# Resting potential

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The relatively static membrane potential of quiescent cells is called the resting membrane potential (or resting voltage), as opposed to the specific dynamic electrochemical phenomena called action potential and graded membrane potential.

Membrane potential is the difference in electric potential between the interior and the exterior of a biological cell. With respect to the exterior of the cell, typical values of membrane potential, normally given in millivolts, range from –40 mV to –80 mV.

In physiology, an action potential occurs when the membrane potential of a specific axon location rapidly rises and falls: this depolarisation then causes adjacent locations to similarly depolarise. Action potentials occur in several types of animal cells, called excitable cells, which include neurons, muscle cells, endocrine cells, glomus cells, and in some plant cells.

## Contents

Apart from the latter two, which occur in excitable cells (neurons, muscles, and some secretory cells in glands), membrane voltage in the majority of non-excitable cells can also undergo changes in response to environmental or intracellular stimuli [ citation needed ]. In principle, there is no difference between resting membrane potential and dynamic voltage changes like action potential from a biophysical point of view: all these phenomena are caused by specific changes in membrane permeabilities for potassium, sodium, calcium, and chloride ions, which in turn result from concerted changes in functional activity of various ion channels, ion transporters, and exchangers. Conventionally, resting membrane potential can be defined as a relatively stable, ground value of transmembrane voltage in animal and plant cells.

A neuron, also known as a neurone or nerve cell, is an electrically excitable cell that communicates with other cells via specialized connections called synapses. It is the main component of nervous tissue. All animals except sponges and placozoans have neurons, but other multicellular organisms such as plants do not.

Muscle is a soft tissue found in most animals. Muscle cells contain protein filaments of actin and myosin that slide past one another, producing a contraction that changes both the length and the shape of the cell. Muscles function to produce force and motion. They are primarily responsible for maintaining and changing posture, locomotion, as well as movement of internal organs, such as the contraction of the heart and the movement of food through the digestive system via peristalsis.

A gland is a group of cells in an animal's body that synthesizes substances for release into the bloodstream or into cavities inside the body or its outer surface.

Voltage is the difference in electric potential between two points, arising from the separation of positive and negative electric charges on opposite sides of a resistive barrier. The typical resting membrane potential of a cell arises from the separation of potassium ions from intracellular, relatively immobile anions across the membrane of the cell. Because the membrane permeability for potassium is much higher than that for other ions (disregarding voltage-gated channels at this stage), and because of the strong chemical gradient for potassium, potassium ions flow from the cytosol into the extracellular space carrying out positive charge, until their movement is balanced by build-up of negative charge on the inner surface of the membrane. Again, because of the high relative permeability for potassium, the resulting membrane potential is almost always close to the potassium reversal potential. But in order for this process to occur, a concentration gradient of potassium ions must first be set up. This work is done by the ion pumps/transporters and/or exchangers and generally is powered by ATP.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two-types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

In the case of the resting membrane potential across an animal cell's plasma membrane, potassium (and sodium) gradients are established by the Na+/K+-ATPase (sodium-potassium pump) which transports 2 potassium ions inside and 3 sodium ions outside at the cost of 1 ATP molecule. In other cases, for example, a membrane potential may be established by acidification of the inside of a membranous compartment (such as the proton pump that generates membrane potential across synaptic vesicle membranes).[ citation needed ]

The cell membrane is a biological membrane that separates the interior of all cells from the outside environment which protects the cell from its environment consisting of a lipid bilayer with embedded proteins. The cell membrane controls the movement of substances in and out of cells and organelles. In this way, it is selectively permeable to ions and organic molecules. In addition, cell membranes are involved in a variety of cellular processes such as cell adhesion, ion conductivity and cell signalling and serve as the attachment surface for several extracellular structures, including the cell wall, the carbohydrate layer called the glycocalyx, and the intracellular network of protein fibers called the cytoskeleton. In the field of synthetic biology, cell membranes can be artificially reassembled.

Na⁺/K⁺-ATPase is an enzyme found in the plasma membrane of all animal cells. It performs several functions in cell physiology.

