Action potential

As an action potential travels down the axon, there is a changein polarity across the membrane. The Na+ and K+ gated ionchannels open and close as the membrane reaches the thresholdpotential, in response to a signal from another neuron. At the be-ginning of the action potential, the Na+ channels open and Na+

moves into the axon, causing depolarization. Repolarization oc-curs when the K+ channels open and K+ moves out of the axon.This creates a change in polarity between the outside of the celland the inside. The impulse travels down the axon in one direc-tion only, to the axon terminal where it signals other neurons.

In physiology, an action potential is a short-lasting eventin which the electrical membrane potential of a cellrapidly rises and falls, following a consistent trajectory.Action potentials occur in several types of animal cells,called excitable cells, which include neurons, musclecells, and endocrine cells, as well as in some plant cells.In neurons, they play a central role in cell-to-cell com-munication. In other types of cells, their main functionis to activate intracellular processes. In muscle cells,for example, an action potential is the first step in thechain of events leading to contraction. In beta cells ofthe pancreas, they provoke release of insulin.[lower-alpha 1]

Action potentials in neurons are also known as "nerveimpulses" or “spikes”, and the temporal sequence of ac-tion potentials generated by a neuron is called its "spiketrain". A neuron that emits an action potential is oftensaid to “fire”.Action potentials are generated by special types ofvoltage-gated ion channels embedded in a cell’s plasmamembrane.[lower-alpha 2] These channels are shut when themembrane potential is near the resting potential of thecell, but they rapidly begin to open if the membrane po-tential increases to a precisely defined threshold value.When the channels open (in response to depolarizationin transmembrane voltage[lower-alpha 2]), they allow an in-ward flow of sodium ions, which changes the electro-

chemical gradient, which in turn produces a further risein the membrane potential. This then causes more chan-nels to open, producing a greater electric current acrossthe cell membrane, and so on. The process proceeds ex-plosively until all of the available ion channels are open,resulting in a large upswing in the membrane potential.The rapid influx of sodium ions causes the polarity of theplasma membrane to reverse, and the ion channels thenrapidly inactivate. As the sodium channels close, sodiumions can no longer enter the neuron, and then they areactively transported back out of the plasma membrane.Potassium channels are then activated, and there is anoutward current of potassium ions, returning the elec-trochemical gradient to the resting state. After an ac-tion potential has occurred, there is a transient negativeshift, called the afterhyperpolarization or refractory pe-riod, due to additional potassium currents. This is themechanism that prevents an action potential from travel-ing back the way it just came.In animal cells, there are two primary types of action po-tentials. One type is generated by voltage-gated sodiumchannels, the other by voltage-gated calcium channels.Sodium-based action potentials usually last for underone millisecond, whereas calcium-based action potentialsmay last for 100 milliseconds or longer. In some typesof neurons, slow calcium spikes provide the driving forcefor a long burst of rapidly emitted sodium spikes. In car-diac muscle cells, on the other hand, an initial fast sodiumspike provides a “primer” to provoke the rapid onset of acalcium spike, which then produces muscle contraction.

1 Overview

1.1 Function

Nearly all cell membranes in animals, plants and fungimaintain an electric potential difference (voltage)—themembrane potential. A typical voltage across an animalcell membrane is –65 mV—approximately one-fifteenthof a volt. Because the cell membrane is very thin, voltagesof this magnitude give rise to very strong electric forcesacross the cell membrane.In the majority of cells, the voltage stays fairly constantover time. There are some types of cells, however, thatare electrically active in the sense that their voltages fluc-tuate. In some of these, the voltages sometimes show veryrapid up-and-down fluctuations that have a stereotypedform: these up-and-down cycles are known as action po-

1

2 2 BIOPHYSICAL BASIS

tentials. The durations of action potentials vary across awide range, and consequently they are analog signals. Inbrain cells of animals, the entire up-and-down cycle maytake place in roughly a few thousandths of a second. Inother types of cells, the cycle may last for several seconds.The electrical properties of an animal cell are deter-mined by the structure of the membrane that surroundsit. A cell membrane consists of a layer of lipid moleculeswith larger protein molecules embedded in it. Thelipid layer is highly resistant to movement of electricallycharged ions, so it functions mainly as an insulator. Thelarge membrane-embedded molecules, in contrast, pro-vide channels through which ions can pass across themembrane, and some of the large molecules are capableof actively moving specific types of ions from one side ofthe membrane to the other.

1.2 Process in a typical neuron

Actionpotential

Volt

ag

e (

mV

)

Depola

riza

tion R

epola

rizatio

n

Threshold

Stimulus

Failedinitiations

Resting state

Refractoryperiod

+40

0

-55

-70

0 1 2 3 4 5

Time (ms)

Approximate plot of a typical action potential shows its variousphases as the action potential passes a point on a cell membrane.The membrane potential starts out at −70 mV at time zero. Astimulus is applied at time = 1 ms, which raises the membranepotential above−55 mV (the threshold potential). After the stim-ulus is applied, the membrane potential rapidly rises to a peakpotential of +40 mV at time = 2 ms. Just as quickly, the poten-tial then drops and overshoots to −90 mV at time = 3 ms, andfinally the resting potential of−70 mV is reestablished at time =5 ms.

All cells in animal body tissues are electrically polar-ized – in other words, they maintain a voltage differ-ence across the cell’s plasma membrane, known as themembrane potential. This electrical polarization resultsfrom a complex interplay between protein structures em-bedded in the membrane called ion pumps and ion chan-nels. In neurons, the types of ion channels in the mem-brane usually vary across different parts of the cell, giv-ing the dendrites, axon, and cell body different electrical

properties. As a result, some parts of the membrane ofa neuron may be excitable (capable of generating actionpotentials), whereas others are not. Recent studies haveshown that the most excitable part of a neuron is the partafter the axon hillock (the point where the axon leavesthe cell body), which is called the initial segment, but theaxon and cell body are also excitable in most cases.Each excitable patch of membrane has two important lev-els of membrane potential: the resting potential, which isthe value the membrane potential maintains as long asnothing perturbs the cell, and a higher value called thethreshold potential. At the axon hillock of a typical neu-ron, the resting potential is around –70 millivolts (mV)and the threshold potential is around –55 mV. Synapticinputs to a neuron cause the membrane to depolarize orhyperpolarize; that is, they cause the membrane poten-tial to rise or fall. Action potentials are triggered whenenough depolarization accumulates to bring the mem-brane potential up to threshold. When an action potentialis triggered, the membrane potential abruptly shoots up-ward, often reaching as high as +100 mV, then equallyabruptly shoots back downward, often ending below theresting level, where it remains for some period of time.The shape of the action potential is stereotyped; that is,the rise and fall usually have approximately the same am-plitude and time course for all action potentials in a givencell. (Exceptions are discussed later in the article.) Inmost neurons, the entire process takes place in about athousandth of a second. Many types of neurons emit ac-tion potentials constantly at rates of up to 10–100 per sec-ond; some types, however, are much quieter, and may gofor minutes or longer without emitting any action poten-tials.

