Uncoupled analysis of stochastic reaction networks in fluctuating environments.
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While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze.In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model.Using several case studies, we demonstrate the significance of the approach.
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Affiliation: Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland.
ABSTRACT
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The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as, for instance, the fluctuations in ribosome copy numbers for a gene regulatory network. While several recent studies demonstrate the importance of accounting for such extrinsic components, the resulting models are typically hard to analyze. In this work we develop a general mathematical framework that allows to uncouple the network from its dynamic environment by incorporating only the environment's effect onto the network into a new model. More technically, we show how such fluctuating extrinsic components (e.g., chemical species) can be marginalized in order to obtain this decoupled model. We derive its corresponding process- and master equations and show how stochastic simulations can be performed. Using several case studies, we demonstrate the significance of the approach. Related in: MedlinePlus |
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Mentions: The mean in Eq.18 is just the unconditional mean of , while the derivative of the expected variance shows an additional negative term, causing it to be smaller than the unconditional variance. Let us for instance consider the case where follows a Cox-Ingersoll-Ross process governed by the SDE (19)with , and as real process parameters and as a standard Wiener process. Note that in this case, Eq. 18 reduces to an autonomous ODE, which for large yields the relative effective noise at stationarity, i.e.,(20)where can be considered a normalized timescale of (see section S.4 in S1 Text). The computation of the effective noise and its dependency on the environmental timescale is illustrated in Fig. 4. |
View Article: PubMed Central - PubMed
Affiliation: Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland.