# Action potential

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An action potential is a pulse-like wave of voltage that can travel on certain types of cell membranes. It occurs most commonly on the membrane of the axon of a neuron, but also appears in other types of excitable cells, such as cardiac muscle cells and even plant cells. The resting voltage across the axonal membrane is typically −60 mV to −70 mV, with the inside being more negative than the outside. This voltage results mainly from a difference in concentrations of potassium inside and outside the cell, as described by the Goldman equation. As an action potential passes through a point, the voltage rises to roughly +40 mV in one millisecond, then returns to −60 mV, usually with an undershoot (Figure 1A). The action potential moves rapidly down the axon, with a conduction velocity as high as 100 meters/second (225 miles per hour). Because of this rapid speed, action potentials are useful in conveying information along neurons, which are sometimes longer than a meter; no material object could be transported as quickly through the body.

An action potential is stimulated by depolarizing the membrane, i.e., by increasing the voltage of the cell's interior relative to the cell's exterior. This depolarization opens voltage-sensitive channels, which allow positive current to flow inwards, further depolarizing the membrane. Weak depolarizations are damped out, restoring the resting potential. A sufficiently strong stimulus, however, will cause the membrane to "fire", initiating a positive feedback loop that suddenly and rapidly increases the voltage. 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. In neurons, the rise and fall of membrane voltage usually lasts a few thousandths of a second; hence, action potentials are sometimes called "spikes".

The passage of an action potential can leave the ionic channels in a non-equilibrium state, making it much more difficult to open them and produce 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 cations; sodium ions enter the cell, and potassium ions leave it, restoring equilibrium. Relatively few ions are required 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 action potential "travels" because it dramatically raises the voltage at one patch of membrane, causing a similar rise at adjacent patches, as described by the cable equation. The axon generally forms many branches, and the action potential usually travels along both forks of a branch point. The action potential stops at the termini of these branches, but may provoke the extracellular release of neurotransmitters at these synapses. These neurotransmitters diffuse and may bind to receptors on an adjacent excitable cell. These receptors are usually ionic channels, although – in contrast to the axonal channels – they are generally opened by chemical binding, not by changes in voltage. The binding of neurotransmitters can help to depolarize the membrane (an excitatory channel) or make shunt any excitatory currents back outside (an inhibitory channel). If these polarizations are sufficiently strong, they can provoke another action potential, beginning the process anew.

## Cellular and biophysical context

### Anatomy of a neuron

Main article: Neuron

Several types of cells support an action potential, such as cells of the heart (cardiac action potential); however, the principal cell type is the neuron, which also has the simplest mechanism. Therefore, we temporarily focus on this cell type, and discuss the differences with other cell types below.

Neurons come in a wide variety of shapes, as described by Santiago Ramón y Cajal around the turn of the 20th century.[1] Nevertheless, all neurons share common traits. Being a eukaryotic cell, they have a single cell nucleus and the usual cellular organelles, such as mitochondria, ribosomes, an endoplasmic reticulum and the Golgi apparatus. Neurons usually have an enlarged central region known as the soma; the nucleus is usually located in the soma, but not always.[2] Most neurons have several long, thin, branched tendrils attached to the soma called dendrites. In addition to these dendrites, most neurons have a single axon, usually thicker and longer than the dendrites; the point at which the axon joins the soma is denoted as the axon hillock. The axon is the only part of the neuron that can support an action potential. This axon usually forks repeatedly near its terminus into many branches, each of which ends in a button-like axon terminal close to another neuron. The (small) space between the two neurons is known as the synapse, with the terminating axon known as the pre-synaptic axon and the other known as the post-synaptic neuron. Most often, these synapses connect an axon terminal with the dendrite of another neuron; however, axons are known to terminate on the soma and even on other axons.[3] The action potential itself does not cross between neurons; rather, the arrival of an action potential stimulates the release of neurotransmitters from the axonal terminal. These neurotransmitters bind to ligand-gated ion channels in the dendritic membrane, stimulating postsynaptic potentials, excitatory and inhibitory, that may depolarize the postsynaptic axon hillock enough to initiate a new action potential. This integration of dendritic signals at the axon hillock and its translation into a temporal code of action potentials is one of the chief mechanisms of neural computing.

