Model of chemically excitable membranes generating autonomous chaotic oscillations

Area of Science:

• Biophysics
• Mathematical Biology
• Computational Neuroscience

Background:

• Chemically excitable membranes are crucial for biological functions.
• Understanding the origins of autonomous oscillations and chaos in biological systems is important.

Purpose of the Study:

• To present a simple mathematical model for chemically excitable membranes exhibiting autonomous chaotic oscillations.
• To explore the role of coupled ion transport systems in generating chaos.

Main Methods:

• Developed a mathematical model incorporating two autocatalytic ion channels (cation and anion).
• Explicitly included counter ions for self-consistency between ion distributions and electric potentials.
• Modeled nonlinear changes in ion channel permeability based on ion densities.

Main Results:

• The model demonstrates autonomous chaotic oscillations by varying coupling strength and ion adsorption rates.
• Cation and anion transport subsystems interact via membrane potential, leading to complex dynamics.
• Various types of chaotic oscillations were generated without external periodic forcing.

Conclusions:

• Coupled ion transport systems can autonomously generate chaos in biological membranes.
• The electric coupling among different ion transport systems may be a source of endogenous biological chaos.
• The proposed model provides a framework for understanding chaotic dynamics in biological systems.