluorescence properties | journal = J. Biol. Chem. | volume = 260 | pages = 3440&ndash;3450}}</ref> [[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).]] While glass micropipette electrodes measure the sum of the currents passing through many ion channels, studying the electrical properties of a single ion channel became possible in the 1970s with the development of the [[patch clamp]] by [[Erwin Neher]] and [[Bert Sakmann]]. For this they were awarded the [[Nobel Prize in Physiology or Medicine]] in 1991.<ref name="nobel_1991">[http://nobelprize.org/medicine/laureates/1991/index.html The Nobel Prize in Physiology or Medicine 1991.]</ref> Patch-clamping verified that ionic channels have discrete states of conductance, such as open, closed and inactivated. ==Neurotoxins== [[Image:Puffer Fish DSC01257.JPG|thumb|right|[[Tetrodotoxin]] is a lethal toxin from the [[pufferfish]] that inhibits the [[voltage-gated ion channel|voltage-sensitive sodium channel]], halting action potentials.]] 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">{{cite journal | author = Nakamura Y, Nakajima S, Grundfest H | date = 1965 | title = The ffect of tetrodotoxin on electrogenic components of squid giant axons | journal = J. Gen. Physiol. | volume = 48 | pages = 985&ndash;996 | doi = 10.1085/jgp.48.6.975}}<br />* {{cite journal | author = Ritchie JM, Rogart RB | date = 1977 | title = The binding of saxitoxin and tetrodotoxin to excitable tissue | journal = Rev. Physiol. Biochem. Pharmacol. | volume = 79 | pages = 1&ndash;50 | doi = 10.1007/BFb0037088}}<br />* {{cite journal | author = Keynes RD, Ritchie JM | date = 1984 | title = On the binding of labelled saxitoxin to the squid giant axon | journal = Proc. R. Soc. Lond. | volume = 239 | pages = 393&ndash;434}}</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. Many other neurotoxins interfere with the transmission of the action potential's effects at the [[chemical synapse|synapses]], especially at the [[neuromuscular junction]]. ==History== [[Image:PurkinjeCell.jpg|thumb|left|Image of two [[Purkinje cell]]s (labeled as '''A''') drawn by [[Santiago Ramón y Cajal]]. Large trees of [[dendrite]]s feed into the [[soma (biology)|soma]], from which a single [[axon]] emerges and moves generally downwards with a few branch points. The smaller cells labeled '''B''' are [[granule cell]]s.]] The role of electricity in the nervous systems of animals was first observed in dissected [[frog]]s by [[Luigi Galvani]], who studied it from 1791 to 1797.<ref name="piccolino_1997">{{cite journal | author = Piccolino M | date = 1997 | title = Luigi Galvani and animal electricity: two centuries after the foundation of electrophysiology | journal = Trends in Neuroscience | volume = 20 | pages = 443&ndash;448 | doi = 10.1016/S0166-2236(97)01101-6}}</ref> Galvani's results stimulated [[Alessandro Volta]] to develop the [[Voltaic pile]]—the earliest known [[battery (electricity)|electric battery]]—with which he studied animal electricity (such as [[electric eel]]s) and the physiological responses to applied [[direct current|direct-current]] [[voltage]]s.<ref name="piccolino_2000">{{cite journal | author = Piccolino M | date = 2000 | title = The bicentennial of the Voltaic battery (1800&ndash;2000): the artificial electric organ | journal = Trends in Neuroscience | volume = 23 | pages = 147&ndash;151 | doi = 10.1016/S0166-2236(99)01544-1}}</ref> Scientists of the 19th century studied the propagation of electrical signals in whole [[nerve]]s (i.e., bundles of [[neuron]]s) and demonstrated that nervous tissue was made up of [[cell (biology)|cells]], instead of an interconnected network of tubes (a ''reticulum'').<ref name="history">{{cite book | author = Brazier MAB | date = 1961 | title = A History of the Electrical Activity of the Brain | publisher = Pitman | location = London}}<br />* {{cite book | author = McHenry LC | date = 1969 | title = Garrison's History of Neurology | publisher = Charles C. Thomas | location = Springfield, IL}}<br />* {{cite book | author = Swazey J, Worden FG | date = 1975 | title = Paths of Discovery in the Neurosciences | publisher = The MIT Press | location = Cambridge, MA}}</ref> [[Carlo Matteucci]] followed up Galvani's studies and demonstrated that [[cell membrane]]s had a voltage across them and could produce [[direct current]]. Matteucci's work inspired the German physiologist, [[Emil du Bois-Reymond]], who discovered the action potential in 1848. The [[conduction velocity]] of action potentials was first measured in 1850 by du Bois-Reymond's friend, [[Hermann von Helmholtz]]. To establish that nervous tissue was made up of discrete cells, the Spanish physician [[Santiago Ramón y Cajal]] and his students used a stain developed by [[Camillo Golgi]] to reveal the myriad shapes of neurons, which they rendered painstakingly. For their discoveries, Golgi and Ramón y Cajal were awarded the 1906 [[Nobel Prize in Physiology or Medicine|Nobel Prize in Physiology]].<ref name="nobel_1906">[http://nobelprize.org/medicine/laureates/1906/index.html The Nobel Prize in Physiology or Medicine 1906.]</ref> Their work resolved a long-standing controversy in the [[neuroanatomy]] of the 19th century; Golgi himself had argued for the network model of the nervous system. [[Image:3b8e.gif|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.]] The 20th century was a golden era for electrophysiology. In 1902 and again in 1912, [[Julius Bernstein]] advanced the hypothesis that the action potential resulted from a change in the [[permeability]] of the axonal membrane to ions.<ref name="bernstein_1902_1912">{{cite journal | author = [[Julius Bernstein|Bernstein J]] | date = 1902 | title = Untersuchungen zur Thermodynamik der bioelektrischen Ströme | journal = Pflüger's Arch. Ges. Physiol. | volume = 92 | pages = 521&ndash;562}}<br />* {{cite book | author = [[Julius Bernstein|Bernstein J]] | date = 1912 | title = Elektrobiologie | publisher = Vieweg und Sohn | location = Braunschweig}}</ref> 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>{{cite journal | author = [[Kenneth Stewart Cole|Cole KS]], Curtis HJ | date = 1939 | title = Electrical impedance of the squid giant axon during activity | journal = J. Gen. Physiol. | volume = 22 | pages = 649&ndash;670 | doi = 10.1085/jgp.22.5.649}}</ref> 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">{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Bernard Katz|Katz B]] | date = 1949 | title = The effect of sodium ions on the electrical activity of the giant axon of the squid | journal = J. Physiology | volume = 108 | pages = 37&ndash;77}}</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">{{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Andrew Huxley|Huxley AF]], [[Bernard Katz|Katz B]] |title = Measurements of current-voltage relations in the membrane of the giant axon of Loligo | journal = Journal of Physiology | year = 1952 | volume = 116 | pages = 424&ndash;448 | pmid = 14946713}}<br />* {{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Andrew Huxley|Huxley AF]] |title = Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo|journal=Journal of Physiology | year = 1952 | volume = 116 | pages = 449&ndash;472 | pmid = 14946713}}<br />* {{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Andrew Huxley|Huxley AF]] | title = The components of membrane conductance in the giant axon of Loligo | journal = J Physiol | year = 1952 | volume = 116 | pages= 473&ndash;496 | pmid = 14946714}}<br />* {{cite journal | author=[[Alan Lloyd Hodgkin|Hodgkin AL]], [[Andrew Huxley|Huxley AF]] | title = The dual effect of membrane potential on sodium conductance in