Membrane potential
A membrane potential is the voltage across an electrochemical double layer, consisting of a membrane and space charges in adjacent electrolyte. If it is in the membrane is a biological membrane as the cell membrane or the membrane of an Zellorganells is the sign convention " inside minus outside potential."
In the diagram opposite are the red and the blue area for the positive and negative excess charges. This can be prevented by the membrane from following their mutual attraction. The envelope curves represent the charge density, which decreases exponentially according to the outside. This also applies to the electric field strength ( purple curve, i W. the path integral of the charge density ), which completely disappears off the membrane, if there is no current, so that the electric potential (green curve, the path integral of the field strength ) where each constant is. The potential difference between these constant values (green arrow) is referred to as membrane potential, also known as transmembrane potential or even electrical gradient, among physicists would understand the field strength.
A membrane potential may occur as in a capacitor by externally applied loads, such as in the portions of myelinated nerve fibers. In contrast, in a biological context more important is the formation of the membrane potential by differences in concentration on both sides of the membrane in conjunction with an ion-selective permeability, controlled permeability and active transport of ions through the membrane.
In extensive cells, such as nerve or muscle cells, the membrane potential varies spatially. It is there the signal line or propagation in sensory cells and the central nervous system and of information processing. In chloroplasts and mitochondria membrane potential of the energetic coupling of processes of energy metabolism is: A process, see electron transport chain transports ions against the tension and makes it work, another, see ATP synthase, is driven by the potential difference.
The measurement of membrane potentials of microscopic structures as possible without electrical, chemical and mechanical control is difficult. The photo shows the derivation of the inner potential of a cell with a fine glass capillary. At the opening of the capillary results in a small diffusion potential, as it is filled with a strong electrolyte in a high concentration, for example 3 M KCl, in order to ensure a defined transition of the metallic conductor, which is located in the capillary and at the image edge can be seen. The time required for the measurement of the membrane potential and entry of foreign potential is not in the image.
- 4.1 The Gibbs free energy of diffusion 4.1.1 Chemical potential - Neutral particles
- 4.1.2 Electric potential - Charged particles
- 4.1.3 Electrochemical potential
- 4.1.4 equilibrium potential
- 4.1.5 Goldman -Hodgkin -Katz equation
Physiological values
The phospholipid bilayer of the membrane unit has a hydrophobic core that holds the space charges about five nm apart. The rest potential of animal cells is -70 mV. This results in a field strength of 107 V / m, or about four times the dielectric strength of air. At voltages of 0.7 to 1.1 volts occurs electroporation.
From the factors field strength, dielectric constant of the membrane material (≥ 2) and electric field constant, a surface charge density results of just 3.10 -4 C / m, which translates to the Faraday constant in 3:10 -6 meq / m².
The characteristic of the exponential decay of the space charge density Debye length is under physiological conditions just one nanometer. In this layer, there are positive and negative mobile charge carriers in a surface concentration of about 2.10 -4 meq / m². Thus, the net charge accounts for only about 1 % of the charge density.
Potential changes as signals
Neurons encode information in the form of short-term changes in potential. These can be divided into two groups, which have different properties and functions:
- Graduated potentials occur as a receptor potential in sensory cells and as a postsynaptic potential at chemical synapses and the motoric end plate.
- Action potentials are generated at the axon hillock and the axon of a nerve cell or to the sub-synaptic membrane of muscle cells.
Comparison at a glance:
Basics
Cause for the diffusion of the ions along a concentration gradient, the Brownian motion. The membrane potential can support this diffusion when the concentration and potential gradient acting in the same direction. When the potential gradient is oppositely directed to the concentration gradient, the ions can only diffuse passively according to the concentration gradient, if the effect of the membrane potential is smaller. If it is greater, then the ions diffuse against the concentration gradient.
Diffusion potential
- Model test
A chamber which is filled with distilled water, is divided by a omnipermeable membrane, for example a filter paper into two half cells. In each half- cell is an electrode, the two electrodes are connected to each other by a voltage meter. Is dissolved in one of the two half-cells (for example, right ) table salt (NaCl ), is first observed a rise in the voltage, which then gradually decreases to zero volts over time.
- Explanation:
Due to the concentration gradient of sodium cations and chloride anions to diffuse through the membrane as long as up to two half cells, the same concentration present. The sodium cation has a smaller diameter than the chloride anion, it may easily diffuse through the pore system of the membrane. Therefore rises at the beginning of experiment their concentration in the cell faster than the left half of the anions. Thus, a voltage difference between the two half-cells is formed from: the left are more positive, more negative charges on the right.
The diffusion rate of the cation but is braked. On the one hand, the concentration gradient becomes weaker, on the other hand, the cations have to diffuse against the building up potential gradient.
In contrast, the diffusion rate of the anions is enhanced by the potential gradient.
Equilibrium potential
- Model test
A chamber which is filled with distilled water is divided by means of a selective semipermeable membrane that passes only the cation in the two half cells. In each half- cell is an electrode, the two electrodes are connected to each other by a voltage meter. Is dissolved in one of the two half-cells (for example, right ) table salt (NaCl ), is first observed a rise in the voltage, which is then retained.
- Explanation:
Due to the concentration gradient, the sodium cations to diffuse through the membrane. Due to the charge separation, a potential gradient based on: the inside of the membrane ( left chamber ) is positive, the outer side ( right ventricle ) is negative. The diffusion rate of the cation but is braked. On the one hand their concentration gradient is weaker, on the other hand, the cations must diffuse against the building up potential gradient.
The diffusion equilibrium is achieved when the driving force of the concentration gradient for the diffusion to the left is the same size as the driving force for the diffusion of the potential gradient to the right.
At equilibrium, the concentrations of the ions inside the concentration outside are different, therefore, a potential difference can be measured.
Reversal potential
The reversal potential of a membrane with open channels, the membrane potential at which the net electric current is zero. The reversal potential is a weighted average of the equilibrium potential of the individual permeable ionic species, wherein the weighting depends on the concentration and permeability below Goldman -Hodgkin -Katz equation.
Mathematical formalisms
The free enthalpy of the diffusion
At the Free? G enthalpy can be read whether particles can be transported through a membrane at a given concentration and potential ratio:
- Is? G = 0, there is balance, the amount of diffusing through the membrane in a direction of the particles is equal to the amount of diffusing particles back through the membrane.
- Is? G <0 the transport is running in one direction voluntarily from where energy is released.
- Is? G > 0, the particles may be transported only under expenditure of energy.
The free enthalpy may also be regarded as a measure of the electrochemical potential which is composed of the two components
- Chemical potential (corresponding to the concentration gradient ) and
- Electric potential (corresponding potential gradient ) is composed.
Chemical potential - Neutral particles
For the transport from the outside to the inside ( imports) the formula is
Explanation:
For T = 298 K and using the logarithm, the equation simplifies to
- When the concentration of substance A is inside the same size as the outside? G = 0, there is equalization of concentration before and there is no mass transport instead.
- If the concentration is bigger on the inside than the outside? G > 0, there is no passive ( " voluntary " ) mass transfer from the outside to the inside instead.
- Is greater than the concentration outside inside,? G <0, there is mass transfer from the outside inwards instead.
Electric potential - Charged particles
Share of cargo transportation on the free enthalpy:
Explanation:
Electrochemical potential
For the import of charged particles, the formula is
Equilibrium potential
For the equilibrium case (? G = 0), the equilibrium potential ΔΨ0 can be calculated for an ion according to the following formula:
For Z = 1 ( the case of Na , K ) and T = 298 K is obtained when using the logarithm to the simplified equation
Example of a membrane potential ( mixed potential ) of -53 mV at 298 K:
Goldman -Hodgkin -Katz equation
By means of the Goldman equation can the membrane equilibrium potential ΔΨ calculate:
Explanation: