thumb|350px|Examples of electrotonic potentials

In physiology, electrotonus refers to the passive spread of charge inside a neuron and between cardiac muscle cells or smooth muscle cells. Passive means that voltage-dependent changes in membrane conductance do not contribute. Neurons and other excitable cells produce two types of electrical potential:

  • Electrotonic potential (or graded potential), a non-propagated local potential, resulting from a local change in ionic conductance (e.g. synaptic or sensory that engenders a local current). When it spreads along a stretch of membrane, it becomes exponentially smaller (decrement).
  • Action potential, a propagated impulse.

Electrotonic potentials represent changes to the neuron's membrane potential that do not lead to the generation of new current by action potentials. However, all action potentials are begun by electrotonic potentials depolarizing the membrane above the threshold potential which converts the electrotonic potential into an action potential. In order to quantify the behavior of electrotonic potentials there are two constants that are commonly used: the membrane time constant τ, and the membrane length constant λ. The membrane time constant measures the amount of time for an electrotonic potential to passively fall to 1/e or 37% of its maximum. A typical value for neurons can be from 1 to 20 ms. The membrane length constant measures how far it takes for an electrotonic potential to fall to 1/e or 37% of its amplitude at the place where it began. Common values for the length constant of dendrites are from .1 to 1 mm.

IPSPs

Electrotonic potentials which decrease the membrane potential are called inhibitory postsynaptic potentials (IPSPs). They hyperpolarize the membrane and make it harder for a cell to have an action potential. IPSPs are associated with Cl<sup>−</sup> entering the cell or K<sup>+</sup> leaving the cell. IPSPs can interact with EPSPs to "cancel out" their effect.

Cable theory

alt=A diagram showing the resistance and capacitance across the cell membrane of an axon. The cell membrane is divided into adjacent regions, each having its own resistance and capacitance between the cytosol and extracellular fluid across the membrane. Each of these regions is in turn connected by an intracellular circuit with a resistance.|thumb|300x300px|[[Equivalent circuit of a neuron constructed with the assumptions of simple cable theory.]]

Cable theory can be useful for understanding how currents flow through the axons of a neuron. In 1855, Lord Kelvin devised this theory as a way to describe electrical properties of transatlantic telegraph cables. Almost a century later in 1946, Hodgkin and Rushton discovered cable theory could be applied to neurons as well. This theory has the neuron approximated as a cable whose radius does not change, and allows it to be represented with the partial differential equation

: <math>

\tau \frac{\partial V}{\partial t} = \lambda^2 \frac{\partial^2 V}{\partial x^2} - V

</math>

where V(x, t) is the voltage across the membrane at a time t and a position x along the length of the neuron, and where λ and τ are the characteristic length and time scales on which those voltages decay in response to a stimulus. Referring to the circuit diagram on the right, these scales can be determined from the resistances and capacitances per unit length.

:<math>

\lambda = \sqrt \frac{r_m}{r_\ell}

</math>

:<math>

\tau =\ r_m c_m \,

</math>

From these equations one can understand how properties of a neuron affect the current passing through it. The length constant λ, increases as membrane resistance becomes larger and as the internal resistance becomes smaller, allowing current to travel farther down the neuron. The time constant τ, increases as the resistance and capacitance of the membrane increase, which causes current to travel more slowly through the neuron.

See also

  • Plateau potentials
  • Cable theory
  • Bioelectrochemistry
  • Voltage-gated ion channel

References

  • Khan Academy: Electrotonic and action potential