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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Veröffentlicht in:	Bulletin of mathematical biology Jg. 81; H. 5; S. 1268 - 1302
Hauptverfasser:	Xu, Bin, Kang, Hye-Won, Jilkine, Alexandra
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2019 Springer Nature B.V
Schlagworte:	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
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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.
AbstractList	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. 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.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.
Author	Xu, Bin Jilkine, Alexandra Kang, Hye-Won
Author_xml	– sequence: 1 givenname: Bin surname: Xu fullname: Xu, Bin email: bxu2@nd.edu organization: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame – sequence: 2 givenname: Hye-Won surname: Kang fullname: Kang, Hye-Won organization: Department of Mathematics and Statistics, University of Maryland Baltimore County – sequence: 3 givenname: Alexandra surname: Jilkine fullname: Jilkine, Alexandra email: ajilkine@nd.edu organization: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame
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CitedBy_id	crossref_primary_10_1091_mbc_E20_10_0666 crossref_primary_10_1007_s11538_019_00575_3 crossref_primary_10_1016_j_jtbi_2020_110242 crossref_primary_10_3390_cells9081769
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Copyright	Society for Mathematical Biology 2019 Bulletin of Mathematical Biology is a copyright of Springer, (2019). All Rights Reserved. Society for Mathematical Biology 2019.
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Snippet	Oscillations occur in a wide variety of essential cellular processes, such as cell cycle progression, circadian clocks and calcium signaling in response to...
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SubjectTerms	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
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Title	Comparison of Deterministic and Stochastic Regime in a Model for Cdc42 Oscillations in Fission Yeast
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Volume	81
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