Coupled beta and high-frequency oscillations emerge from synchronized bursting in a minimal model of the parkinsonian subthalamic nucleus
- 1Department of Neurology, University of Minnesota, Minneapolis, Minnesota, United States of America
- 2Department of Psychiatry & Behavioral Sciences, University of Minnesota, Minneapolis, Minnesota, United States of America
Abstract
Local field potentials (LFPs) recorded from the subthalamic nucleus (STN) in Parkinson's disease (PD) exhibit a distinctive multiscale spectral signature: exaggerated beta-band oscillations (13–30 Hz) coupled to high-frequency oscillations (HFOs, 200–400 Hz), with HFO amplitude being phase-locked to the beta cycle. This phase-amplitude coupling (PAC) has been identified as a promising biomarker of the parkinsonian state, yet no biophysical model has explained how it emerges, what determines the HFO frequency, or how HFOs can exist without beta modulation in the medicated STN. Here we show that a heterogeneous population of excitatory Izhikevich neurons with recurrent coupling produces three dynamical regimes: (i) asynchronous tonic firing, (ii) asynchronous bursting, in which neurons burst individually producing broadband HFO power but without coherent population-level PAC, and (iii) synchronous bursting, which gives rise to beta-HFO PAC. The regimes are governed by two biophysically interpretable parameters that capture complementary effects of dopamine depletion: one reflecting changes in intrinsic neuronal excitability, the other reflecting changes in synaptic coupling strength. The transition from asynchronous to synchronous bursting in this model emulates the emergence of pathological STN neuronal activity in the parkinsonian state. HFO peak frequency varies continuously across the two-parameter landscape, suggesting a possible mechanism of the clinically observed shift from slow (200–300 Hz) to fast (300–400 Hz) HFOs between medication states. The character of the synchronization transition depends on baseline excitability, ranging from a sharp co-emergence of bursting and synchrony at low excitability to a decoupled transition at intermediate excitability, where the bursting fraction saturates while the population synchronization continues to increase with coupling. The asynchronous-to-synchronous bursting transition and the beta-HFO PAC in the STN population also arise in an extended version of the model with reciprocal coupling to an inhibitory population of globus pallidus externa (GPe)-like neurons, with the beta frequency varying with the delay in the synaptic coupling between the two populations. The model generates testable predictions for future clinical and experimental studies, provides a numerical dissection of how mesoscopic LFP features could map onto microscopic neuronal dynamics, and serves as a computational building block for future circuit-level models that may inform brain stimulation strategies tailored to the patient-specific dynamical state of the STN. Author summary: In Parkinson's disease, local field potentials (LFP) from the subthalamic nucleus (STN) contain two prominent rhythms: a slow beta rhythm (13–30 Hz) and fast oscillations (200–400 Hz). In the parkinsonian state, these rhythms become coupled, with fast oscillation amplitude varying systematically with beta phase, a relationship absent in the medicated state. We built a biophysical spiking neuron network model that represents two key effects of dopamine depletion on STN neuronal activity: changes in the intrinsic neuronal excitability and changes in synaptic coupling strength. The model produces fast oscillations from rapid intraburst firing, while the slow beta rhythm and its coupling to fast oscillations emerge with the onset of synchronized bursting across the population. Importantly, the frequency of the fast oscillations shifts continuously depending on both parameters, offering a possible explanation for a puzzling clinical observation that these oscillations change frequency between medication states. The model also reproduces the modulation pattern in the spike-triggered average of HFO envelope amplitude reported in patient recordings, and is thus consistent with single-unit observations as well as LFP-level spectral features. By mapping how multi-timescale LFP spectral features relate to the dynamical regime of the underlying neuronal population, this work suggests a framework that may inform brain stimulation strategies based on patient-specific dynamical states.
