Monotone dynamics of two cells dynamically coupled by a voltage-dependent gap junction.

Area of Science:

• Biophysics
• Computational Biology
• Cellular Electrophysiology

Background:

• Cells communicate electrically through gap junctions.
• Gap junction channels exhibit dynamic conductance states.
• Voltage dependence of channel gating is crucial for cellular communication.

Purpose of the Study:

• To develop and analyze a simple model of two non-excitable cells coupled via gap junctions.
• To investigate the relationship between system dynamics and the Jacobian matrix determinant.
• To explore conditions leading to multiple steady states in coupled cells.

Main Methods:

• Mathematical modeling of two dynamically coupled non-excitable cells.
• Analysis of gap junction channel conductance states (low and high).
• Investigation of voltage-dependent transition rates between channel states.
• Examination of the Jacobian matrix and its determinant for steady-state analysis.

Main Results:

• A simple relationship exists between the number/stability of steady states and the Jacobian determinant.
• The system exhibits monotonicity under specific voltage-dependent gating conditions.
• A tridiagonal Jacobian matrix indicates that all initial conditions evolve to a steady state.
• Multiple steady states are possible within this model.

Conclusions:

• The model provides insights into the complex dynamics of gap junction-coupled cells.
• Voltage-dependent gating of gap junctions can lead to multiple stable cellular states.
• Understanding these dynamics is vital for comprehending intercellular electrical signaling.