by Ka Nap Tse, G. Bard Ermentrout, Jonathan E. RubinRecent computational studies of Parkinson’s disease have yielded contradictory findings regarding the role of the subthalamic nucleus (STN) in pathological beta oscillations, with some models implicating STN as essential for beta generation and others suggesting that STN suppresses oscillations. This work addresses these discrepancies by systematically investigating how the specific features of the integrate-and-fire neurons used in these models influence simulated basal ganglia network dynamics. Using both rate models and spiking network simulations incorporating coupled subthalamopallidal and pallidostriatal circuits, we demonstrate that the choice between leaky integrate-and-fire (LIF) and quadratic integrate-and-fire (QIF) models to represent STN neurons fundamentally impacts the phase relationship between STN and external globus pallidus prototypical (Proto) neuron populations. QIF STN neurons establish in-phase coupling with Proto neurons, which enhances beta oscillation amplitude, while LIF STN neurons develop anti-phase relationships, which suppresses beta power. Through intervention experiments and parameter sweeps across physiologically relevant firing rates, we show that these phase-related effects persist robustly across network conditions, and we mathematically establish conditions under which these results are guaranteed to hold. Our findings reveal that the fundamental mathematical structure underlying spike generation, rather than other biophysical details, determines whether the subthalamopallidal loop acts as a beta amplifier or suppressor. This mechanistic insight reconciles contradictory findings in the literature, demonstrates that seemingly minor modeling choices can have profound consequences for understanding disease mechanisms and therapeutic targets, and offers predictions for determining which model framework reflects the biological reality.