Membrane potential

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Membrane potential (or transmembrane potential) is the voltage difference (or electrical potential difference) between the interior and exterior of a cell. Because the fluid inside and outside a cell is highly conductive, while a cell's plasma membrane is highly resistive, the voltage change in moving from a point outside to a point inside occurs largely within the narrow width of the membrane itself. Therefore, it is common to speak of the membrane potential as the voltage across the membrane.

The plasma membrane surrounds the cell to provide a stable environment for biological processes. The membrane potential arises from the action of ion channels, ion pumps, and ion transporters embedded in the membrane which maintain different ion concentrations inside and outside the cell. The term "membrane potential" is sometimes used interchangeably with cell potential but is applicable to any lipid bilayer or membrane.

Three special cases of physiological membrane potential with underlying mechanisms and the concept of equilibrium or reversal potential, which constitute the subject of electrophysiology and cellular biophysics, are addressed in this article. The former are resting membrane potential, action potential, and graded (postsynaptic) membrane potentials. The membrane potential of most not-excitable cells is kept at relatively stable value of resting potential. In contrast, electrically excitable cells like neurons and myocytes can "fire" action potentials. Neurons are specialized to use changes in membrane potential for fast communication, with other neurons, muscles, and secretory cells. When cell membrane depolarizes from resting potential and produces action potential, it travels down the axon to the synapses: the magnitude of the axonal membrane potential varies dynamically along its length. On reaching a (chemical) synapse, a neurotransmitter is released causing a localized change in potential in the postsynaptic membrane of the target neuron by opening ion channels in its membrane. Importantly, every occasion of action potential firing results from spatial and temporal summation of often a very large number of minuscule graded postsynaptic responses of both positive (membrane depolarization) and negative (membrane hyperpolarization) polarities. Ultimately, such important aspects as value of resting potential, maximum amplitude and after-hyperpolarization phase of action potential can be easily understood utilizing the concept of equilibrium potential.

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 is needed}

[edit] Reversal potential

An equilibrium or reversal potential of an ion is the value of transmembrane voltage at which the electric force generated by diffusional movement of the ion down its concentration gradient becomes equal to the molecular force of that diffusion. This means that the transmembrane voltage exactly matches (resists) the force of diffusion of the ion (or vice versa), such that the net current of the ion across the membrane is zero and unchanging. The equilibrium potential of a particular ion is designated by the notation E_ion.The equilibrium potential for any ion can be calculated using the Nernst equation.^[1] For example, reversal potential for potassium ions will be as follows:

Failed to parse (Cannot write to or create math output directory): E_{eq,K^+} = \frac{RT}{zF} \ln \frac{[K^+]_{o}}{[K^+]_{i}} ,

where

• E_eq,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 the intracellular concentration of potassium

Apparently, even if two different ions have the same charge (ie. K⁺ and Na⁺), they can still have very different equilibrium potentials, provided their outside and/or inside concentrations differ. Take, for example, the equilibrium potentials of potassium and sodium in neurons. The potassium equilibrium potential E_K is -84 mV with 5 mM potassium outside and 140 mM inside. The sodium equilibrium potential, on the other hand, E_Na is approximately +40 mV with approximately 12 mM sodium inside and 140 mM outside.^{[note 1]}

Resting potential and action potential are often referred as "potassium" and "sodium" potentials, respectively. This stems from the origin of the resting potential (proximity to the E_K), and the origin (activation of sodium channels) and the peak amplitude of the action potential (proximity to the E_Na).

[edit] Resting membrane potential

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 the potassium ions to move down the concentration gradient.

Relatively static membrane potential of quiescent cells is called resting membrane potential (or resting voltage), as opposed to the dynamic electrochemical phenomenona called action potential and graded membrane potential. Apart from the latter two, which occur in excitable cells (neurons, muscles, and some secretory cells in glands), membrane voltage in the non-excitable cells can also undergo changes in response to environmental or intracellular stimuli. For example, depolarization of the plasma membrane appears to be an important step in programmed cell death.^[2] In principle, there is no difference between resting membrane potential and dynamic voltage changes like action potential from biophysical point of view: all these phenomena are caused by specific changes in membrane permeabilities for potassium, sodium, calcium, and chloride, which in turn result from concerted changes in functional activity of various ion channels, ion pumps, exchangers, and transporters. Conventionally, resting membrane potential can be defined as a relatively stable, ground, value of transmembrane voltage in animal and plant cells.

Generation of resting membrane potential is explicitly explained by Goldman equation.^[3] It is essentially the Nernst equation, in that it is based on the charges of the ions in question, as well as the difference between their inside and outside concentrations. However, it also takes into consideration the relative permeability of the plasma membrane to each ion in question.

Failed to parse (Cannot write to or create math output directory): E_{m} = \frac{RT}{F} \ln{ \left( \frac{ P_{\mathrm{K}}[\mathrm{K}^{+}]_\mathrm{out} + P_{\mathrm{Na}}[\mathrm{Na}^{+}]_\mathrm{out} + P_{\mathrm{Cl}}[\mathrm{Cl}^{-}]_\mathrm{in}}{ P_{\mathrm{K}}[\mathrm{K}^{+}]_\mathrm{in} + P_{\mathrm{Na}}[\mathrm{Na}^{+}]_\mathrm{in} + P_{\mathrm{Cl}}[\mathrm{Cl}^{-}]_\mathrm{out}} \right) }

for the three monovalent ions most important to action potentials: potassium (K⁺), sodium (Na⁺), and chloride (Cl⁻). Being an anion, the chloride terms are treated differently than the cation terms; the inside concentration is in the numerator, and the outside concentration is in the denominator, which is reversed from the cation terms. P_i stands for the permeability of the ion type i. If calcium ions are also considered, which are critically important for action potentials in muscles, the formula for the equilibrium potential becomes more complicated.^[4] The resting plasma membrane of the most animal cells is much more permeable to K⁺, which results in the resting potential to be close to the potassium equilibrium potential.^[5][6]

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 E_K. Na⁺ entering the cell will tend to drag the membrane potential toward the reversal potential for sodium E_Na. 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 E_Na and E_K. As E_Na and E_K 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 are 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 pumps. 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 and -80 mV for potassium. Thus the membrane potential will not be right at E_K, but rather depolarized from E_K by an amount of approximately 5% of the 140 mV difference between E_K and E_Na. 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 (Goldman equation). The size of each weight is the relative permeability of each ion. In the normal case, where three ions contribute to the membrane potential:

Failed to parse (Cannot write to or create math output directory): E_{m} = \frac{P_{K^+}} {P_{tot}} E_{K^+} + \frac{P_{Na^+}} {P_{tot}} E_{Na^+} + \frac{P_{Cl^-}} {P_{tot}} E_{Cl^-}

, where

• E_m is the membrane potential, measured in volts
• E_X is the equilibrium potential for ion X, also in volts
• P_X is the relative permeability of ion X in arbitrary units (e.g. siemens for electrical conductance)
• P_tot is the total permeability of all permeant ions, in this case P_tot = P_K⁺ + P_Na⁺ + P_Cl^-

It is important to understand that ionic and water permeability of a pure lipid bilayer is very small, and it is similarly negligible for ions of comparable size, such as Na⁺ and K⁺. The cell membranes, however, contain a large number of ion channels, water channels (aquaporins), and various ionic pumps, exchangers, and transporters, which can selectively increase permeability of the membrane for different ions. The relatively high membrane permeability for potassium ions at resting potential results from inward-rectifier potassium ion channels which are open at negative voltages, and so called leak potassium conductances such as two-barrel open rectifier K⁺ channel (ORK⁺) which is locked in the open state irrespective of voltage. These potassium channels should not be confused with voltage-activated K⁺ channels responsible for membrane repolarization during action potential.

