Bifurcation analysis of a two-compartment hippocampal pyramidal cell model

Area of Science:

• Computational Neuroscience
• Mathematical Biology
• Neuroscience

Background:

• The Pinsky-Rinzel model is a widely used, non-smooth computational model of CA3 pyramidal cells.
• Analyzing complex neuronal dynamics in non-smooth models presents significant challenges.

Purpose of the Study:

• To develop a smooth, modified Pinsky-Rinzel model suitable for numerical continuation methods.
• To perform a comprehensive bifurcation and fast-slow analysis of CA3 pyramidal cell behavior.

Main Methods:

• Modification of the Pinsky-Rinzel model to achieve a smooth system.
• Application of numerical continuation techniques for bifurcation analysis.
• Utilizing fast-slow analysis to investigate underlying mechanisms of neuronal dynamics.

Main Results:

• Identified key bifurcations governing transitions between resting, bursting, and spiking states.
• Demonstrated how reduced calcium conductance eliminates bursting behavior.
• Revealed the influence of phase differences between calcium and dendritic voltage on irregular spiking and potassium currents.
• Established that calcium concentration drives intraburst dynamics, while the afterhyperpolarization current's gate influences interburst intervals.

Conclusions:

• The smooth model accurately captures the qualitative dynamics of the original Pinsky-Rinzel model.
• Bifurcation analysis provides critical insights into the emergence and disappearance of bursting in CA3 pyramidal cells.
• Understanding these dynamics is crucial for interpreting neuronal activity, including during sharp-wave ripples in larger networks.