Membrane potential

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The membrane potential (more precisely: the transmembrane voltage ) is a special electrical voltage between two fluid spaces in which charged particles ( ions ) are present in different concentrations . A membrane potential arises when the fluid spaces are separated by a membrane that allows at least one of these types of particles to pass through, but cannot be passed through equally well by all types of particles ( semi-permeability ). Driven by random particle movement, more ions of one type then switch to the side with the lower concentration than in the opposite direction ( diffusion ), resulting in charge separation and thus the transmembrane voltage. The charge separation also means an increasing electrical repulsion force on the following particles, which ultimately becomes just as strong as the diffusion. In this state of equilibrium , particles of the type under consideration are still moving across the membrane, but at any moment the same number in both directions; the net current is zero and the membrane potential is stable. Stable membrane potentials also exist when several types of particles are involved; In this case, the net current for each individual type of particle is almost always not equal to zero, while the net current calculated over all particles is also zero.

Membrane potentials are of paramount importance in biology; all living cells build up a membrane potential. To create and maintain the differences in concentration, they use molecular pumps such as sodium-potassium ATPase ; selective permeability is created through specific ion channels . Cells use the membrane potential for transport across the membrane ; Temporally variable membrane potentials coordinate the heart's action and guide and integrate information in the brain and nerves.

Physical formulation

Course of electrical quantities across a membrane and adjacent electrolytes. In principle, the picture does not change if charges that are bound to the membrane surface are taken into account.

A membrane potential is the electrical voltage across an electrochemical double layer , which consists of a membrane and space charges in adjacent electrolytes . In the diagram opposite, the red and blue areas represent the positive and negative excess charges, respectively . The enveloping curves represent the charge density . This drops off steeply towards the center; this is where the hydrophobic part of the membrane is, which charges with a hydrated shell avoid. The charge density drops exponentially towards the outside. This also applies to the electrical field strength (purple curve, generally the path integral of the charge density), which disappears completely away from the membrane if no current flows there , so that the electrical potential (green curve, path integral of the field strength) remains constant there is. The potential difference (voltage) between these constant values ​​(green arrow) is referred to as the membrane potential , also as the transmembrane potential or even electrical gradient , which physicists understand as the field strength.

As with a capacitor, a membrane potential can arise from an externally supplied charge, for example in the myelinated sections of nerve fibers. In a biological context, however, the formation of the membrane potential through differences in concentration on both sides of the membrane in connection with ion-selective permeability , controlled permeability and active transport of ions through the membrane is more important.

In the case of large cells, such as nerve or muscle cells , the membrane potential varies spatially. There it is used for signal transmission and propagation, and also for information processing in sensory cells and the central nervous system . In chloroplasts and mitochondria , the membrane potential serves the energetic coupling of processes of the energy metabolism : One process, see electron transport chain , transports ions against the voltage and does work , another, see ATP synthase , is driven by the potential difference.

Measurement

Measuring the membrane potential of a Xenopus laevis oocyte by inserting a microelectrode.

Since the potential on both sides of the membrane (assuming the absence of currents) hardly changes after a short distance from the membrane, an electrode somewhere in the two electrolyte solutions is sufficient to measure the transmembrane voltage. The physiological sign convention is generally “inside minus outside potential”. For the measurement of the plasma membrane potential, this means that one of the two electrodes must be inserted into the cytosol ; the measured membrane potential can then also be interpreted as the potential of the cytosol if the extracellular fluid is selected as the reference point.

The measurement of membrane potentials on microscopic structures, if possible without electrical, chemical and mechanical interference, is difficult. The photo shows the derivation of the internal potential of a cell with a fine glass capillary. At the opening of the capillary there is a small diffusion potential because it is filled with a strong electrolyte in high concentration, e.g. B. 3  M  KCl to ensure a defined transition to the metallic conductor, which is located in the capillary and can be seen at the edge of the picture. The recording of the external potential, which is also necessary for measuring the membrane potential, is not included in the picture.

Physiological values

The phospholipid double layer of the unit membrane has a hydrophobic core that keeps the space charges apart a good five nm . The resting potential of animal cells is −70 mV. This results in a field strength of over 10 ⁷  V / m or about four times the dielectric strength of air. Electroporation occurs at voltages from 0.7 to 1.1 volts .

The factors field strength, permittivity number of the membrane material (≥ 2) and electrical field constant result in a surface charge density of almost 3 · 10 ⁻⁴  C / m², which translates into 3 · 10 ⁻⁶ mEq / m² with the Faraday constant .  

