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Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks
Abstract Noise is often indispensable to key cellul …
Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces.
actions with two-dimensional state spaces.  +
Authors X. Flora Meng, Ania-Ariadna Baetica, Vipul Singhal, Richard M. Murray  +
Flags Biocircuits  +
Funding Theory-Based Engineering of Biomolecular Circuits in Living Cells +
ID 2017f  +
Source ''Royal Society Interface'', 14(130), 2017  +
Tag mbsm17-rsi  +
Title Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks +
Type Journal paper  +
Categories Papers
Modification date
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26 January 2019 15:54:42  +
URL
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https://doi.org/10.1098/rsif.2017.0157  +
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Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks + Title
 

 

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