the giant axon of Loligo | journal = J Physiol | year = 1952 | volume = 116 | pages = 497&ndash;506 | pmid = 14946715}}<br />* {{cite journal | author = [[Alan Lloyd Hodgkin|Hodgkin AL]], [[Andrew Huxley|Huxley AF]] | title = A quantitative description of membrane current and its application to conduction and excitation in nerve | journal = J Physiol | year = 1952 | volume = 117 | pages = 500&ndash;544 | pmid = 12991237}}</ref> 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">{{cite journal | author = [[Erwin Neher|Neher E]], [[Bert Sakmann|Sakmann B]] | date = 1976 | title = Single-channel currents recorded from membrane of denervated frog muscle fibres | journal = Nature | volume = 260 | pages = 779&ndash;802}}<br />* {{cite journal | author = Hamill OP, Marty A, [[Erwin Neher|Neher E]], [[Bert Sakmann|Sakmann B]], Sigworth FJ | date = 1981 | title = Improved patch-clamp techniques for high-resolution current recording from cells and cell-free membrane patches | journal = Pflugers Arch. | volume = 391 | pages = 85&ndash;100 | doi = 10.1007/BF00656997}}<br />* {{cite journal | author = [[Erwin Neher|Neher E]], [[Bert Sakmann|Sakmann B]] | date = 1992 | title = The patch clamp technique | journal = Scientific American | volume = 266 | pages = 44&ndash;51}}</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">{{cite journal | author = Yellen G | date = 2002 | title = The voltage-gated potassium channels and their relatives | journal = Nature | volume = 419 | pages = 35&ndash;42 | doi = 10.1038/nature00978}}</ref> through the atomic-resolution [[X-ray crystallography|crystal structures]],<ref name="doyle_1998">{{cite journal | author = Doyle DA, Morais Cabral J, Pfuetzner RA, Kuo A, Gulbis JM, Cohen SL, ''et al.'' | date = 1998 | title = The structure of the potassium channel, molecular basis of K<sup>+</sup> conduction and selectivity | journal = Science | volume = 280 | pages = 69&ndash;77 | doi = 10.1126/science.280.5360.69 | pmid = 9525859}}<br />* {{cite journal | author = Zhou Y, Morias-Cabrak JH, Kaufman A, MacKinnon R | date = 2001 | title = Chemistry of ion coordination and hydration revealed by a K<sup>+</sup>-Fab complex at 2.0 A resolution | journal = Nature | volume = 414 | pages = 43&ndash;48 | doi = 10.1038/35102009}}<br />* {{cite journal | author = Jiang Y, Lee A, Chen J, Ruta V, Cadene M, Chait BT, MacKinnon R | date = 2003 | title = X-ray structure of a voltage-dependent K<sup>+</sup> channel | journal = Nature | volume = 423 | pages = 33&ndash;41 | doi = 10.1038/nature01580}}</ref> fluorescence distance measurements<ref name="FRET">{{cite journal | author = Cha A, Snyder GE, Selvin PR, Bezanilla F | date = 1999 | title = Atomic-scale movement of the voltage-sensing region in a potassium channel measured via spectroscopy | journal = Nature | volume = 402 | pages = 809&ndash;813 | doi = 10.1038/45552}}<br />* {{cite journal | author = Glauner KS, Mannuzzu LM, Gandhi CS, Isacoff E | date = 1999 | title = Spectroscopic mapping of voltage sensor movement in the ''Shaker'' potassium channel | journal = Nature | volume = 402 | pages = 813&ndash;817 | doi = 10.1038/45561}}<br />* {{cite journal | author = Bezanilla F | date = 2000 | title = The voltage sensor in voltage-dependent ion channels | journal = Physiol. Rev. | volume = 80 | pages = 555&ndash;592}}</ref> and [[cryo-electron microscopy]] studies.<ref name="cryoEM">{{cite journal | author = Catterall WA | date = 2001 | title = A 3D view of sodium channels | journal = Nature | volume = 409 | pages = 988&ndash;999 | doi = 10.1038/35059188}}<br />* {{cite journal | author = Sato C, Ueno Y, Asai K, Takahashi K, Sato M, Engel A, ''et al.'' | date = 2001 | title = The voltage-sensitive sodium channel is a bell-shaped molecule with several cavities | journal = Nature | volume = 409 | pages = 1047&ndash;1051 | doi = 10.1038/35059098}}</ref> Julius Bernstein was also the first to introduce the [[Nernst equation]] for [[resting potential]] across the membrane; this was generalized by David E. Goldman to the eponymous [[Goldman equation]] in 1943.