Bursting, beating, and chaos in an excitable membrane model

Area of Science:

• Computational Biology
• Biophysics
• Cellular Electrophysiology

Background:

• The pancreatic beta-cell exhibits complex electrical activity crucial for insulin secretion.
• Hodgkin-Huxley type models are essential for simulating cellular electrophysiology.
• Understanding oscillations in excitable cells is key to metabolic regulation.

Purpose of the Study:

• To investigate periodic and aperiodic behaviors in a Hodgkin-Huxley type model of the pancreatic beta-cell.
• To characterize deterministic chaos in an endogenously active excitable membrane model.
• To develop a simplified model for analyzing calcium dynamics.

Main Methods:

• Numerical solutions of the Chay-Keizer model for pancreatic beta-cells.
• Variation of the glucose-dependent parameter kCa to observe dynamic pattern changes.
• Development of a one-variable, discrete-time model for intracellular calcium evolution.

Main Results:

• Observed regimes of periodic beating (continuous spiking) and bursting modes.
• Identified aperiodic responses in the transition between periodic and bursting modes.
• Characterized deterministic chaos in the pancreatic beta-cell model, consistent with non-biophysical systems.

Conclusions:

• The pancreatic beta-cell model exhibits diverse dynamic behaviors, including deterministic chaos.
• A simplified discrete-time model effectively captures the essential dynamics of intracellular calcium.
• This research provides insights into the complex electrical activity of pancreatic beta-cells.