Modeling the geometry of circadian synchronization and period across aging.

Circadian freerunning periods change across the lifespan, yet most computational models do not reproduce these shifts without assuming additional mechanisms. Although the maturation and later deterioration of the suprachiasmatic nucleus (SCN) shape behavioral and humoral rhythms, the underlying driver of period change is more general. We show that it arises from an inherent property of a positively skewed frequency distribution, which naturally follows from a symmetric Gaussian distribution of intrinsic periods. Using a Kuramoto framework with a time-dependent coupling strength and age-related widening of period variability, we map the geometry of synchronization and macroscopic period and trace a developmental trajectory across this surface. Strong coupling in early adulthood pulls the synchronized period below the mean, matching data from C57BL/6 mice, whereas declining coupling and greater heterogeneity in late life lengthen the period and reduce amplitude. The same mechanism explains the negative correlation between amplitude and macroscopic period when period variability is high. This "circadian geometry" reveals that age-dependent variations in the macroscopic period are sufficiently explained by coupling and the width of the period distribution, and provides a parsimonious framework applicable to the SCN and other oscillator populations for understanding long-term changes in circadian dynamics during development and aging.