Exploiting circadian memory to hasten recovery from circadian misalignment

Abstract

Recent years have seen a sustained interest in the development of circadian reentrainment strategies to limit the deleterious effects of jet lag. Due to the dynamical complexity of many circadian models, phase-based model reduction techniques are often an imperative first step in the analysis. However, amplitude coordinates that capture lingering effects (i.e., memory) from past inputs are often neglected. In this work, we focus on these amplitude coordinates using an operational phase and an isostable coordinate framework in the context of the development of jet-lag amelioration strategies. By accounting for the influence of circadian memory, we identify a latent phase shift that can prime one’s circadian cycle to reentrain more rapidly to an expected time-zone shift. A subsequent optimal control problem is proposed that balances the trade-off between control effort and the resulting latent phase shift. Data-driven model identification techniques for the inference of necessary reduced order, phase-amplitude-based models are considered in situations where the underlying model equations are unknown, and numerical results are illustrated in both a simple planar model and in a coupled population of circadian oscillators.

Periodic solutions to perturbed nonlinear oscillators with memory

“…• Jet-lag effects on humans suggest the opportunity of developing strategies that may control or even contrast them. Proposed mathematical models to describe quantitatively the phenomenon involve population of oscillators with circadian effects [1]; so they require the insertion of a delay. • Looking at a spatial scale smaller than the one of an entire organism, we see that transcription, translation, diffusion, and transport processes in gene networks have different duration: diffuse delay occurs, depending on the structure of gene networks.…”

“…. If we derive the balance equations from the resulting Hamiltonian, solve with respect to qi , we obtain that the resulting dynamics of the target particle is described by a structure falling within the scheme (1). Here, the N − 1 particles behave as a thermal bath (see [52] for pertinent proofs and further detailed analyses).…”