### Transport across the plasma membrane

[Image:CellMembraneDrawing.jpg|thumb|300px|The hydrophobic cell membrane prevents charged molecules from easily diffusing through it, permitting a potential difference to exist across the membrane.]]

#### Ion pumps

Main article: Ion transporter

#### Ion channels

Main article: Ion channel

### Resting potential

Main article: Resting potential

The resting potential is what would be maintained were there no action potentials, synaptic potentials, or other changes to the membrane potential. In neurons the resting potential is approximately −70 mV (the negative sign signifies excess negative charge inside the cell relative to the outside). The resting potential is mostly determined by the ion concentrations in the fluids on both sides of the cell membrane and the ion transport proteins in the cell membrane. The term resting is somewhat misleading, for the cell must constantly do work to maintain the resting potential. The establishment of this potential difference involves several factors, the most important of which are the transport of ions across the cell membrane and the selective permeability of the membrane to these ions.

The active transport of potassium and sodium ions into and out of the cell, respectively, is accomplished by a number of sodium-potassium pumps scattered across the cell membrane. Each pump transports two ions of potassium into the cell for every three ions of sodium pumped out. This establishes a particular distribution of positively charged ions across the cell membrane, with more sodium present outside the cell than inside. In some situations, the electrogenic sodium-potassium pumps make a significant contribution to the resting membrane potential, but in most cells there are potassium leak channels that dominate the value of the resting potential.

Sodium and potassium ions diffuse through open ion channels under the influence of their electrochemical gradients. At the resting potential, the net movement of sodium into the cell equals the net movement of potassium out of the cell. However, the resting cell membrane is approximately 75 times more permeable to potassium than to sodium because potassium leak channels are always open. As a result, the cell's resting membrane potential is closer to the equilibrium potential of potassium (=EK=−90 mV) than the equilibrium potential of sodium (=ENa=+60 mV).

Like the resting potential, action potentials depend upon the permeability of the cell membrane to sodium and potassium ions. Transient changes in conductance for different ions cause the changes in membrane potential necessary to initiate, sustain, and terminate action potentials.

The sequence of events that underlie the action potential are outlined below:

### Resting potential

At rest in many neurons, potassium channels (both the inward-rectifier potassium ion channel and tandem pore domain potassium channel are open while sodium channels are closed. Though no net current flows, the resting potential is pulled toward the K+ reversal potential as K+ is the primary permeant ion. Other tissue types, such as skeletal muscle, can also have a large resting Cl- conductance, increasing the resting potential to more positive values.

## Sequence of events

An action potential is a depolarizing all-or-nothing stimulus that propagates along a cell's surface without losing intensity. There is always a difference in electrostatic potential between the inside and outside of a cell, i.e. the cell is polarized. This membrane potential is the result of the distribution of ions across the cell membrane and the selective permeability of the membrane to these ions. The voltage of an inactive cell remains close to a resting potential with excess negative charge inside the cell. When the membrane of an excitable cell becomes depolarized beyond a threshold, the cell undergoes an action potential (it "fires"), often called a "spike" (see Threshold and initiation).

An action potential is a rapid change of the polarity of the voltage from negative to positive and then vice versa, the entire cycle lasting on the order of milliseconds. Each cycle — and therefore each action potential — has a rising phase, a falling phase, and finally an undershoot (see Phases). In specialized muscle cells of the heart, such as cardiac pacemaker cells, a plateau phase of intermediate voltage may precede the falling phase, extending the action potential duration into hundreds of milliseconds.

The action potential does not dwell in one location of the cell's membrane, but travels along the membrane (see Propagation). It can travel along an axon for long distances, for example to carry signals from the spinal cord to the muscles of the foot. After traveling the whole length of the axon, the action potential reaches a synapse, where it stimulates the release of neurotransmitters. These neurotransmitters can immediately induce an action potential in the next neuron to propagate the signal, but the response is usually more complex.

Both the speed and complexity of action potentials vary between different types of cells, but their amplitudes tend to be roughly the same. Within any one cell, consecutive action potentials are typically indistinguishable. Neurons are thought to transmit information by generating sequences of action potentials called "spike trains". By varying both the rate as well as the precise timing of the action potentials they generate, neurons can change the information that they transmit.

## Phases

### Stimulation

A local membrane depolarization caused by an excitatory stimulus causes some voltage-gated sodium channels in the axon hillock membrane to open, causing net inward movement of sodium ions through the channels along their electrochemical gradient. This movement of sodium ions across the membrane is an example of facilitated diffusion.[4] Because they are positively charged, the inward moving sodium ions make the potential difference across the membrane less negative inside. This initial inward movement of sodium ions is favored by both the negative-inside membrane potential and the concentration gradient of sodium ions across the membrane (less sodium inside). The movement of individual sodium ions involves many random molecular collisions and at any particular moment a sodium ion might be moving outward, but the net movement of sodium is inward, as determined by the electrochemical gradient.

### Depolarization ("Rising phase")

As sodium ions enter and the membrane potential becomes less negative, more sodium channels open, causing an even greater influx of sodium ions. This is an example of positive feedback. As more sodium channels open, the sodium current dominates over the potassium leak current and the membrane potential becomes positive inside. Recent experiments on cortical neurons suggest that sodium channels open cooperatively,[5] allowing for a much faster uptake than is possible for Hodgkin-Huxley–type dynamics.

### Peak

By the time the membrane potential has reached a peak value of around +50 mV, time-dependent inactivation gates on the sodium channels have already started to close, reducing and finally preventing further influx of sodium ions. While this occurs, the voltage-sensitive activation gates on the voltage-gated potassium channels begin to open.

It is important to appreciate that very few ions actually cross the membrane at any stage in the action potential. There is no 'flood' of sodium into the cell; the gross intracellular and extracellular concentrations of sodium and potassium change so little during the action potential as to be negligible. Instead, the change in membrane polarity occurs due to the permeability for sodium, PNa, increasing greatly via the positive feedback system described (depolarization causes voltage-gated sodium channels to open, so membrane becomes more depolarized etc). Increasing PNa relative to potassium permeability (PK) affects voltage because it lifts the membrane potential towards that of the equilibrium potential for sodium (ENa), which is approximately +55 mV.

This can be measured quantitatively using the Goldman equation,

$V = \frac{RT}{F} \ln \frac{P_{\hbox{K}}[\hbox{K}^+]_{\hbox{extracellular}} + P_{\hbox{Na}}[\hbox{Na}^+]_{\hbox{extracellular}}}{P_{\hbox{K}}[\hbox{K}^+]_{\hbox{intracellular}} + P_{\hbox{Na}}[\hbox{Na}^+]_{\hbox{intracellular}}}$

Concentrations of Na and K in and out of the cell do not change much, but PNa and PK values do change markedly, and it is this that changes the value for V.

### Repolarization ("Falling phase")

As voltage-gated potassium channels open, there is a large outward movement of potassium ions driven by the potassium concentration gradient and initially favored by the positive-inside electrical gradient. As potassium ions diffuse out, this movement of positive charge causes a reversal of the membrane potential to negative-inside and repolarization of the neuron back towards the large negative-inside resting potential.

Again, it is not the movement of potassium ions that changes membrane voltage. It is the value for PK rising above that for PNa, dragging membrane voltage back towards the equilibrium constant for potassium (around -70 mV) (see Goldman Constant Field Equation).

### Hyperpolarization ("Undershoot")

Closing of voltage-gated potassium channels is both voltage- and time-dependent. As potassium exits the cell, the resulting membrane repolarization initiates the closing of voltage-gated potassium channels. These channels do not close immediately in response to a change in membrane potential; rather, voltage-gated potassium channels (also called delayed rectifier potassium channels) have a delayed response, such that potassium continues to flow out of the cell even after the membrane has fully repolarized. Thus the membrane potential dips below the normal resting membrane potential of the cell for a brief moment; this dip of hyperpolarization is known as the undershoot.

