Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation
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Del Vecchio_Stochastic analysis.pdf
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Author(s)
Ghaemi, Reza
Del Vecchio, Domitilla
Date Issued
June 2012
Journal
Proceedings of the 2012 American Control Conference (ACC)
Publisher
Institute of Electrical and Electronics Engineers
Citation
Ghaemi, Reza and Domitilla Del Vecchio. "Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation." In 2012 American Control Conference
Fairmont Queen Elizabeth, Montréal, Canada June 27-June 29, 2012. Proceedings. IEEE.
Version
Author's final manuscript
Abstract
The input/output dynamic behavior of a biomolecular system is affected by interconnection to other downstream systems through impedance-like effects called retroactivity. In this paper, we study the effects of retroactivity at the interconnection between two transcriptional modules, focusing on stochastic behavior. In particular, we describe the system through the Master equation and develop a singular perturbation theory to obtain a reduced Master equation. We prove that the solution of the original Master equation converges fast to an e neighbor of the solution of the reduced Master equation, in which e is the singular perturbation parameter. Our analysis shows that the upstream system and the downstream one are statistically independent at the steady state. However, the interconnection slows down the dynamics of both the expectation and the variance of the output of the upstream transcriptional module.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6315645