Values of resting membrane potential in the most of the mature (differentiated) animal cells usually vary between E_K and around -40 mV. Resting voltage in the excitable cells capable of producing action potentials is usually balanced around -60 mV because more depolarized voltage would lead to spontaneous activation of voltage-activated sodium channels and generate action potential. Immature or not-differentiated cells demonstrate highly variable values of resting voltage usually significantly more positive than that in the differentiated cells.^[7] In such cells, the resting potential value correlates well with the degree of differentiation: undifferentiated cells can demonstrate resting potential value as low as 0 mV.

Maintenance of resting potential can be very costly for a cell, especially when the cell function requires a rather depolarized value of membrane voltage. For example, resting potential in day light-adapted blowfly (Calliphora vicina) photoreceptors can be as high as -30 mV.^[8]. In insect photoreceptors depolarization is provided by light-activated TRP channels which cause fluctuations in membrane voltage in response to changing ambient light intensity. These changes in voltage then propagate as graded membrane responses to the synapses with a second-order neuron. At -30 mV, blowfly photoreceptor input resistance and membrane time constant can be as low as 10 MΩ and 1.5 ms, respectively, and the corner frequency of the voltage response power spectrum as high as 120 Hz. Such remarkably high corner frequency allows Calliphora vicina to produce the fastest functional responses ever recorded from an ocular photoreceptor.^[9] This excellent visual ability, however, is very expensive metabolically, because such a low membrane resistance results from numerous open voltage-activated potassium and light-activated TRP channels, which, in turn, requires high level of Na+/K+-ATPase activity to maintain the proper ionic gradients. As a result, blowfly retina is one of the most, if not the most, energy demanding tissues in the fly both under dark- and light-adapted conditions.^[10][11][12] Maintenance of resting potential in such cells may cost more than 20% of overall cellular ATP.^[12]
On the other hand, high resting potential in the not-differentiated cells can be rather a great metabolic advantage, and not a burden for non-active cells such as stem cells. This apparent paradox is easily resolved by careful examination of the origin of that resting potential. Low-differentiated cells are characterized by extremely high input resistance^[7] which implies that leak and inward rectifier potassium channels, which are responsible for high potassium permeability at rest, as well as other leak conductances (cloride and sodium, for example), are not expressed at this stage of cell life. As an apparent result, potassium permeability becomes similar to that for sodium ions, which places resting potential in-between the reversal potentials for sodium and potassium as discussed above. And because all ionic permeabilities in such cells are virtually the basic ionic leaks of a lipid bilayer, very little metabolic cost may be associated with maintenance of resting potential in such cells.

[edit] Action potential

Figure 1. A. view of an idealized action potential illustrates its various phases as the action potential passes a point on a cell membrane. B. Actual recordings of action potentials are often distorted compared to the schematic view because of variations in electrophysiological techniques used to make the recording.

Figure 2. Train of action potentials is evoked by a depolarizing current stimulus. This is a whole-cell current clamp recording (voltage is allowed to change freely while current amplitude is held constant)

Neurons communicate with other neurons, muscles, and organs via action potentials (APs), brief transient waveforms quickly "moving" along neuronal axons. The typical duration of an action potential registered with a pointed electrode is about 1 ms, which includes fast depolarization from the resting potential by means of opening of voltage-activated sodium channels, followed by slower repolarization of the membrane as a result of opening of voltage-activated potassium channels. After-hyperpolarization or "undershoot" is the final phase of an action potential which results from the activity of Na+/K+-ATPase (two K⁺ ions in, three Na⁺ ions out per cycle of pumping results in the net one positive charge leaving the cell, i.e. one negative charge entering the cell), opening of calcium- and sodium-activated potassium channels, and deactivating delayed-rectifier potassium channels.