2 Biophysical basis

Action potentials result from the presence in a cell’s mem-brane of special types of voltage-gated ion channels. Avoltage-gated ion channel is a cluster of proteins embed-ded in the membrane that has three key properties:

1. It is capable of assuming more than one conforma-tion.

2. At least one of the conformations creates a channelthrough the membrane that is permeable to specifictypes of ions.

3. The transition between conformations is influencedby the membrane potential.

Thus, a voltage-gated ion channel tends to be open forsome values of the membrane potential, and closed forothers. In most cases, however, the relationship betweenmembrane potential and channel state is probabilistic andinvolves a time delay. Ion channels switch between con-formations at unpredictable times: The membrane poten-

3

Action potential propagation along an axon

tial determines the rate of transitions and the probabilityper unit time of each type of transition.Voltage-gated ion channels are capable of producing ac-tion potentials because they can give rise to positive feed-back loops: The membrane potential controls the state ofthe ion channels, but the state of the ion channels controlsthe membrane potential. Thus, in some situations, a risein the membrane potential can cause ion channels to open,thereby causing a further rise in the membrane potential.An action potential occurs when this positive feedbackcycle proceeds explosively. The time and amplitude tra-jectory of the action potential are determined by the bio-physical properties of the voltage-gated ion channels thatproduce it. Several types of channels that are capable ofproducing the positive feedback necessary to generate anaction potential exist. Voltage-gated sodium channels areresponsible for the fast action potentials involved in nerveconduction. Slower action potentials in muscle cells andsome types of neurons are generated by voltage-gated cal-cium channels. Each of these types comes in multiplevariants, with different voltage sensitivity and differenttemporal dynamics.The most intensively studied type of voltage-dependention channels comprises the sodium channels involved in

fast nerve conduction. These are sometimes known asHodgkin-Huxley sodium channels because they were firstcharacterized by Alan Hodgkin and Andrew Huxley intheir Nobel Prize-winning studies of the biophysics of theaction potential, but can more conveniently be referredto as NaV channels. (The “V” stands for “voltage”.) AnNaV channel has three possible states, known as deac-tivated, activated, and inactivated. The channel is per-meable only to sodium ions when it is in the activatedstate. When the membrane potential is low, the channelspends most of its time in the deactivated (closed) state.If the membrane potential is raised above a certain level,the channel shows increased probability of transitioningto the activated (open) state. The higher the membranepotential the greater the probability of activation. Oncea channel has activated, it will eventually transition tothe inactivated (closed) state. It tends then to stay in-activated for some time, but, if the membrane potentialbecomes low again, the channel will eventually transitionback to the deactivated state. During an action poten-tial, most channels of this type go through a cycle deacti-vated→activated→inactivated→deactivated. This is onlythe population average behavior, however — an individ-ual channel can in principle make any transition at anytime. However, the likelihood of a channel’s transitioningfrom the inactivated state directly to the activated state isvery low: A channel in the inactivated state is refractoryuntil it has transitioned back to the deactivated state.The outcome of all this is that the kinetics of the NaVchannels are governed by a transition matrix whose ratesare voltage-dependent in a complicated way. Since thesechannels themselves play a major role in determining thevoltage, the global dynamics of the system can be quitedifficult to work out. Hodgkin and Huxley approachedthe problem by developing a set of differential equationsfor the parameters that govern the ion channel states,known as the Hodgkin-Huxley equations. These equa-tions have been extensively modified by later research,but form the starting point for most theoretical studiesof action potential biophysics.As the membrane potential is increased, sodium ion chan-nels open, allowing the entry of sodium ions into the cell.This is followed by the opening of potassium ion channelsthat permit the exit of potassium ions from the cell. Theinward flow of sodium ions increases the concentration ofpositively charged cations in the cell and causes depolar-ization, where the potential of the cell is higher than thecell’s resting potential. The sodium channels close at thepeak of the action potential, while potassium continuesto leave the cell. The efflux of potassium ions decreasesthe membrane potential or hyperpolarizes the cell. Forsmall voltage increases from rest, the potassium currentexceeds the sodium current and the voltage returns to itsnormal resting value, typically −70 mV.[1][2][3] However,if the voltage increases past a critical threshold, typically15 mV higher than the resting value, the sodium currentdominates. This results in a runaway condition whereby

4 3 NEUROTRANSMISSION

the positive feedback from the sodium current activateseven more sodium channels. Thus, the cell fires, pro-ducing an action potential.[1][4][5][note 1] The frequency atwhich cellular action potentials are produced is known asits firing rate.Currents produced by the opening of voltage-gated chan-nels in the course of an action potential are typically sig-nificantly larger than the initial stimulating current. Thus,the amplitude, duration, and shape of the action potentialare determined largely by the properties of the excitablemembrane and not the amplitude or duration of the stim-ulus. This all-or-nothing property of the action potentialsets it apart from graded potentials such as receptor po-tentials, electrotonic potentials, and synaptic potentials,which scale with the magnitude of the stimulus. A vari-ety of action potential types exist in many cell types andcell compartments as determined by the types of voltage-gated channels, leak channels, channel distributions, ionicconcentrations, membrane capacitance, temperature, andother factors.The principal ions involved in an action potential aresodium and potassium cations; sodium ions enter the cell,and potassium ions leave, restoring equilibrium. Rela-tively few ions need to cross the membrane for the mem-brane voltage to change drastically. The ions exchangedduring an action potential, therefore, make a negligiblechange in the interior and exterior ionic concentrations.The few ions that do cross are pumped out again bythe continuous action of the sodium–potassium pump,which, with other ion transporters, maintains the nor-mal ratio of ion concentrations across the membrane.Calcium cations and chloride anions are involved in afew types of action potentials, such as the cardiac actionpotential and the action potential in the single-cell algaAcetabularia, respectively.Although action potentials are generated locally onpatches of excitable membrane, the resulting currents cantrigger action potentials on neighboring stretches of mem-brane, precipitating a domino-like propagation. In con-trast to passive spread of electric potentials (electrotonicpotential), action potentials are generated anew alongexcitable stretches of membrane and propagate withoutdecay.[6] Myelinated sections of axons are not excitableand do not produce action potentials and the signal ispropagated passively as electrotonic potential. Regularlyspaced unmyelinated patches, called the nodes of Ran-vier, generate action potentials to boost the signal. Knownas saltatory conduction, this type of signal propagationprovides a favorable tradeoff of signal velocity and axondiameter. Depolarization of axon terminals, in general,triggers the release of neurotransmitter into the synapticcleft. In addition, backpropagating action potentials havebeen recorded in the dendrites of pyramidal neurons,which are ubiquitous in the neocortex.[lower-alpha 3] Theseare thought to have a role in spike-timing-dependent plas-ticity.

3 Neurotransmission

Main article: Neurotransmission

3.1 Anatomy of a neuron

Several types of cells support an action potential, suchas plant cells, muscle cells, and the specialized cells ofthe heart (in which occurs the cardiac action potential).However, the main excitable cell is the neuron, which alsohas the simplest mechanism for the action potential.Neurons are electrically excitable cells composed, in gen-eral, of one or more dendrites, a single soma, a single axonand one or more axon terminals. Dendrites are cellularprojections whose primary function is to receive synap-tic signals. Their protrusions, or spines, are designed tocapture the neurotransmitters released by the presynapticneuron. They have a high concentration of ligand-gatedion channels. These spines have a thin neck connectinga bulbous protrusion to the dendrite. This ensures thatchanges occurring inside the spine are less likely to affectthe neighboring spines. The dendritic spine can, with rareexception (see LTP), act as an independent unit. The den-drites extend from the soma, which houses the nucleus,and many of the “normal” eukaryotic organelles. Unlikethe spines, the surface of the soma is populated by voltageactivated ion channels. These channels help transmit thesignals generated by the dendrites. Emerging out fromthe soma is the axon hillock. This region is characterizedby having a very high concentration of voltage-activatedsodium channels. In general, it is considered to be thespike initiation zone for action potentials.[7] Multiple sig-nals generated at the spines, and transmitted by the somaall converge here. Immediately after the axon hillock isthe axon. This is a thin tubular protrusion traveling awayfrom the soma. The axon is insulated by a myelin sheath.Myelin is composed of either Schwann cells (in the pe-ripheral nervous system) or oligodendrocytes (in the cen-tral nervous system), both of which are types of glial cells.Although glial cells are not involved with the transmis-sion of electrical signals, they communicate and provideimportant biochemical support to neurons.[8] To be spe-cific, myelin wraps multiple times around the axonal seg-ment, forming a thick fatty layer that prevents ions fromentering or escaping the axon. This insulation preventssignificant signal decay as well as ensuring faster signalspeed. This insulation, however, has the restriction thatno channels can be present on the surface of the axon.There are, therefore, regularly spaced patches of mem-brane, which have no insulation. These nodes of Ran-vier can be considered to be “mini axon hillocks”, as theirpurpose is to boost the signal in order to prevent signifi-cant signal decay. At the furthest end, the axon loses itsinsulation and begins to branch into several axon termi-nals. These presynaptic terminals, or synaptic boutons,are a specialized area within the axon of the presynap-

3.4 “All-or-none” principle 5

tic cell that contains neurotransmitters enclosed in smallmembrane-bound spheres called synaptic vesicles.

