Coupled beta and high-frequency oscillations emerge from synchronized bursting in a minimal model of the parkinsonian subthalamic nucleus

Local field potentials recorded from the subthalamic nucleus (STN) in Parkinsons 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 captures the emergence of pathological STN neuronal activity in the parkinsonian state. HFO peak frequency varies continuously across the two-parameter landscape, providing a mechanistic account 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 two-stage process at intermediate excitability where burst recruitment precedes synchronization. The model generates testable predictions for future clinical and experimental studies, provides a numerical dissection of how mesoscopic LFP features map onto microscopic neuronal dynamics, and serves as a computational building block for future circuit-level models that can guide brain stimulation strategies tailored to the patient-specific dynamical state of the STN. Author summaryIn Parkinsons 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 captures 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, explaining 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, confirming consistency 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 offers a framework for brain stimulation strategies informed by patient-specific dynamical states.