The Debye length, which is characteristic of the exponential decrease in the space charge density, is just under one nanometer under physiological conditions. In this layer there are positive and negative mobile charge carriers in a surface concentration of about 2 · 10 ⁻⁴  mEq / m². The net charge is therefore only about 1% of the charge density.

Changes in potential as signals

Nerve cells encode information in the form of short-term changes in potential. These can be divided into two groups that have different properties and functions:

• Graduated potentials occur as receptor potential in sensory cells and as postsynaptic potential in chemical synapses and the motor endplate .
• Action potentials are generated on the axon hill and on the axon of a nerve cell or on the subsynaptic membrane of muscle cells.

Comparison in the overview:

	graduate potential	Action potential
1	amplitude modulated	frequency modulated
2	graduated amplitude	constant amplitude
3	not refractory	refractory
4th	Summation possible	no summation possible ("all or nothing principle")
5	Passive propagation with a decrease in amplitude	Active propagation with preservation of the amplitude
6th	no trigger threshold	defined trigger threshold
7th	Depolarization or hyperpolarization with subsequent repolarization	only depolarization with subsequent repolarization
8th	unspecific cation channels	fast, voltage-gated sodium ion channels
9	Duration 40 to 4000 ms	Duration 4 ms

Basics of creation

diffusion

Dissolved particles are in constant motion as an expression of their thermal energy . This movement is called Brownian molecular movement and is completely undirected. If there is a connection between two locations that differ in the concentration of a particle type, which can be passed by this particle type, net particles move in the direction of the lower concentration until the same concentrations are finally reached. This process is called diffusion ; it is not driven by a force, but results solely from the accidental movement. A single particle can also move in the other direction; with a large number of particles, however, there is always an equalization of the concentration because this is likely or, in other words, thermodynamically favorable.

Equilibrium potential

When charged particles ( ions ) diffuse, the situation becomes more complicated because charge separation is associated with diffusion. This generates an increasing electrostatic force, which accelerates the ions in the direction of the higher concentration, so that their movement is no longer completely undirected and therefore no complete concentration compensation can result. But here, too, at some point an equilibrium (a state without net current) will be established, namely when the electrical and the stochastic drive exactly cancel each other out. The electrical voltage at which this is the case is called equilibrium potential and can be calculated using the Nernst equation .

Model test

A chamber filled with saline solution is divided into two half-cells by a selective, semipermeable membrane that only allows the sodium cation to pass through. There is an electrode in each half-cell ; the two electrodes are connected to each other by a voltmeter, which at this point shows zero. If more table salt is dissolved in one of the two half-cells (for example the right one), an increase in voltage is observed first, which then remains as "equilibrium voltage".

Explanation

Due to the concentration gradient, sodium ions diffuse through the membrane. Due to the charge separation, a potential gradient builds up: the inside of the membrane (left chamber) becomes positive, the outside (right chamber) becomes negative. Due to the potential gradient that builds up, the diffusion speed is getting slower. The diffusion equilibrium is reached when the driving force of the concentration gradient for the diffusion to the left is just as great as the driving force of the potential gradient for the diffusion to the right. The net charge that has flowed up to that point is so small that the concentrations in the two half-cells have not changed significantly.

General membrane potential

If a membrane is permeable to several ions for which the equilibrium potentials differ, no thermodynamic equilibrium is possible at the given concentrations . Nevertheless, a temporarily stable state is also established here: the zero current potential. At this voltage, there are net currents for individual types of ions, but all currents together add up to zero. The membrane potential is closer to the equilibrium potential of an ion species, the higher the permeability for this ion species; the exact value can be calculated using the Goldman equation .

Keeping the concentrations constant

The ion currents in the case of the general membrane potential would reduce the concentration differences in the long term, so that the voltage would change and eventually reach zero. For a constant membrane potential, a mechanism is necessary that transports the ions back against the direction of the passive currents. This transport is active , i. H. he needs Gibbs energy . The sodium-potassium pump is of great importance in biological systems . It creates three sodium ions in exchange for two potassium ions from the cell, the Gibbs energy comes from the hydrolysis of an ATP into ADP and phosphate . The sodium-potassium ATPase indirectly drives further ion return transports via cotransporters; this is referred to as secondary or tertiary active membrane transport .

Derivation via free enthalpy

passive transport through open ion channels

From the free enthalpy Δ G it can be read whether at a given membrane potential and given concentration ratios, particles move net across a membrane:

• If Δ G = 0, there is a thermodynamic equilibrium : the number of particles diffusing through the membrane per period is the same in both directions.
• If Δ G <0, the transport is exergonic , i.e. it takes place voluntarily in the considered direction.
• If Δ G > 0, the transport is endergonic , i.e. only takes place in the considered direction if it is coupled to an exergonic process (such as the hydrolysis of ATP).

The free enthalpy can also be viewed as a measure of the electrochemical potential that results from the two components

• chemical potential (corresponds to the concentration difference ) and
• electrical potential (corresponds to the potential difference).

Chemical potential - neglecting the potential difference

The formula applies to transport from outside to inside (import)

${\displaystyle \Delta G=R\cdot T\cdot \ln {\frac {c(A_{i})}{c(A_{a})}}}$.

Explanation:

R : General gas constant R = 8.3143 J mol ⁻¹ K ⁻¹

T : temperature in Kelvin

c (A _i ), c (A _a ): Mole concentrations of substance A inside, outside

ln: natural logarithm

For T = 298 K and using the decadic logarithm, the equation is simplified to

${\displaystyle \Delta G=5{,}7\,\mathrm {kJ/mol} \cdot \lg {\frac {c(A_{i})}{c(A_{a})}}}$.

• If the concentration of substance A inside is exactly as large as outside, then Δ G = 0, there is concentration equalization and no substance transport takes place.
• If the concentration inside is greater than outside, Δ G > 0, there is no passive (“voluntary”) transport of substances from outside to inside.
• If the concentration outside is greater than inside, Δ G <0, mass transport takes place from outside to inside.

Electric potential - neglecting the difference in concentration

The free enthalpy for pure charge transport is

${\displaystyle \Delta G_{\text{Ladungstransport}}=Z\cdot F\cdot \Delta \Psi }$.

Explanation:

Z : The number of charges Z corresponds to the ion charge of the particle to be transported. It is positive for cations and negative for anions.

F : Faraday constant F = 96485 C · mol ⁻¹

ΔΨ: membrane potential

Electrochemical potential

For the import of charged particles results from addition

${\displaystyle \Delta G=R\cdot T\cdot \ln {\frac {c(A_{i})}{c(A_{a})}}+Z\cdot F\cdot \Delta \Psi }$.

Nernst equation

In the case of equilibrium (Δ G = 0), the equilibrium potential ΔΨ ₀ for an ion can be determined by rearranging the above equation:

${\displaystyle \Delta \Psi _{0}=-{\frac {\mathrm {R} \cdot T}{Z\cdot F}}\cdot \ln {\frac {c(A_{i})}{c(A_{a})}}}$

for Z = 1 (for Na ⁺ , K ⁺ ) and T = 298 K, using the decadic logarithm results in the simplified equation

${\displaystyle \Delta \Psi _{0}=-59{,}1\,\mathrm {mV} \cdot \lg {\frac {c(A_{i})}{c(A_{a})}}}$.

Goldman-Hodgkin-Katz equation

The Goldman equation provides the zero current potential when considering several ions, it is listed here without derivation:

${\displaystyle \Delta \Psi ={\frac {RT}{F}}\cdot \ln {\frac {\Sigma [P_{\mathrm {ka} }\cdot c_{\mathrm {ka-a} }]+\Sigma [P_{\mathrm {an} }\cdot c_{\mathrm {an-i} }]}{\Sigma [P_{\mathrm {ka} }\cdot c_{\mathrm {ka-i} }]+\Sigma [P_{\mathrm {an} }\cdot c_{\mathrm {an-a} }]}}}$

Explanation:

P : permeability of the channels for anions (an) and cations (ka)

c : Concentration of anions and cations inside (-i) or outside (-a) the cell

Example for a membrane potential (mixed potential) ΔΨ of –53 mV at 298 K:

Ion species	c eq (A outside )	c eq (A inside )	ΔΨ 0	ΔG for a transport from the outside to the inside
Na +	400 mmol / l	20 mmol / l	+76 mV	+2.3 kJ / mol
K +	50 mmol / l	440 mmol / l	−55 mV	−10.5 kJ / mol
Cl -	108	560	+43 mV	−11.0 kJ / mol

literature

• Jacob Kraicer, Samuel Jeffrey Dixon: Measurement and Manipulation of Intracellular Ions. Academic Press, 1995, ISBN 0-08-053646-8 , limited preview in Google Book Search

Web links

• Cell physiology