Hyperbolic distance reveals functional communication pathways in the Drosophila circadian clock network

Circadian clocks are widespread across organisms, regulating behavioral and physiological processes. Drosophila, with its relatively small number of neurons and fully mapped connectome, provides an ideal model for investigating functional interactions among circadian clock neurons. To explore the communication pathways within the circadian clock network, we constructed a network of 242 neurons based on synaptic connectivity and embedded it in hyperbolic space, enabling navigation based on hyperbolic distances. The results demonstrated that hyperbolic distance effectively captures functional interactions within the Drosophila circadian clock network. Notably, neurons in LNITP, DN3, and DN1p play central roles in mediating global information flow, while pairs of subgroups such as DN3–DN3, DN3–DN1p, and DN3–LNITP exhibit strong functional coupling despite being spatially separated. Moreover, efficient navigation can be achieved within the network embedded in hyperbolic space. We further identified key pathways and subgroups—particularly LNITP and DN3—as crucial for contralateral communication, and revealed that certain right hemisphere neurons are more critical for contralateral communication than left counterparts. These results are verified through simulations of collective dynamics among neurons using the Kuramoto model. In conclusion, hyperbolic geometry not only provides a more accurate representation of functional interactions in the Drosophila circadian clock network but also offers new geometric insights into neuronal routing mechanisms and synchronization properties.