  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.