<ref name="goldman_1943">{{cite journal | author = Goldman DE | date = 1943 | title = Potential, impedance and rectification in membranes | journal = J. Gen. Physiol. | volume = 27 | pages = 37&ndash;60 | doi = 10.1085/jgp.27.1.37}}</ref> The [[Na+/K+-ATPase|sodium–potassium pump]] was identified in 1957<ref>{{cite journal | author = Skou J | title = The influence of some cations on an adenosine triphosphatase from peripheral nerves | journal = Biochim Biophys Acta | volume = 23 | issue = 2 | pages = 394&ndash;401 | year = 1957 | pmid = 13412736 | doi = 10.1016/0006-3002(57)90343-8}}<br />* [http://nobelprize.org/chemistry/laureates/1997/index.html The Nobel Prize in Chemistry 1997.] Nobelprize.org. Retrieved on [[2007-04-21]].</ref> and its properties gradually elucidated,<ref name="hodgkin_1955" /><ref name="caldwell_1960" /><ref name="caldwell_1957">{{cite journal | author = Caldwell PC, Keynes RD | date = 1957 | title = The utilization of phosphate bond energy for sodium extrusion from giant axons | journal = J. Physiol. (London) | volume = 137 | pages = 12&ndash;13P}}</ref> culminating in the determination of its atomic-resolution structure by [[X-ray crystallography]].<ref name="Na_K_pump_structure">{{cite journal | author = Morth JP, Pedersen PB, Toustrup-Jensen MS, Soerensen TLM, Petersen J, Andersen JP, Vilsen B, Nissen P | date = 2007 | title = Crystal structure of the sodium–potassium pump | journal = Nature | volume = 450 | pages = 1043&ndash;1049 | doi = 10.1038/nature06419}}</ref> The crystal structures of related ionic pumps have also been solved, giving a broader view of how these molecular machines work.<ref>{{cite journal | author = Lee AG, East JM | date = 2001 | title = What the structure of a calcium pump tells us about its mechanism | journal = Biochemical Journal | volume = 356 | pages = 665&ndash;683|pmid= 11389676 | doi = 10.1042/0264-6021:3560665}}</ref> ==Quantitative models== {{Main|Quantitative models of the action potential}} [[Image:MembraneCircuit.jpg|thumb|right|300px|Equivalent electrical circuit for the Hodgkin–Huxley model of the action potential. ''I''<sub>''m''</sub> and ''V''<sub>''m''</sub> represent the current through, and the voltage across, a small patch of membrane, respectively. The ''C''<sub>''m''</sub> 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]]. ]] 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 these 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" /> Although the Hodgkin–Huxley model may be a simplification of a realistic nervous membrane, its complexity has inspired several even-more-simplified models,<ref>{{cite book | author = Hoppensteadt FC | date = 1986 | title = An introduction to the mathematics of neurons | publisher = Cambridge University Press | location = Cambridge | isbn = 0-521-31574-3}}<br />* {{cite journal | author = FitzHugh R | date = 1960 | title = Thresholds and plateaus in the Hodgkin-Huxley nerve equations | journal = J. Gen. Physiol. | volume = 43 | pages = 867&ndash;896 | doi = 10.1085/jgp.43.5.867 | pmid = 13823315}}<br />* {{cite journal | author = Kepler TB, Abbott LF | date = 1992 | title = Reduction of conductance-based neuron models | journal = Biological Cybernetics | volume = 66 | pages = 381&ndash;387 | doi = 10.1007/BF00197717 | unused_data = |Marder E}}</ref> such as the Morris–Lecar model<ref name="morris_1981">{{cite journal | author = Morris C, Lecar H | date = 1981 | title = Voltage oscillations in the barnacle giant muscle fiber | journal = Biophysical Journal | volume = 35 | pages = 193&ndash;213}}</ref> and the [[FitzHugh–Nagumo model]],<ref name="fitzhugh">{{cite journal | author = FitzHugh R | date = 1961 | title = Impulses and physiological states in theoretical models of nerve membrane | journal = Biophysical Journal | volume = 1 | pages = 445&ndash;466}}<br />* {{cite journal | author = Nagumo J, Arimoto S, Yoshizawa S | date = 1962 | title = An active pulse transmission line simulating nerve axon | journal = Proceedings of the IRE | volume = 50 | pages = 2061&ndash;2070 | doi = 10.1109/JRPROC.1962.288235}}</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">{{cite journal | author = Bonhoeffer KF | date = 1948 | title = Activation of Passive Iron as a Model for the Excitation of Nerve | journal = J. Gen. Physiol. | volume = 32 | pages = 69&ndash;91 | doi = 10.1085/jgp.32.1.69}}<br />* {{cite journal | author = Bonhoeffer KF | date = 1953 | title = Modelle der Nervenerregung | journal = Naturwissenschaften | volume = 40 | pages = 301&ndash;311 | doi = 10.1007/BF00632438}}<br />* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]] | date = 1926 | title = On relaxation-oscillations | journal = Philosophical Magazine | volume = 2 | pages = 978&ndash;992}}<br />* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]], van der Mark J | date = 1928 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Philosophical Magazine | volume = 6 | pages = 763&ndash;775}}<br />* {{cite journal | author = [[Balthasar van der Pol|van der Pol B]], van der Mark J | date = 1929 | title = The heartbeat considered as a relaxation oscillation, and an electrical model of the heart | journal = Arch. Neerl. Physiol. | volume = 14 | pages = 418&ndash;443}}</ref> have been well-studied within mathematics,<ref name="math_studies">{{cite book | author = Sato S, Fukai H, Nomura T, Doi S | date = 2005 | chapter = Bifurcation Analysis of the Hodgkin-Huxley Equations | title = Modeling in the Neurosciences: From Biological Systems to Neuromimetic Robotics | edition = 2nd edition | editor = Reeke GN, Poznanski RR, Lindsay KA, Rosenberg JR, Sporns O| publisher = CRC Press | location = Boca Raton | isbn = 978-0415328685 | pages = pp. 459&ndash;478}}<br />* {{cite journal | author = Evans JW | date = 1972 | title = Nerve axon equations. I. Linear approximations | journal = Indiana U. Math. Journal | volume = 21 | pages = 877&ndash;885 | doi = 10.1512/iumj.1972.21.21071}}<br />* {{cite journal | author = Evans JW, Feroe J | date = 1977 | title = Local stability theory of the nerve impulse | journal = Math. Biosci. | volume = 37 | pages = 23&ndash;50 | doi = 10.1016/0025-5564(77)90076-1}}<br />* {{cite book | author = FitzHugh R | date = 1969 | chapter = Mathematical models of axcitation and propagation in nerve | title = Biological Engineering | editor = HP Schwann | publisher = McGraw-Hill | location = New York | pages = pp. 1&ndash;85}}<br />* {{cite book | author = [[John Guckenheimer|Guckenheimer J]], [[Philip Holmes|Holmes P]] | date = 1986 | title = Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields | edition = 2nd printing, revised and corrected | publisher = Springer Verlag | location = New York | isbn = 0-387-90819-6| pages = pp. 12&ndash;16}}</ref> computation<ref name="computational_studies">{{cite book | author = Nelson ME, Rinzel J| year= 1994|chapter= The Hodgkin-Huxley Model|title=The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System| editor= Bower J, Beeman D | publisher = Springer Verlag | location = New York|pages= pp. 29–49 | chapterurl=http://www.genesis-sim.org/GENESIS/iBoG/iBoGpdf/chapt4.pdf}}<br />* {{cite book | author = Rinzel J, Ermentrout GB | date = 1989 | chapter = Analysis of Neural Excitability and Oscillations | title = Methods in Neuronal Modeling: From Synapses to Networks | editor = [[Christof Koch|C. Koch]], I Segev | publisher = Bradford Book, The MIT Press | location = Cambridge, MA | isbn = 0-262-11133-0 | pages = pp. 135&ndash;169}}</ref> and electronics.