In a neuron, synaptic vesicles store various neurotransmitters that are released at the synapse. The release is regulated by a voltage-dependent calcium channel. Vesicles are essential for propagating nerve impulses between neurons and are constantly recreated by the cell. The area in the axon that holds groups of vesicles is an axon terminal or "terminal bouton". Up to 130 vesicles can be released per bouton over a ten-minute period of stimulation at 0.2 Hz. In the visual cortex of the human brain, synaptic vesicles have an average diameter of 39.5 nanometers (nm) with a standard deviation of 5.1 nm.

## Electroneutrality

In most quantitative treatments of membrane potential, such as the derivation of Goldman equation, electroneutrality is assumed; that is, that there is no measurable charge excess in any side of the membrane. So, although there is an electric potential across the membrane due to charge separation, there is no actual measurable difference in the global concentration of positive and negative ions across the membrane (as it is estimated below), that is, there is no actual measurable charge excess on either side. That occurs because the effect of charge on electrochemical potential is hugely greater than the effect of concentration so an undetectable change in concentration creates a great change in electric potential. [ citation needed ]

The Goldman–Hodgkin–Katz voltage equation, more commonly known as the Goldman equation, is used in cell membrane physiology to determine the reversal potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane.

In electrochemistry, the electrochemical potential, μ, sometimes abbreviated to ECP, is a thermodynamic measure of chemical potential that does not omit the energy contribution of electrostatics. Electrochemical potential is expressed in the unit of J/mol.

## Generation of the resting potential

Cell membranes are typically permeable to only a subset of ions. These usually include potassium ions, chloride ions, bicarbonate ions, and others. To simplify the description of the ionic basis of the resting membrane potential, it is most useful to consider only one ionic species at first, and consider the others later. Since trans-plasma-membrane potentials are almost always determined primarily by potassium permeability, that is where to start.

• Panel 1 of the diagram shows a diagrammatic representation of a simple cell where a concentration gradient has already been established. This panel is drawn as if the membrane has no permeability to any ion. There is no membrane potential because despite there being a concentration gradient for potassium, there is no net charge imbalance across the membrane. If the membrane were to become permeable to a type of ion that is more concentrated on one side of the membrane, then that ion would contribute to membrane voltage because the permeant ions would move across the membrane with net movement of that ion type down the concentration gradient. There would be net movement from the side of the membrane with a higher concentration of the ion to the side with lower concentration. Such a movement of one ion across the membrane would result in a net imbalance of charge across the membrane and a membrane potential. This is a common mechanism by which many cells establish a membrane potential.
• In panel 2 of the diagram, the cell membrane has been made permeable to potassium ions, but not the anions (An) inside the cell. These anions are mostly contributed by protein. There is energy stored in the potassium ion concentration gradient that can be converted into an electrical gradient when potassium (K+) ions move out of the cell. Note that potassium ions can move across the membrane in both directions but by the purely statistical process that arises from the higher concentration of potassium ions inside the cell, there will be more potassium ions moving out of the cell. Because there is a higher concentration of potassium ions inside the cells, their random molecular motion is more likely to encounter the permeability pore (ion channel) that is the case for the potassium ions that are outside and at a lower concentration. An internal K+ is simply "more likely" to leave the cell than an extracellular K+ is to enter it. It is a matter of diffusion doing work by dissipating the concentration gradient. As potassium leaves the cell, it is leaving behind the anions. Therefore, a charge separation is developing as K+ leaves the cell. This charge separation creates a transmembrane voltage. This transmembrane voltage is the membrane potential. As potassium continues to leave the cell, separating more charges, the membrane potential will continue to grow. The length of the arrows (green indicating concentration gradient, red indicating voltage), represents the magnitude of potassium ion movement due to each form of energy. The direction of the arrow indicates the direction in which that particular force is applied. Thus, the building membrane voltage is an increasing force that acts counter to the tendency for net movement of potassium ions down the potassium concentration gradient.
• In Panel 3, the membrane voltage has grown to the extent that its "strength" now matches the concentration gradients. Since these forces (which are applied to K+) are now the same strength and oriented in opposite directions, the system is now in equilibrium. Put another way, the tendency of potassium to leave the cell by running down its concentration gradient is now matched by the tendency of the membrane voltage to pull potassium ions back into the cell. K+ continues to move across the membrane, but the rate at which it enters and leaves the cell are the same, thus, there is no net potassium current. Because the K+ is at equilibrium, membrane potential is stable, or "resting" (EK).

Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore. Their functions include establishing a resting membrane potential, shaping action potentials and other electrical signals by gating the flow of ions across the cell membrane, controlling the flow of ions across secretory and epithelial cells, and regulating cell volume. Ion channels are present in the membranes of all excitable cells. Ion channels are one of the two classes of ionophoric proteins, the other being ion transporters.

Diffusion is the net movement of molecules or atoms from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in chemical potential of the diffusing species.

The resting voltage is the result of several ion-translocating enzymes (uniporters, cotransporters, and pumps) in the plasma membrane, steadily operating in parallel, whereby each ion-translocator has its characteristic electromotive force (= reversal potential = 'equilibrium voltage'), depending on the particular substrate concentrations inside and outside (internal ATP included in case of some pumps). H+ exporting ATPase render the membrane voltage in plants and fungi much more negative than in the more extensively investigated animal cells, where the resting voltage is mainly determined by selective ion channels.

In most neurons the resting potential has a value of approximately −70 mV. The resting potential is mostly determined by the concentrations of the ions in the fluids on both sides of the cell membrane and the ion transport proteins that are in the cell membrane. How the concentrations of ions and the membrane transport proteins influence the value of the resting potential is outlined below.

The resting potential of a cell can be most thoroughly understood by thinking of it in terms of equilibrium potentials. In the example diagram here, the model cell was given only one permeant ion (potassium). In this case, the resting potential of this cell would be the same as the equilibrium potential for potassium.

However, a real cell is more complicated, having permeabilities to many ions, each of which contributes to the resting potential. To understand better, consider a cell with only two permeant ions, potassium, and sodium. Consider a case where these two ions have equal concentration gradients directed in opposite directions, and that the membrane permeabilities to both ions are equal. K+ leaving the cell will tend to drag the membrane potential toward EK. Na+ entering the cell will tend to drag the membrane potential toward the reversal potential for sodium ENa. Since the permeabilities to both ions were set to be equal, the membrane potential will, at the end of the Na+/K+ tug-of-war, end up halfway between ENa and EK. As ENa and EK were equal but of opposite signs, halfway in between is zero, meaning that the membrane will rest at 0 mV.

Note that even though the membrane potential at 0 mV is stable, it is not an equilibrium condition because neither of the contributing ions is in equilibrium. Ions diffuse down their electrochemical gradients through ion channels, but the membrane potential is upheld by continual K+ influx and Na+ efflux via ion transporters. Such situation with similar permeabilities for counter-acting ions, like potassium and sodium in animal cells, can be extremely costly for the cell if these permeabilities are relatively large, as it takes a lot of ATP energy to pump the ions back. Because no real cell can afford such equal and large ionic permeabilities at rest, resting potential of animal cells is determined by predominant high permeability to potassium and adjusted to the required value by modulating sodium and chloride permeabilities and gradients.

In a healthy animal cell Na+ permeability is about 5% of the K+ permeability or even less, whereas the respective reversal potentials are +60 mV for sodium (ENa)and −80 mV for potassium (EK). Thus the membrane potential will not be right at EK, but rather depolarized from EK by an amount of approximately 5% of the 140 mV difference between EK and ENa. Thus, the cell's resting potential will be about −73 mV.

In a more formal notation, the membrane potential is the weighted average of each contributing ion's equilibrium potential. The size of each weight is the relative conductance of each ion. In the normal case, where three ions contribute to the membrane potential:

${\displaystyle E_{m}={\frac {g_{K^{+}}}{g_{tot}}}E_{K^{+}}+{\frac {g_{Na^{+}}}{g_{tot}}}E_{Na^{+}}+{\frac {g_{Cl^{-}}}{g_{tot}}}E_{Cl^{-}}}$,

where

• Em is the membrane potential, measured in volts
• EX is the equilibrium potential for ion X, also in volts
• gX/gtot is the relative conductance of ion X, which is dimensionless
• gtot is the total conductance of all permeant ions in arbitrary units (e.g. siemens for electrical conductance), in this case gK+ + gNa+ + gCl

## Membrane transport proteins

For determination of membrane potentials, the two most important types of membrane ion transport proteins are ion channels and ion transporters. Ion channel proteins create paths across cell membranes through which ions can passively diffuse without direct expenditure of metabolic energy. They have selectivity for certain ions, thus, there are potassium-, chloride-, and sodium-selective ion channels. Different cells and even different parts of one cell (dendrites, cell bodies, nodes of Ranvier) will have different amounts of various ion transport proteins. Typically, the amount of certain potassium channels is most important for control of the resting potential (see below). Some ion pumps such as the Na+/K+-ATPase are electrogenic, that is, they produce charge imbalance across the cell membrane and can also contribute directly to the membrane potential. Most pumps use metabolic energy (ATP) to function.

## Equilibrium potentials

For most animal cells potassium ions (K+) are the most important for the resting potential. [1] Due to the active transport of potassium ions, the concentration of potassium is higher inside cells than outside. Most cells have potassium-selective ion channel proteins that remain open all the time. There will be net movement of positively charged potassium ions through these potassium channels with a resulting accumulation of excess negative charge inside of the cell. The outward movement of positively charged potassium ions is due to random molecular motion (diffusion) and continues until enough excess negative charge accumulates inside the cell to form a membrane potential which can balance the difference in concentration of potassium between inside and outside the cell. "Balance" means that the electrical force (potential) that results from the build-up of ionic charge, and which impedes outward diffusion, increases until it is equal in magnitude but opposite in direction to the tendency for outward diffusive movement of potassium. This balance point is an equilibrium potential as the net transmembrane flux (or current) of K+ is zero. A good approximation for the equilibrium potential of a given ion only needs the concentrations on either side of the membrane and the temperature. It can be calculated using the Nernst equation:

${\displaystyle E_{eq,K^{+}}={\frac {RT}{zF}}\ln {\frac {[K^{+}]_{o}}{[K^{+}]_{i}}},}$

where

• Eeq,K+ is the equilibrium potential for potassium, measured in volts
• R is the universal gas constant, equal to 8.314 joules·K−1·mol−1
• T is the absolute temperature, measured in kelvins (= K = degrees Celsius + 273.15)
• z is the number of elementary charges of the ion in question involved in the reaction
• F is the Faraday constant, equal to 96,485 coulombs·mol−1 or J·V−1·mol−1
• [K+]o is the extracellular concentration of potassium, measured in mol·m−3 or mmol·l−1
• [K+]i is likewise the intracellular concentration of potassium

Potassium equilibrium potentials of around −80 millivolts (inside negative) are common. Differences are observed in different species, different tissues within the same animal, and the same tissues under different environmental conditions. Applying the Nernst Equation above, one may account for these differences by changes in relative K+ concentration or differences in temperature.

For common usage the Nernst equation is often given in a simplified form by assuming typical human body temperature (37 °C), reducing the constants and switching to Log base 10. (The units used for concentration are unimportant as they will cancel out into a ratio). For Potassium at normal body temperature one may calculate the equilibrium potential in millivolts as:

${\displaystyle E_{eq,K^{+}}=61.54mV\log {\frac {[K^{+}]_{o}}{[K^{+}]_{i}}},}$

Likewise the equilibrium potential for sodium (Na+) at normal human body temperature is calculated using the same simplified constant. You can calculate E assuming an outside concentration, [K+]o, of 10mM and an inside concentration, [K+]i, of 100mM. For chloride ions (Cl) the sign of the constant must be reversed (−61.54 mV). If calculating the equilibrium potential for calcium (Ca2+) the 2+ charge halves the simplified constant to 30.77 mV. If working at room temperature, about 21 °C, the calculated constants are approximately 58 mV for K+ and Na+, −58 mV for Cl and 29 mV for Ca2+. At physiological temperature, about 29.5 °C, and physiological concentrations (which vary for each ion), the calculated potentials are approximately 67 mV for Na+, −90 mV for K+, −86 mV for Cl and 123 mV for Ca2+.

## Resting potentials

The resting membrane potential is not an equilibrium potential as it relies on the constant expenditure of energy (for ionic pumps as mentioned above) for its maintenance. It is a dynamic diffusion potential that takes this mechanism into accountwholly unlike the equilibrium potential, which is true no matter the nature of the system under consideration. The resting membrane potential is dominated by the ionic species in the system that has the greatest conductance across the membrane. For most cells this is potassium. As potassium is also the ion with the most negative equilibrium potential, usually the resting potential can be no more negative than the potassium equilibrium potential. The resting potential can be calculated with the Goldman-Hodgkin-Katz voltage equation using the concentrations of ions as for the equilibrium potential while also including the relative permeabilities of each ionic species. Under normal conditions, it is safe to assume that only potassium, sodium (Na+) and chloride (Cl) ions play large roles for the resting potential:

${\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {P_{Na^{+}}[Na^{+}]_{o}+P_{K^{+}}[K^{+}]_{o}+P_{Cl^{-}}[Cl^{-}]_{i}}{P_{Na^{+}}[Na^{+}]_{i}+P_{K^{+}}[K^{+}]_{i}+P_{Cl^{-}}[Cl^{-}]_{o}}}\right)}}$

This equation resembles the Nernst equation, but has a term for each permeant ion. Also, z has been inserted into the equation, causing the intracellular and extracellular concentrations of Cl to be reversed relative to K+ and Na+, as chloride's negative charge is handled by inverting the fraction inside the logarithmic term. *Em is the membrane potential, measured in volts *R, T, and F are as above *Ps is the relative permeability of ion s *[s]Y is the concentration of ion s in compartment Y as above. Another way to view the membrane potential, considering instead the conductance of the ion channels rather than the permeability of the membrane, is using the Millman equation (also called the Chord Conductance Equation):

${\displaystyle E_{m}={\frac {g_{K^{+}}E_{eq,K^{+}}+g_{Na^{+}}E_{eq,Na^{+}}+g_{Cl^{-}}E_{eq,Cl^{-}}}{g_{K^{+}}+g_{Na^{+}}+g_{Cl^{-}}}}}$

or reformulated

${\displaystyle E_{m}={\frac {g_{K^{+}}}{g_{tot}}}E_{eq,K^{+}}+{\frac {g_{Na^{+}}}{g_{tot}}}E_{eq,Na^{+}}+{\frac {g_{Cl^{-}}}{g_{tot}}}E_{eq,Cl^{-}}}$

where gtot is the combined conductance of all ionic species, again in arbitrary units. The latter equation portrays the resting membrane potential as a weighted average of the reversal potentials of the system, where the weights are the relative conductances of each ion species (gX/gtot). During the action potential, these weights change. If the conductances of Na+ and Cl are zero, the membrane potential reduces to the Nernst potential for K+ (as gK+ = gtot). Normally, under resting conditions gNa+ and gCl− are not zero, but they are much smaller than gK+, which renders Em close to Eeq,K+. Medical conditions such as hyperkalemia in which blood serum potassium (which governs [K+]o) is changed are very dangerous since they offset Eeq,K+, thus affecting Em. This may cause arrhythmias and cardiac arrest. The use of a bolus injection of potassium chloride in executions by lethal injection stops the heart by shifting the resting potential to a more positive value, which depolarizes and contracts the cardiac cells permanently, not allowing the heart to repolarize and thus enter diastole to be refilled with blood.

Although the GHK voltage equation and Millman's equation are related, they are not equivalent. The critical difference is that Millman's equation assumes the current-voltage relationship to be ohmic, whereas the GHK voltage equation takes into consideration the small, instantaneous rectifications predicted by the GHK flux equation caused by the concentration gradient of ions. Thus, a more accurate estimate of membrane potential can be calculated using the GHK equation than with Millman's equation. [2]

## Measuring resting potentials

In some cells, the membrane potential is always changing (such as cardiac pacemaker cells). For such cells there is never any "rest" and the "resting potential" is a theoretical concept. Other cells with little in the way of membrane transport functions that change with time have a resting membrane potential that can be measured by inserting an electrode into the cell. [3] Transmembrane potentials can also be measured optically with dyes that change their optical properties according to the membrane potential.

## Summary of resting potential values in different types of cells

Cell types Resting potential
Skeletal muscle cells -95 mV [4]
Astroglia -80 to -90 mV
Neurons -60 to -70 mV [5]
Smooth muscle cells -60 mV
Aorta Smooth muscle tissue -45mV [5]
Photoreceptor cells -40 mV
Hair cell (Cochlea)-15 to -40mV [6]
Erythrocytes -8.4 mV [7]
Chondrocytes -8mV [5]

## History

Resting currents in nerves were measured and described by Julius Bernstein in 1902 where he proposed a "Membrane Theory" that explained the resting potential of nerve and muscle as a diffusion potential. [8]

## Related Research Articles

In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the system. Usually, this state results when the forward reaction proceeds at the same rate as the reverse reaction. The reaction rates of the forward and backward reactions are generally not zero, but equal. Thus, there are no net changes in the concentrations of the reactant(s) and product(s). Such a state is known as dynamic equilibrium.

