Why is leakage current control important

Rest and action potential

Abstract

The interaction of different tissues or organs requires good coordination between the individual cells and therefore often very fast communication over long distances. Fast cell communication can be ensured through the transmission of electrochemical signals. For this purpose, charged particles are transported, so-called ions, the distribution of which in cells is precisely controlled. If this results in a change in the cell's charge, it is referred to as electrogenic transport. In contrast to this, with electronically neutral transport either only uncharged substances are transported or the transported charges balance each other so that the overall charge of the cell remains unchanged.

The distribution of charge carriers along the cell membrane creates a potential difference that is known as the resting potential and energy has to be used to maintain it. The transport of charge carriers through a cell membrane leads to a change in the potential along the membrane and can be used specifically for the transmission of information. If the change in potential is large enough, what is known as an action potential is formed.

Charge distribution inside and outside the cell

Since different charged ions (see also: electrolytes) are present in different concentrations inside and outside of cells, a characteristic charge distribution occurs on cell membranes - a "potential". In addition to the classic electrolytes, negatively charged proteins (especially intracellular) also contribute to the distribution of charge. In the following, concentration information for the most important extra- and intracellular charge carriers is given based on the idealized model of a nerve cell.

Chemical basics of excitation conduction

An ion solution conducts electricity. The decisive factor for the speed of ion transport is the electric field strength. It is quantified via the ionic strength, which includes both the concentration of the ions and their charge.

  • Ionic strength: Measure of the strength of the electrical field created by ions in a solution
  • Molar conductivity: electrical conductivity of an electrolyte solution based on the concentration of the solution
    • Formula: Λm = Λm0 - K × √c
      • Unit: S × cm2/ mol
      • Λm = Molar conductivity, Λm0 = Standard molar conductivity, K = constant, c = ion concentration
  • Electrochemical potential: Indicates how much work has to be done in order to increase the amount of substance of the ion type i at the same temperature and the same pressure
    • Formula: μi = μi + z × F × φ
  • Potential calculations on biomembranes: If there is a concentration gradient of ions on a membrane, the difference in charge on both sides of the membrane creates a voltage (= membrane potential). This can be determined using two equations:
    • Nernst equation: With a concentration gradient of one type of ion
      • Formula: UG = (60 mV / z) × lg (cexternal / cinternally)
        • UG = Equilibrium potential, z = charge of the ions under consideration, cexternal = Concentration of ions outside the cell, cinternally = Concentration of ions within the cell
        • Derived from the Nernst equation for concentration cells
    • Goldman equation: With a concentration gradient of several types of ions
      • Formula: UM. = RT / F × ln ((PN / A × cWell, ext + PK × cK, ext, ext + PCl × cCl, int) / (PN / A × cWell, int + PK × cK, int, int + PCl × cCl, ext))
        • UM. = Membrane potential, R = gas constant, T = temperature, F = Faraday constant, P = permeability of the membrane for the respective ion, cext = Concentration of ions outside the cell, cint = Concentration of ions within the cell
        • Goldman equation is derived from the Nernst equation for concentration cells (see above)
  • Ion flow: Describes the flow rate of ions depending on how well ions can pass through a membrane and a voltage difference on both sides of the membrane as the driving force for the ion movement
    • Formula: ion flow J = membrane conductivity Λ × driving voltage difference ΔU

Physical principles of excitation conduction

On cell membranes, electrical currents run between excited and unexcited membrane sections. Electrophysical laws can be used to describe this “current flow”.

principle

  • Depolarization of the membrane: the tension on a section of the membrane becomes more positive on the inside due to an influx of cations
  • Electrotonic forwarding
    • Depolarization of a membrane section automatically leads to a depolarization of neighboring areas (passive)
    • This effect can be described with the help of the membrane resistance (in the case of nerve cells, the existing insulation by myelin sheaths and the internal longitudinal resistance must also be taken into account) and the shape of the electrical conductor (axon diameter = thickness of the nerve cell process)

Physical laws for the conduction of stimuli along a cell membrane

The laws are derived from cable theory.

  • Series resistance Ri
    • Definition: Resistance that the cytosol presents to a longitudinal movement of charge carriers
    • Formula: Ri = ρ × l / A
      • R.i = Resistance, ρ = specific resistance, l = length, A = cross-sectional area
      • Unit: Ω (Ohm)
    • Influence on the spread of excitation: The lower the longitudinal resistance, the better and faster the spread of excitation
    • Influence of nerve fiber thickness: the thicker a nerve fiber, the lower the longitudinal resistance
  • Membrane resistance RM.
    • Definition: resistance of a cell membrane to the passage of charge carriers
    • Influence on the propagation of excitation: the higher the membrane resistance, the better the excitation conduction (little loss of charge carriers)
    • Influence of the nerve fiber thickness: the thicker a nerve fiber, the lower the membrane resistance (since this also increases the surface area of ​​the nerve fiber and it is easier for particles to pass through the membrane)
  • Longitudinal membrane constant λ
    • Definition: Distance from a stimulus location after which the electrical potential has dropped to only 37% of the original amplitude
    • Calculation: from the internal longitudinal resistance and the membrane resistance
  • Membrane capacity CM.
    • Definition: Nerve fiber membranes act as a kind of capacitor and can absorb a certain amount of electrical charge, which is no longer passed on by the membrane
    • Formula: CM. = Q / U
    • Unit: F (Farad = Coulomb / Volt)
    • Influence on the spread of excitation: the higher the membrane capacity, the worse the conduction of excitation
    • Influence of nerve fiber thickness: the thicker a nerve fiber, the greater the membrane capacity (since the larger the nerve fiber's surface area, the larger the area where tension can build up)

Membrane resistance and capacitance are inversely proportional to each other (the higher the resistance, the smaller the capacitance)!

For the internodes, this means that a high membrane resistance, a low membrane capacity and a low internal longitudinal resistance increase the speed at which an electrical potential is transmitted!

The conduction speed in continuous stimulus conduction is proportional to the radius of the nerve fiber - the thicker the nerve, the faster the continuous stimulus conduction!

The resting potential

The resting potential (RP) is the membrane potential of an excitable cell (e.g. nerve cells or muscle cells) at rest. It is about the "ground state", which more or less corresponds to the sum of all diffusion potentials (i.e. potentials in constant equilibrium) of the intra- and extracellular ions (see above: charge distribution in the cell). The size of the RP varies depending on the cell type; it is in the range from approx. -70mV to -90mV.

The RP corresponds more or less to the K+- Equilibrium potential, which varies according to the ion channels present in the cell: neurons ≈ -70mV, muscle cells (skeleton and heart) ≈ -90mV, glial cells ≈ -90mV!

The action potential

The charge along a membrane cannot be shielded by it, so that a diffusion potential occurs on the membrane, which is called the resting potential. It is usually -70mV. Electrochemical communication now takes place by changing this resting potential. This change is known as the action potential; it usually arises in the same way. An exception are the heart muscle cells, whose action potentials look different and are formed. For details, see: Heart excitation.

Phases of the action potential

phaseDescription of the phase Cellular processespotential
Resting potential

-70 mV

(Inside - / outside +)

Threshold potential
  • Beginning of an increase in cell potential over a critical threshold
    • Ensures that only relevant stimuli are passed on
  • Neurotransmitters bind externally to receptors in the cell membrane
    • Leads to the opening of the Na connected to the receptors+Channels → Na+-A stream
  • If the threshold potential of about -55mV is reached, voltage-dependent Na also open+-Channels; K+-Channels start to close
  • Stimulus below the activation threshold does not lead to an opening of the voltage-dependent Na+-Channels
-70 mV to -50 mV
Depolarization
  • Conversion of the stimulus into a conductive electrochemical potential
  • Includes the steeply rising part of the potential curve (upstroke) from the stimulus threshold (approx. -70 to -50mV) to the stimulus maximum of the AP (approx. +30 mV)
  • Mainly responsible cation: sodium (Na+)
    • Massive Na+Ion influx through voltage-dependent Na+-Channels
      • Membrane approaches the Na+-Equilibrium potential (+ 60mV)
  • K+-Channels almost completely closed
> -50 mV
excess
  • Potential range in which the opening probability of the Na+Channels are highest and the membrane potential is positive
  • At the apex of the curve there are many Na+-Channels already inactive again
  • K+-Channels almost completely closed

+30 mV

(Inside + / outside -)

Repolarization
  • Return to the basic state
  • Mainly responsible cation: potassium (K+)
    • Voltage-dependent K+-Channels open
    • Beginning K+- outflow
  • Inactivation of the voltage-dependent Na+-Channels
    • Decreased Na+-A stream
+30 mV to -90 mV
Hyperpolarization
  • State of Na+-Channels changes from closed-inactive to closed-can be activated
  • After the repolarization there are still a few K+-Channels open
    • The cause is the increased activity of the K+Channels through Ca. that flowed in during the depolarization2+that is slowly removed
    • Furthermore, K+- Outflow and approach to K+-Equilibrium potential
approx. -90 mV (inside - / outside +)
Refractory period
  • Term for the time after a depolarization, in which the cell cannot be excited or only with difficulty and weakly
    • Regulation of the AP frequency
    • Prevents a stimulus from running back
  • Absolute refractory phase: Na+-Channels are inactivated and no new AP can be triggered, regardless of how strong the incoming stimulus is
  • Relative refractory phase
    • Some na+-Channels can be reactivated, but have an increased stimulus threshold so that only a strong stimulus can trigger a new AP
    • This AP then also has a lower amplitude than a "normal" AP

-70 mV

(Inside - / outside +)

In order to exceed the threshold potential and trigger an action potential, the membrane potential of a nerve cell must be shifted by approx. 10–30 mV!

Ion flow that takes place in an uncontrolled manner and can only be traced back to the reduction of the concentration gradient is called leakage current!

Epileptical attack
During an epileptic seizure, synchronous, high-frequency discharges from nerve cells in the cerebral cortex occur. Due to the high action potential frequency, the ion currents (high potassium extracellular, high sodium intracellular) can no longer fully pass through the relatively slow Na+/ K+-ATPase towards the resting membrane potential (high potassium intracellular, high sodium extracellular). The K+-Concentration consequently increases extracellularly. In addition, there is an increased consumption of oxygen and energy as well as an increased release of glutamate.

Duration of action potentials

The duration of an action potential depends on what type of cell it is. The most important are listed here.