<ref name="keener_1983">{{cite journal | author = Keener JP | date = 1983 | title = Analogue circuitry for the van der Pol and FitzHugh-Nagumo equations | journal = IEEE Trans. On Systems, Man and Cybernetics | volume = 13 | pages = 1010&ndash;1014}}</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), researches can study [[neural computation]]<ref>{{cite book | author = [[Warren Sturgis McCulloch|McCulloch WS]] | date = 1988 | title = Embodiments of Mind | publisher = The MIT Press | location = Cambridge MA | isbn = 0-262-63114-8 | pages = pp. 19&ndash;39, 46&ndash;66, 72&ndash;141}}<br />* {{cite book | title = Neurocomputing:Foundations of Research | editors = JA Anderson, E Rosenfeld | publisher = The MIT Press | location = Cambridge, MA | isbn = 0-262-01097-6 | pages = 15&ndash;41}}</ref> and simple [[reflex]]es, such as [[escape reflex]]es and others controlled by [[central pattern generator]]s.<ref name="cpg">{{cite book | author = Getting PA | date = 1989 | chapter = Reconstruction of Small Neural Networks | title = Methods in Neuronal Modeling: From Synapses to Networks | editor = [[Christof Koch|C Koch]] and I Segev | publisher = Bradford Book, The MIT Press | location = Cambridge, MA | isbn = 0-262-11133-0 | pages = pp. 171&ndash;194}}<br />* Hooper, Scott L. "Central Pattern Generators." ''Embryonic ELS'' (1999) http://www.els.net/elsonline/figpage/I0000206.html (2 of 2) [2/6/2001 11:42:28 AM] Online: Accessed 27 November 2007 [http://crab-lab.zool.ohiou.edu/hooper/cpg.pdf]</ref> ==See also== * [[Bursting]] * [[Signals (biology)]] * [[Central pattern generator]] ==Notes== <references group=note/> ==References== {{reflist|2}} ==Bibliography== * {{cite book | author = Aidley DJ, Stanfield PR | date = 1996 | title = Ion Channels: Molecules in Action | publisher = Cambridge University Press | location = Cambridge | isbn = 978-0521498821}} * {{cite book | author = Bear MF, Connors BW, Paradiso MA | year = 2001 | title = Neuroscience: Exploring the Brain | publisher = Lippincott | location = Baltimore | isbn = 0781739446}} * {{cite book | author = [[Theodore Holmes Bullock|Bullock TH]], Orkand R, Grinnell A | year = 1977 | title = Introduction to Nervous Systems | publisher = W. H. Freeman | location = New York | isbn = 0-7167-0030-1}} * {{cite journal|author=Clay JR|title= Axonal excitability revisited|journal=Prog Biophys Mol Biol|year= 2005|month= May|volume=88|issue=1|pages=59&ndash;90|pmid=15561301|doi=10.1016/j.pbiomolbio.2003.12.004}} * {{cite book | author = Deutsch S, [[Evangelia Micheli-Tzanakou|Micheli-Tzanakou E]] | date = 1987 | title = Neuroelectric Systems | publisher = New York University Press | location = New York | isbn = 0-8147-1782-9}} * {{cite book | author = [[Bertil Hille|Hille B]] | date = 2001 | title = Ion Channels of Excitable Membranes | edition = 3rd edition | publisher = Sinauer Associates | location = Sunderland, MA | isbn = 978-0878933211}} * {{cite book | author = Hoppensteadt FC | year = 1986 | title = An Introduction to the Mathematics of Neurons | publisher = Cambridge University Press | location = Cambridge | isbn = 0-521-31574-3}} * {{cite book | author = Johnston D, Wu SM-S | date = 1995 | title = Foundations of Cellular Neurophysiology | publisher = Bradford Book, The MIT Press | location = Cambridge, MA | isbn = 0-262-10053-3}} * {{cite book | author = Junge D | year = 1981 | title = Nerve and Muscle Excitation | edition = 2nd ed. | publisher = Sinauer Associates | location = Sunderland MA | isbn = 0-87893-410-3}} * {{cite book | author = [[Eric R. Kandel|Kandel ER]], Schwartz JH, Jessell TM | year = 2000 | title = [[Principles of Neural Science]] | edition = 4th ed. | publisher = McGraw-Hill | location = New York | isbn = 