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The synchronization dynamics for the circadian gene expression in the suprachiasmatic nucleus is investigated using a transcriptional circadian clock gene oscillator model. With global coupling in constant dark (DD) conditions, the model exhibits a one-cluster phase synchronized state, in dim light (dim LL), bistability between one- and two-cluster states and in bright LL, a two-cluster state. The two-cluster phase synchronized state, where some oscillator pairs synchronize in-phase, and some anti-phase, can explain the splitting of the circadian clock, i.e., generation of two bouts of daily activities with certain species, e.g., with hamsters. The one- and two-cluster states can be reached by transferring the animal from DD or bright LL to dim LL, i.e., the circadian synchrony has a memory effect. The stability of the one- and two-cluster states was interpreted analytically by extracting phase models from the ordinary differential equation models. In a modular network with two strongly coupled oscillator populations with weak intragroup coupling, with appropriate initial conditions, one group is synchronized to the one-cluster state and the other group to the two-cluster state, resulting in a weak-chimera state. Computational modeling suggests that the daily rhythms in sleep–wake depend on light intensity acting on bilateral networks of suprachiasmatic nucleus (SCN) oscillators. Addition of a network heterogeneity (coupling between the left and right SCN) allowed the system to exhibit chimera states. The simulations can guide experiments in the circadian rhythm research to explore the effect of light intensity on the complexities of circadian desynchronization.
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Kuranet: Systems of coupled oscillators that learn to synchronize
Networks of coupled oscillators are some of the most studied objects in the theory of dynamical systems. Two important areas of current interest are the study of synchrony in highly disordered systems and the modeling of systems with adaptive network structures. Here, we present a single approach to both of these problems in the form of "KuraNet", a deep-learning-based system of coupled oscillators that can learn to synchronize across a distribution of disordered network conditions. The key feature of the model is the replacement of the traditionally static couplings with a coupling function which can learn optimal interactions within heterogeneous oscillator populations. We apply our approach to the eponymous Kuramoto model and demonstrate how KuraNet can learn data-dependent coupling structures that promote either global or cluster synchrony. For example, we show how KuraNet can be used to empirically explore the conditions of global synchrony in analytically impenetrable models with disordered natural frequencies, external field strengths, and interaction delays. In a sequence of cluster synchrony experiments, we further show how KuraNet can function as a data classifier by synchronizing into coherent assemblies. In all cases, we show how KuraNet can generalize to both new data and new network scales, making it easy to work with small systems and form hypotheses about the thermodynamic limit. Our proposed learning-based approach is broadly applicable to arbitrary dynamical systems with wide-ranging relevance to modeling in physics and systems biology.
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- Award ID(s):
- 1740741
- PAR ID:
- 10294916
- Date Published:
- Journal Name:
- ArXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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