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Axon Stretch Growth: The Mechanotransduction of Neuronal Growth
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Delayed feedback model of axonal length sensing.

Bhargav R Karamched1, Paul C Bressloff1

  • 1Department of Mathematics, University of Utah, Salt Lake City, Utah.

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|May 9, 2015
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Summary
This summary is machine-generated.

This study models how neurons sense axonal length using oscillating signals. Longer axons produce lower frequency signals, with motor transport fluctuations impacting accuracy.

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Area of Science:

  • Cell Biology
  • Neuroscience
  • Biophysics

Background:

  • Cell size and organelle regulation are fundamental biological questions.
  • Neuronal axons present unique size homeostasis challenges due to their extreme lengths.
  • A proposed mechanism links axonal length to the frequency of retrograde molecular motor signals.

Purpose of the Study:

  • To develop a mathematical model of the proposed molecular-motor-based axonal length-sensing mechanism.
  • To investigate the relationship between axonal length and signal frequency.
  • To predict the impact of molecular motor transport dynamics on length sensing reliability.

Main Methods:

  • Coupling advection-diffusion equations for bidirectional motor transport with a chemical signaling network.
  • Analyzing emergent chemical oscillations via Hopf bifurcation analysis.
  • Simulating the effects of molecular motor knockdown and transport fluctuations.

Main Results:

  • Chemical oscillations emerge from delayed negative feedback, acting as a length-encoding signal.
  • Oscillation frequency is a monotonically decreasing function of axonal length.
  • Kinesin or dynein knockdown increases oscillation frequency, predicting longer axons.
  • Model predicts reduced reliability of length sensing for longer axons due to transport fluctuations.

Conclusions:

  • The developed mathematical model supports a frequency-based mechanism for axonal length sensing.
  • Delayed negative feedback in signaling networks drives emergent oscillations for length encoding.
  • Axonal length sensing accuracy is potentially limited by the stochasticity of molecular motor transport.