0-8385-7701-6}} * {{cite book | author = [[Richard Keynes|Keynes RD]], Aidley DJ | year = 1991 | title = Nerve and Muscle | edition = 2nd ed. | publisher = Cambridge University Press | location = Cambridge | isbn = 0-521-41042-8}} * {{cite book | author = Miller C | date = 1987 | chapter = How ion channel proteins work | title = Neuromodulation: The Biochemical Control of Neuronal Excitability | editor = LK Kaczmarek, IB Levitan | publisher = Oxford University Press | location = New York | isbn = 978-0195040975 | pages = pp. 39&ndash;63}} * {{cite book | author = Nelson DL, Cox MM | date = 2008 | title = Lehninger Principles of Biochemistry | edition = 5th ed. | publisher = W. H. Freeman | location = New York | isbn= 978-0-7167-7108-1}} * {{cite book | author = Purves D, Augustine GJ, Fitzpatrick D, Hall WC, Lamantia A-S, McNamara JO, Williams SM | title = Neuroscience | edition= 2nd ed. | year = 2001| publisher = Sinauer Associates | location = Sunderland, MA |chapter= Release of Transmitters from Synaptic Vesicles | isbn = 0878937250 | chapterurl=http://www.ncbi.nlm.nih.gov/books/bv.fcgi?rid=neurosci.section.326}} * {{cite book | author = Purves D, Augustine GJ, Fitzpatrick D, Hall WC, Lamantia A-S, McNamara JO, White LE | title = Neuroscience | edition= 4th ed. | year = 2008 | publisher = Sinauer Associates | location = Sunderland, MA | isbn = 978-0-87893-697-7}} * {{cite book | author = [[Knut Schmidt-Nielsen|Schmidt-Nielsen K]] | date = 1997 | title = Animal Physiology: Adaptation and Environment | edition = 5th ed. | publisher = Cambridge University Press | location = Cambridge | isbn = 978-0521570985}} * {{cite book | author = Stevens CF | date = 1966 | title = Neurophysiology: A Primer | publisher = John Wiley and Sons | location = New York}}{{LCCN|66|0|15872}}. ==External links== {{Spoken Wikipedia|Action_potential.ogg|2005-06-22}} ;Animations * [http://www.blackwellpublishing.com/matthews/channel.html Ionic flow in action potentials] at [[Blackwell Publishing]] * [http://www.blackwellpublishing.com/matthews/actionp.html Action potential propagation in myelinated and unmyelinated axons] at [[Blackwell Publishing]] * [http://bcs.whfreeman.com/thelifewire/content/chp44/4402001.html Resting membrane potential] from ''Life: The Science of Biology'', by WK Purves, D Sadava, GH Orians, and HC Heller, 8th edition, New York: WH Freeman, ISBN 978-0716776710. * [http://www.nernstgoldman.physiology.arizona.edu/ Ionic motion and the Goldman voltage for arbitrary ionic concentrations] at [[University of Arizona]] * [http://www.brainu.org/action_potential_cartoon.swf] An excellent cartoon illustrating the action potential. ;Lecture notes and other materials * [http://www.du.edu/~kinnamon/3640/actionpotential/ap1.html The Action Potential] John Kinnamon, [[University of Denver]] * [http://trc.ucdavis.edu/biosci10v/bis10v/week10/06potential.html Resting and Action Membrane Potentials] Teaching Resources Center, [[UC Davis]]. Animated tutorials * [http://cese.sourceforge.net/ Open-source software to simulate neuronal and cardiac action potentials] at [[SourceForge.net]] {{featured article}} [[Category:Neural coding]] [[Category:Electrophysiology]] [[Category:Computational neuroscience]] [[Category:Cellular neuroscience]] {{Link FA|es}} <!-- The below are interlanguage links. --> [[ar:كمون الفعل]] [[ca:Potencial d'acció]] [[de:Aktionspotential]] [[es:Potencial de acción]] [[fi:Toimintapotentiaali]] [[fr:Potentiel d'action]] [[he:דחף עצבי]] [[id:Potensial aksi]] [[it:Potenziale d'azione]] [[ja:活動電位]] [[ko:활동전위]] [[lv:Darbības potenciāls]] [[ms:Potensi aksi]] [[nl:Actiepotentiaal]] [[pl:Potencjał czynnościowy]] [[ps:کړنی-سېک]] [[pt:Potencial de ação]] [[ro:Potenţial de acţiune]] [[ru:Потенциал действия]] [[simple:Nerve impulse]] [[sl:Akcijski potencial]] [[sv:Aktionspotential]] [[zh:动作电位]]