Action potential
An action potential occurs when the
In neurons, action potentials play a central role in cell–cell communication by providing for—or with regard to saltatory conduction, assisting—the propagation of signals along the neuron's axon toward synaptic boutons situated at the ends of an axon; these signals can then connect with other neurons at synapses, or to motor cells or glands. In other types of cells, their main function is to activate intracellular processes. In muscle cells, for example, an action potential is the first step in the chain of events leading to contraction. In beta cells of the pancreas, they provoke release of insulin.[a] Action potentials in neurons are also known as "nerve impulses" or "spikes", and the temporal sequence of action potentials generated by a neuron is called its "spike train". A neuron that emits an action potential, or nerve impulse, is often said to "fire".
Action potentials are generated by special types of
In animal cells, there are two primary types of action potentials. One type is generated by
Overview
Nearly all cell membranes in animals, plants and fungi maintain a voltage difference between the exterior and interior of the cell, called the membrane potential. A typical voltage across an animal cell membrane is −70 mV. This means that the interior of the cell has a negative voltage relative to the exterior. In most types of cells, the membrane potential usually stays fairly constant. Some types of cells, however, are electrically active in the sense that their voltages fluctuate over time. In some types of electrically active cells, including neurons and muscle cells, the voltage fluctuations frequently take the form of a rapid upward (positive) spike followed by a rapid fall. These up-and-down cycles are known as action potentials. In some types of neurons, the entire up-and-down cycle takes place in a few thousandths of a second. In muscle cells, a typical action potential lasts about a fifth of a second. In plant cells, an action potential may last three seconds or more.[4]
The electrical properties of a cell are determined by the structure of its membrane. A cell membrane consists of a lipid bilayer of molecules in which larger protein molecules are embedded. The lipid bilayer is highly resistant to movement of electrically charged ions, so it functions as an insulator. The large membrane-embedded proteins, in contrast, provide channels through which ions can pass across the membrane. Action potentials are driven by channel proteins whose configuration switches between closed and open states as a function of the voltage difference between the interior and exterior of the cell. These voltage-sensitive proteins are known as voltage-gated ion channels.
Process in a typical neuron
All cells in animal body tissues are
Each excitable patch of membrane has two important levels of membrane potential: the resting potential, which is the value the membrane potential maintains as long as nothing perturbs the cell, and a higher value called the threshold potential. At the axon hillock of a typical neuron, the resting potential is around –70 millivolts (mV) and the threshold potential is around –55 mV. Synaptic inputs to a neuron cause the membrane to depolarize or hyperpolarize; that is, they cause the membrane potential to rise or fall. Action potentials are triggered when enough depolarization accumulates to bring the membrane potential up to threshold. When an action potential is triggered, the membrane potential abruptly shoots upward and then equally abruptly shoots back downward, often ending below the resting level, where it remains for some period of time. The shape of the action potential is stereotyped; this means that the rise and fall usually have approximately the same amplitude and time course for all action potentials in a given cell. (Exceptions are discussed later in the article). In most neurons, the entire process takes place in about a thousandth of a second. Many types of neurons emit action potentials constantly at rates of up to 10–100 per second. However, some types are much quieter, and may go for minutes or longer without emitting any action potentials.
Biophysical basis
This section needs additional citations for verification. (February 2014) |
Action potentials result from the presence in a cell's membrane of special types of voltage-gated ion channels.[6] A voltage-gated ion channel is a transmembrane protein that has three key properties:
- It is capable of assuming more than one conformation.
- At least one of the conformations creates a channel through the membrane that is permeable to specific types of ions.
- The transition between conformations is influenced by the membrane potential.
Thus, a voltage-gated ion channel tends to be open for some values of the membrane potential, and closed for others. In most cases, however, the relationship between membrane potential and channel state is probabilistic and involves a time delay. Ion channels switch between conformations at unpredictable times: The membrane potential determines the rate of transitions and the probability per unit time of each type of transition.
Voltage-gated ion channels are capable of producing action potentials because they can give rise to positive feedback loops: The membrane potential controls the state of the ion channels, but the state of the ion channels controls the membrane potential. Thus, in some situations, a rise in 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 feedback cycle (Hodgkin cycle) proceeds explosively. The time and amplitude trajectory of the action potential are determined by the biophysical properties of the voltage-gated ion channels that produce it. Several types of channels capable of producing the positive feedback necessary to generate an action potential do exist. Voltage-gated sodium channels are responsible for the fast action potentials involved in nerve conduction. Slower action potentials in muscle cells and some types of neurons are generated by voltage-gated calcium channels. Each of these types comes in multiple variants, with different voltage sensitivity and different temporal dynamics.
The most intensively studied type of voltage-dependent ion channels comprises the sodium channels involved in fast nerve conduction. These are sometimes known as Hodgkin-Huxley sodium channels because they were first characterized by
The outcome of all this is that the kinetics of the NaV channels are governed by a transition matrix whose rates are voltage-dependent in a complicated way. Since these channels themselves play a major role in determining the voltage, the global dynamics of the system can be quite difficult to work out. Hodgkin and Huxley approached the problem by developing a set of differential equations for the parameters that govern the ion channel states, known as the Hodgkin-Huxley equations. These equations have been extensively modified by later research, but form the starting point for most theoretical studies of action potential biophysics.
