Resting potential

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The Na
/K
-ATPase, as well as effects of diffusion of the involved ions, are major mechanisms to maintain the resting potential across the membranes of animal cells. Sodium-potassium pump and diffusion.png
The Na
/K
-ATPase
, as well as effects of diffusion of the involved ions, are major mechanisms to maintain the resting potential across the membranes of animal cells.

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. The resting membrane potential has a value of approximately -70mV or -0.07V. [1]

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. The resting potential exists due to the differences in membrane permeabilities for potassium, sodium, calcium, and chloride ions, which in turn result from 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.

Because the membrane permeability for potassium is much higher than that for other ions, and because of the strong chemical gradient for potassium, potassium ions flow from the cytosol out to 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.

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 ]

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 on either 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 ]

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.

A diagram showing the progression in the development of a membrane potential from a concentration gradient (for potassium). Green arrows indicate net movement of K down a concentration gradient. Red arrows indicate net movement of K due to the membrane potential. The diagram is misleading in that while the concentration of potassium ions outside of the cell increases, only a small amount of K needs to cross the membrane in order to produce a membrane potential with a magnitude large enough to counter the tendency of the potassium ions to move down the concentration gradient. Membrane potential development.jpg
A diagram showing the progression in the development of a membrane potential from a concentration gradient (for potassium). Green arrows indicate net movement of K down a concentration gradient. Red arrows indicate net movement of K due to the membrane potential. The diagram is misleading in that while the concentration of potassium ions outside of the cell increases, only a small amount of K needs to cross the membrane in order to produce a membrane potential with a magnitude large enough to counter the tendency of the potassium ions to move down the concentration gradient.

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:

,

where

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. [2] 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:

where

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:

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 pillows 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:

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):

or reformulated

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. [3]

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

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. [9]

See also

Related Research Articles

In a chemical reaction, chemical equilibrium is the state in which both the 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. 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 they are equal. Thus, there are no net changes in the concentrations of the reactants and products. Such a state is known as dynamic equilibrium.

In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction from the standard electrode potential, absolute temperature, the number of electrons involved in the redox reaction, and activities of the chemical species undergoing reduction and oxidation respectively. It was named after Walther Nernst, a German physical chemist who formulated the equation.

<span class="mw-page-title-main">Action potential</span> Neuron communication by electric impulses

An action potential occurs when the membrane potential of a specific cell rapidly rises and falls. This depolarization then causes adjacent locations to similarly depolarize. Action potentials occur in several types of excitable cells, which include animal cells like neurons and muscle cells, as well as some plant cells. Certain endocrine cells such as pancreatic beta cells, and certain cells of the anterior pituitary gland are also excitable cells.

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.

<span class="mw-page-title-main">Depolarization</span> Change in a cells electric charge distribution

In biology, depolarization or hypopolarization 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 compared to the outside. Depolarization is essential to the function of many cells, communication between cells, and the overall physiology of an organism.

<span class="mw-page-title-main">Membrane potential</span> Electric potential difference between interior and exterior of a biological cell

Membrane potential is the difference in electric potential between the interior and the exterior of a biological cell. It equals the interior potential minus the exterior potential. This is the energy per charge which is required to move a positive charge at constant velocity across the cell membrane from the exterior to the interior.

In a biological membrane, the reversal potential is the membrane potential at which the direction of ionic current reverses. At the reversal potential, there is no net flow of ions from one side of the membrane to the other. For channels that are permeable to only a single type of ion, the reversal potential is identical to the equilibrium potential of the ion.

<span class="mw-page-title-main">Threshold potential</span> Critical potential value

In electrophysiology, the threshold potential is the critical level to which a membrane potential must be depolarized to initiate an action potential. In neuroscience, 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.

<span class="mw-page-title-main">Cardiac action potential</span> Biological process in the heart

Unlike the action potential in skeletal muscle cells, the cardiac action potential is not initiated by nervous activity. Instead, it arises from a group of specialized cells known as pacemaker cells, that have automatic action potential generation capability. In healthy hearts, these cells form the cardiac pacemaker and are found in the sinoatrial node in the right atrium. They produce roughly 60–100 action potentials every minute. The action potential passes along the cell membrane causing the cell to contract, therefore the activity of the sinoatrial node results in a resting heart rate of roughly 60–100 beats per minute. All cardiac muscle cells are electrically linked to one another, by intercalated discs which allow the action potential to pass from one cell to the next. This means that all atrial cells can contract together, and then all ventricular cells.

<span class="mw-page-title-main">Voltage-gated ion channel</span> Type of ion channel transmembrane protein

Voltage-gated ion channels are a class of transmembrane proteins that form ion channels that are activated by changes in a cell's 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.

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

<span class="mw-page-title-main">Electrochemical gradient</span> Gradient of electrochemical potential, usually for an ion that can move across a 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:

<span class="mw-page-title-main">Axolemma</span> Cell membrane of an axon

In neuroscience, the axolemma is the cell membrane of an axon, the branch of a neuron through which signals are transmitted. The axolemma is a three-layered, bilipid membrane. Under standard electron microscope preparations, the structure is approximately 8 nanometers thick.

<span class="mw-page-title-main">Hodgkin–Huxley model</span> Describes how neurons transmit electric signals

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 engineering characteristics of excitable cells such as neurons and muscle cells. It is a continuous-time dynamical system.

The Na–K–Cl cotransporter (NKCC) is a transport protein that aids in the secondary 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.

<span class="mw-page-title-main">Gibbs–Donnan effect</span> Behaviour of charged particles near a semi-permeable membrane

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.

The Goldman–Hodgkin–Katz flux equation describes the ionic flux across a cell membrane as a function of the transmembrane potential and the concentrations of the ion inside and outside of the cell. Since both the voltage and the concentration gradients influence the movement of ions, this process is a simplified version of electrodiffusion. Electrodiffusion is most accurately defined by the Nernst–Planck equation and the GHK flux equation is a solution to the Nernst–Planck equation with the assumptions listed below.

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.

<span class="mw-page-title-main">Sodium in biology</span> Use of sodium by organisms

Sodium ions are necessary in small amounts for some types of plants, but sodium as a nutrient is more generally needed in larger amounts by animals, due to their use of it for generation of nerve impulses and for maintenance of electrolyte balance and fluid balance. In animals, sodium ions are necessary for the aforementioned functions and for heart activity and certain metabolic functions. The health effects of salt reflect what happens when the body has too much or too little sodium. Characteristic concentrations of sodium in model organisms are: 10 mM in E. coli, 30 mM in budding yeast, 10 mM in mammalian cell and 100 mM in blood plasma.

References

  1. "Resting Membrane Potential - Nernst - Generation". TeachMePhysiology. Retrieved 2024-09-18.
  2. 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.
  3. Hille, Bertil (2001) Ion Channels of Excitable Membranes, 3 ed.
  4. 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).
  5. "Muscles". users.rcn.com. 2015-01-24. Archived from the original on 2015-11-07. Retrieved 2016-06-01.
  6. 1 2 3 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   3229839 . PMID   21328349.
  7. 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. Bibcode:1986Natur.322..368A. doi:10.1038/322368a0. PMID   2426595. S2CID   4371640.
  8. 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. S2CID   19693916.
  9. 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. S2CID   2842501.