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 impact of environmental fluctuations on a dynamical system of interest is as diverse as the timescale on which they operate. For instance, extrinsic noise in the context of gene expression might be slowly varying (e.g., correlates well with the cell-cycle [29], [30]), while fluctuations in transcription factor abundance might be significantly faster than the expression kinetics downstream. From a technical point of view, timescales range from constant environmental conditions that are random but fixed [31] to regimes where the fluctuations are very fast, such that quasi-steady-state (QSS) assumptions become applicable [16], [32]. A QSS-based approach for simulating a system in the presence of extrinsic noise corresponds to simulating the conditional CTMC , where is replaced by the mean of . Alternatively, one may try to replace a fluctuating environment through a random but fixed environment of same variance but this leads to an overestimation of the process variance in [5], as discussed in a later section. To investigate the two above simplifying assumptions and compare them to the exact solution obtained via SSA and MSA, we performed a simulation study on a linear three-stage birth-death model given in Fig. 3a. In this case only species C is considered of interest whose uncoupled dynamics are obtained by marginalizing A and B. The results from Fig. 3b and Fig. 3c show that MSA facilitates accurate and fast approximations also under intermediate environmental time-scales where QSS- and static environmental assumptions break down. |
View Article: PubMed Central - PubMed
Affiliation: Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland.