Deterministic-Like Model Reduction for a Class of Multi-Scale Stochastic Differential Equations with Application to Biomolecular Systems
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ModelReductionSDE_TechnicalNote.pdf
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509.8 KB
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Author(s)
Herath, Narmada K
Del Vecchio, Domitilla
Date Issued
May 2018
Journal
IEEE Transactions on Automatic Control
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Herath, Narmada, and Domitilla Del Vecchio. “Deterministic-Like Model Reduction for a Class of Multi-Scale Stochastic Differential Equations with Application to Biomolecular Systems.” IEEE Transactions on Automatic Control (2018): 1–1.
Version
Author's final manuscript
Abstract
We consider a class of singularly perturbed stochastic differential equations with linear drift terms, and present a reduced-order model that approximates both slow and fast variable dynamics when the time-scale separation is large. We show that, on a finite time interval, moments of all orders of the slow variables for the original system become closer to those of the reduced-order model as time-scale separation is increased. A similar result holds for the first and second moments of the fast variable approximation. Biomolecular systems with linear propensity functions, modeled by the chemical Langevin equation fit the class of systems considered in this work. Thus, as an application example, we analyze the trade-offs between noise and information transmission in a typical gene regulatory network motif, for which both slow and fast variables are required.
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-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1109/TAC.2018.2829461
