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

Autor: Hye-Won Kang, Bin Xu, Alexandra Jilkine
Rok vydání: 2019
Předmět:
0301 basic medicine
Stochastic modelling
General Mathematics
Immunology
Dynamical system
Models
Biological
General Biochemistry
Genetics and Molecular Biology
03 medical and health sciences
0302 clinical medicine
Limit cycle
Schizosaccharomyces
Computer Simulation
Limit (mathematics)
Statistical physics
Infinite-period bifurcation
cdc42 GTP-Binding Protein
General Environmental Science
Pharmacology
Physics
Stochastic Processes
Steady state
Fourier Analysis
Oscillation
General Neuroscience
Cell Polarity
Mathematical Concepts
Kinetics
030104 developmental biology
Computational Theory and Mathematics
030220 oncology & carcinogenesis
Linear Models
Schizosaccharomyces pombe Proteins
General Agricultural and Biological Sciences
Algorithms
Rho Guanine Nucleotide Exchange Factors
Deterministic system
Zdroj: Bulletin of Mathematical Biology. 81:1268-1302
ISSN: 1522-9602
0092-8240
DOI: 10.1007/s11538-019-00573-5
Popis: 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.
Databáze: OpenAIRE
Externí odkaz: