A bifurcation analysis of neuronal subthreshold oscillations

Area of Science:

• Neuroscience
• Computational Neuroscience
• Biophysics

Background:

• Subthreshold oscillations are crucial for neuronal function in the entorhinal cortex.
• Understanding the ionic mechanisms underlying these oscillations is essential for comprehending network dynamics.

Purpose of the Study:

• To analyze the conditions for generating subthreshold oscillations using a two-variable neuronal model.
• To identify the roles of specific ionic currents (sodium, potassium/cation) in oscillation generation and properties.

Main Methods:

• Nonlinear dynamical techniques and bifurcation analysis were applied to a two-differential-equation neuronal model.
• Mathematical descriptions of membrane currents were based on voltage-clamp data from entorhinal cortical neurons.
• The influence of ionic conductance magnitudes and kinetic properties on oscillations was investigated.

Main Results:

• The model identified ranges of sodium, potassium/cation, and leakage conductances supporting subthreshold oscillations.
• Potassium/cation current threshold and activation time constant significantly impacted oscillation robustness and frequency.
• Sodium activation curve characteristics influenced the gradual emergence and extended range of oscillations.

Conclusions:

• The findings implicate slow inward rectifier or a novel slow outward current in entorhinal cortical oscillations.
• Model results provide insights into the biophysical basis of subthreshold oscillations and their dependence on specific ionic currents.