FROM HETEROGENEITY TO GEOMETRY: STATE-INVARIANT LIMIT-CYCLE ATTRACTOR OF MEDIAL SEPTAL THETA OSCILLATION

The medial septum (MS) is essential for organizing hippocampal theta rhythms during memory, yet its constituent neurons are strikingly diverse and weakly synchronized. Using large-scale Neuropixels recordings from freely moving rats, we demonstrate that this paradox is resolved at the ensemble level. Specifically,we show that MS population activity exhibits structured statistical properties that constrain its covariance, giving rise to coherent population dynamics despite pronounced single-cell heterogeneity. This emergent “ring” constitutes a limit-cycle attractor, stabilized by a steep U-shaped potential that actively corrects amplitude perturbations.

The ring architecture is a state-invariant feature of the circuit: its geometry is preserved during locomotion and REM sleep, while population activity collapses toward the origin during NREM sleep. We further uncover a simple rule governing neuronal recruitment into the ring: a neuron’s contribution is strongly predicted by its spectral coherence with the hippocampal field—reflecting network membership strength—rather than by its precise spike timing.

Functionally, the MS population state serves as a high-precision global temporal reference. It predicts hippocampal place-cell spike timing with significantly greater accuracy than the local field potential, providing a stable population-level clock that supports precise temporal coordination of hippocampal activity across behavioral and sleep states.