Hyperbolic distance modulated coupling enhances collective rhythms and biological consistency in circadian clock networks

Stable circadian rhythms rely on synchronized neuronal oscillations in the suprachiasmatic nucleus (SCN), which is profoundly influenced by network coupling structures. Coupling structures defined solely by network topology in existing models cannot accurately quantify functional interactions between neurons. In this paper, we introduced a distance-modulated coupling mechanism into the Poincaré model and compared Euclidean and hyperbolic distances as functional distance metrics. The coupling structure was derived from functional networks reconstructed from mouse SCN slices during TTX-resynchronization experiments, while distances mean that between neurons. Simulations demonstrate that the hyperbolic distance-modulated coupling exhibits higher synchronization degree and approximate experimental result. Moreover, it slightly enhances oscillation amplitudes while preserving stable collective rhythms. These findings indicate that effective information flow in the SCN depends on functional rather than spatial proximity alone. Hyperbolic distance enables a more accurate description of effective interactions in circadian networks and provides a geometric modeling framework linking structure, function, and collective dynamics in complex neural systems.