The effects of long-range connections on navigation in suprachiasmatic nucleus networks

In the mammalian suprachiasmatic nucleus (SCN), the cellular oscillators communicate within a neuronal network to regulate the circadian rhythms of physiological and behavioral activity. However, how the network topology drives the information communication in the SCN remains poorly understood, especially for the effects of long-range connections. In this work, using a decentralized navigation protocol in spatially embedded networks, we investigated long-range links' effects on navigation in SCN networks. We showed that the SCN networks could be embedded into hidden hyperbolic metric spaces with a simple connectivity law, and the hyperbolic distances can determine the long-range connections. Strikingly, after removing a small fraction of connections with long hyperbolic distances, the residual SCN network can still maintain the robustness of the system and relatively efficient information communication. In contrast, after removing the same fraction of connections with long distances in Euclidean space, the network becomes very vulnerable, and the navigability between the left and right SCN is seriously damaged. In the end, we adopted a biophysical model to verify the findings in navigation and showed that highly efficient navigation in hyperbolic space implies the system can support the circadian rhythm better. Our results suggest that distances in the underlying hyperbolic space provide new insights into the effects of long-range connections and information communication in SCN networks.