As the membrane potential is increased,
Currents produced by the opening of voltage-gated channels in the course of an action potential are typically significantly larger than the initial stimulating current. Thus, the amplitude, duration, and shape of the action potential are determined largely by the properties of the excitable membrane and not the amplitude or duration of the stimulus. This
The principal ions involved in an action potential are sodium and potassium cations; sodium ions enter the cell, and potassium ions leave, restoring equilibrium. Relatively few ions need to cross the membrane for the membrane voltage to change drastically. The ions exchanged during an action potential, therefore, make a negligible change in the interior and exterior ionic concentrations. The few ions that do cross are pumped out again by the continuous action of the
Although action potentials are generated locally on patches of excitable membrane, the resulting currents can trigger action potentials on neighboring stretches of membrane, precipitating a domino-like propagation. In contrast to passive spread of electric potentials (
In the Hodgkin–Huxley membrane capacitance model, the speed of transmission of an action potential was undefined and it was assumed that adjacent areas became depolarized due to released ion interference with neighbouring channels. Measurements of ion diffusion and radii have since shown this not to be possible.[citation needed] Moreover, contradictory measurements of entropy changes and timing disputed the capacitance model as acting alone.[citation needed] Alternatively, Gilbert Ling's adsorption hypothesis, posits that the membrane potential and action potential of a living cell is due to the adsorption of mobile ions onto adsorption sites of cells.[13]
Maturation of the electrical properties of the action potential
A
In the early development of many organisms, the action potential is actually initially carried by calcium current rather than sodium current. The opening and closing kinetics of calcium channels during development are slower than those of the voltage-gated sodium channels that will carry the action potential in the mature neurons. The longer opening times for the calcium channels can lead to action potentials that are considerably slower than those of mature neurons.[14] Xenopus neurons initially have action potentials that take 60–90 ms. During development, this time decreases to 1 ms. There are two reasons for this drastic decrease. First, the inward current becomes primarily carried by sodium channels.[15] Second, the delayed rectifier, a potassium channel current, increases to 3.5 times its initial strength.[14]
In order for the transition from a calcium-dependent action potential to a sodium-dependent action potential to proceed new channels must be added to the membrane. If Xenopus neurons are grown in an environment with
This maturation of electrical properties is seen across species. Xenopus sodium and potassium currents increase drastically after a neuron goes through its final phase of mitosis. The sodium current density of rat cortical neurons increases by 600% within the first two postnatal weeks.[14]
Neurotransmission
Anatomy of a neuron
Several types of cells support an action potential, such as plant cells, muscle cells, and the specialized cells of the heart (in which occurs the cardiac action potential). However, the main excitable cell is the neuron, which also has the simplest mechanism for the action potential.
Neurons are electrically excitable cells composed, in general, of one or more dendrites, a single
Initiation
Before considering the propagation of action potentials along axons and their termination at the synaptic knobs, it is helpful to consider the methods by which action potentials can be initiated at the axon hillock. The basic requirement is that the membrane voltage at the hillock be raised above the threshold for firing.[7][8][20][21] There are several ways in which this depolarization can occur.
Dynamics
Action potentials are most commonly initiated by
Neurotransmission can also occur through electrical synapses.[23] Due to the direct connection between excitable cells in the form of gap junctions, an action potential can be transmitted directly from one cell to the next in either direction. The free flow of ions between cells enables rapid non-chemical-mediated transmission. Rectifying channels ensure that action potentials move only in one direction through an electrical synapse.[citation needed] Electrical synapses are found in all nervous systems, including the human brain, although they are a distinct minority.[24]
"All-or-none" principle
The amplitude of an action potential is often thought to be independent of the amount of current that produced it. In other words, larger currents do not create larger action potentials. Therefore, action potentials are said to be all-or-none signals, since either they occur fully or they do not occur at all.[d][e][f] This is in contrast to receptor potentials, whose amplitudes are dependent on the intensity of a stimulus.[25] In both cases, the frequency of action potentials is correlated with the intensity of a stimulus.
Despite the classical view of the action potential as a stereotyped, uniform signal having dominated the field of neuroscience for many decades, newer evidence does suggest that action potentials are more complex events indeed capable of transmitting information through not just their amplitude, but their duration and phase as well, sometimes even up to distances originally not thought to be possible.[26][27][28][29]
Sensory neurons
In
Pacemaker potentials
In sensory neurons, action potentials result from an external stimulus. However, some excitable cells require no such stimulus to fire: They spontaneously depolarize their axon hillock and fire action potentials at a regular rate, like an internal clock.[32] The voltage traces of such cells are known as pacemaker potentials.[33] The cardiac pacemaker cells of the sinoatrial node in the heart provide a good example.[g] Although such pacemaker potentials have a natural rhythm, it can be adjusted by external stimuli; for instance, heart rate can be altered by pharmaceuticals as well as signals from the sympathetic and parasympathetic nerves.[34] The external stimuli do not cause the cell's repetitive firing, but merely alter its timing.[33] In some cases, the regulation of frequency can be more complex, leading to patterns of action potentials, such as bursting.
