The membrane potential changes which occur during nerve impulse propagation are collectively called the "action potential". In order to understand these, we must first know something about the structure of a neuron.
A neuron is a cell with protrusions, one of which is very long compared to the cell body. The small protrusions are called "dendrites", and on their ends are the "synapses" which receive chemical signals from other neurons. The long protrusion is called the "axon"; at its far end are nerve endings which can release chemical signals to be received on the synapses of neurons in its neighborhood. The width of an axon varies greatly among species: the diameter of a squid axon is about 500 mm, lobster nerve and frog muscle axons are about 75 mm, and mammalian motor neurons average about 10 mm. Axons attached to many neurons, including mamalian motor neurons, are coated with a protein ("myelin") sheath. The sheath acts as an insulator, preventing ion leakage and hence increasing impulse propagation speed. These myelinated axons have small (1 mm long) interuptions in the sheath every 2 mm. These interruptions are called "Nodes of Ranvier", and are the sole places where ion transfer takes place. The density of ion channels is much greater in these nodes: while there are only about 20 Na channels per square micrometer in a nonmyelinated axon, there are about 10 4 per square micrometer at each Node of Ranvier in a myelinated axon.
The propagation of a nerve impulse along an axon begins when the synapses receives neurotransmitters from nerve endings nearby. The neuron then increases its internal potential, setting off a chain of events which is repeated for each Node of Ranvier as the nerve impulse "jumps" down the axon (this is known as "saltatory" conduction):
A movie of this process (50K quicktime animation) shows the influx of sodium as a function of distance along the axon and time. One on the vertical scale indicates the peak of the action potential; the movie makes it clear that the propagation of the impulse occurs much faster (22 ms between node firings for an axon radius of 5 m) than the time scale of the action potential at a single node (1-2 ms).
A higher stimulus intensity is reflected in increased frequency of impulses, not in higher voltages: all action potentials look essentially the same. The speed of propagation for mammalian motor neurons is 10 - 120 m / s, while for nonmyelinated sensory neurons it's about 5 - 25 m / s (nonmyelinated neurons fire in a continuous fashion, without the jumps; ion leakage allows effectively complete circuits, but slows the rate of propagation).
It is interesting to note that ethanol intoxication produces its behavioral side effects at this biophysical level. The metabolism of ethanol has as a by-product fatty acid ethyl esters. These ethyl esters can block the potassium channels open, allowing potassium ions to leave the neuron when it is in the rest state. This effectively lowers the membrane potential, making it harder for the potential to reach the threshold necessary for impulse conduction. The result is increased difficulty in both mental and motor functions. This situation can also be caused by taking in excessive amounts of potassium; in both cases, death can result from nervous system failure.
The "Axon Propagation" Mathematica notebook allows us to specify the Na influx and axon radius, as well as the ion velocity inside the axon. It then computes the charge inside the node as a function of time. It compares two models of charge distribution: one models the internal charge as a line, while the other models it as a disk located at the node. The model equations for the electrical potential are derived from adding together the contributions from all of the "bits" of charge in the configuration (this step requires calculus; we will ignore the details). Note that these are limiting models of what is in reality very complicated (probably something like an expanding shell inside the axon, since the intracellular fluid is approximately equipotential).
By watching the changes in the potential at the next node, we can find the time at which the next node reaches threshold, and compute from that the propagation speed. By repeating this for a range of axon radii, we can find the dependence of propagation speed on axon radius. Which model is closer to the linear dependency expected? Typical values quoted for myelinated axons are 6 to 9 m / s per micron diameter.
The next section is on circuit topology.
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©1996, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.
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