In electrochemistry, the Nernst equation is an equation that relates the reduction potential of an electrochemical reaction to the standard electrode potential, temperature, and activities of the chemical species undergoing reduction and oxidation. It was named after Walther Nernst, a German physical chemist who formulated the equation.

Refractoriness is the fundamental property of any object of autowave nature not to respond on stimuli, if the object stays in the specific refractory state. In common sense, refractory period is the characteristic recovery time, a period of time that is associated with the motion of the image point on the left branch of the isocline .

Hyperpolarization is a change in a cell's membrane potential that makes it more negative. It is the opposite of a depolarization. It inhibits action potentials by increasing the stimulus required to move the membrane potential to the action potential threshold.

In biology, depolarization is a change within a cell, during which the cell undergoes a shift in electric charge distribution, resulting in less negative charge inside the cell. Depolarization is essential to the function of many cells, communication between cells, and the overall physiology of an organism.

In a biological membrane, the reversal potential of an ion is the membrane potential at which there is no net (overall) flow of that particular ion from one side of the membrane to the other. In the case of post-synaptic neurons, the reversal potential is the membrane potential at which a given neurotransmitter causes no net current flow of ions through that neurotransmitter receptor's ion channel.

In neuroscience, the threshold potential is the critical level to which a membrane potential must be depolarized to initiate an action potential. Threshold potentials are necessary to regulate and propagate signaling in both the central nervous system (CNS) and the peripheral nervous system (PNS).

In cellular biology, membrane transport refers to the collection of mechanisms that regulate the passage of solutes such as ions and small molecules through biological membranes, which are lipid bilayers that contain proteins embedded in them. The regulation of passage through the membrane is due to selective membrane permeability - a characteristic of biological membranes which allows them to separate substances of distinct chemical nature. In other words, they can be permeable to certain substances but not to others.

The cardiac action potential is a brief change in voltage across the cell membrane of heart cells. This is caused by the movement of charged atoms between the inside and outside of the cell, through proteins called ion channels. The cardiac action potential differs from action potentials found in other types of electrically excitable cells, such as nerves. Action potentials also vary within the heart; this is due to the presence of different ion channels in different cells.

In neuroscience, repolarization refers to the change in membrane potential that returns it to a negative value just after the depolarization phase of an action potential has changed the membrane potential to a positive value. The repolarization phase usually returns the membrane potential back to the resting membrane potential. The efflux of K+ ions results in the falling phase of an action potential. The ions pass through the selectivity filter of the K+ channel pore.

Voltage-gated ion channels are a class of transmembrane proteins that form ion channels that are activated by changes in the electrical membrane potential near the channel. The membrane potential alters the conformation of the channel proteins, regulating their opening and closing. Cell membranes are generally impermeable to ions, thus they must diffuse through the membrane through transmembrane protein channels. They have a crucial role in excitable cells such as neuronal and muscle tissues, allowing a rapid and co-ordinated depolarization in response to triggering voltage change. Found along the axon and at the synapse, voltage-gated ion channels directionally propagate electrical signals. Voltage-gated ion-channels are usually ion-specific, and channels specific to sodium (Na+), potassium (K+), calcium (Ca2+), and chloride (Cl) ions have been identified. The opening and closing of the channels are triggered by changing ion concentration, and hence charge gradient, between the sides of the cell membrane.

An electrochemical gradient is a gradient of electrochemical potential, usually for an ion that can move across a membrane. The gradient consists of two parts, the chemical gradient, or difference in solute concentration across a membrane, and the electrical gradient, or difference in charge across a membrane. When there are unequal concentrations of an ion across a permeable membrane, the ion will move across the membrane from the area of higher concentration to the area of lower concentration through simple diffusion. Ions also carry an electric charge that forms an electric potential across a membrane. If there is an unequal distribution of charges across the membrane, then the difference in electric potential generates a force that drives ion diffusion until the charges are balanced on both sides of the membrane.

The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes. It is a continuous time model, unlike, for example, the Rulkov map.