Phases
The course of the action potential can be divided into five parts: the rising phase, the peak phase, the falling phase, the undershoot phase, and the refractory period. During the rising phase the membrane potential depolarizes (becomes more positive). The point at which depolarization stops is called the peak phase. At this stage, the membrane potential reaches a maximum. Subsequent to this, there is a falling phase. During this stage the membrane potential becomes more negative, returning towards resting potential. The undershoot, or afterhyperpolarization, phase is the period during which the membrane potential temporarily becomes more negatively charged than when at rest (hyperpolarized). Finally, the time during which a subsequent action potential is impossible or difficult to fire is called the refractory period, which may overlap with the other phases.[35]
The course of the action potential is determined by two coupled effects.[36] First, voltage-sensitive ion channels open and close in response to changes in the membrane voltage Vm. This changes the membrane's permeability to those ions.[37] Second, according to the Goldman equation, this change in permeability changes the equilibrium potential Em, and, thus, the membrane voltage Vm.[h] Thus, the membrane potential affects the permeability, which then further affects the membrane potential. This sets up the possibility for positive feedback, which is a key part of the rising phase of the action potential.[7][10] A complicating factor is that a single ion channel may have multiple internal "gates" that respond to changes in Vm in opposite ways, or at different rates.[38][i] For example, although raising Vm opens most gates in the voltage-sensitive sodium channel, it also closes the channel's "inactivation gate", albeit more slowly.[39] Hence, when Vm is raised suddenly, the sodium channels open initially, but then close due to the slower inactivation.
The voltages and currents of the action potential in all of its phases were modeled accurately by
Stimulation and rising phase
A typical action potential begins at the
For a neuron at rest, there is a high concentration of sodium and chloride ions in the
The critical threshold voltage for this runaway condition is usually around −45 mV, but it depends on the recent activity of the axon. A cell that has just fired an action potential cannot fire another one immediately, since the Na+ channels have not recovered from the inactivated state. The period during which no new action potential can be fired is called the absolute refractory period.[43][44][45] At longer times, after some but not all of the ion channels have recovered, the axon can be stimulated to produce another action potential, but with a higher threshold, requiring a much stronger depolarization, e.g., to −30 mV. The period during which action potentials are unusually difficult to evoke is called the relative refractory period.[43][44][45]
Peak phase
The positive feedback of the rising phase slows and comes to a halt as the sodium ion channels become maximally open. At the peak of the action potential, the sodium permeability is maximized and the membrane voltage Vm is nearly equal to the sodium equilibrium voltage ENa. However, the same raised voltage that opened the sodium channels initially also slowly shuts them off, by closing their pores; the sodium channels become inactivated.[39] This lowers the membrane's permeability to sodium relative to potassium, driving the membrane voltage back towards the resting value. At the same time, the raised voltage opens voltage-sensitive potassium channels; the increase in the membrane's potassium permeability drives Vm towards EK.[39] Combined, these changes in sodium and potassium permeability cause Vm to drop quickly, repolarizing the membrane and producing the "falling phase" of the action potential.[43][46][21][47]
Afterhyperpolarization
The depolarized voltage opens additional voltage-dependent potassium channels, and some of these do not close right away when the membrane returns to its normal resting voltage. In addition, further potassium channels open in response to the influx of calcium ions during the action potential. The intracellular concentration of potassium ions is transiently unusually low, making the membrane voltage Vm even closer to the potassium equilibrium voltage EK. The membrane potential goes below the resting membrane potential. Hence, there is an undershoot or hyperpolarization, termed an afterhyperpolarization, that persists until the membrane potassium permeability returns to its usual value, restoring the membrane potential to the resting state.[48][46]
Refractory period
Each action potential is followed by a refractory period, which can be divided into an absolute refractory period, during which it is impossible to evoke another action potential, and then a relative refractory period, during which a stronger-than-usual stimulus is required.[43][44][45] These two refractory periods are caused by changes in the state of sodium and potassium channel molecules. When closing after an action potential, sodium channels enter an "inactivated" state, in which they cannot be made to open regardless of the membrane potential—this gives rise to the absolute refractory period. Even after a sufficient number of sodium channels have transitioned back to their resting state, it frequently happens that a fraction of potassium channels remains open, making it difficult for the membrane potential to depolarize, and thereby giving rise to the relative refractory period. Because the density and subtypes of potassium channels may differ greatly between different types of neurons, the duration of the relative refractory period is highly variable.
The absolute refractory period is largely responsible for the unidirectional propagation of action potentials along axons.[49] At any given moment, the patch of axon behind the actively spiking part is refractory, but the patch in front, not having been activated recently, is capable of being stimulated by the depolarization from the action potential.
Propagation
The action potential generated at the axon hillock propagates as a wave along the axon.
Once an action potential has occurred at a patch of membrane, the membrane patch needs time to recover before it can fire again. At the molecular level, this absolute refractory period corresponds to the time required for the voltage-activated sodium channels to recover from inactivation, i.e., to return to their closed state.
Myelin and saltatory conduction
In order to enable fast and efficient transduction of electrical signals in the nervous system, certain neuronal axons are covered with
Myelin prevents ions from entering or leaving the axon along myelinated segments. As a general rule, myelination increases the
Action potentials cannot propagate through the membrane in myelinated segments of the axon. However, the current is carried by the cytoplasm, which is sufficient to depolarize the first or second subsequent node of Ranvier. Instead, the ionic current from an action potential at one node of Ranvier provokes another action potential at the next node; this apparent "hopping" of the action potential from node to node is known as saltatory conduction. Although the mechanism of saltatory conduction was suggested in 1925 by Ralph Lillie,[q] the first experimental evidence for saltatory conduction came from Ichiji Tasaki[r] and Taiji Takeuchi[s][54] and from Andrew Huxley and Robert Stämpfli.[t] By contrast, in unmyelinated axons, the action potential provokes another in the membrane immediately adjacent, and moves continuously down the axon like a wave.