### Refractory period

During the next, ~ 1–3 ms, action potential initiation becomes difficult. This is the Refractory Period, consisting of an absolute and relative phase. In the absolute refractory period, the Na+ Channels cannot be opened by a stimulus; they have entered an inactivated state. This is time-dependent, and during this phase no action potential, irrespective of applied voltage, will be fired. In the relative refractory period (immediately after the absolute phase), action potentials can be initiated, but the threshold is greater. There are two reasons for this: the cell may still be slightly hyperpolarized due to still higher than resting value for PK, so more voltage is required to reach threshold, and also the threshold itself is higher than usual because some of the sodium channels will still be inactivated. (Note that the sodium channel therefore has at least three states: closed, open and inactivated — closed and not able to open). The refractory period is important because it ensures unidirectional (one way) propagation of the action potential.

There is a common misconception that the Na+/K+ pump restores the resting potential during the action potential falling phase by actively pumping Na+ out of, and K+ into the neuron. This (along with the misconception that sodium 'floods' the cell to cause the action potential), is not correct. The Na+/K+/ATPase (another name for the pump) does ultimately maintain the resting potential by maintaining the concentration gradients for Na and K, but does so on a much slower time scale; days as opposed to milliseconds. During the falling phase of the action potential, the resting potential is restored exclusively by PK rising to once again be far larger than PNa (i.e. membrane permeability to potassium far exceeds its permeability to sodium, thus bringing the membrane potential back down towards EK (the potassium equilibrium potential). The time-course of the role of the Na+/K+/ATPase in maintaining resting potentials can be demonstrated by the fact that the poison Ouabain inactivates the Na+/K+/ATPase, yet many thousands of action potentials can still be fired without significantly running down the concentration gradients.

## Threshold and initiation

Action potentials are triggered when an initial depolarization reaches the threshold. This threshold potential varies, but generally is about 15 millivolts more positive than the cell's resting membrane potential, occurring when the inward sodium current exceeds the outward potassium current. The net influx of positive charges carried by sodium ions depolarizes the membrane potential, leading to the further opening of voltage-gated sodium channels. These channels support greater inward current causing further depolarization, creating a positive-feedback cycle that drives the membrane potential to a very depolarized level.

The action potential threshold can be shifted by changing the balance between sodium and potassium currents. For example, if some of the sodium channels are in an inactivated state, then a given level of depolarization will open fewer sodium channels and a greater depolarization will be needed to trigger an action potential. This is the basis for the refractory period.

Action potentials are largely dictated by the interplay between sodium and potassium ions (although there are minor contributions from other ions such as calcium and chloride), and are often modeled using hypothetical cells containing only two transmembrane ion channels (a voltage-gated sodium channel and a non-voltage-gated potassium channel). The origin of the action potential threshold may be studied using I/V curves (right) that plot currents through ion channels against the cell's membrane potential. (Note that the illustrated I/V is an "instantaneous" current voltage relationship. It represents the peak current through channels at a given voltage before any inactivation has taken place (i.e. ~ 1 ms after stepping to that voltage) for the Na current. The most positive voltages in this plot are only attainable by the cell through artificial means: voltages imposed by the voltage-clamp apparatus).

Four significant points in the I/V curve are indicated by arrows in the figure:

1. The green arrow indicates the resting potential of the cell and also the value of the equilibrium potential for potassium (Ek). As the K+ channel is the only one open at these negative voltages, the cell will rest at Ek.
2. The yellow arrow indicates the equilibrium potential for Na+ (ENa). In this two-ion system, ENa is the natural limit of membrane potential beyond which a cell cannot pass. Current values illustrated in this graph that exceed ENa are measured by artificially pushing the cell's voltage past its natural limit. Note however, that ENa could only be reached if the potassium current were absent.
3. The blue arrow indicates the maximum voltage that the peak of the action potential can approach. This is the actual natural maximum membrane potential that this cell can reach. It cannot reach ENa because of the counteracting influence of the potassium current.
4. The red arrow indicates the action potential threshold. This is where Isum becomes net-inward. Note that this is a zero-current crossing, but with a negative slope. Any such "negative slope crossing" of the zero current level in an I/V plot is an unstable point. At any voltage negative to this crossing, the current is outward and so a cell will tend to return to its resting potential. At any voltage positive of this crossing, the current is inward and will tend to depolarize the cell. This depolarization leads to more inward current, thus the sodium current become regenerative. The point at which the green line reaches its most negative value is the point where all sodium channels are open. Depolarizations beyond that point thus decrease the sodium current as the driving force decreases as the membrane potential approaches ENa.

