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Bulletin of Mathematical Biology

, Volume 81, Issue 5, pp 1268–1302 | Cite as

Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast

  • Bin XuEmail author
  • Hye-Won Kang
  • Alexandra JilkineEmail author
Article

Abstract

Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to stimuli. It remains unclear how intrinsic stochasticity can influence these oscillatory systems. Here, we focus on oscillations of Cdc42 GTPase in fission yeast. We extend our previous deterministic model by Xu and Jilkine to construct a stochastic model, focusing on the fast diffusion case. We use SSA (Gillespie’s algorithm) to numerically explore the low copy number regime in this model, and use analytical techniques to study the long-time behavior of the stochastic model and compare it to the equilibria of its deterministic counterpart. Numerical solutions suggest noisy limit cycles exist in the parameter regime in which the deterministic system converges to a stable limit cycle, and quasi-cycles exist in the parameter regime where the deterministic model has a damped oscillation. Near an infinite period bifurcation point, the deterministic model has a sustained oscillation, while stochastic trajectories start with an oscillatory mode and tend to approach deterministic steady states. In the low copy number regime, metastable transitions from oscillatory to steady behavior occur in the stochastic model. Our work contributes to the understanding of how stochastic chemical kinetics can affect a finite-dimensional dynamical system, and destabilize a deterministic steady state leading to oscillations.

Keywords

Biochemical oscillations Stochastic model Cell polarity Noise-induced phenomena 

Notes

Acknowledgements

BX is supported by the Robert and Sara Lumpkins Endowment for Postdoctoral Fellows in Applied and Computational Math and Statistics at the University of Notre Dame. HWK is supported by NSF Grant DMS-1620403. AJ is supported by NSF Grant DMS-1615800. AJ and BX acknowledge the assistance of the Notre Dame Center for Research Computing (CRC).

Supplementary material

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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  1. 1.Department of Applied and Computational Mathematics and StatisticsUniversity of Notre DameNotre DameUSA
  2. 2.Department of Mathematics and StatisticsUniversity of Maryland Baltimore CountyBaltimoreUSA

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