Myelin has two important advantages: fast conduction speed and energy efficiency. For axons larger than a minimum diameter (roughly 1
The length of axons' myelinated segments is important to the success of saltatory conduction. They should be as long as possible to maximize the speed of conduction, but not so long that the arriving signal is too weak to provoke an action potential at the next node of Ranvier. In nature, myelinated segments are generally long enough for the passively propagated signal to travel for at least two nodes while retaining enough amplitude to fire an action potential at the second or third node. Thus, the
Some diseases degrade myelin and impair saltatory conduction, reducing the conduction velocity of action potentials.[w] The most well-known of these is multiple sclerosis, in which the breakdown of myelin impairs coordinated movement.[57]
Cable theory
The flow of currents within an axon can be described quantitatively by
where V(x, t) is the voltage across the membrane at a time t and a position x along the length of the neuron, and where λ and τ are the characteristic length and time scales on which those voltages decay in response to a stimulus. Referring to the circuit diagram on the right, these scales can be determined from the resistances and capacitances per unit length.[60]
These time and length-scales can be used to understand the dependence of the conduction velocity on the diameter of the neuron in unmyelinated fibers. For example, the time-scale τ increases with both the membrane resistance rm and capacitance cm. As the capacitance increases, more charge must be transferred to produce a given transmembrane voltage (by
Termination
Chemical synapses
In general, action potentials that reach the synaptic knobs cause a
Electrical synapses
Some synapses dispense with the "middleman" of the neurotransmitter, and connect the presynaptic and postsynaptic cells together.[ac] When an action potential reaches such a synapse, the ionic currents flowing into the presynaptic cell can cross the barrier of the two cell membranes and enter the postsynaptic cell through pores known as connexons.[ad] Thus, the ionic currents of the presynaptic action potential can directly stimulate the postsynaptic cell. Electrical synapses allow for faster transmission because they do not require the slow diffusion of neurotransmitters across the synaptic cleft. Hence, electrical synapses are used whenever fast response and coordination of timing are crucial, as in escape reflexes, the retina of vertebrates, and the heart.
Neuromuscular junctions
A special case of a chemical synapse is the
Other cell types
Cardiac action potentials
The cardiac action potential differs from the neuronal action potential by having an extended plateau, in which the membrane is held at a high voltage for a few hundred milliseconds prior to being repolarized by the potassium current as usual.[ai] This plateau is due to the action of slower calcium channels opening and holding the membrane voltage near their equilibrium potential even after the sodium channels have inactivated.
The cardiac action potential plays an important role in coordinating the contraction of the heart.
Muscular action potentials
The action potential in a normal skeletal muscle cell is similar to the action potential in neurons.[61] Action potentials result from the depolarization of the cell membrane (the sarcolemma), which opens voltage-sensitive sodium channels; these become inactivated and the membrane is repolarized through the outward current of potassium ions. The resting potential prior to the action potential is typically −90mV, somewhat more negative than typical neurons. The muscle action potential lasts roughly 2–4 ms, the absolute refractory period is roughly 1–3 ms, and the conduction velocity along the muscle is roughly 5 m/s. The action potential releases calcium ions that free up the tropomyosin and allow the muscle to contract. Muscle action potentials are provoked by the arrival of a pre-synaptic neuronal action potential at the neuromuscular junction, which is a common target for neurotoxins.[ag]
Plant action potentials
The initial influx of calcium ions also poses a small cellular depolarization, causing the voltage-gated ion channels to open and allowing full depolarization to be propagated by chloride ions.
Some plants (e.g.
However, plenty of research has been done on action potentials and how they affect movement and clockwork within the Venus flytrap. To start, the resting membrane potential of the Venus flytrap (-120mV) is lower than animal cells (usually -90mV to -40mV).[66][67] The lower resting potential makes it easier to activate an action potential. Thus, when an insect lands on the trap of the plant, it triggers a hair-like mechanoreceptor.[66] This receptor then activates an action potential which lasts around 1.5 ms.[68] Ultimately, this causes an increase of positive Calcium ions into the cell, slightly depolarizing it.
However, the flytrap does not close after one trigger. Instead, it requires the activation of 2 or more hairs.[65][66] If only one hair is triggered, it throws the activation as a false positive. Further, the second hair must be activated within a certain time interval (0.75 s - 40 s) for it to register with the first activation.[66] Thus, a buildup of calcium starts and slowly falls from the first trigger. When the second action potential is fired within the time interval, it reaches the Calcium threshold to depolarize the cell, closing the trap on the prey within a fraction of a second.[66]
Together with the subsequent release of positive potassium ions the action potential in plants involves an
Unlike the rising phase and peak, the falling phase and after-hyperpolarization seem to depend primarily on cations that are not calcium. To initiate repolarization, the cell requires movement of potassium out of the cell through passive transportation on the membrane. This differs from neurons because the movement of potassium does not dominate the decrease in membrane potential; In fact, to fully repolarize, a plant cell requires energy in the form of ATP to assist in the release of hydrogen from the cell – utilizing a transporter commonly known as H+-ATPase.[70][66]
Taxonomic distribution and evolutionary advantages
Action potentials are found throughout
Animal | Cell type | Resting potential (mV) | AP increase (mV) | AP duration (ms) | Conduction speed (m/s) |
---|---|---|---|---|---|
Squid (Loligo) | Giant axon | −60 | 120 | 0.75 | 35 |
Earthworm (Lumbricus) | Median giant fiber | −70 | 100 | 1.0 | 30 |
Cockroach (Periplaneta) | Giant fiber | −70 | 80–104 | 0.4 | 10 |
Frog (Rana) | Sciatic nerve axon | −60 to −80 | 110–130 | 1.0 | 7–30 |
Cat (Felis) | Spinal motor neuron | −55 to −80 | 80–110 | 1–1.5 | 30–120 |
Given its conservation throughout evolution, the action potential seems to confer evolutionary advantages. One function of action potentials is rapid, long-range signaling within the organism; the conduction velocity can exceed 110 m/s, which is one-third the
The common prokaryotic/eukaryotic ancestor, which lived perhaps four billion years ago, is believed to have had voltage-gated channels. This functionality was likely, at some later point, cross-purposed to provide a communication mechanism. Even modern single-celled bacteria can utilize action potentials to communicate with other bacteria in the same biofilm.[72]
Experimental methods
The study of action potentials has required the development of new experimental methods. The initial work, prior to 1955, was carried out primarily by
The first problem was solved by studying the
The second problem was addressed with the crucial development of the
The third problem, that of obtaining electrodes small enough to record voltages within a single axon without perturbing it, was solved in 1949 with the invention of the glass micropipette electrode,
While glass micropipette electrodes measure the sum of the currents passing through many ion channels, studying the electrical properties of a single ion channel became possible in the 1970s with the development of the patch clamp by Erwin Neher and Bert Sakmann. For this discovery, they were awarded the Nobel Prize in Physiology or Medicine in 1991.[lower-Greek 3] Patch-clamping verified that ionic channels have discrete states of conductance, such as open, closed and inactivated.
Neurotoxins
Several
History
The role of electricity in the nervous systems of animals was first observed in dissected
In the 19th century scientists studied the propagation of electrical signals in whole
The 20th century saw significant breakthroughs in electrophysiology. In 1902 and again in 1912,
Julius Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane; this was generalized by David E. Goldman to the eponymous Goldman equation in 1943.[h] The sodium–potassium pump was identified in 1957[bl][lower-Greek 6] and its properties gradually elucidated,[bm][bn][bo] culminating in the determination of its atomic-resolution structure by X-ray crystallography.[bp] The crystal structures of related ionic pumps have also been solved, giving a broader view of how these molecular machines work.[bq]
Quantitative models
Mathematical and computational models are essential for understanding the action potential, and offer predictions that may be tested against experimental data, providing a stringent test of a theory. The most important and accurate of the early neural models is the
See also
Notes
- ^ In general, while this simple description of action potential initiation is accurate, it does not explain phenomena such as excitation block (the ability to prevent neurons from eliciting action potentials by stimulating them with large current steps) and the ability to elicit action potentials by briefly hyperpolarizing the membrane. By analyzing the dynamics of a system of sodium and potassium channels in a membrane patch using computational models, however, these phenomena are readily explained.[lower-Greek 1]
- Purkinje fibers are muscle fibers and not related to the Purkinje cells, which are neurons found in the cerebellum.
References
Footnotes
- PMID 12991237.
- PMID 6257554.
- ^ "Cardiac Muscle Contraction". Retrieved 28 May 2021.
- S2CID 5026557.
- PMID 29378864.
- ^ Purves D, Augustine GJ, Fitzpatrick D, et al., eds. (2001). "Voltage-Gated Ion Channels". Neuroscience (2nd ed.). Sunderland, MA: Sinauer Associates. Archived from the original on 5 June 2018. Retrieved 29 August 2017.
- ^ a b c d e f g h Bullock, Orkand & Grinnell 1977, pp. 150–151.
- ^ a b c d e Junge 1981, pp. 89–90.
- ^ a b Schmidt-Nielsen 1997, p. 484.
- ^ a b c Purves et al. 2008, pp. 48–49; Bullock, Orkand & Grinnell 1977, p. 141; Schmidt-Nielsen 1997, p. 483; Junge 1981, p. 89.
- ^ Stevens 1966, p. 127.
- ^ Schmidt-Nielsen, p. 484.
- PMID 26821050.
- ^ OCLC 762720374.
- ISBN 9780849388071.
- ISBN 978-1-4613-2717-2. Archivedfrom the original on 17 July 2017.
- ISBN 9780080584621.
- ^ Bullock, Orkand & Grinnell 1977, p. 11.
- ^ Silverthorn 2010, p. 253.
- ^ a b c Purves et al. 2008, pp. 49–50; Bullock, Orkand & Grinnell 1977, pp. 140–141; Schmidt-Nielsen 1997, pp. 480–481.
- ^ a b c d Schmidt-Nielsen 1997, pp. 483–484.
- ^ Bullock, Orkand & Grinnell 1977, pp. 177–240; Schmidt-Nielsen 1997, pp. 490–499; Stevens 1966, p. 47–68.
- ^ Bullock, Orkand & Grinnell 1977, pp. 178–180; Schmidt-Nielsen 1997, pp. 490–491.
- ^ Purves et al. 2001.
- ^ Purves et al. 2008, pp. 26–28.
- ^ "Myelination Increases the Spatial Extent of Analog Modulation of Synaptic Transmission: A Modeling Study". Frontiers in Cellular Neuroscience.
- PMID 31105529.
- S2CID 8295969.
- PMID 34346782.
- ^ Schmidt-Nielsen 1997, pp. 535–580; Bullock, Orkand & Grinnell 1977, pp. 49–56, 76–93, 247–255; Stevens 1966, pp. 69–79.
- ^ Bullock, Orkand & Grinnell 1977, pp. 53; Bullock, Orkand & Grinnell 1977, pp. 122–124.
- ^ Junge 1981, pp. 115–132.
- ^ a b Bullock, Orkand & Grinnell 1977, pp. 152–153.
- ^ Bullock, Orkand & Grinnell 1977, pp. 444–445.
- ^ Purves et al. 2008, p. 38.
- ^ Stevens 1966, pp. 127–128.
- ^ Purves et al. 2008, pp. 61–65.
- ^ Purves et al. 2008, pp. 64–74; Bullock, Orkand & Grinnell 1977, pp. 149–150; Junge 1981, pp. 84–85; Stevens 1966, pp. 152–158.
- ^ a b c Purves et al. 2008, p. 47; Purves et al. 2008, p. 65; Bullock, Orkand & Grinnell 1977, pp. 147–148; Stevens 1966, p. 128.
- ^ Goldin, AL in Waxman 2007, Neuronal Channels and Receptors, pp. 43–58.
- ^ Stevens 1966, p. 49.
- ^ Purves et al. 2008, p. 34; Bullock, Orkand & Grinnell 1977, p. 134; Schmidt-Nielsen 1997, pp. 478–480.
- ^ a b c d Purves et al. 2008, p. 49.
- ^ a b c d Stevens 1966, pp. 19–20.
- ^ a b c Bullock, Orkand & Grinnell 1977, p. 151; Junge 1981, pp. 4–5.
- ^ a b Bullock, Orkand & Grinnell 1977, p. 152.
- ^ Bullock, Orkand & Grinnell 1977, pp. 147–149; Stevens 1966, pp. 126–127.
- ^ Purves et al. 2008, p. 37.
- ^ a b Purves et al. 2008, p. 56.
- ^ Bullock, Orkand & Grinnell 1977, pp. 160–164.
- ^ Stevens 1966, pp. 21–23.
- ^ Bullock, Orkand & Grinnell 1977, pp. 161–164.
- ^ Bullock, Orkand & Grinnell 1977, p. 509.
- ^ Tasaki, I in Field 1959, pp. 75–121
- ^ Schmidt-Nielsen 1997, Figure 12.13.
- ^ Bullock, Orkand & Grinnell 1977, p. 163.
- ^ Waxman, SG in Waxman 2007, Multiple Sclerosis as a Neurodegenerative Disease, pp. 333–346.
- ^ a b Rall, W in Koch & Segev 1989, Cable Theory for Dendritic Neurons, pp. 9–62.
- OCLC 18384545.
- ^ Purves et al. 2008, pp. 52–53.
- ^ Ganong 1991, pp. 59–60.
- ISSN 0019-5235.
- S2CID 5059716.
- S2CID 9246114.
- ^ PMID 26804557.
- ^ PMID 29336976.
- ^ Purves D, Augustine GJ, Fitzpatrick D, et al., editors. Neuroscience. 2nd edition. Sunderland (MA): Sinauer Associates; 2001. Electrical Potentials Across Nerve Cell Membranes.Available from: [1]
- PMID 19516982.
- ^ Gradmann, D; Mummert, H in Spanswick, Lucas & Dainty 1980, Plant action potentials, pp. 333–344.
- ^ Opritov, V A, et al. "Direct Coupling of Action Potential Generation in Cells of a Higher Plant (Cucurbita Pepo) with the Operation of an Electrogenic Pump." Russian Journal of Plant Physiology, vol. 49, no. 1, 2002, pp. 142–147.
- ^ Bullock & Horridge 1965.
- PMID 27780067.
- ISBN 9781610693387.
- ^ Junge 1981, pp. 63–82.
- ^ Kettenmann & Grantyn 1992.
- ^ Snell, FM in Lavallée, Schanne & Hébert 1969, Some Electrical Properties of Fine-Tipped Pipette Microelectrodes.
- ^ Brazier 1961; McHenry & Garrison 1969; Worden, Swazey & Adelman 1975.
- )
- ^ Olesko, Kathryn M., and Frederic L. Holmes. "Experiment, Quantification and Discovery: Helmholtz's Early Physiological Researches, 1843-50". In Hermann von Helmholtz and the Foundations of Nineteenth Century Science, ed. David Cahan, 50-108. Berkeley; Los Angeles; London: University of California, 1994.
- ^ Bernstein 1912.
- PMID 16407565.
- ^ Hoppensteadt 1986.