The Na-K-Cl cotransporter (NKCC) is a protein that aids in the active transport of sodium, potassium, and chloride into cells. In humans there are two isoforms of this membrane transport protein, NKCC1 and NKCC2, encoded by two different genes. Two isoforms of the NKCC1/Slc12a2 gene result from keeping or skipping exon 21 in the final gene product.

The Gibbs–Donnan effect is a name for the behaviour of charged particles near a semi-permeable membrane that sometimes fail to distribute evenly across the two sides of the membrane. The usual cause is the presence of a different charged substance that is unable to pass through the membrane and thus creates an uneven electrical charge. For example, the large anionic proteins in blood plasma are not permeable to capillary walls. Because small cations are attracted, but are not bound to the proteins, small anions will cross capillary walls away from the anionic proteins more readily than small cations.

In neurophysiology, several mathematical models of the action potential have been developed, which fall into two basic types. The first type seeks to model the experimental data quantitatively, i.e., to reproduce the measurements of current and voltage exactly. The renowned Hodgkin–Huxley model of the axon from the Loligo squid exemplifies such models. Although qualitatively correct, the H-H model does not describe every type of excitable membrane accurately, since it considers only two ions, each with only one type of voltage-sensitive channel. However, other ions such as calcium may be important and there is a great diversity of channels for all ions. As an example, the cardiac action potential illustrates how differently shaped action potentials can be generated on membranes with voltage-sensitive calcium channels and different types of sodium/potassium channels. The second type of mathematical model is a simplification of the first type; the goal is not to reproduce the experimental data, but to understand qualitatively the role of action potentials in neural circuits. For such a purpose, detailed physiological models may be unnecessarily complicated and may obscure the "forest for the trees". The Fitzhugh-Nagumo model is typical of this class, which is often studied for its entrainment behavior. Entrainment is commonly observed in nature, for example in the synchronized lighting of fireflies, which is coordinated by a burst of action potentials; entrainment can also be observed in individual neurons. Both types of models may be used to understand the behavior of small biological neural networks, such as the central pattern generators responsible for some automatic reflex actions. Such networks can generate a complex temporal pattern of action potentials that is used to coordinate muscular contractions, such as those involved in breathing or fast swimming to escape a predator.

## References

1. An example of an electrophysiological experiment to demonstrate the importance of K+ for the resting potential. The dependence of the resting potential on the extracellular concentration of K+ is shown in Figure 2.6 of Neuroscience, 2nd edition, by Dale Purves, George J. Augustine, David Fitzpatrick, Lawrence C. Katz, Anthony-Samuel LaMantia, James O. McNamara, S. Mark Williams. Sunderland (MA): Sinauer Associates, Inc.; 2001.
2. Hille, Bertil (2001) Ion Channels of Excitable Membranes, 3 ed.
3. An illustrated example of measuring membrane potentials with electrodes is in Figure 2.1 of Neuroscience by Dale Purves, et al. (see reference #1, above).
4. "Muscles". users.rcn.com. 2015-01-24. Archived from the original on 2015-11-07. Retrieved 2016-06-01.
5. Lewis, Rebecca; Asplin, Katie E.; Bruce, Gareth; Dart, Caroline; Mobasheri, Ali; Barrett-Jolley, Richard (2011-11-01). "The role of the membrane potential in chondrocyte volume regulation". Journal of Cellular Physiology. 226 (11): 2979–2986. doi:10.1002/jcp.22646. ISSN   1097-4652. PMC  . PMID   21328349.
6. Ashmore, J. F.; Meech, R. W. (1986-07-24). "Ionic basis of membrane potential in outer hair cells of guinea pig cochlea". Nature. 322 (6077): 368–371. doi:10.1038/322368a0.
7. Cheng, K; Haspel, HC; Vallano, ML; Osotimehin, B; Sonenberg, M (1980). "Measurement of membrane potentials (psi) of erythrocytes and white adipocytes by the accumulation of triphenylmethylphosphonium cation". J. Membr. Biol. 56 (3): 191–201. doi:10.1007/bf01869476. PMID   6779011.
8. Seyfarth, Ernst-August (2006-01-01). "Julius Bernstein (1839-1917): pioneer neurobiologist and biophysicist". Biological Cybernetics. 94 (1): 2–8. doi:10.1007/s00422-005-0031-y. ISSN   0340-1200. PMID   16341542.