ROUGH DRAFT authorea.com/10527

Abstract

# Abstract

“Coupled oscillators are not only of great biological importance, but also very interesting from a dynamical systems point of view. In a systems biology context, the interconnection between two periodic processes such the circadian rhythm and the cell cycle represents an ideal analyzable system at the single-cell level. The analysis of a large dataset from time-lapse imaging of single mouse fibroblast showed, in our previous study, that circadian and cell cycle are robustly synchronized. This synchronization state is observed over a wide range of conditions resulting from a predominant influence of the cell cycle on the circadian cycle. Moreover, parameters of the coupling functions has been identified with stochastic modeling of two interacting phase oscillators. Here, we reconstruct a non-parametric model of the phase dynamics, identifying new potential interactions between the two processes. This allows us to make more specific predictions on precise cell cycle events that could influence the circadian clock, such the condensation of chromosomes coinciding with transcriptional shutdown, and subsequently testing those prediction using different markers of cell cycle events. By analyzing several conditions we found that the phase relationship of the two systems presents shifts characteristic of resonating oscillators. In conclusion, we highlight how the use of a statistical model allows the understanding of the interaction between two important cellular processes by reducing the complex dynamics to a low dimensional phase model. ”

# Author Summary

150–200 word non-technical summary written in the first-person voice, Aim to highlight where your work fits within a broader context; present the significance or possible implications of your work simply and objectively; and avoid the use of acronyms and complex terminology wherever possible. “-Impact of cell cycle perturbation on circadian clock/ Understanding the properties of the circadian clock - Low dimensionality”

# Introduction

\label{sec:Introduction}

The circadian clock and the cell cycle oscillators represent two cellular processes having a period in the range of one day. At the single-cell level, the circadian rhythm is carried out by a network of transcriptional and translational feedback loops that drive rhythmic expression of genes with a period of about 24 hours (Buhr 2013). This cell autonomous rhythm is self-sustained (Westermark 2009) and is considered to temporally orchestrate many important cell physiological processes such as metabolism (Nakahata 2009) (Eckel-Mahan 2013), redox balance and chromatin conformation (Aguilar-Arnal 2013). The cell cycle can also be considered as a periodic process lasting on the order of one day in dividing mammalian cells (Hahn 2009). Consequently, is reasonable to expect that, when circadian and cell cycles run in parallel in the same cell, their coupling could lead to synchronization, also called mode-locking.

Evidences in mammalian cells (Liu 2007), (Yoo 2004) showed synchronization between circadian and cell cycles oscillators which is compatible with the 1:1 mode-locking state. Moreover, many studied described circadian rhythms of cell divisions or clock-dependent variations of mitotic indexes in different types of mammalian cells (Matsuo 2003), (Kowalska 2013), (Reddy 2005). These observations could be explained by a model denominated “circadian gating of the cell-cycle”, defined as a control operated by the circadian clock that determines temporal windows in which certain cell cycle transitions are either allowed or restricted. A deeper understanding of how the two biological systems interact is currently of great interest, notably to better understand the role of circadian clocks in proliferating tissues such as the epidermis, immune or stem cells and in cancer (Plikus 2015).

In a previous work (Bieler 2014), we performed a systematic analysis based on time-lapse imaging of circadian cycles in dividing mammalian NIH3T3 cells. We used Rev-Erb$$\alpha$$-YFP as a transcriptional circadian reporter and detected the times of its maximal expression, or circadian peaks. For the cell cycle we detected the cell divisions via tracking and manually validated both peak and divisions times. The study of a large collection of these times in different conditions clearly indicated that both oscillators tick in a tightly synchronized state, showing a unimodal distribution of circadian phase at division centered about $$0.75 \times 2\pi$$, with division occurring about five hours before divisions. The influence of the cell cycle on the circadian clock was apparent in the dependence of the length of circadian intervals on the timing of divisions, as already shown by Nagoshi et al. (Nagoshi 2004). In addition, the circadian intervals were consistently shorter in dividing cells than in non-dividing ones. In order to further probe the system, we performed a number of perturbations affecting both the circadian clock and the cell cycle. In all conditions the two oscillators remained synchronized, and the data were consistent with a scenario in which the coupling is predominantly from the cell cycle to the circadian clock. Moreover, we fitted a parametric form of the coupling functions to the data via maximum likelihood. This clearly identified an acceleration of circadian phase after the division, but the stochastic nature of the problem, the large number of parameters and the particular parametric form of the coupling functions made identifying further interaction points challenging. Thus, contrary to our expectations, we found that the cell cycle progression exerts a predominant influence on the circadian clock within single cells. While fruitful, this analysis in term of peak and division times, implicitly assumes that the phase goes linearly between two events, and thus neglect fast components of the phase dynamic (Kralemann 2008).

In a recent study Feillet et al. (Feillet 2014) performed similar experiments in NIH-3T3 cells, using the same Rev-Erb$$\alpha$$