The propagation of the nerve impulse

Area of Science:

• Biophysics
• Computational Neuroscience
• Mathematical Biology

Background:

• Action potential propagation is fundamental to neuronal signaling.
• Existing models often simplify the complex nonlinear ionic currents involved.
• Understanding the physical basis of these currents is crucial for accurate modeling.

Purpose of the Study:

• To derive a partial differential equation for the propagated action potential.
• To incorporate gating charge and nonlinear ionic currents using fundamental physical principles.
• To provide a physically grounded approximation for action potential propagation.

Main Methods:

• Derivation of partial differential equations using symmetry, charge conservation, and Ohm's law.
• Analysis of gating charge in the laboratory and a reference frame with zero capacitive currents.
• Expressing nonlinear ionic current in terms of voltage-dependent membrane capacitance C(V).

Main Results:

• A novel relation between orthogonal ionic current components was found.
• The ionic current was expressed using C(V) and axial current satisfying Ohm's law.
• Quasilinear partial differential equations were developed, yielding analytical solutions for action potentials.

Conclusions:

• The derived quasilinear equations approximate propagated action potentials effectively.
• These equations reveal the physical content of the FitzHugh-Nagumo model.
• The study enhances understanding of action potential dynamics and nonlinear current behavior.