The transition between stochastic and deterministic behavior in an excitable gene circuit

We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramat...

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Bibliographic Details
Published in:PloS one 2012-04, Vol.7 (4), p.e34536-e34536
Main Authors: Hilborn, Robert C, Brookshire, Benjamin, Mattingly, Jenna, Purushotham, Anusha, Sharma, Anuraag
Format: Article
Language:English
Subjects:
Analysis
Bifurcations
Biology
Chemical reactions
Circadian rhythm
Computer Science
Computer simulation
Copy number
Differential equations
DNA Copy Number Variations - genetics
DNA methylation
Dynamical systems
Epigenetic inheritance
Gene expression
Gene Regulatory Networks - genetics
Genes
Mathematical models
Mathematics
Methylation
Models, Genetic
Monte Carlo simulation
Nervous system
Noise
Ordinary differential equations
Oscillations
Phase transitions
Physics
Probability distribution
Proteins
Simulation
Statistical mechanics
Stochastic models
Stochastic Processes
Stochasticity
Transcription, Genetic - genetics
Yeast
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Summary:We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on the gene copy number and find very slow convergence to the large number limit near the bifurcation point. The implications for understanding the dynamics of gene circuits and other birth-death dynamical systems with small numbers of constituents are discussed.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0034536