Delay models for the early embryonic cell cycle oscillator.

Jan Rombouts,Lendert Gelens,Alexandra Vandervelde

doi:10.1371/journal.pone.0194769

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.

Highlights

The cell cycle is one of the most fundamental processes in living organisms
In order to reduce this complexity, we focus on the fast cell cycles 2–12, where Tsai et al [20] have experimentally demonstrated that the ratio of Cdc25/Wee1 is increased such that Wee1 is no longer able to generate a bistable response of Cdk1 activity vs. cyclin B
The model is deceptively simple, we believe it captures the essence of the cell cycle oscillator and we demonstrate that implementing the time delay differently can have a large impact on the resulting oscillations

Summary

Introduction

The cell cycle is one of the most fundamental processes in living organisms. In order to survive and grow, a cell needs to proceed in a well-controlled fashion through DNA replication, mitosis and growth. Each cycle only takes about 25 minutes each (Fig 1A), where the cells switch between S phase and M phase, without any gap phases or checkpoints in between These regular oscillations even persist with exactly the same period when parthenogenetically activated (Fig 1B). Such SCWs are changes in the pigmentation of the egg cortex that occur before each cell divides [2], and it is believed that these SCWs are associated to waves traveling through the egg, triggering the cell to divide [3, 4] The fact that these early embryonic oscillations are so regular, and occur in the absence of checkpoints and fertilization, makes this cell cycle more amenable to detailed study, both in the lab and using mathematical models.

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Conclusion