(361n) Limits of Entrainment of Circadian Neuronal Networks

Circadian Rhythmicity is at the center of various important physiological and behavioral processes in mammals, such as sleep, metabolism, homeostasis, mood changes and more [1]. It has been shown that this rhythm arises from self-sustained biomolecular oscillations of a neuronal network located in the Suprachiasmatic Nucleus (SCN). Under normal circumstances, this network remains synchronized to the day-night cycle due to signaling from the retina. Misalignment of these neuronal oscillations with the external light signal can disrupt numerous physiological functions and take a long-lasting toll on health and well-being.

In this work, we study a state-of-the-art computational neuroscience model [2] to determine, using modern scientific computing algorithms, the limits of circadian synchronization to the external light signal. We employ a matrix-free approach [3] to locate high-dimensional periodic steady states for various forcing frequencies and duty cycles. Our algorithmic pipeline enables numerical continuation and the construction of bifurcation diagrams w.r.t. forcing parameters. We also computationally explore the effect of heterogeneity in the circadian neuronal network as well as the effect of corrective therapeutic interventions, such as that of the drug molecule Longdaysin.

[1] M. H. Hastings, E. S. Maywood, M. Brancaccio, Generation of circadian rhythms in the suprachiasmatic nucleus, Nature Reviews Neuroscience 19 (8) (2018) 453–469.

[2] C. Vasalou, E. Herzog, M. Henson, Multicellular model for intercellular synchronization in circadian neural networks, Biophysical Journal 101 (1) (2011) 12–20.

[3] Kelley, C. T., Kevrekidis, I. G., & Qiao, L. (2004). Newton-Krylov solvers for time-steppers. arXiv preprint math/0404374.