Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺
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Author(s)
Herath, Narmada K
Del Vecchio, Domitilla
Date Issued
March 2018
Journal
The Journal of Chemical Physics
Publisher
American Institute of Physics (AIP)
Citation
Herath, Narmada and Domitilla Del Vecchio. “Reduced Linear Noise Approximation for Biochemical Reaction Networks with Time-Scale Separation: The Stochastic tQSSA⁺.” The Journal of Chemical Physics 148, 9 (March 2018): 094108 © 2018 Author(s)
Version
Final published version
Abstract
Biochemical reaction networks often involve reactions that take place on different time scales, giving rise to "slow" and "fast" system variables. This property is widely used in the analysis of systems to obtain dynamical models with reduced dimensions. In this paper, we consider stochastic dynamics of biochemical reaction networks modeled using the Linear Noise Approximation (LNA). Under time-scale separation conditions, we obtain a reduced-order LNA that approximates both the slow and fast variables in the system. We mathematically prove that the first and second moments of this reduced-order model converge to those of the full system as the time-scale separation becomes large. These mathematical results, in particular, provide a rigorous justification to the accuracy of LNA models derived using the stochastic total quasi-steady state approximation (tQSSA). Since, in contrast to the stochastic tQSSA, our reduced-order model also provides approximations for the fast variable stochastic properties, we term our method the "stochastic tQSSA⁺". Finally, we demonstrate the application of our approach on two biochemical network motifs found in gene-regulatory and signal transduction networks.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Department of Mechanical Engineering
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Creative Commons Attribution 4.0 International License
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DOI of Published Version
https://doi.org/10.1063/1.5012752
