Modelling in vivo action potential propagation along a giant axon

Area of Science:

• Computational Neuroscience
• Biophysics
• Mathematical Biology

Background:

• Investigates current flow in excitable, unmyelinated axons using a 3D partial differential equation model.
• Compares a 3D model to the 1D cable equation for axon electrophysiology.

Purpose of the Study:

• To evaluate the accuracy of the 1D cable equation approximation for action potential propagation in axons.
• To compare 3D model predictions with cable equation results for squid giant axons in vitro and in vivo settings.

Main Methods:

• Developed and applied a three-dimensional partial differential equation model for axonal current flow.
• Compared simulation results from the 3D model with the established 1D cable equation.
• Analyzed differences in action potential wave profiles and propagation speeds under varying conditions.

Main Results:

• In vitro, the 3D model and cable equation showed minimal differences for squid giant axons, validating the cable equation's accuracy in this specific context.
• In vivo, significant discrepancies emerged between the 3D model and cable equation regarding wave profile and propagation speed.
• The cable equation was found to overestimate the increase in propagation velocity with increasing axon radius in the in vivo scenario.

Conclusions:

• The 1D cable equation is a valid approximation for squid giant axons in vitro but less so in vivo.
• Differences in extracellular conductivity significantly impact the accuracy of the cable equation for action potential propagation.
• Findings have implications for understanding the evolutionary trade-offs between axon radius and action potential propagation speed.