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The cell cycle and the circadian clock are essential cyclic cellular processes often synchronous in healthy cells. In this work, we use previously developed mathematical models of the mammalian cell cycle and circadian cellular clock in order to investigate their dynamical interactions. Firstly, we study unidirectional cell cycle → clock coupling by proposing a mechanism of mitosis promoting factor (MPF)-controlled REV-ERB α degradation. Secondly, we analyse a bidirectional coupling configuration, where we add the CLOCK : BMAL1-mediated MPF repression via the WEE1 kinase to the first system. Our simulations reproduce ratios of clock to cell cycle period in agreement with experimental observations and give predictions of the system’s synchronization state response to a variety of control parameters. Specifically, growth factors accelerate the coupled oscillators and dexamethasone (Dex) drives the system from a 1 : 1 to a 3 : 2 synchronization state. Furthermore, simulations of a Dex pulse reveal that certain time regions of pulse application drive the system from 1 : 1 to 3 : 2 synchronization while others have no effect, revealing the existence of a responsive and an irresponsive system’s phase, a result we contextualize with observations on the segregation of Dex-treated cells into two populations.

Abstract:The cellular division cycle is an essential process to ensure healthy tissue homeostasis, which can, due to its periodicity, be interpreted as a biological oscillator. This work focuses on identifying the main mechanisms underlying cell cycle rhythms in mammals and propose a mathematical model to describe them. The model is based on post-translational modifications of cyclin Bcdk1, also called mitosis promoting factor (MPF), known to be the essential protein of the mammalian cell cycle, as well as in its degradation by the APC:cdc20 complex. The final result is a two variable reduced model of the mammalian cell cycle that is able to reproduce oscillatory behaviors and properties consistent with observations, namely the period being tunable by an external input of growth factor. We calibrate and validate this model and study its behavior in a simple open-loop control configuration, showing that it can exhibit bistability and oscillations. The model presents an advantage to work with due to its low variable and parameter size.

Guedes Soares (2016) Data assimilation with the ensemble Kalman filter in a high-resolution wave forecasting model for coastal areas,

We merge the Kessler-Levine simple discrete model for Dictyostelium cyclic adenosine monophosphate (cAMP) production and diffusion with the Dilão-Hauser directional sensing aggregation mechanism. The resulting compound model describes all the known transient patterns that emerge during Dictyostelium aggregation, which include the spontaneous formation of cAMP self-sustained target and spiral waves and streaming. We show that the streaming patterns depend on the speed of the amoebae, on the relaxation time for the production of cAMP, on the cAMP degradation rate, and on directional sensing. Moreover, we show that different signaling centers emerge during Dictyostelium aggregation.

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The mammalian clock and cell cycle are two essential biological oscillators. In this work we investigate the coupling of these oscillators via non-linear dynamical modeling. We use previously developed reduced models of these systems and study a molecular interaction of MPF (mitosis promoting factor) repression by the CLOCK:BMAL1 protein complex, via induction of the repressor wee1. Furthermore, we propose an hypothesis whereby the clock responds to cell cycle Growth Factors (GFs) via a pathway involving the non-essential cell cycle complex cyclin D/cdk4 and study this interaction in the context of unidirectional clock → cell cycle coupling. We observe 1:1, 3:2, 4:3, 5:4 ratios of clock to cell cycle period and identify GF and the coupling strength c b as decisive control parameters for the system's state of synchronization. Synchronization ratios differing from 1:1, namely 3:2 and 5:4, have been observed in cells treated with the corticosteroid Dexamethasone (Dex). Here, we study Dex application and are able to reproduce the induction of ratios differing from 1:1. Finally, because slowing down the cell cycle is very relevant in the context of cancer therapies, we devise particular protocols of cell cycle period control with the use of clock inputs that are successful in substantially slowing down the cell cycle by the use of the system's synchronization dynamics, obtaining 2:3, 3:4, 4:5 ratios of clock to cell cycle period.

In this work, we study period control of the mammalian cell cycle via coupling with the cellular clock. For this, we make use of the oscillators’ synchronization dynamics and investigate methods of slowing down the cell cycle with the use of clock inputs. Clock control of the cell cycle is well established via identified molecular mechanisms, such as the CLOCK:BMAL1-mediated induction of the wee1 gene, resulting in the WEE1 kinase that represses the active form of mitosis promoting factor (MPF), the essential cell cycle component. To investigate the coupling dynamics of these systems, we use previously developed models of the clock and cell cycle oscillators and center our studies on unidirectional clock [Formula: see text] cell cycle coupling. Moreover, we propose an hypothesis of a Growth Factor (GF)-responsive clock, involving a pathway of the non-essential cell cycle complex cyclin D/CDK4. We observe a variety of rational ratios of clock to cell cycle period, such as: 1:1, 3:2, 4:3, and 5:4. Finally, our protocols of period control are successful in effectively slowing down the cell cycle by the use of clock modulating inputs, some of which correspond to existing drugs.