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Membrane Length Constant Calculator

Quantifies how far an electrical signal can travel along a neuron before decaying to 37% of its original amplitude.

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Membrane Length Constant

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Overview

The membrane length constant (λ) is a crucial parameter in neurophysiology, representing the distance over which a steady-state voltage change across the neuronal membrane decays to 1/e (approximately 37%) of its initial value. It is determined by the square root of the ratio of membrane resistance (Rm) to internal resistance (Ri). A larger length constant indicates that a signal can propagate further along the neuron with less attenuation, which is vital for efficient signal transmission in the nervous system.

Symbols

Variables

\lambda = Membrane Length Constant, R_m = Membrane Resistance, R_i = Internal Resistance

Membrane Length Constant
Membrane Resistance
Internal Resistance

Apply it well

When To Use

When to use: Use this equation to understand the passive electrical properties of neurons and how far a local potential change will spread. It's applied when analyzing the efficiency of signal propagation in axons and dendrites, particularly in response to subthreshold stimuli. Knowing the length constant helps predict how effectively a synaptic input at one point will influence the membrane potential at a distant point.

Why it matters: The membrane length constant is fundamental to understanding neuronal communication. It dictates the spatial summation of synaptic potentials and the speed and reliability of action potential propagation. Variations in length constant due to changes in membrane or internal resistance can significantly impact neuronal function, affecting everything from sensory perception to motor control and learning.

Avoid these traps

Common Mistakes

  • Confusing length constant with time constant.
  • Incorrectly interpreting the units of Rm and Ri.
  • Assuming active propagation when only passive spread is considered.

One free problem

Practice Problem

A neuron has a membrane resistance (Rm) of 10000 Ω·cm² and an internal resistance (Ri) of 100 Ω·cm. Calculate its membrane length constant (λ).

Membrane Resistance10000 Ω·cm²
Internal Resistance100 Ω·cm

Solve for:

Hint: Remember to take the square root of the ratio.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Principles of Neural Science, Sixth Edition by Kandel, Schwartz, Jessell, Siegelbaum, Hudspeth
  2. Neuroscience, Sixth Edition by Purves, Augustine, Fitzpatrick, Hall, LaMantia, Mooney, Platt, White
  3. Wikipedia: Length constant
  4. Principles of Neural Science, 6th Edition, Kandel, Schwartz, Jessell, Siegelbaum, Hudspeth
  5. Neuroscience, 6th Edition, Purves, Augustine, Fitzpatrick, Hall, LaMantia, McNamara, White
  6. Kandel, Schwartz, Jessell, Siegelbaum, Hudspeth, 'Principles of Neural Science', 6th ed., Chapter 8
  7. Johnston and Wu, 'Foundations of Cellular Neurophysiology', 2nd ed., Chapter 3
  8. Purves, Augustine, Fitzpatrick, Hall, LaMantia, Mooney, Platt, White, 'Neuroscience', 6th ed., Chapter 2