Abstract

Brain rhythms appear as transient spindle-shaped bursts with waxing and waning envelopes. Yet, the general principles governing their emergence remain unclear, obscured by biophysical complexity. Here, by recording 4–16 Hz EEG α-spindles alongside the concurrent firing of large populations of thalamic and cortical excitatory and inhibitory neurons with Neuropixels electrode in anesthetized mice, we introduce a minimal modeling framework—a two-dimensional stochastic system with a stable focus—to explain how spindle amplitude and frequency vary with anesthesia depth. We show that α-spindle amplitude is determined by the excitation–inhibition balance and neuronal firing variability. Coupling two such systems with variable interaction strength generates faster or slower spindle types, linking network interactions to mixed-frequency dynamics. Our results uncover a parsimonious dynamical principle governing spindle generation and the control of their amplitude and frequency, bridging single-neuron activity, network rhythms, and anesthesia depth monitoring.