3.2 Initiation

Before considering the propagation of action potentialsalong axons and their termination at the synaptic knobs,it is helpful to consider the methods by which action po-tentials can be initiated at the axon hillock. The basicrequirement is that the membrane voltage at the hillockbe raised above the threshold for firing.[1][2][9][10] Thereare several ways in which this depolarization can occur.

When an action potential arrives at the end of the pre-synapticaxon (top), it causes the release of neurotransmitter moleculesthat open ion channels in the post-synaptic neuron (bottom).The combined excitatory and inhibitory postsynaptic potentials ofsuch inputs can begin a new action potential in the post-synapticneuron.

3.3 Dynamics

Action potentials are most commonly initiated byexcitatory postsynaptic potentials from a presynapticneuron.[11] Typically, neurotransmitter molecules are re-leased by the presynaptic neuron. These neurotransmit-ters then bind to receptors on the postsynaptic cell. Thisbinding opens various types of ion channels. This open-ing has the further effect of changing the local permeabil-ity of the cell membrane and, thus, the membrane poten-tial. If the binding increases the voltage (depolarizes themembrane), the synapse is excitatory. If, however, thebinding decreases the voltage (hyperpolarizes the mem-brane), it is inhibitory. Whether the voltage is increasedor decreased, the change propagates passively to nearbyregions of the membrane (as described by the cable equa-tion and its refinements). Typically, the voltage stimulusdecays exponentially with the distance from the synapseand with time from the binding of the neurotransmitter.Some fraction of an excitatory voltage may reach the axonhillock and may (in rare cases) depolarize the membraneenough to provoke a new action potential. More typically,the excitatory potentials from several synapses must worktogether at nearly the same time to provoke a new actionpotential. Their joint efforts can be thwarted, however,by the counteracting inhibitory postsynaptic potentials.

Neurotransmission can also occur through electricalsynapses.[12] Due to the direct connection between ex-citable cells in the form of gap junctions, an action poten-tial can be transmitted directly from one cell to the nextin either direction. The free flow of ions between cellsenables rapid non-chemical-mediated transmission. Rec-tifying channels ensure that action potentials move onlyin one direction through an electrical synapse. Electricalsynapses are found in all nervous systems, including thehuman brain, although they are a distinct minority.[13]

3.4 “All-or-none” principle

The amplitude of an action potential is independent of theamount of current that produced it. In other words, largercurrents do not create larger action potentials. There-fore, action potentials are said to be all-or-none signals,since either they occur fully or they do not occur atall.[lower-alpha 4][lower-alpha 5][lower-alpha 6] This is in contrast toreceptor potentials, whose amplitudes are dependent onthe intensity of a stimulus.[14] In both cases, the frequencyof action potentials is correlated with the intensity of astimulus.

3.5 Sensory neurons

Main article: Sensory neuron

In sensory neurons, an external signal such as pressure,temperature, light, or sound is coupled with the open-ing and closing of ion channels, which in turn alter theionic permeabilities of the membrane and its voltage.[15]

These voltage changes can again be excitatory (depolar-izing) or inhibitory (hyperpolarizing) and, in some sen-sory neurons, their combined effects can depolarize theaxon hillock enough to provoke action potentials. Exam-ples in humans include the olfactory receptor neuron andMeissner’s corpuscle, which are critical for the sense ofsmell and touch, respectively. However, not all sensoryneurons convert their external signals into action poten-tials; some do not even have an axon![16] Instead, they mayconvert the signal into the release of a neurotransmitter,or into continuous graded potentials, either of which maystimulate subsequent neuron(s) into firing an action po-tential. For illustration, in the human ear, hair cells con-vert the incoming sound into the opening and closingof mechanically gated ion channels, which may causeneurotransmitter molecules to be released. In similarmanner, in the human retina, the initial photoreceptorcells and the next layer of cells (comprising bipolar cellsand horizontal cells) do not produce action potentials;only some amacrine cells and the third layer, the ganglioncells, produce action potentials, which then travel up theoptic nerve.

6 4 PHASES

3.6 Pacemaker potentials

Main article: Pacemaker potentialIn sensory neurons, action potentials result from an ex-

-70

-60

-50

-40

-30

-20

-10

0

10

Pacemaker Action Potential

PREPOTENTIAL

K+

Ca++(T)

In pacemaker potentials, the cell spontaneously depolarizes(straight line with upward slope) until it fires an action potential.

ternal stimulus. However, some excitable cells require nosuch stimulus to fire: They spontaneously depolarize theiraxon hillock and fire action potentials at a regular rate,like an internal clock.[17] The voltage traces of such cellsare known as pacemaker potentials.[18] The cardiac pace-maker cells of the sinoatrial node in the heart provide agood example.[lower-alpha 7] Although such pacemaker po-tentials have a natural rhythm, it can be adjusted by ex-ternal stimuli; for instance, heart rate can be altered bypharmaceuticals as well as signals from the sympatheticand parasympathetic nerves.[19] The external stimuli donot cause the cell’s repetitive firing, but merely alter itstiming.[18] In some cases, the regulation of frequency canbe more complex, leading to patterns of action potentials,such as bursting.

4 Phases

The course of the action potential can be divided into fiveparts: the rising phase, the peak phase, the falling phase,the undershoot phase, and the refractory period. Duringthe rising phase the membrane potential depolarizes (be-comes more positive). The point at which depolarizationstops is called the peak phase. At this stage, the mem-brane potential reaches a maximum. Subsequent to this,there is a falling phase. During this stage the membranepotential becomes more negative, returning towards rest-ing potential. The undershoot, or afterhyperpolarization,phase is the period during which the membrane poten-tial temporarily becomes more negatively charged thanwhen at rest (hyperpolarized). Finally, the time duringwhich a subsequent action potential is impossible or dif-ficult to fire is called the refractory period, which mayoverlap with the other phases.[20]

The course of the action potential is determined by two

coupled effects.[21] First, voltage-sensitive ion channelsopen and close in response to changes in the membranevoltage Vm. This changes the membrane’s permeabil-ity to those ions.[22] Second, according to the Goldmanequation, this change in permeability changes in the equi-librium potential Em, and, thus, the membrane voltageVm.[lower-alpha 8] Thus, the membrane potential affects thepermeability, which then further affects the membranepotential. This sets up the possibility for positive feed-back, which is a key part of the rising phase of the ac-tion potential.[1][4] A complicating factor is that a singleion channel may have multiple internal “gates” that re-spond to changes in Vm in opposite ways, or at differ-ent rates.[23][lower-alpha 9] For example, although raisingVmopens most gates in the voltage-sensitive sodium chan-nel, it also closes the channel’s “inactivation gate”, albeitmore slowly.[24] Hence, when Vm is raised suddenly, thesodium channels open initially, but then close due to theslower inactivation.The voltages and currents of the action potential in allof its phases were modeled accurately by Alan LloydHodgkin and Andrew Huxley in 1952,[lower-alpha 9] forwhich they were awarded the Nobel Prize in Physiologyor Medicine in 1963.[lower-greek 2] However, their modelconsiders only two types of voltage-sensitive ion chan-nels, and makes several assumptions about them, e.g.,that their internal gates open and close independentlyof one another. In reality, there are many types ofion channels,[25] and they do not always open and closeindependently.[lower-alpha 10]

4.1 Stimulation and rising phase

A typical action potential begins at the axon hillock[26]

with a sufficiently strong depolarization, e.g., a stimulusthat increases Vm. This depolarization is often caused bythe injection of extra sodium cations into the cell; thesecations can come from a wide variety of sources, such aschemical synapses, sensory neurons or pacemaker poten-tials.For a neuron at rest, there is a high concentration ofsodium and chlorine ions in the extracellular fluid com-pared to the intracellular fluid while there is a high con-centration of potassium ions in the intracellular fluidcompared to the extracellular fluid. This concentrationgradient along with potassium leak channels present onthe membrane of the neuron causes an efflux of potas-sium ions making the resting potential close to EK≈ –75 mV.[27] The depolarization opens both the sodiumand potassium channels in the membrane, allowing theions to flow into and out of the axon, respectively. Ifthe depolarization is small (say, increasing Vm from −70mV to −60 mV), the outward potassium current over-whelms the inward sodium current and the membranerepolarizes back to its normal resting potential around−70 mV.[1][2][3]However, if the depolarization is largeenough, the inward sodium current increases more than

4.4 Refractory period 7

the outward potassium current and a runaway condition(positive feedback) results: the more inward current thereis, the more Vm increases, which in turn further in-creases the inward current.[1][4] A sufficiently strong de-polarization (increase in Vm) causes the voltage-sensitivesodium channels to open; the increasing permeability tosodium drives Vm closer to the sodium equilibrium volt-age ENₐ≈ +55 mV. The increasing voltage in turn causeseven more sodium channels to open, which pushes Vmstill further towards ENₐ. This positive feedback contin-ues until the sodium channels are fully open and Vm isclose to ENₐ.[1][2][9][10] The sharp rise in Vm and sodiumpermeability correspond to the rising phase of the actionpotential.[1][2][9][10]

The critical threshold voltage for this runaway conditionis usually around −45 mV, but it depends on the recentactivity of the axon. A membrane that has just firedan action potential cannot fire another one immediately,since the ion channels have not returned to the deacti-vated state. The period during which no new action po-tential can be fired is called the absolute refractory pe-riod.[28][29][30] At longer times, after some but not all ofthe ion channels have recovered, the axon can be stim-ulated to produce another action potential, but with ahigher threshold, requiring a much stronger depolariza-tion, e.g., to −30 mV. The period during which actionpotentials are unusually difficult to evoke is called the rel-ative refractory period.[28][29][30]

4.2 Peak and falling phase

The positive feedback of the rising phase slows andcomes to a halt as the sodium ion channels become max-imally open. At the peak of the action potential, thesodium permeability is maximized and the membranevoltageVm is nearly equal to the sodium equilibrium volt-age ENₐ. However, the same raised voltage that openedthe sodium channels initially also slowly shuts them off,by closing their pores; the sodium channels become in-activated.[24] This lowers the membrane’s permeabilityto sodium relative to potassium, driving the membranevoltage back towards the resting value. At the sametime, the raised voltage opens voltage-sensitive potassiumchannels; the increase in the membrane’s potassium per-meability drives Vm towards EK.[24] Combined, thesechanges in sodium and potassium permeability cause Vmto drop quickly, repolarizing the membrane and produc-ing the “falling phase” of the action potential.[28][31][10][32]

4.3 Afterhyperpolarization

The raised voltage opened many more potassium chan-nels than usual, and some of these do not close rightaway when the membrane returns to its normal restingvoltage. In addition, further potassium channels open inresponse to the influx of calcium ions during the action

potential. The potassium permeability of the membraneis transiently unusually high, driving the membrane volt-age Vm even closer to the potassium equilibrium voltageEK. Hence, there is an undershoot or hyperpolarization,termed an afterhyperpolarization in technical language,that persists until the membrane potassium permeabilityreturns to its usual value.[33][31]

4.4 Refractory period

Each action potential is followed by a refractory pe-riod, which can be divided into an absolute refrac-tory period, during which it is impossible to evokeanother action potential, and then a relative refrac-tory period, during which a stronger-than-usual stimu-lus is required.[28][29][30] These two refractory periodsare caused by changes in the state of sodium and potas-sium channel molecules. When closing after an actionpotential, sodium channels enter an “inactivated” state,in which they cannot be made to open regardless of themembrane potential—this gives rise to the absolute re-fractory period. Even after a sufficient number of sodiumchannels have transitioned back to their resting state, itfrequently happens that a fraction of potassium channelsremains open, making it difficult for the membrane po-tential to depolarize, and thereby giving rise to the relativerefractory period. Because the density and subtypes ofpotassium channels may differ greatly between differenttypes of neurons, the duration of the relative refractoryperiod is highly variable.The absolute refractory period is largely responsible forthe unidirectional propagation of action potentials alongaxons.[34] At any given moment, the patch of axon be-hind the actively spiking part is refractory, but the patchin front, not having been activated recently, is capableof being stimulated by the depolarization from the actionpotential.

5 Propagation

Main article: Nerve conduction velocity

The action potential generated at the axon hillock prop-agates as a wave along the axon.[35] The currents flowinginwards at a point on the axon during an action poten-tial spread out along the axon, and depolarize the adja-cent sections of its membrane. If sufficiently strong, thisdepolarization provokes a similar action potential at theneighboring membrane patches. This basic mechanismwas demonstrated by Alan Lloyd Hodgkin in 1937. Af-ter crushing or cooling nerve segments and thus blockingthe action potentials, he showed that an action potentialarriving on one side of the block could provoke anotheraction potential on the other, provided that the blockedsegment was sufficiently short.[lower-alpha 11]

8 5 PROPAGATION

Once an action potential has occurred at a patch of mem-brane, the membrane patch needs time to recover be-fore it can fire again. At the molecular level, this abso-lute refractory period corresponds to the time requiredfor the voltage-activated sodium channels to recover frominactivation, i.e., to return to their closed state.[29] Thereare many types of voltage-activated potassium channelsin neurons, some of them inactivate fast (A-type cur-rents) and some of them inactivate slowly or not inac-tivate at all; this variability guarantees that there will bealways an available source of current for repolarization,even if some of the potassium channels are inactivatedbecause of preceding depolarization. On the other hand,all neuronal voltage-activated sodium channels inactivatewithin several millisecond during strong depolarization,thus making following depolarization impossible until asubstantial fraction of sodium channels have returned totheir closed state. Although it limits the frequency offiring,[36] the absolute refractory period ensures that theaction potential moves in only one direction along anaxon.[34] The currents flowing in due to an action potentialspread out in both directions along the axon.[37] However,only the unfired part of the axon can respond with an ac-tion potential; the part that has just fired is unresponsiveuntil the action potential is safely out of range and cannotrestimulate that part. In the usual orthodromic conduc-tion, the action potential propagates from the axon hillocktowards the synaptic knobs (the axonal termini); propaga-tion in the opposite direction—known as antidromic con-duction—is very rare.[38] However, if a laboratory axonis stimulated in its middle, both halves of the axon are“fresh”, i.e., unfired; then two action potentials will begenerated, one traveling towards the axon hillock and theother traveling towards the synaptic knobs.

In saltatory conduction, an action potential at one node of Ran-vier causes inwards currents that depolarize the membrane at thenext node, provoking a new action potential there; the action po-tential appears to “hop” from node to node.

5.1 Myelin and saltatory conduction

Main articles: Myelination and Saltatory conduction

In order to enable fast and efficient transduction of elec-trical signals in the nervous system, certain neuronal ax-ons are covered with myelin sheaths. Myelin is a mul-tilamellar membrane that enwraps the axon in segmentsseparated by intervals known as nodes of Ranvier. It isproduced by specialized cells: Schwann cells exclusivelyin the peripheral nervous system, and oligodendrocytesexclusively in the central nervous system. Myelin sheathreduces membrane capacitance and increases membraneresistance in the inter-node intervals, thus allowing afast, saltatory movement of action potentials from nodeto node.[lower-alpha 12][lower-alpha 13][lower-alpha 14] Myelinationis found mainly in vertebrates, but an analogous systemhas been discovered in a few invertebrates, such as somespecies of shrimp.[lower-alpha 15] Not all neurons in verte-brates are myelinated; for example, axons of the neuronscomprising the autonomous nervous system are not, ingeneral, myelinated.Myelin prevents ions from entering or leaving the axonalong myelinated segments. As a general rule, myelina-tion increases the conduction velocity of action poten-tials and makes them more energy-efficient. Whethersaltatory or not, the mean conduction velocity of an ac-tion potential ranges from 1 meter per second (m/s) toover 100 m/s, and, in general, increases with axonaldiameter.[lower-alpha 16]

