Axial Resistance and Passive Cable Properties of Axons

Before any voltage-gated channel opens, an axon behaves like a leaky electrical cable. Cable theory treats the axon as a core conductor whose interior (axial, or longitudinal) resistance, membrane resistance, and membrane capacitance together determine how a local potential spreads and decays along its length. These passive properties set the stage for the active action potential and govern how far and how fast subthreshold signals travel.

Definition

Passive cable properties describe an axon as a core conductor in which axial (intracellular longitudinal) resistance, membrane resistance, and membrane capacitance determine the electrotonic spread of potential; the length constant sets the distance over which a steady potential decays and the time constant sets how quickly the membrane potential responds to current.

Scope

This topic covers the passive electrical properties of the axon: axial resistance, membrane resistance and capacitance, the length constant, and the time constant, and how they govern electrotonic spread and influence conduction. It treats the axon as a core conductor and is reference physiology, not clinical guidance.

Core questions

• What does it mean to treat an axon as an electrical cable?
• How do axial resistance, membrane resistance, and capacitance determine the length and time constants?
• How do passive cable properties influence the speed of impulse conduction?
• Why does a larger fibre diameter lower axial resistance and increase conduction velocity?

Key concepts

• Axial (longitudinal) resistance
• Membrane resistance
• Membrane capacitance
• Length constant (lambda)
• Time constant (tau)
• Electrotonic (passive) spread
• Core conductor model

Key theories

Cable (core-conductor) theory

A treatment of the axon as a cylindrical conductor with distributed axial resistance, membrane resistance, and membrane capacitance, from which the length constant, time constant, and the dependence of conduction on geometry are derived.

Mechanisms

Current injected at one point of an axon divides between flowing longitudinally through the cytoplasm, against the axial resistance, and leaking outward across the membrane resistance while charging the membrane capacitance. The balance of axial and membrane resistance fixes the length constant, the distance over which a steady-state potential falls to about 37 percent of its value; a low axial resistance or a high membrane resistance gives a longer length constant and farther spread. The product of membrane resistance and capacitance fixes the time constant, which determines how rapidly the membrane potential changes in response to current. Because axial resistance falls as fibre cross-sectional area rises, larger-diameter axons have longer length constants and faster passive spread, which, together with the active currents described by Hodgkin and Huxley, makes them conduct action potentials more quickly. Cable theory thus links axon geometry and membrane properties to both subthreshold signalling and conduction velocity.

Clinical relevance

Cable properties explain why fibre diameter and membrane insulation affect conduction speed and why passive signal spread is limited over distance. This entry is descriptive reference material on normal biophysics and is not a basis for individual clinical decisions.

Evidence & guidelines

The framework derives from core-conductor (cable) analyses of nerve fibres and from the biophysical measurements underlying the Hodgkin-Huxley model; these are mechanistic and theoretical treatments rather than clinical guidelines.

History

Cable analysis of biological fibres has roots in the nineteenth-century theory of the telegraph cable, adapted to nerve in the twentieth century. Rushton's 1951 treatment of medullated nerve formalised how fibre size shapes conduction, and Rall later extended core-conductor theory to the branching geometry of neurons, making cable theory a foundation for understanding both passive integration and impulse propagation.

Key figures

• William Rushton
• Alan Hodgkin
• Andrew Huxley
• Wilfrid Rall

Seminal works

• rushton-1951
• hodgkin-huxley-1952

Frequently asked questions

What is the length constant of an axon?

It is the distance over which a steady, passively spreading potential decays to about 37 percent of its original size; it grows when axial resistance is low or membrane resistance is high, allowing signals to spread farther.

Why do thicker axons conduct faster?

A larger cross-sectional area lowers the internal axial resistance, lengthening the length constant so that depolarisation spreads farther and faster to bring the next region of membrane to threshold.