E3 Impulse propagation (cable theory and Saltatory conduction)

Topic

The propagation of the nerve impulse along the axon is described by cable theory, which treats the axon as a circuit distributed along its length, characterized at every point by internal axial resistance, membrane resistance, and membrane capacitance—all expressed per unit length of the axon.

The ratio of membrane resistance to internal axial resistance defines the axon's length constant, which determines the extent of spatial attenuation of a passive signal as it travels along the axon: the larger the length constant, the less the passive signal attenuates over a given distance. Meanwhile, the product of the axon's membrane resistance and capacitance defines its time constant—the same time constant previously defined for the resting neuronal membrane.

In unmyelinated axons, conduction velocity scales approximately with the square root of the axonal diameter: the larger the diameter, the higher the conduction velocity, although this improvement becomes less pronounced as the diameter continues to increase. In myelinated axons, by contrast, conduction is saltatory: the impulse jumps from one Node of Ranvier to the next rather than propagating continuously; this causes conduction velocity to scale linearly with axonal diameter and results in a much higher velocity than in an unmyelinated fiber of the same caliber.

The axonal conduction safety factor compares the available current generated by an active node with the threshold current required to excite the next axonal segment: as long as the current available at the active node exceeds the threshold current of the subsequent segment, the safety factor ensures reliable propagation of the action potential along the entire axon. Taken together, it is this very axon—described by cable theory as a distributed circuit characterized by its length constant, time constant, and conduction safety factor—that determines whether the action potential propagates reliably from one end of the axon to the other.

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