Action potentials cannot propagate through the mem-brane in myelinated segments of the axon. However,the current is carried by the cytoplasm, which is suffi-cient to depolarize the first or second subsequent nodeof Ranvier. Instead, the ionic current from an actionpotential at one node of Ranvier provokes another ac-tion potential at the next node; this apparent “hopping”of the action potential from node to node is knownas saltatory conduction. Although the mechanism ofsaltatory conduction was suggested in 1925 by RalphLillie,[lower-alpha 17] the first experimental evidence forsaltatory conduction came from Ichiji Tasaki[lower-alpha 18]

and Taiji Takeuchi[lower-alpha 19][39] and from AndrewHuxley and Robert Stämpfli.[lower-alpha 20] By contrast, inunmyelinated axons, the action potential provokes an-other in the membrane immediately adjacent, and movescontinuously down the axon like a wave.Myelin has two important advantages: fast conductionspeed and energy efficiency. For axons larger than aminimum diameter (roughly 1 micrometre), myelinationincreases the conduction velocity of an action potential,typically tenfold.[lower-alpha 22] Conversely, for a given con-duction velocity, myelinated fibers are smaller than theirunmyelinated counterparts. For example, action poten-tials move at roughly the same speed (25 m/s) in a myeli-nated frog axon and an unmyelinated squid giant axon, but

5.2 Cable theory 9

Comparison of the conduction velocities of myelinated and un-myelinated axons in the cat. The conduction velocity v of myeli-nated neurons varies roughly linearly with axon diameter d (thatis, v ∝ d),[lower-alpha 16] whereas the speed of unmyelinated neu-rons varies roughly as the square root (v ∝√ d).[lower-alpha 21] Thered and blue curves are fits of experimental data, whereas thedotted lines are their theoretical extrapolations.

the frog axon has a roughly 30-fold smaller diameter and1000-fold smaller cross-sectional area. Also, since theionic currents are confined to the nodes of Ranvier, farfewer ions “leak” across the membrane, saving metabolicenergy. This saving is a significant selective advantage,since the human nervous system uses approximately 20%of the body’s metabolic energy.[lower-alpha 22]

The length of axons’ myelinated segments is importantto the success of saltatory conduction. They should be aslong as possible to maximize the speed of conduction, butnot so long that the arriving signal is too weak to provokean action potential at the next node of Ranvier. In na-ture, myelinated segments are generally long enough forthe passively propagated signal to travel for at least twonodes while retaining enough amplitude to fire an actionpotential at the second or third node. Thus, the safetyfactor of saltatory conduction is high, allowing transmis-sion to bypass nodes in case of injury. However, actionpotentials may end prematurely in certain places wherethe safety factor is low, even in unmyelinated neurons; acommon example is the branch point of an axon, whereit divides into two axons.[40]

Some diseases degrade myelin and impair saltatory con-duction, reducing the conduction velocity of actionpotentials.[lower-alpha 23] The most well-known of these ismultiple sclerosis, in which the breakdown of myelin im-pairs coordinated movement.[41]

5.2 Cable theory

Main article: Cable theoryThe flow of currents within an axon can be de-

Figure.1: Cable theory’s simplified view of a neuronal fiber. Theconnected RC circuits correspond to adjacent segments of a pas-sive neurite. The extracellular resistances rₑ (the counterparts ofthe intracellular resistances rᵢ) are not shown, since they are usu-ally negligibly small; the extracellular medium may be assumedto have the same voltage everywhere.

scribed quantitatively by cable theory[42] and its elabo-rations, such as the compartmental model.[43] Cable the-ory was developed in 1855 by Lord Kelvin to model thetransatlantic telegraph cable[lower-alpha 24] and was shownto be relevant to neurons by Hodgkin and Rushton in1946.[lower-alpha 25] In simple cable theory, the neuron istreated as an electrically passive, perfectly cylindricaltransmission cable, which can be described by a partialdifferential equation[42]

τ∂V

∂t= λ2 ∂

2V

∂x2− V

whereV(x, t) is the voltage across the membrane at a timet and a position x along the length of the neuron, andwhere λ and τ are the characteristic length and time scaleson which those voltages decay in response to a stimulus.Referring to the circuit diagram on the right, these scalescan be determined from the resistances and capacitancesper unit length.[44]

τ = rmcm

λ =

√rmrl

These time and length-scales can be used to understandthe dependence of the conduction velocity on the diam-eter of the neuron in unmyelinated fibers. For example,

10 7 OTHER CELL TYPES

the time-scale τ increases with both the membrane re-sistance rm and capacitance cm. As the capacitance in-creases, more charge must be transferred to produce agiven transmembrane voltage (by the equation Q=CV); asthe resistance increases, less charge is transferred per unittime, making the equilibration slower. In similar man-ner, if the internal resistance per unit length ri is lowerin one axon than in another (e.g., because the radius ofthe former is larger), the spatial decay length λ becomeslonger and the conduction velocity of an action potentialshould increase. If the transmembrane resistance rm is in-creased, that lowers the average “leakage” current acrossthe membrane, likewise causing λ to become longer, in-creasing the conduction velocity.

6 Termination

6.1 Chemical synapses

Main articles: Chemical synapse, Neurotransmitter,Excitatory postsynaptic potential and Inhibitory postsy-naptic potential

In general, action potentials that reach the synapticknobs cause a neurotransmitter to be released into thesynaptic cleft.[lower-alpha 26] Neurotransmitters are smallmolecules that may open ion channels in the postsynap-tic cell; most axons have the same neurotransmitter atall of their termini. The arrival of the action potentialopens voltage-sensitive calcium channels in the presynap-tic membrane; the influx of calcium causes vesicles filledwith neurotransmitter to migrate to the cell’s surface andrelease their contents into the synaptic cleft.[lower-alpha 27]

This complex process is inhibited by the neurotoxinstetanospasmin and botulinum toxin, which are responsi-ble for tetanus and botulism, respectively.[lower-alpha 28]

Intercellular space

Hydrophilic channel2-4 nm space

Connexon

Plasma membranes

connexin monomer

Closed Open

Electrical synapses between excitable cells allow ions to passdirectly from one cell to another, and are much faster thanchemical synapses.

6.2 Electrical synapses

Main articles: Electrical synapse, Gap junction andConnexin

Some synapses dispense with the “middleman” of theneurotransmitter, and connect the presynaptic and post-synaptic cells together.[lower-alpha 29] When an action po-tential reaches such a synapse, the ionic currents flowinginto the presynaptic cell can cross the barrier of the twocell membranes and enter the postsynaptic cell throughpores known as connexons.[lower-alpha 30] Thus, the ioniccurrents of the presynaptic action potential can directlystimulate the postsynaptic cell. Electrical synapses al-low for faster transmission because they do not requirethe slow diffusion of neurotransmitters across the synap-tic cleft. Hence, electrical synapses are used wheneverfast response and coordination of timing are crucial, as inescape reflexes, the retina of vertebrates, and the heart.