The action potential threshold is often confused with the "threshold" of sodium channel opening. This is incorrect, because sodium channels have no threshold. Instead, they open in response to depolarization in a stochastic manner. Depolarization does not so much open the channel as increases the probability of it being open. Even at hyperpolarized potentials, a sodium channel will open very occasionally. In addition, the threshold of an action potential is not the voltage at which sodium current becomes significant; it is the point where it exceeds the potassium current.

Biologically in neurons, depolarization typically originates in the dendrites at synapses. In principle, however, an action potential may be initiated anywhere along a nerve fiber. In his discovery of "animal electricity," Luigi Galvani made a leg of a dead frog kick as in life by touching a sciatic nerve with his scalpel, to which he had inadvertently transferred a negative, static-electric charge, thus initiating an action potential.

## Propagation

Main article: Cable theory

The influx of positively charged ions during an action potential changes the voltage across the membrane from its resting value (-65 mV) to a positive value (roughly +40 mV), but initially only in the vicinity of where the ionic channels were opened. The interior cytosol has a reasonably high ionic strength, typically 100 mM, and therefore can conduct electricity. Hence, if the interior voltage varies along the length of a neuron, then current will flow from the point of higher voltage (say, +40 mV) to the point of lower voltage (say, the resting potential -65 mV). This current will depolarize the latter point, and if sufficiently strong, will initiate a new action potential there.

This flow of current within the axon can be described by cable theory[6] and its elaborations, such as the compartmental model.[7] In simple cable theory, the neuron is treated as an electrically passive transmission cable, which is readily described by the partial differential equation[6]

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

where V(x,t) is the voltage across the membrane at a time t and a position x along the length of the neuron, and where λ and τ are the characteristic length and time scales on which those voltages decay in response to a stimulus. Given the circuit diagram above, these scales can be determined from the resistances and capacitances per unit length

$\tau = r_{m} c_{m}$
Failed to parse (syntax error): \lambda = \sqrt{\frac{r_{m}}{r_{i} + r_{e}}

Thus, if we decrease the capacitance cm, we decrease τ and, thus, speed up the neuron's response to a stimulus. Similarly, if we decrease the "leakage" current by increasing the membrane resistance rm, the spatial decay constant λ becomes longer. Both effects may be accomplished by wrapping the axon in a fatty, low-dielectric substance such as myelin, which is made up of Schwann cells. This allows for much faster axonal conduction between well-separated points, the nodes of Ranvier.

In unmyelinated axons, action potentials propagate as an interaction between passively spreading membrane depolarization and voltage-gated sodium channels. When one patch of cell membrane is depolarized enough to open its voltage-gated sodium channels, sodium ions enter the cell by facilitated diffusion. Once inside, positively-charged sodium ions "nudge" adjacent ions down the axon by electrostatic repulsion (analogous to the principle behind Newton's cradle) and attract negative ions away from the adjacent membrane. As a result, a wave of positivity moves down the axon without any individual ion moving very far. Once the adjacent patch of membrane is depolarized, the voltage-gated sodium channels in that patch open, regenerating the cycle. The process repeats itself down the length of the axon, with an action potential regenerated at each segment of membrane.

### Speed of propagation

Action potentials propagate faster in axons of larger diameter, other things being equal. They typically travel from 10–100 m/s. The main reason is that the axial resistance of the axon lumen is lower with larger diameters, because of an increase in the ratio of cross-sectional area to membrane surface area. As the membrane surface area is the chief factor impeding action potential propagation in an unmyelinated axon, increasing this ratio is a particularly effective way of increasing conduction speed.

An extreme example of an animal using axon diameter to speed action potential conduction is found in the Atlantic squid. The squid giant axon controls the muscle contraction associated with the squid's predator escape response. This axon can be more than 1 mm in diameter, and is presumably an adaptation to allow very fast activation of the escape behavior. The velocity of nerve impulses in these fibers is among the fastest in nature. Squids are notable examples of organisms with unmyelinated axons; the first tests to try to determine the mechanism by which impulses travel along axons, involving the detection of a potential difference between the inside and the surface of a neuron, were undertaken in the 1940s by Alan Hodgkin and Andrew Huxley using squid giant axons because of their relatively large axon diameter. Hodgkin and Huxley won their shares of the 1963 Nobel Prize in Physiology or Medicine for their work on the electrophysiology of nerve action potentials.[8]

In the autonomic nervous system in mammals, postganglionic neurons are unmyelinated. The small diameter of these axons (about 2 µ) results in a propagatory speed of approximately 1 m/s, as opposed to approximately 18 m/s in myelinated nerve fibers of comparable diameter, thus highlighting the effect of myelination on the speed of transmission of impulses.

### Saltatory conduction

In myelinated axons, saltatory conduction is the process by which an action potential appears to jump along the length of an axon, being regenerated only at uninsulated segments (the nodes of Ranvier). Saltatory conduction increases nerve conduction velocity without having to dramatically increase axon diameter.

Saltatory conduction has played an important role in the evolution of larger and more complex organisms whose nervous systems must rapidly transmit action potentials across greater distances. Without saltatory conduction, conduction velocity would need large increases in axon diameter, resulting in organisms with nervous systems too large for their bodies.

#### Detailed mechanism

The main impediment to conduction speed in unmyelinated axons is membrane capacitance. In an electric circuit, the capacitance of a capacitor can be decreased by decreasing the cross-sectional area of its plates, or by increasing the distance between plates. The nervous system uses myelin as its main strategy to decrease membrane capacitance. Myelin is an insulating sheath wrapped around axons by Schwann cells in the peripheral nervous system (PNS) and oligodendrocytes, in the Central Nervous System (CNS) neuroglia that flatten their cytoplasm to form large sheets made up mostly of plasma membrane. These sheets wrap around the axon, moving the conducting plates (the intra- and extracellular fluid) farther apart to decrease membrane capacitance.

The resulting insulation allows the rapid (essentially instantaneous) conduction of ions through a myelinated segment of axon, but prevents the regeneration of action potentials through those segments. Action potentials are only regenerated at the unmyelinated nodes of Ranvier which are spaced intermittently between myelinated segments. An abundance of voltage-gated sodium channels on these bare segments (up to three orders of magnitude greater than their density in unmyelinated axons[9]) allows action potentials to be efficiently regenerated at the nodes of Ranvier.

As a result of myelination, the insulated portion of the axon behaves like a passive wire: it conducts action potentials rapidly because its membrane capacitance is low, and minimizes the degradation of action potentials because its membrane resistance is high. When this passively propagated signal reaches a node of Ranvier, it initiates an action potential, which subsequently travels passively to the next node where the cycle repeats.

#### Resilience to injury

The length of myelinated segments of axon is important to saltatory conduction. They should be as long as possible to maximize the length of fast passive conduction, but not so long that the decay of the passive signal is too great to reach threshold at the next node of Ranvier. In reality, myelinated segments are 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.

#### Role in disease

Some diseases degrade saltatory conduction and reduce the speed of action potential conductance. The most well-known of these diseases is multiple sclerosis, in which the breakdown of myelin impairs coordinated movement.

## Refractory period

Where membrane has undergone an action potential, a refractory period follows. Thus, although the passive transmission of action potentials across myelinated segments would suggest that action potentials propagate in either direction, most action potentials travel unidirectionally because the node behind the propagating action potential is refractory.

This period arises primarily because of the time-dependent inactivation of sodium channels, as described by Hodgkin and Huxley in 1952. Immediately after an action potential, during the absolute refractory period, virtually all sodium channels are inactivated and thus it is impossible to fire another action potential in that segment of membrane.

