Full system bifurcation analysis of endocrine bursting models

Area of Science:

• Neuroscience
• Cellular Electrophysiology
• Mathematical Biology

Background:

• Plateau bursting is a common firing pattern in electrically excitable cells like endocrine cells and neurons.
• This bursting is typically modulated by the interaction of voltage-gated calcium channels and calcium-sensitive potassium channels.
• Distinct bursting patterns, such as square-wave and pseudo-plateau, exist and are linked to specific bifurcation types.

Purpose of the Study:

• To investigate the mechanisms underlying square-wave and pseudo-plateau bursting patterns in endocrine cell models.
• To perform a detailed bifurcation analysis of the fast-slow system for these bursting patterns.
• To determine the relevance of Hopf bifurcation criticality in characterizing routes to bursting.

Main Methods:

• Utilized the Hindmarsh and Rose polynomial model, preserving key biophysical properties.
• Conducted a comprehensive bifurcation analysis of the full fast-slow system.
• Examined the influence of the fixed point's location relative to homoclinic bifurcations.

Main Results:

• Both square-wave and pseudo-plateau bursting patterns exhibit two potential routes to bursting.
• The criticality of the Hopf bifurcation in the fast subsystem does not determine the route to bursting.
• The specific route to bursting is contingent upon the position of the full system's fixed point relative to fast subsystem homoclinic bifurcations.

Conclusions:

• The criticality of the Hopf bifurcation is not a determining factor for the routes to bursting in endocrine cells.
• Endocrine bursting dynamics are more complex than suggested by standard fast-slow analysis.
• A full-system bifurcation analysis is crucial for understanding the nuanced properties of endocrine bursting.