A one-dimensional moving-boundary model for tubulin-driven axonal growth

Area of Science:

• Biophysics
• Cell Biology
• Neuroscience

Background:

• Axonal elongation is crucial for neural development.
• Tubulin dynamics within the growth cone are key to this process.
• Understanding the mechanical and chemical factors governing axon growth is essential.

Purpose of the Study:

• To develop a continuum-mechanical model of axonal elongation.
• To analyze the role of tubulin assembly in the growth cone.
• To determine how biological parameters influence steady-state axon lengths and stability.

Main Methods:

• A one-dimensional continuum-mechanical model was formulated.
• The model utilizes a coupled system of three differential equations.
• Steady-state solutions were analyzed, and numerical simulations were performed.

Main Results:

• The model categorizes all steady-state solutions, predicting zero, one, or two possible steady-state axon lengths.
• Explicit expressions for stationary concentration distributions were derived.
• Numerical simulations showed that longer axon lengths correspond to stable states, while shorter lengths are unstable.

Conclusions:

• The model provides a framework for understanding axonal elongation based on tubulin dynamics.
• It allows for the examination of individual biological parameter influences on axon growth.
• For typical parameters, free tubulin concentration in the axon is lower than in the soma and growth cone.