6.3 Neuromuscular junctions

Main articles: Neuromuscular junction, Acetylcholinereceptor and Cholinesterase enzyme

A special case of a chemical synapse is the neuromuscularjunction, in which the axon of a motor neuron termi-nates on a muscle fiber.[lower-alpha 31] In such cases, thereleased neurotransmitter is acetylcholine, which bindsto the acetylcholine receptor, an integral membrane pro-tein in the membrane (the sarcolemma) of the musclefiber.[lower-alpha 32] However, the acetylcholine does not re-main bound; rather, it dissociates and is hydrolyzed bythe enzyme, acetylcholinesterase, located in the synapse.This enzyme quickly reduces the stimulus to the muscle,which allows the degree and timing of muscular contrac-tion to be regulated delicately. Some poisons inactivateacetylcholinesterase to prevent this control, such as thenerve agents sarin and tabun,[lower-alpha 33] and the insecti-cides diazinon and malathion.[lower-alpha 34]

7 Other cell types

7.1 Cardiac action potentials

Main articles: Cardiac action potential, Electrical con-duction system of the heart, Cardiac pacemaker andArrhythmiaThe cardiac action potential differs from the neuronal

action potential by having an extended plateau, in whichthe membrane is held at a high voltage for a few hundredmilliseconds prior to being repolarized by the potassiumcurrent as usual.[lower-alpha 35] This plateau is due to the ac-tion of slower calcium channels opening and holding themembrane voltage near their equilibrium potential even

7.3 Plant action potentials 11

4

0

1 2

3

4

Phases of a cardiac action potential. The sharp rise in volt-age (“0”) corresponds to the influx of sodium ions, whereas thetwo decays (“1” and “3”, respectively) correspond to the sodium-channel inactivation and the repolarizing eflux of potassiumions. The characteristic plateau (“2”) results from the openingof voltage-sensitive calcium channels.

after the sodium channels have inactivated.The cardiac action potential plays an important rolein coordinating the contraction of the heart.[lower-alpha 35]

The cardiac cells of the sinoatrial node provide thepacemaker potential that synchronizes the heart. The ac-tion potentials of those cells propagate to and throughthe atrioventricular node (AV node), which is normallythe only conduction pathway between the atria and theventricles. Action potentials from the AV node travelthrough the bundle of His and thence to the Purkinjefibers.[note 2] Conversely, anomalies in the cardiac ac-tion potential—whether due to a congenital mutationor injury—can lead to human pathologies, especiallyarrhythmias.[lower-alpha 35] Several anti-arrhythmia drugsact on the cardiac action potential, such as quinidine,lidocaine, beta blockers, and verapamil.[lower-alpha 36]

7.2 Muscular action potentials

Main articles: Neuromuscular junction and Musclecontraction

The action potential in a normal skeletal muscle cell issimilar to the action potential in neurons.[45] Action po-tentials result from the depolarization of the cell mem-brane (the sarcolemma), which opens voltage-sensitivesodium channels; these become inactivated and the mem-brane is repolarized through the outward current of potas-sium ions. The resting potential prior to the action po-tential is typically −90mV, somewhat more negative thantypical neurons. The muscle action potential lasts roughly2–4 ms, the absolute refractory period is roughly 1–3 ms,and the conduction velocity along the muscle is roughly5 m/s. The action potential releases calcium ions thatfree up the tropomyosin and allow the muscle to con-tract. Muscle action potentials are provoked by the ar-rival of a pre-synaptic neuronal action potential at theneuromuscular junction, which is a common target for

neurotoxins.[lower-alpha 33]

7.3 Plant action potentials

Plant and fungal cells [lower-alpha 37] are also electri-cally excitable. The fundamental difference to an-imal action potentials is that the depolarization inplant cells is not accomplished by an uptake of pos-itive sodium ions, but by release of negative chlorideions.[lower-alpha 38][lower-alpha 39][lower-alpha 40] Together withthe following release of positive potassium ions, which iscommon to plant and animal action potentials, the actionpotential in plants infers, therefore, an osmotic loss ofsalt (KCl), whereas the animal action potential is osmot-ically neutral, when equal amounts of entering sodiumand leaving potassium cancel each other osmotically. Theinteraction of electrical and osmotic relations in plantcells [lower-alpha 41] indicates an osmotic function of elec-trical excitability in the common, unicellular ancestorsof plants and animals under changing salinity conditions,whereas the present function of rapid signal transmissionis seen as a younger accomplishment of metazoan cellsin a more stable osmotic environment.[46] It must be as-sumed that the familiar signalling function of action po-tentials in some vascular plants (e.g. Mimosa pudica),arose independently from that in metazoan excitable cells.

8 Taxonomic distribution and evo-lutionary advantages

Action potentials are found throughout multicellularorganisms, including plants, invertebrates suchas insects, and vertebrates such as reptiles andmammals.[lower-alpha 42] Sponges seem to be the mainphylum of multicellular eukaryotes that does not transmitaction potentials, although some studies have suggestedthat these organisms have a form of electrical signaling,too.[lower-alpha 43] The resting potential, as well as thesize and duration of the action potential, have notvaried much with evolution, although the conductionvelocity does vary dramatically with axonal diameter andmyelination.

Given its conservation throughout evolution, the actionpotential seems to confer evolutionary advantages. Onefunction of action potentials is rapid, long-range signalingwithin the organism; the conduction velocity can exceed110 m/s, which is one-third the speed of sound. For com-parison, a hormone molecule carried in the bloodstreammoves at roughly 8 m/s in large arteries. Part of thisfunction is the tight coordination of mechanical events,such as the contraction of the heart. A second functionis the computation associated with its generation. Being

12 10 NEUROTOXINS

an all-or-none signal that does not decay with transmis-sion distance, the action potential has similar advantagesto digital electronics. The integration of various dendriticsignals at the axon hillock and its thresholding to form acomplex train of action potentials is another form of com-putation, one that has been exploited biologically to formcentral pattern generators and mimicked in artificial neu-ral networks.

9 Experimental methods

See also: ElectrophysiologyThe study of action potentials has required the devel-

The giant axons of the European squid (Loligo vulgaris) werecrucial for scientists to understand the action potential.

opment of new experimental methods. The initial work,prior to 1955, focused on three goals: isolating signalsfrom single neurons or axons, developing fast, sensitiveelectronics, and shrinking electrodes enough that the volt-age inside a single cell could be recorded.The first problem was solved by studying the gi-ant axons found in the neurons of the squid genusLoligo.[lower-alpha 44] 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 themeasy to extract and manipulate.[lower-alpha 9][lower-alpha 45]

However, the Loligo axons are not representative of allexcitable cells, and numerous other systems with actionpotentials have been studied.The second problem was addressed with the crucial de-velopment of the voltage clamp,[lower-alpha 46] which per-mitted experimenters to study the ionic currents underly-ing an action potential in isolation, and eliminated a keysource of electronic noise, the current IC associated withthe capacitance C of the membrane.[48] Since the currentequals C times the rate of change of the transmembranevoltage Vm, the solution was to design a circuit that keptVm fixed (zero rate of change) regardless of the currentsflowing across the membrane. Thus, the current requiredto keep Vm at a fixed value is a direct reflection of the

current flowing through the membrane. Other electronicadvances included the use of Faraday cages and electron-ics with high input impedance, so that the measurementitself did not affect the voltage being measured.[49]

The third problem, that of obtaining electrodessmall enough to record voltages within a sin-gle axon without perturbing it, was solved in1949 with the invention of the glass micropipetteelectrode,[lower-alpha 47] which was quickly adopted byother researchers.[lower-alpha 48][lower-alpha 49] Refinementsof this method are able to produce electrode tips that areas fine as 100 Å (10 nm), which also confers high inputimpedance.[50] Action potentials may also be recordedwith small metal electrodes placed just next to a neuron,with neurochips containing EOSFETs, or optically withdyes that are sensitive to Ca2+ or to voltage.[lower-alpha 50]

As revealed by a patch clamp electrode, an ion channel has twostates: open (high conductance) and closed (low conductance).

