Hypothesis driven single cell dual oscillator mathematical model of circadian rhythms

Abstract

Molecular mechanisms responsible for 24 h circadian oscillations, entrainment to external cues, encoding of day length and the time-of-day effects have been well studied experimentally. However, it is still debated from the molecular network point of view whether each cell in suprachiasmatic nuclei harbors two molecular oscillators, where one tracks dawn and the other tracks dusk activities. A single cell dual morning and evening oscillator was proposed by Daan et al., based on the molecular network that has two sets of similar non-redundant per1/cry1 and per2/cry2 circadian genes and each can independently maintain their endogenous oscillations. Understanding of dual oscillator dynamics in a single cell at molecular level may provide insight about the circadian mechanisms that encodes day length variations and its response to external zeitgebers. We present here a realistic dual oscillator model of circadian rhythms based on the series of hypotheses proposed by Daan et al., in which they conjectured that the circadian genes per1/cry1 track dawn while per2/cry2 tracks dusk and they together constitute the morning and evening oscillators (dual oscillator). Their hypothesis also provides explanations about the encoding of day length in terms of molecular mechanisms of per/cry expression. We frame a minimal mathematical model with the assumption that per1 acts a morning oscillator and per2 acts as an evening oscillator and to support and interpret this assumption we fit the model to the experimental data of per1/per2 circadian temporal dynamics, phase response curves (PRC's), and entrainment phenomena under various light-dark conditions. We also capture different patterns of splitting phenomena by coupling two single cell dual oscillators with neuropeptides vasoactive intestinal polypeptide (VIP) and arginine vasopressin (AVP) as the coupling agents and provide interpretation for the occurrence of splitting in terms of ME oscillators, though they are not required to explain the morning and evening oscillators. The proposed dual oscillator model based on Daan's hypothesis supports per1 and per2 playing the role of morning and evening oscillators respectively and this may be the first step towards the understanding of the core molecular mechanism responsible for encoding the day length.

Weak coupling between intracellular feedback loops explains dissociation of clock gene dynamics

“…Based on differences in free-running oscillation phases and light responses, Daan et al . hypothesized that Per1 and Cry1 may constitute a M oscillator, while Per2 and Cry2 act as an E oscillator within a single cell [64], a concept that was later studied computationally [65]. Nuesslein-Hildesheim et al .…”

Multi-scale modeling of the circadian modulation of learning and memory

“…In this work, we assumed most of the molecular mechanisms and therefore, resorted to simple molecular models. We could have considered more realistic models like morning and evening (ME) oscillators [30], where it explained how circadian clock genes control morning and evening activities, but again to know how the GRN model communicates with the conductance model through neurotransmitters or other coupling agents is a big challenge. This can be at best speculated to model the process.…”

Aging in a Relativistic Biological Space-Time

“…When studied in isolation, biological clocks can be described and predicted with periodic functions, which may speed up, slow down, or even stop and start over the course of a persons' lifetime. The more complex case of multiple integrated biological clocks can be modeled with coupled oscillators and dynamical systems theory (Shiju and Sriram, 2017 ). However, a fundamental assumption of these approaches is that the rate of change of these biological clocks are measured with respect to a linear passage of time and that the rate is independent from the biological space in which the biological clocks operate.…”