Open AccessDelay models for the early embryonic cell cycle oscillator
Author(s) -
Jan Rombouts,
Alexandra Vandervelde,
Lendert Gelens
Publication year - 2018
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0194769
Subject(s) - xenopus , control theory (sociology) , computer science , limit cycle , dynamics (music) , negative feedback , biological system , physics , biology , nonlinear system , voltage , artificial intelligence , biochemistry , control (management) , quantum mechanics , gene , acoustics
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.