With time, sodium channels are reactivated in a stochastic manner. As they become available, it becomes possible to fire an action potential, albeit one with a much higher threshold. This is the relative refractory period and together with the absolute refractory period, lasts approximately five milliseconds.

## Termination and consequences

An action potential proceeding along a membrane is prevented from reversing its direction by the refractory period, and will eventually depolarize the entire cell. When the action potential reaches an area where all the cell membrane is already depolarized or still in the refractory period, the action potential can no longer propagate. Because an action potential propagates only along contiguous membrane, another mechanism is necessary to transmit action potentials between cells. Neurons communicate with each other at a chemical synapse. Other cell types, such as cardiac muscle cells, can communicate action potentials via electrical synapses.

The synapse is a very small gap between neurons that allows one-way communication. As the presynaptic neuron undergoes an action potential, voltage-sensitive calcium channels open and cause the release of neurotransmitters into the synapse. These chemical transmitters can initiate an action potential in the postsynaptic neuron, allowing communication between neurons. Some neurotransmitters inhibit action potentials, and the interaction of excitatory and inhibitory signals allows complex modulation of signals in the nervous system.

The action potential, as a method of long-distance communication, fits a particular biological need seen most readily when considering the transmission of information along a nerve axon. To move a signal from one end of an axon to the other, nature must contend with physics similar to those that govern the movement of electrical signals along a wire. Due to the resistance and capacitance of a wire, signals tend to degrade as they travel along that wire over a distance. These properties, known collectively as cable properties set the physical limits over which signals can travel. Thus, nonspiking neurons (which carry signals without action potentials) tend to be small. Proper function of the body requires that signals be delivered from one end of an axon to the other without loss. An action potential does not so much propagate along an axon, as it is newly regenerated by the membrane voltage and current at each stretch of membrane along its path. In other words, the nerve membrane recreates the action potential at its full amplitude as it travels down the axon, thus overcoming the limitations imposed by cable physics.

## Plant action potentials

Many plants also exhibit action potentials that travel via their phloem to coordinate activity. 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.

## Alternative models

The model of electrical signal propagation in neurons employing voltage-gated ion channels described above is accepted by almost all scientists working in the field. However there are a few observations not easily reconciled with the model:

• A signal traveling along a neuron is accompanied by a slight local thickening of the membrane and a force acting outwards.[10]
• An action potential traveling along a neuron results in a slight increase in temperature followed by a decrease in temperature;[11] electrical charges traveling through a resistor however always produce heat.

One recent alternative, the soliton model, attempts to explain signals in neurons as pressure (or sound) solitons traveling along the membrane, accompanied by electrical field changes resulting from piezo-electric effects.

## Experimental methods

Action potentials are measured with the recording techniques of electrophysiology and more recently with neurochips containing EOSFETs. An oscilloscope recording the membrane potential from a single point on an axon shows each stage of the action potential as the wave passes. These phases trace an arc that resembles a distorted sine wave; its amplitude depends on whether the action potential wave has reached that point on the membrane or has passed it and if so, how long ago.

## Mathematics

The action potential features both positive and negative feedback and, under constant stimulation, forms a kind of blocking oscillator. Various sets of non-linear equations have been proposed to model the action potential, to help understand its physiological behavior and to study it as a dynamical system, particularly its bifurcation properties[12] and entrainment behavior.[13]

The most physiologically accurate equations are those of Alan Lloyd Hodgkin and Andrew Huxley;[14] However, these equations are difficult to study systematically and exhaustively, being nonlinear and having four dimensions: the transmembrane voltage V, and the probabilities m, n and h of the sodium and potassium ion channels being open or inactivated. The voltage equation is clearly non-linear

$C \frac{dV}{dt} = I_{\mathrm{ext}} - g_{Na} m^{3} h \left( V - V_{\mathrm{Na}}\right) - g_{K} n^{4} \left( V - V_{\mathrm{K}}\right) - g_{L} \left( V - V_{L} \right)$

where Iext is the external current stimulus. By contrast, the probability dynamics seem pseudo-first-author, e.g.,