Action potential is initiated when membrane is depolarized above action potential activation threshold, which is approximately 20 mV above the resting potential level in neurons (-60 mV). In neurons in vivo, initial depolarization is caused by spatio-temporal summation of graded excitatory postsynaptic potentials (EPSPs), which is the "natural" mechanism of action potential initiation in neuronal networks. For example, it may require hundreds and thousands of EPSPs simultaneously or almost simultaneously converging on the neuron to evoke an action potential because a typical amplitude of an EPSP is 0.1 mV and the excitatory graded potentials are offset by their inhibitory counterparts, inhibitory postsynaptic potentials (IPSPs). Alternatively, action potentials can be initiated by external injection of a brief depolarizing current pulse in vitro and in vivo, during physiological experiments and in certain medical devices (see cardiac pacemaker). Sodium and potassium channels are key components of AP generation and propagation. Voltage-activated sodium channels, which are predominantly closed at resting voltage levels, react to a depolarizing perturbation by further opening, first gradually and linearly, but then, beyond a certain threshold, in a robust avalanche-like manner.^[13] The principal mechanism of AP generation was discovered by Hodgkin & Huxsley ^[14] and discussed in detail elsewhere (see Action Potential).
Inactivation of sodium channels is responsible for the so called "absolute refractory period" after action potential. During that period of an order of few milliseconds duration no consequtive AP can be evoked by no matter how large depolarization. During the relative refractory period, a sufficient number of sodium channels (but not all) have recovered that an action potential can be provoked, but only with a stimulus much stronger than usual. These refractory periods ensure that the action potential travels in only one direction along the axon.^[15]

Action potentials usually originate at the axon hillock, where voltage-activated sodium channel density is the highest and their activation voltage threshold is the lowest, but they can be initiated in any part of neuron including dendrites and soma, if density of sodium channels allows it. Action potentials, originating from dendrites and soma have different shapes (broader in dendrites), and the critical amplitude of depolarizing perturbation (AP threshold level) changes as: dendrites > soma > axon hillock. APs usually propagate from axon hillock toward axonal synapses, but can also propagate back to soma and dendrites, although the biological significance and network calculation benefits of this phenomenon are not yet established.^[16]

[edit] Graded membrane potential

Figure 3. Graph displaying an EPSP, an IPSP, and the summation of an EPSP and an IPSP. When the two are summed together the potential is still below the action potential threshold.

A graded membrane potential is a gradient of transmembrane potential difference along a length of cell membrane. Graded potentials are particularly important in neurons that lack action potentials, such as some types of retinal neurons. Graded potentials that depolarize the membrane, increasing the membrane potential above the resting potential, are important as "triggering potentials" that can spread along the surface of neuronal cell bodies to axon initial segments (the first part of the axon as it leaves the cell body) and trigger action potentials. Graded potentials that hyperpolarize the membrane potential to values more negative than the resting potential can inhibit the generation of action potentials. Graded potentials can arise at either portions of cells that function as sensory receptors or at synapses that are activated by neurotransmitters. These two types of graded potentials are called receptor potentials or synaptic potentials. Graded potentials are distinct from action potentials in that graded potentials spread electric potential changes along cell membranes without activating the kind of constant magnitude propagating signal that is characteristic of the action potential. Graded potentials are highest at a source and decay with increasing distance from the source.

[edit] All other values of membrane potential

From the viewpoint of biophysics, there is nothing particularly special about the resting membrane potential. It is merely the membrane potential that results from the membrane permeabilities that predominate when the cell is resting. The above equation of weighted averages always applies, but the following approach may be easier to visualize. At any given moment, there are two factors for an ion that determine how much influence that ion will have over the membrane potential of a cell.

1. That ion's driving force and,
2. That ion's permeability

Intuitively, this is easy to understand. If the driving force is high, then the ion is being "pushed" across the membrane hard (more correctly stated: it is diffusing in one direction faster than the other). If the permeability is high, it will be easier for the ion to diffuse across the membrane. But what are 'driving force' and 'permeability'?

• Driving force: the driving force is the net electrical force available to move that ion across the membrane. It is calculated as the difference between the voltage that the ion "wants" to be at (its equilibrium potential) and the actual membrane potential (E_m). So formally, the driving force for an ion = E_m - E_ion

• For example, at our earlier calculated resting potential of −73 mV, the driving force on potassium is 7 mV ((−73 mV) − (−80 mV) = 7 mV. The driving force on sodium would be (−73 mV) − (60 mV) = −133 mV.

• Permeability: is simply a measure of how easily an ion can cross the membrane. It is normally measured as the (electrical) conductance and the unit, siemens, corresponds to 1 C·s^-1·V^-1, that is one charge per second per volt of potential.

So in a resting membrane, while the driving force for potassium is low, its permeability is very high. Sodium has a huge driving force, but almost no resting permeability. In this case, the math tells us that potassium carries about 20 times more current than sodium, and thus has 20 times more influence over E_m than does sodium.

However, consider another case—the peak of the action potential. Here permeability to Na is high and K permeability is relatively low. Thus the membrane moves to near E_Na and far from E_K.

The more ions are permeant, the more complicated it becomes to predict the membrane potential. However, this can be done using the Goldman-Hodgkin-Katz equation or the weighted means equation. By simply plugging in the concentration gradients and the permeabilities of the ions at any instant in time, one can determine the membrane potential at that moment. What the GHK equations says, basically, is that at any time, the value of the membrane potential will be a weighted average of the equilibrium potentials of all permeant ions. The "weighting" is the ions relative permeability across the membrane.

[edit] Effects and implications

While cells expend energy to transport ions and establish a transmembrane potential, they use this potential in turn to transport other ions and metabolites such as sugar. The transmembrane potential of the mitochondria drives the production of ATP, which is the common currency of biological energy.

Cells may draw on the energy they store in the resting potential to drive action potentials or other forms of excitation. These changes in the membrane potential enable communication with other cells (as with action potentials) or initiate changes inside the cell, which happens in an egg when it is fertilized by a sperm.

In neuronal cells, an action potential begins with a rush of sodium ions into the cell through sodium channels, resulting in depolarization, while recovery involves an outward rush of potassium through potassium channels. Both these fluxes occur by passive diffusion.

[edit] See also

• Action potential
• Electrochemical potential
• Goldman Equation
• Membrane biophysics
• Signal (biology)

[edit] Notes

1. ^ Note that the sign of E_Na and E_K are opposite. This is because the concentration gradient for potassium is directed out of the cell, while the concentration gradient for sodium is directed into the cell. Membrane potentials are defined relative to the exterior of the cell; thus, a potential of −70 mV implies that the interior of the cell is negative relative to the exterior.

[edit] References

[edit] Further reading

• Alberts et al. Molecular Biology of the Cell. Garland Publishing; 4th Bk&Cdr edition (March, 2002). ISBN 0-8153-3218-1. Undergraduate level.
• Guyton, Arthur C., John E. Hall. Textbook of medical physiology. W.B. Saunders Company; 10th edition (August 15, 2000). ISBN 0-7216-8677-X. Undergraduate level.
• Hille, B. Ionic Channel of Excitable Membranes Sinauer Associates, Sunderland, MA, USA; 1st Edition, 1984. ISBN 0-87893-322-0
• Nicholls, J.G., Martin, A.R. and Wallace, B.G. From Neuron to Brain Sinauer Associates, Inc. Sunderland, MA, USA 3rd Edition, 1992. ISBN 0-87893-580-0
• Ove-Sten Knudsen. Biological Membranes: Theory of Transport, Potentials and Electric Impulses. Cambridge University Press (September 26, 2002). ISBN 0-521-81018-3. Graduate level.
• National Medical Series for Independent Study. Physiology. Lippincott Williams & Wilkins. Philadelphia, PE, USA 4th Edition, 2001. ISBN 0-638-30603-0

[edit] External links

• Nernst/Goldman Equation Simulator