The effect of the feedback inhibition of heterogeneous external globus pallidus on beta oscillations in an extended basal ganglia network

Pathological $\beta$-band oscillations (13–35 Hz) in the basal ganglia (BG) are strongly associated with Parkinson's disease (PD). Recent evidence shows that subpopulations of external globus pallidus (GPe) neurons exhibit distinct responses to pathological conditions, and that their inhibitory feedback to the striatum strongly shape BG dynamics, features often overlooked in conventional models. To address this, we developed an extended BG network using a modified Hodgkin–Huxley framework, incorporating two GPe subclasses, arkypallidal (TA) and prototypical (TI), along with striatal medium spiny neurons (MSNs) and fast-spiking interneurons (FSIs). Simulations revealed that mutual inhibition within the GPe drives TI neurons from tonic firing into $\beta$-bursting, retrogradely suppressing striatal activity through the GPe–FSI–MSN loop and disrupting direct/indirect pathway balance. We further show that GPe-TA projections exert strong inhibitory control over striatal populations, and that reducing MSN M-current reproduces $\beta$ oscillations that propagate downstream. Blocking D2 MSN $\to$ GPe-TI and GPe-TI $\to$ GPe-TA synapses restores normal TI firing. Our results emphasize the role of GPe heterogeneity in pathological oscillations and suggest circuit-level therapeutic strategies for PD.