$\frac{dm}{dt} = f(\theta) \left[ \alpha_{m} (1 - m) - \beta_{m} m \right]$

and analogously for n and h'; the function f(θ) captures their temperature dependence. However, the coefficients α and β depend strongly (exponentially) on the transmembrane voltage V. The simplest way to study such complex dynamical systems is to consider their behavior in the vicinity of a fixed point. This analysis shows that the Hodgkin-Huxley system undergoes a transition from stable decay to equilibrium to oscillations as the stimulating current is increased above a treshold; interestingly, the system becomes stable again at much larger external currents.[15]

Therefore, various simplifications of the Hodgkin-Huxley equations have been developed that exhibit qualitatively similar behavior.[16] the Fitzhugh-Nagumo model is a canonical example of such simplified systems. Based on the tunnel diode, the FHN model has only two dimensions, but exhibits a similar stability behavior.[13]

$L\frac{dI}{dt} = E - V - RI$
$C dV/dt = I - g(v)$

The FHN model is similar to other "flush and fill" models of the action potential, the basic idea being that the neuronal membrane integrated the input current until the accumulated charge exceeds the threshold voltage, initiating another action potential.

## Circuit model

Cell membranes that contain ion channels can be modeled as RC circuits to better understand the propagation of action potentials in biological membranes. In such a circuit, the resistor represents the membrane's ion channels, while the capacitor models the insulating lipid membrane. Variable resistors are used for voltage-gated ion channels, as their resistance changes with voltage. A fixed resistor represents the potassium leak channels that maintain the membrane's resting potential. The sodium and potassium gradients across the membrane are modeled as voltage sources (batteries).

## References

1. Ramón y Cajal S (1911). Histologie du Systeme Nerveux de l'Homme et des Vertebretes, Paris: A. Maloine.
2. Bullock et al., p. X.
3. Bullock et al., p. X.
4. Bertil Hille and William A. Catterall (1999). "Electrical Excitability and Ion Channels" in Basic Neurochemistry sixth edition, Chapter 6. Lippincott Williams and Wilkins. ISBN 0-397-51820-X Retrieved on 2008-03-27.
5. Björn Naundorf, Fred Wolf and Maxim Volgushev (2006-04-20). Unique features of action potential initiation in cortical neurons 440: 1060–1063.
6. 6.0 6.1 Rall W (1989). "Cable Theory for Dendritic Neurons" C. Koch and I. Segev Methods in Neuronal Modeling: From Synapses to Networks, Cambridge MA: Bradford Books, MIT Press.
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### General sources

• Bear MF, Connors BW, Paradiso MA (2001). Neuroscience: Exploring the Brain, Baltimore: Lippincott.
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• Hoppensteadt FC (1986). An Introduction to the Mathematics of Neurons, Cambridge: Cambridge University Press.
• Junge D (1981). Nerve and Muscle Excitation, 2nd ed., Sunderland MA: Sinauer Associates.
• Kandel ER, Schwartz JH, Jessell TM (2000). Principles of Neural Science, 4th ed., New York: McGraw-Hill.
• Dale Purves, et al. Neuroscience, 2nd ed. 2001. Sinauer Associates, Inc. Ion Channels Underlying Action Potentials. ISBN 0878937250 Release of Transmitters from Synaptic Vesicles
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### Original sources

• Hodgkin AL, Huxley AF. "Currents carried by sodium and potassium ions through the membrane of the giant axon of Loligo". J Physiol. 1952 Apr;116(4):449–72. PMID 14946713
• Hodgkin AL, Huxley AF. "The components of membrane conductance in the giant axon of Loligo". J Physiol. 1952 Apr;116(4):473–96. PMID 14946714
• Hodgkin AL, Huxley AF. "The dual effect of membrane potential on sodium conductance in the giant axon of Loligo". J Physiol. 1952 Apr;116(4):497–506. PMID 14946715
• Hodgkin AL, Huxley AF. "A quantitative description of membrane current and its application to conduction and excitation in nerve". J Physiol. 1952 Aug;117(4):500–44. PMID 12991237
• Clay JR. "Axonal excitability revisited". Prog Biophys Mol Biol. 2005 May;88(1):59–90. PMID 15561301