- ^ Sato, S; Fukai, H; Nomura, T; Doi, S in Reeke et al. 2005, Bifurcation Analysis of the Hodgkin-Huxley Equations, pp. 459–478.
* FitzHugh, R in Schwann 1969, Mathematical models of axcitation and propagation in nerve, pp. 12–16.
* Guckenheimer & Holmes 1986, pp. 12–16 - ^ Nelson, ME; Rinzel, J in Bower & Beeman 1995, The Hodgkin-Huxley Model, pp. 29–49.
* Rinzel, J & Ermentrout, GB; in Koch & Segev 1989, Analysis of Neural Excitability and Oscillations, pp. 135–169. - S2CID 15326972.
- ^ McCulloch 1988, pp. 19–39, 46–66, 72–141; Anderson & Rosenfeld 1988, pp. 15–41.
- ^ Getting, PA in Koch & Segev 1989, Reconstruction of Small Neural Networks, pp. 171–194.
Journal articles
- PMID 16464129.
- ^ from the original on 8 July 2011.
- S2CID 2915815.
- ^ Sasaki, T., Matsuki, N., Ikegaya, Y. 2011 Action-potential modulation during axonal conduction Science 331 (6017), pp. 599–601
- S2CID 34131910.
- S2CID 4147174.
- ^ PMID 19873371.
- ^ PMID 12991237.
- S2CID 1328840. Archived from the original(PDF) on 20 December 2018. Retrieved 24 September 2019.
- PMID 16994886.
- )
- S2CID 14720760.
- S2CID 45470194.
- PMID 10395528.
- ^ .
- PMID 19872151. See also Keynes & Aidley 1991, p. 78
- .
- S2CID 44315437.
- PMID 14825228.
- PMID 14889433.
- ^ S2CID 10033356.
- S2CID 12441377.
- S2CID 178547827.
- PMID 20281590.
- PMID 18064409.
- PMID 16840708.
- PMID 10865130.
- S2CID 22414506.
- S2CID 46371790.
- PMID 17573397.
- S2CID 1888352.
- ^ S2CID 211234081.
- PMID 16337171.
- ^ S2CID 21823003.
- PMID 14754423.
- PMID 130926.
- S2CID 22063907.
- doi:10.1071/pp01017.
- PMID 17280895.
- S2CID 24190001.
- PMID 17263772.
- PMID 10101111.
- PMID 2541698.
- S2CID 1355280.
- ^ Cole KS (1949). "Dynamic electrical characteristics of the squid axon membrane". Arch. Sci. Physiol. 3: 253–8.
- PMID 15410483.
- .
- PMID 12991232.
- PMID 3838314.
- PMID 19289075.
- S2CID 11465181.
- S2CID 23394494.
- S2CID 393323.
- S2CID 33229139.
- PMID 19873125.
- ^ Lapicque L (1907). "Recherches quantitatives sur l'excitationelectrique des nerfs traitee comme une polarisation". J. Physiol. Pathol. Gen. 9: 620–635.
- PMID 18128147.
- PMID 1374932.
- S2CID 4420877.
- S2CID 4347957.
- S2CID 18629998.
- S2CID 4430165.
- S2CID 32516710.
- PMID 14368574.
- PMID 13806926.
- S2CID 222188054.
- S2CID 4344526.
- PMID 11389676.
- S2CID 6789007.
- PMID 7260316.
- S2CID 51648050.
- , van der Mark J (1929). "The heartbeat considered as a relaxation oscillation, and an electrical model of the heart". Arch. Neerl. Physiol. 14: 418–443.
- .
- S2CID 20077648.
- S2CID 11388348.
Books
- Anderson JA, Rosenfeld E, eds. (1988). Neurocomputing: Foundations of Research. Cambridge, Massachusetts: The MIT Press. OCLC 15860311.
- OCLC 11358569.
- Bower JM, Beeman D (1995). The Book of GENESIS: Exploring Realistic Neural Models with the GEneral NEural SImulation System. Santa Clara, Calif.: TELOS. OCLC 30518469.
- Brazier MA (1961). A History of the Electrical Activity of the Brain. London: Pitman. OCLC 556863.
- OCLC 558128.
- OCLC 2048177.
- Field J, ed. (1959). Handbook of Physiology: a Critical, Comprehensive Presentation of Physiological Knowledge and Concepts: Section 1: Neurophysiology. Vol. 1. Washington, DC: American Physiological Society. OCLC 830755894.
- Ganong, WF (1991). Review of Medical Physiology (15th ed.). Norwalk, Conn.: Appleton and Lange. )
- Guckenheimer J, Holmes P, eds. (1986). Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Applied Mathematical Sciences. Vol. 42 (2nd ed.). New York: Springer Verlag. OCLC 751129941.
- Hoppensteadt FC (1986). An Introduction to the Mathematics of Neurons. Cambridge studies in mathematical biology. Vol. 6. Cambridge: Cambridge University Press. OCLC 12052275.
- Junge D (1981). Nerve and Muscle Excitation (2nd ed.). Sunderland, Mass.: Sinauer Associates. OCLC 6486925.
- Kettenmann H, Grantyn R, eds. (1992). Practical Electrophysiological Methods: A Guide for in Vitro Studies in Vertebrate Neurobiology. New York: Wiley. OCLC 25204689.
- OCLC 25204483.
- OCLC 18384545.