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BibTeX
@article{sheheitli2026coupled,
title = {{Coupled beta and high-frequency oscillations emerge from synchronized bursting in a minimal model of the parkinsonian subthalamic nucleus}},
author = {Hiba Sheheitli and Luke A. Johnson and Jing Wang and Joshua E. Aman and Jerrold L. Vitek},
journal = {PLOS Computational Biology},
year = {2026},
month = oct,
doi = {10.1371/journal.pcbi.1014921},
url = {https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014921},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Coupled beta and high-frequency oscillations emerge from synchronized bursting in a minimal model of the parkinsonian subthalamic nucleus
AU - Hiba Sheheitli
AU - Luke A. Johnson
AU - Jing Wang
AU - Joshua E. Aman
AU - Jerrold L. Vitek
PY - 2026
DA - 2026/10/30
JO - PLOS Computational Biology
DO - 10.1371/journal.pcbi.1014921
UR - https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1014921
AB - Local field potentials (LFPs) recorded from the subthalamic nucleus (STN) in Parkinson's disease (PD) exhibit a distinctive multiscale spectral signature: exaggerated beta-band oscillations (13–30 Hz) coupled to high-frequency oscillations (HFOs, 200–400 Hz), with HFO amplitude being phase-locked to the beta cycle. This phase-amplitude coupling (PAC) has been identified as a promising biomarker of the parkinsonian state, yet no biophysical model has explained how it emerges, what determines the HFO frequency, or how HFOs can exist without beta modulation in the medicated STN. Here we show that a heterogeneous population of excitatory Izhikevich neurons with recurrent coupling produces three dynamical regimes: (i) asynchronous tonic firing, (ii) asynchronous bursting, in which neurons burst individually producing broadband HFO power but without coherent population-level PAC, and (iii) synchronous bursting, which gives rise to beta-HFO PAC. The regimes are governed by two biophysically interpretable parameters that capture complementary effects of dopamine depletion: one reflecting changes in intrinsic neuronal excitability, the other reflecting changes in synaptic coupling strength. The transition from asynchronous to synchronous bursting in this model emulates the emergence of pathological STN neuronal activity in the parkinsonian state. HFO peak frequency varies continuously across the two-parameter landscape, suggesting a possible mechanism of the clinically observed shift from slow (200–300 Hz) to fast (300–400 Hz) HFOs between medication states. The character of the synchronization transition depends on baseline excitability, ranging from a sharp co-emergence of bursting and synchrony at low excitability to a decoupled transition at intermediate excitability, where the bursting fraction saturates while the population synchronization continues to increase with coupling. The asynchronous-to-synchronous bursting transition and the beta-HFO PAC in the STN population also arise in an extended version of the model with reciprocal coupling to an inhibitory population of globus pallidus externa (GPe)-like neurons, with the beta frequency varying with the delay in the synaptic coupling between the two populations. The model generates testable predictions for future clinical and experimental studies, provides a numerical dissection of how mesoscopic LFP features could map onto microscopic neuronal dynamics, and serves as a computational building block for future circuit-level models that may inform brain stimulation strategies tailored to the patient-specific dynamical state of the STN. Author summary: In Parkinson's disease, local field potentials (LFP) from the subthalamic nucleus (STN) contain two prominent rhythms: a slow beta rhythm (13–30 Hz) and fast oscillations (200–400 Hz). In the parkinsonian state, these rhythms become coupled, with fast oscillation amplitude varying systematically with beta phase, a relationship absent in the medicated state. We built a biophysical spiking neuron network model that represents two key effects of dopamine depletion on STN neuronal activity: changes in the intrinsic neuronal excitability and changes in synaptic coupling strength. The model produces fast oscillations from rapid intraburst firing, while the slow beta rhythm and its coupling to fast oscillations emerge with the onset of synchronized bursting across the population. Importantly, the frequency of the fast oscillations shifts continuously depending on both parameters, offering a possible explanation for a puzzling clinical observation that these oscillations change frequency between medication states. The model also reproduces the modulation pattern in the spike-triggered average of HFO envelope amplitude reported in patient recordings, and is thus consistent with single-unit observations as well as LFP-level spectral features. By mapping how multi-timescale LFP spectral features relate to the dynamical regime of the underlying neuronal population, this work suggests a framework that may inform brain stimulation strategies based on patient-specific dynamical states.
SN - 1553-7358
SN - 1553-734X
ER -