Intermittent synchronization in a network of bursting neurons

TL;DR

This paper investigates the mechanism behind intermittent synchronization in neural networks, using a simplified model of coupled bursting neurons analyzed through geometric and perturbation methods, with implications for understanding Parkinson's disease.

Contribution

It introduces a reduced mathematical model explaining intermittent phase-locking in bursting neurons, highlighting the role of slow variables and synaptic strength.

Findings

Intermittent synchrony arises from overlapped spiking influenced by slow phase plane geometry.

Two slow variables generate overlapped spiking activity patterns.

The model's parameters relate to biophysical factors affected in Parkinson's disease.

Abstract

Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical network of the basal ganglia, formed by excitatory and inhibitory bursters of the subthalamic nucleus and globus pallidus, involved in motor control and affected in Parkinson's disease. Recent experiments have demonstrated the intermittent nature of the phase-locking of neural activity in this network. Here we explore one potential mechanism to explain the intermittent phase-locking in a network. We simplify the network to obtain a model of two inhibitory coupled elements and explore its dynamics. We used geometric analysis and singular perturbation methods for dynamical systems to reduce the full model to a simpler set of equations. Mathematical analysis was completed using three slow variables with two different time scales. Intermittently synchronous oscillations are generated by overlapped spiking which crucially depends on the geometry of the slow phase plane and the interplay between slow variables as well as the strength of synapses. Two slow variables are responsible for the generation of activity patterns with overlapped spiking and the other slower variable enhances the robustness of an irregular and intermittent activity pattern. While the analyzed network and the explored mechanism of intermittent synchrony appear to be quite generic, the results of this analysis can be used to trace particular values of biophysical parameters (synaptic strength and parameters of calcium dynamics), which are known to be impacted in Parkinson's disease.