While glass micropipette electrodes measure the sum ofthe currents passing through many ion channels, study-ing the electrical properties of a single ion channel be-came possible in the 1970s with the development of thepatch clamp by Erwin Neher and Bert Sakmann. Forthis they were awarded the Nobel Prize in Physiologyor Medicine in 1991.[lower-greek 3] Patch-clamping verifiedthat ionic channels have discrete states of conductance,such as open, closed and inactivated.Optical imaging technologies have been developed in re-cent years to measure action potentials, either via simulta-neous multisite recordings or with ultra-spatial resolution.Using voltage-sensitive dyes, action potentials have beenoptically recorded from a tiny patch of cardiomyocytemembrane.[lower-alpha 51]

10 Neurotoxins

Several neurotoxins, both natural and synthetic, aredesigned to block the action potential. Tetrodotoxinfrom the pufferfish and saxitoxin from the Gonyaulax(the dinoflagellate genus responsible for "red tides")block action potentials by inhibiting the voltage-sensitivesodium channel;[lower-alpha 52] similarly, dendrotoxin fromthe black mamba snake inhibits the voltage-sensitivepotassium channel. Such inhibitors of ion channels servean important research purpose, by allowing scientists to“turn off” specific channels at will, thus isolating the other

13

Tetrodotoxin is a lethal toxin found in pufferfish that inhibits thevoltage-sensitive sodium channel, halting action potentials.

channels’ contributions; they can also be useful in puri-fying ion channels by affinity chromatography or in as-saying their concentration. However, such inhibitors alsomake effective neurotoxins, and have been considered foruse as chemical weapons. Neurotoxins aimed at the ionchannels of insects have been effective insecticides; oneexample is the synthetic permethrin, which prolongs theactivation of the sodium channels involved in action po-tentials. The ion channels of insects are sufficiently dif-ferent from their human counterparts that there are fewside effects in humans. Many other neurotoxins interferewith the transmission of the action potential’s effects atthe synapses, especially at the neuromuscular junction.

11 History

The role of electricity in the nervous systems of ani-mals was first observed in dissected frogs by Luigi Gal-vani, who studied it from 1791 to 1797.[lower-alpha 53] Gal-vani’s results stimulated Alessandro Volta to develop theVoltaic pile—the earliest-known electric battery—withwhich he studied animal electricity (such as electric eels)and the physiological responses to applied direct-currentvoltages.[lower-alpha 54]

Scientists of the 19th century studied the propagationof electrical signals in whole nerves (i.e., bundles ofneurons) and demonstrated that nervous tissue was madeup of cells, instead of an interconnected network of tubes(a reticulum).[51] Carlo Matteucci followed up Galvani’sstudies and demonstrated that cell membranes had a volt-age across them and could produce direct current. Mat-teucci’s work inspired the German physiologist, Emil duBois-Reymond, who discovered the action potential in1848. The conduction velocity of action potentials wasfirst measured in 1850 by du Bois-Reymond’s friend,Hermann von Helmholtz. To establish that nervous tis-sue is made up of discrete cells, the Spanish physician

Image of two Purkinje cells (labeled as A) drawn by SantiagoRamón y Cajal in 1899. Large trees of dendrites feed into thesoma, from which a single axon emerges and moves generallydownwards with a few branch points. The smaller cells labeledB are granule cells.

Santiago Ramón y Cajal and his students used a staindeveloped by Camillo Golgi to reveal the myriad shapesof neurons, which they rendered painstakingly. For theirdiscoveries, Golgi and Ramón y Cajal were awarded the1906 Nobel Prize in Physiology.[lower-greek 4] Their workresolved a long-standing controversy in the neuroanatomyof the 19th century; Golgi himself had argued for the net-work model of the nervous system.The 20th century was a golden era for electrophysi-ology. In 1902 and again in 1912, Julius Bernsteinadvanced the hypothesis that the action potential re-sulted from a change in the permeability of the ax-onal membrane to ions.[lower-alpha 55][52] Bernstein’s hy-pothesis was confirmed by Ken Cole and Howard Cur-tis, who showed that membrane conductance increasesduring an action potential.[lower-alpha 56] In 1907, LouisLapicque suggested that the action potential was gener-ated as a threshold was crossed,[lower-alpha 57] what wouldbe later shown as a product of the dynamical systemsof ionic conductances. In 1949, Alan Hodgkin andBernard Katz refined Bernstein’s hypothesis by consider-ing that the axonal membrane might have different per-meabilities to different ions; in particular, they demon-strated the crucial role of the sodium permeability for theaction potential.[lower-alpha 58] They made the first actualrecording of the electrical changes across the neuronalmembrane that mediate the action potential.[lower-greek 5]

This line of research culminated in the five 1952 pa-pers of Hodgkin, Katz and Andrew Huxley, in whichthey applied the voltage clamp technique to determine

14 12 QUANTITATIVE MODELS

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 dependence of the axonal membrane’s permeabili-ties to sodium and potassium ions on voltage and time,from which they were able to reconstruct the actionpotential quantitatively.[lower-alpha 9] Hodgkin and Huxleycorrelated the properties of their mathematical modelwith discrete ion channels that could exist in severaldifferent states, including “open”, “closed”, and “in-activated”. Their hypotheses were confirmed in themid-1970s and 1980s by Erwin Neher and Bert Sak-mann, who developed the technique of patch clamp-ing to examine the conductance states of individual ionchannels.[lower-alpha 59] In the 21st century, researchers arebeginning to understand the structural basis for theseconductance states and for the selectivity of channelsfor their species of ion,[lower-alpha 60] through the atomic-resolution crystal structures,[lower-alpha 61] fluorescence dis-tance measurements[lower-alpha 62] and cryo-electron mi-croscopy studies.[lower-alpha 63]

Julius Bernstein was also the first to introduce the Nernstequation for resting potential across the membrane;this was generalized by David E. Goldman to theeponymous Goldman equation in 1943.[lower-alpha 8]

The sodium–potassium pump was identified in1957[lower-alpha 64][lower-greek 6] and its properties grad-ually elucidated,[lower-alpha 65][lower-alpha 66][lower-alpha 67]

culminating in the determination of its atomic-resolutionstructure by X-ray crystallography.[lower-alpha 68] Thecrystal structures of related ionic pumps have also beensolved, giving a broader view of how these molecular

machines work.[lower-alpha 69]

12 Quantitative models

Main article: Quantitative models of the action potentialMathematical and computational models are essential

gNa+

ENa+ EK+ ECl- ELeak

gLeakgCl-gK+ Cm

ILeakICl-IK+INa+

Extracellular

Intracellular

Vm--- ---

++++++

Im

Equivalent electrical circuit for the Hodgkin–Huxley model of theaction potential. I andV represent the current through, and thevoltage across, a small patch of membrane, respectively. The Crepresents the capacitance of the membrane patch, whereas thefour g's represent the conductances of four types of ions. The twoconductances on the left, for potassium (K) and sodium (Na), areshown with arrows to indicate that they can vary with the appliedvoltage, corresponding to the voltage-sensitive ion channels. Thetwo conductances on the right help determine the resting mem-brane potential.

for understanding the action potential, and offer pre-dictions that may be tested against experimental data,providing a stringent test of a theory. The most im-portant and accurate of the early neural models is theHodgkin–Huxley model, which describes the action po-tential by a coupled set of four ordinary differential equa-tions (ODEs).[lower-alpha 9] Although the Hodgkin–Huxleymodel may be a simplification with few limitations[53]

compared to the realistic nervous membrane as it existsin nature, its complexity has inspired several even-more-simplified models,[54][lower-alpha 70] such as the Morris–Lecar model[lower-alpha 71] and the FitzHugh–Nagumomodel,[lower-alpha 72] both of which have only two cou-pled ODEs. The properties of the Hodgkin–Huxleyand FitzHugh–Nagumo models and their relatives, suchas the Bonhoeffer–van der Pol model,[lower-alpha 73] havebeen well-studied within mathematics,[55][lower-alpha 74]

computation[56] and electronics.[lower-alpha 75] However thesimple models of generator potential and action po-tential fail to accurately reproduce the near thresholdneural spike rate and spike shape, specifically for themechanoreceptors like the Pacinian corpuscle.[57] Moremodern research has focused on larger and more inte-grated systems; by joining action-potential models withmodels of other parts of the nervous system (such asdendrites and synapses), researchers can study neuralcomputation[58] and simple reflexes, such as escape re-

15

flexes and others controlled by central pattern genera-tors.[59][lower-alpha 76]

13 See also

• Anode break excitation

• Bursting

• Central pattern generator

• Chronaxie

• Neural accommodation

• Single-unit recording

• Soliton model in neuroscience

14 Notes[1] In general, while this simple description of action po-

tential initiation is accurate, it does not explain phe-nomena such as excitation block (the ability to pre-vent neurons from eliciting action potentials by stim-ulating them with large current steps) and the abilityto elicit action potentials by briefly hyperpolarizing themembrane. By analyzing the dynamics of a system ofsodium and potassium channels in a membrane patch us-ing computational models, however, these phenomena arereadily explained.[lower-greek 1]

[2] Note that these Purkinje fibers are muscle fibers and notrelated to the Purkinje cells, which are neurons found inthe cerebellum.

