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

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...

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Bibliographic Details
Published in:Bulletin of mathematical biology Vol. 81; no. 5; pp. 1268 - 1302
Main Authors: Xu, Bin, Kang, Hye-Won, Jilkine, Alexandra
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2019
Springer Nature B.V
Subjects:
Algorithms
Bifurcations
Biological clocks
Calcium signalling
cdc42 GTP-Binding Protein - metabolism
Cdc42 protein
Cell Biology
Cell cycle
Cell Polarity
Circadian rhythms
Computer Simulation
Copy number
Diffusion rate
Economic models
Fission
Fourier Analysis
Guanosine triphosphatases
Kinetics
Life Sciences
Linear Models
Mathematical and Computational Biology
Mathematical Concepts
Mathematical models
Mathematics
Mathematics and Statistics
Models, Biological
Organic chemistry
Oscillations
Parameters
Reaction kinetics
Rho Guanine Nucleotide Exchange Factors - metabolism
Schizosaccharomyces - cytology
Schizosaccharomyces - metabolism
Schizosaccharomyces pombe Proteins - metabolism
Steady state
Stochastic models
Stochastic Processes
Stochasticity
Yeast
Stochastic model
Cell polarity
Biochemical oscillations
Noise-induced phenomena
ISSN:0092-8240, 1522-9602, 1522-9602
Online Access:Get full text
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Summary: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.
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ISSN:0092-8240
1522-9602
1522-9602
DOI:10.1007/s11538-019-00573-5