Journal
JOURNAL OF THE ROYAL SOCIETY INTERFACE
Volume 13, Issue 114, Pages -Publisher
ROYAL SOC
DOI: 10.1098/rsif.2015.0772
Keywords
bursting noise; piecewise deterministic Markov process; stochastic processes; first passage times; weak noise limit; coarse-grained models
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Funding
- Engineering and Physical Sciences Research Council EPSRC (UK) [EP/K037145/1]
- EPSRC [EP/K037145/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/K037145/1] Funding Source: researchfish
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The dynamics of short-lived mRNA results in bursts of protein production in gene regulatory networks. We investigate the propagation of bursting noise between different levels of mathematical modelling and demonstrate that conventional approaches based on diffusion approximations can fail to capture bursting noise. An alternative coarse-grained model, the so-called piecewise deterministic Markov process (PDMP), is seen to outperform the diffusion approximation in biologically relevant parameter regimes. We provide a systematic embedding of the PDMP model into the landscape of existing approaches, and we present analytical methods to calculate its stationary distribution and switching frequencies.
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