15 Footnotes[1] Bullock, Orkand & Grinnell 1977, pp. 150-151.

[2] Junge 1981, pp. 89-90.

[3] Schmidt-Nielsen 1997, p. 484.

[4] Purves et al. 2008, pp. 48-49; Bullock, Orkand & Grin-nell 1977, p. 141; Schmidt-Nielsen 1997, p. 483; Junge1981, p. 89.

[5] Stevens 1966, p. 127.

[6] Schmidt-Nielsen, p. 484.

[7] Bullock, Orkand & Grinnell 1977, p. 11.

[8] Silverthorn 2010, p. 253.

[9] Purves et al. 2008, pp. 49-50; Bullock, Orkand & Grin-nell 1977, pp. 140-141; Schmidt-Nielsen 1997, pp. 480-481.

[10] Schmidt-Nielsen 1997, pp. 483-484.

[11] Bullock, Orkand & Grinnell 1977, pp. 177-240; Schmidt-Nielsen 1997, pp. 490-499; Stevens 1966, p. 47-68.

[12] Bullock, Orkand & Grinnell 1977, pp. 178-180; Schmidt-Nielsen 1997, pp. 490-491.

[13] Purves et al. 2001.

[14] Purves et al. 2008, pp. 26-28.

[15] Schmidt-Nielsen 1997, pp. 535-580; Bullock, Orkand &Grinnell 1977, pp. 49-56, 76-93, 247-255; Stevens 1966,pp. 69-79.

[16] Bullock, Orkand & Grinnell 1977, pp. 53; Bullock,Orkand & Grinnell 1977, pp. 122-124.

[17] Junge 1981, pp. 115-132.

[18] Bullock, Orkand & Grinnell 1977, pp. 152-153.

[19] Bullock, Orkand & Grinnell 1977, pp. 444-445.

[20] Purves et al. 2008, p. 38.

[21] Stevens 1966, pp. 127-128.

[22] Purves et al. 2008, p. 61-65.

[23] Purves et al. 2008, pp. 64-74; Bullock, Orkand & Grin-nell 1977, pp. 149-150; Junge 1981, pp. 84-85; Stevens1966, pp. 152-158.

[24] Purves et al. 2008, p. 47; Purves et al. 2008, p. 65;Bullock, Orkand & Grinnell 1977, pp. 147-148; Stevens1966, p. 128.

[25] Goldin, AL in Waxman 2007, Neuronal Channels and Re-ceptors, pp. 43-58.

[26] Stevens 1966, p. 49.

[27] Purves et al. 2008, p. 34; Bullock, Orkand & Grinnell1977, p. 134; Schmidt-Nielsen 1997, pp. 478-480.

[28] Purves et al. 2008, p. 49.

[29] Stevens 1966, pp. 19-20.

[30] Bullock, Orkand & Grinnell 1977, p. 151; Junge 1981,pp. 4-5.

[31] Bullock, Orkand & Grinnell 1977, p. 152.

[32] Bullock, Orkand & Grinnell 1977, pp. 147-149; Stevens1966, pp. 126-127.

[33] Purves et al. 2008, p. 37.

[34] Purves et al. 2008, p. 56.

[35] Bullock, Orkland & Grinnell 1977, pp. 160-164.

[36] Stevens 1966, pp. 21-23.

[37] Bullock, Orkland & Grinnell 1977, pp. 161-164.

[38] Bullock, Orkland & Grinnell 1977, p. 509.

[39] Tasaki, I in Field 1959, pp. 75–121

[40] Bullock, Orkland & Grinnell 1977, p. 163.

16 16 REFERENCES

[41] Waxman, SG in Waxman 2007, Multiple Sclerosis as aNeurodegenerative Disease, pp. 333-346.

[42] Rall, W in Koch & Segev 1989, Cable Theory for Den-dritic Neurons, p. 9-62.

[43] Segev, I; Fleshman, JW; Burke, RE in Koch & Segev1989, Compartmental Models of Complex Neurons, pp.63-96.

[44] Purves et al. 2008, pp. 52-53.

[45] Ganong 1991, pp. 59-60.

[46] Gradmann, D; Mummert, H in Spanswick, Lucas &Dainty 1980, Plant action potentials, pp. 333-344.

[47] Bullock 1965.

[48] Junge 1981, pp. 63-82.

[49] Kettenmann & Grantyn 1992.

[50] Snell, FM in Lavallee, Schanne & Hebert 1969, SomeElectrical Properties of Fine-Tipped Pipette Microelec-trodes.

[51] Brazier 1961; McHenry & Garrison 1969; Worden,Swazey & Adelman 1975.

[52] Bernstein 1912.

[53] Baranauskas, G.; Martina, M. (2006). “Sodium Cur-rents Activate without a Hodgkin and Huxley-Type De-lay in Central Mammalian Neurons”. J. Neurosci. 26 (2):671–684. doi:10.1523/jneurosci.2283-05.2006. PMID16407565.

[54] Hoppensteadt 1986.

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[2] “The Nobel Prize in Physiology or Medicine 1963” (Pressrelease). The Royal Swedish Academy of Science. 1963.Retrieved 2010-02-21.

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17 Further reading• Aidley DJ, Stanfield PR (1996). Ion Channels:Molecules in Action. Cambridge: Cambridge Uni-versity Press. ISBN 978-0-521-49882-1.

• Bear MF, Connors BW, Paradiso MA (2001). Neu-roscience: Exploring the Brain. Baltimore: Lippin-cott. ISBN 0-7817-3944-6.

• Clay JR (May 2005). “Axonal excitability re-visited”. Prog Biophys Mol Biol 88 (1): 59–90. doi:10.1016/j.pbiomolbio.2003.12.004. PMID15561301.

• Deutsch S, Micheli-Tzanakou E (1987). Neuroelec-tric Systems. New York: New York University Press.ISBN 0-8147-1782-9.

• Hille B (2001). Ion Channels of Excitable Mem-branes (3rd ed.). Sunderland, MA: Sinauer Asso-ciates. ISBN 978-0-87893-321-1.

• Johnston D, Wu SM-S (1995). Foundations of Cel-lular Neurophysiology. Cambridge, MA: BradfordBook, The MIT Press. ISBN 0-262-10053-3.

• Kandel ER, Schwartz JH, Jessell TM (2000).Principles of Neural Science (4th ed.). New York:McGraw-Hill. ISBN 0-8385-7701-6.

• Miller C (1987). “How ion channel proteins work”.In LK Kaczmarek, IB Levitan. Neuromodulation:The Biochemical Control of Neuronal Excitability.New York: Oxford University Press. pp. 39–63.ISBN 978-0-19-504097-5.

• Nelson DL, Cox MM (2008). Lehninger Principlesof Biochemistry (5th ed.). New York: W. H. Free-man. ISBN 978-0-7167-7108-1.

18 External linksAnimations

• Ionic flow in action potentials at Blackwell Publish-ing

22 18 EXTERNAL LINKS

• Action potential propagation in myelinated and un-myelinated axons at Blackwell Publishing

• Generation of AP in cardiac cells and generation ofAP in neuron cells

• Resting membrane potential from Life: The Scienceof Biology, by WK Purves, D Sadava, GH Orians,and HC Heller, 8th edition, New York: WH Free-man, ISBN 978-0-7167-7671-0.

• Ionic motion and the Goldman voltage for arbitraryionic concentrations at The University of Arizona

• A cartoon illustrating the action potential

• Action potential propagation

• Production of the action potential: voltage and cur-rent clamping simulations

• Open-source software to simulate neuronal and car-diac action potentials at SourceForge.net

• Introduction to the Action Potential, NeuroscienceOnline (electronic neuroscience textbook by UTHouston Medical School)

• Khan Academy: Electrotonic and action potential

23

19 Text and image sources, contributors, and licenses

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