XB-ART-54729

PLoS One
January 1, 2018;
13
(3):
e0194769.
## Delay models for the early embryonic cell cycle oscillator.

Rombouts J
,
Vandervelde A
,
Gelens L
.

Abstract

Time delays are known to play a crucial role in generating biological oscillations. The early embryonic cell cycle in the frog Xenopus laevis is one such example. Although various mathematical models of this oscillating system exist, it is not clear how to best model the required time delay. Here, we study a simple cell cycle model that produces oscillations due to the presence of an ultrasensitive, time-delayed negative feedback loop. We implement the time delay in three qualitatively different ways, using a fixed time delay, a distribution of time delays, and a delay that is state-dependent. We analyze the dynamics in all cases, and we use experimental observations to interpret our results and put constraints on unknown parameters. In doing so, we find that different implementations of the time delay can have a large impact on the resulting oscillations.

PubMed ID: 29579091

PMC ID: PMC5868829

Article link: PLoS One

Species referenced: Xenopus laevis

Genes referenced: cdk1

GO keywords: cell division

Article Images: [+] show captions

References [+] :

Anderson,

*Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of Xenopus laevis Development.*2017, Pubmed, Xenbase
Anderson,

Ashyraliyev,

Babtie,

Barrio,

Bollen,

Chang,

Eurich,

Feng,

Ferrell,

François,

Félix,

Gelens,

Gelens,

Goldbeter,

Gonze,

Goodwin,

Hara,

Heim,

Hoffmann,

Jüngling,

Kim,

Leier,

Lewis,

Lillacci,

Ma,

Mahaffy,

Marlovits,

Martínez-Llinàs,

Mattingly,

McGowan,

Meyer,

Mitchell,

Mochida,

Mochida,

Mochida,

Monk,

Novak,

Novák,

Pines,

Pomerening,

Pomerening,

Rateitschak,

Ruoff,

Salazar,

Salazar,

Sha,

Srividhya,

Srividhya,

Tang,

Trunnell,

Tsai,

Yang,

Zhu,

*Desynchronizing Embryonic Cell Division Waves Reveals the Robustness of Xenopus laevis Development.*2017, Pubmed , XenbaseAshyraliyev,

*Systems biology: parameter estimation for biochemical models.*2009, PubmedBabtie,

*How to deal with parameters for whole-cell modelling.*2017, PubmedBarrio,

*Reduction of chemical reaction networks through delay distributions.*2013, PubmedBollen,

*Mitotic phosphatases: from entry guards to exit guides.*2010, PubmedChang,

*Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle.*2013, Pubmed , XenbaseEurich,

*Distributed delays stabilize ecological feedback systems.*2005, PubmedFeng,

*Modeling delayed processes in biological systems.*2016, PubmedFerrell,

*Modeling the cell cycle: why do certain circuits oscillate?*2011, Pubmed , XenbaseFrançois,

*Adaptive temperature compensation in circadian oscillations.*2013, PubmedFélix,

*Triggering of cyclin degradation in interphase extracts of amphibian eggs by cdc2 kinase.*1990, Pubmed , XenbaseGelens,

*Spatial trigger waves: positive feedback gets you a long way.*2015, Pubmed , XenbaseGelens,

*How Does the Xenopus laevis Embryonic Cell Cycle Avoid Spatial Chaos?*2016, Pubmed , XenbaseGoldbeter,

*A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase.*1991, PubmedGonze,

*The Goodwin model: behind the Hill function.*2014, PubmedGoodwin,

*Oscillatory behavior in enzymatic control processes.*1966, PubmedHara,

*A cytoplasmic clock with the same period as the division cycle in Xenopus eggs.*1980, Pubmed , XenbaseHeim,

*Protein phosphatase 1 is essential for Greatwall inactivation at mitotic exit.*2016, Pubmed , XenbaseHoffmann,

*Phosphorylation and activation of human cdc25-C by cdc2--cyclin B and its involvement in the self-amplification of MPF at mitosis.*1993, Pubmed , XenbaseJüngling,

*Determining the sub-Lyapunov exponent of delay systems from time series.*2015, PubmedKim,

*Substrate competition as a source of ultrasensitivity in the inactivation of Wee1.*2007, Pubmed , XenbaseLeier,

*Exact model reduction with delays: closed-form distributions and extensions to fully bi-directional monomolecular reactions.*2014, PubmedLewis,

*Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator.*2003, PubmedLillacci,

*Parameter estimation and model selection in computational biology.*2010, PubmedMa,

*Detection of time delays and directional interactions based on time series from complex dynamical systems.*2018, PubmedMahaffy,

*Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis.*1998, PubmedMarlovits,

*Modeling M-phase control in Xenopus oocyte extracts: the surveillance mechanism for unreplicated DNA.*1998, Pubmed , XenbaseMartínez-Llinàs,

*Dynamical properties induced by state-dependent delays in photonic systems.*2015, PubmedMattingly,

*The Design Space of the Embryonic Cell Cycle Oscillator.*2017, Pubmed , XenbaseMcGowan,

*Human Wee1 kinase inhibits cell division by phosphorylating p34cdc2 exclusively on Tyr15.*1993, PubmedMeyer,

*Distributed delays stabilize neural feedback systems.*2008, PubmedMitchell,

*Effect of state-dependent delay on a weakly damped nonlinear oscillator.*2011, PubmedMochida,

*Protein phosphatases and their regulation in the control of mitosis.*2012, PubmedMochida,

*Greatwall phosphorylates an inhibitor of protein phosphatase 2A that is essential for mitosis.*2011, Pubmed , XenbaseMochida,

*Two Bistable Switches Govern M Phase Entry.*2018, PubmedMonk,

*Oscillatory expression of Hes1, p53, and NF-kappaB driven by transcriptional time delays.*2003, PubmedNovak,

*Numerical analysis of a comprehensive model of M-phase control in Xenopus oocyte extracts and intact embryos.*1994, Pubmed , XenbaseNovák,

*Design principles of biochemical oscillators.*2008, PubmedPines,

*Cubism and the cell cycle: the many faces of the APC/C.*2011, PubmedPomerening,

*Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2.*2003, Pubmed , XenbasePomerening,

*Systems-level dissection of the cell-cycle oscillator: bypassing positive feedback produces damped oscillations.*2005, Pubmed , XenbaseRateitschak,

*Intracellular delay limits cyclic changes in gene expression.*2007, PubmedRuoff,

*The Goodwin oscillator: on the importance of degradation reactions in the circadian clock.*2000, PubmedSalazar,

*Versatile regulation of multisite protein phosphorylation by the order of phosphate processing and protein-protein interactions.*2007, PubmedSalazar,

*Multisite protein phosphorylation--from molecular mechanisms to kinetic models.*2009, PubmedSha,

*Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts.*2003, Pubmed , XenbaseSrividhya,

*A simple time delay model for eukaryotic cell cycle.*2007, PubmedSrividhya,

*The effects of time delays in a phosphorylation-dephosphorylation pathway.*2007, PubmedTang,

*Two distinct mechanisms for negative regulation of the Wee1 protein kinase.*1994, Pubmed , XenbaseTrunnell,

*Ultrasensitivity in the Regulation of Cdc25C by Cdk1.*2011, Pubmed , XenbaseTsai,

*Changes in oscillatory dynamics in the cell cycle of early Xenopus laevis embryos.*2014, Pubmed , XenbaseYang,

*The Cdk1-APC/C cell cycle oscillator circuit functions as a time-delayed, ultrasensitive switch.*2013, Pubmed , XenbaseZhu,

*Incomplete phase-space method to reveal time delay from scalar time series.*2016, Pubmed