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

Zihan Li; Xia Shi; Bei Bai; Zihan Li; Xia Shi; Bei Bai

doi:10.3934/era.2025270

Electronic Research Archive

2025, Volume 33, Issue 10: 6070-6095. doi: 10.3934/era.2025270

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

Zihan Li ¹,
Xia Shi ^{2,3
,
,},
Bei Bai ²

1.
School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China
2.
School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China
3.
Key Laboratory of Mathematics and Information Networks (Beijing University of Posts and Telecommunications), Ministry of Education, Beijing 100876, China

Received: 16 August 2025 Revised: 09 October 2025 Accepted: 14 October 2025 Published: 17 October 2025

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 $ \rightarrow $ GPe-TI and GPe-TI $ \rightarrow $ 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.
- heterogeneous GPe,
- Bursting,
- $\beta$-band oscillations,
- Parkinson's disease,
- basal ganglia
Citation: Zihan Li, Xia Shi, Bei Bai. The effect of the feedback inhibition of heterogeneous external globus pallidus on beta oscillations in an extended basal ganglia network[J]. Electronic Research Archive, 2025, 33(10): 6070-6095. doi: 10.3934/era.2025270

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Abstract

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 $ \rightarrow $ GPe-TI and GPe-TI $ \rightarrow $ 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.

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