- Lavallée M, Schanne OF, Hébert NC, eds. (1969). Glass Microelectrodes. New York: Wiley. OCLC 686.
- OCLC 237280.
- McHenry LC, Garrison FH (1969). Garrison's History of Neurology. Springfield, Ill.: Charles C. Thomas. OCLC 429733931.
- Silverthorn DU (2010). Human Physiology: An Integrated Approach (5th ed.). San Francisco: Pearson. OCLC 268788623.
- Spanswick RM, Lucas WJ, Dainty J, eds. (1980). Plant Membrane Transport: Current Conceptual Issues. Developments in Plant Biology. Vol. 4. Amsterdam: Elsevier Biomedical Press. OCLC 5799924.
- Purves D, Augustine GJ, Fitzpatrick D, Hall WC, Lamantia AS, McNamara JO, Williams SM (2001). "Release of Transmitters from Synaptic Vesicles". Neuroscience (2nd ed.). Sunderland, MA: Sinauer Associates. OCLC 806472664.
- Purves D, Augustine GJ, Fitzpatrick D, Hall WC, Lamantia AS, McNamara JO, White LE (2008). Neuroscience (4th ed.). Sunderland, MA: Sinauer Associates. OCLC 144771764.
- Reeke GN, Poznanski RR, Sporns O, Rosenberg JR, Lindsay KA, eds. (2005). Modeling in the Neurosciences: from Biological Systems to Neuromimetic Robotics. Boca Raton, Fla.: Taylor & Francis. OCLC 489024131.
- OCLC 35744403.
- Schwann HP, ed. (1969). Biological Engineering. Inter-University Electronics Series. Vol. 9. New York: McGraw-Hill. OCLC 51993.
- Stevens CF (1966). Neurophysiology: A Primer. New York: John Wiley and Sons. OCLC 1175605.
- Waxman SG, ed. (2007). Molecular Neurology. Burlington, Mass.: Elsevier Academic Press. OCLC 154760295.
- Worden FG, Swazey JP, Adelman G, eds. (1975). The Neurosciences, Paths of Discovery. Cambridge, Massachusetts: The MIT Press. OCLC 1500233.
Web pages
- .
- ^ "The Nobel Prize in Physiology or Medicine 1963" (Press release). The Royal Swedish Academy of Science. 1963. Archived from the original on 16 July 2007. Retrieved 21 February 2010.
- ^ "The Nobel Prize in Physiology or Medicine 1991" (Press release). The Royal Swedish Academy of Science. 1991. Archived from the original on 24 March 2010. Retrieved 21 February 2010.
- ^ "The Nobel Prize in Physiology or Medicine 1906" (Press release). The Royal Swedish Academy of Science. 1906. Archived from the original on 4 December 2008. Retrieved 21 February 2010.
- ^ Warlow C (June 2007). "The Recent Evolution of a Symbiotic Ion Channel in the Legume Family Altered Ion Conductance and Improved Functionality in Calcium Signaling". Practical Neurology. 7 (3). BMJ Publishing Group: 192–197. Archived from the original on 14 March 2012. Retrieved 23 March 2013.
- ^ "The Nobel Prize in Chemistry 1997" (Press release). The Royal Swedish Academy of Science. 1997. Archived from the original on 23 October 2009. Retrieved 21 February 2010.
Further reading
- Aidley DJ, Stanfield PR (1996). Ion Channels: Molecules in Action. Cambridge: Cambridge University Press. ISBN 978-0-521-49882-1.
- Bear MF, Connors BW, Paradiso MA (2001). Neuroscience: Exploring the Brain. Baltimore: Lippincott. ISBN 0-7817-3944-6.
- Clay JR (May 2005). "Axonal excitability revisited". Progress in Biophysics and Molecular Biology. 88 (1): 59–90. PMID 15561301.
- Deutsch S, ISBN 0-8147-1782-9.
- ISBN 978-0-87893-321-1.
- Johnston D, Wu SM (1995). Foundations of Cellular Neurophysiology. Cambridge, Massachusetts: Bradford Book, The MIT Press. ISBN 0-262-10053-3.
- ISBN 0-8385-7701-6.
- Miller C (1987). "How ion channel proteins work". In Kaczmarek LK, Levitan IB (eds.). 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 Principles of Biochemistry (5th ed.). New York: W. H. Freeman. ISBN 978-0-7167-7108-1.
External links
- Ionic flow in action potentials at Blackwell Publishing
- Action potential propagation in myelinated and unmyelinated axons at Blackwell Publishing
- Generation of AP in cardiac cells and generation of AP in neuron cells
- Resting membrane potential from Life: The Science of Biology, by WK Purves, D Sadava, GH Orians, and HC Heller, 8th edition, New York: WH Freeman, ISBN 978-0-7167-7671-0.
- Ionic motion and the Goldman voltage for arbitrary ionic concentrations at The University of Arizona
- A cartoon illustrating the action potential
- Action potential propagation
- Production of the action potential: voltage and current clamping simulations[permanent dead link]
- Open-source software to simulate neuronal and cardiac action potentials at SourceForge.net
- Introduction to the Action Potential, Neuroscience Online (electronic neuroscience textbook by UT Houston Medical School)
- Khan Academy: Electrotonic and action potential Archived 2 July 2014 at the Wayback Machine