A stochastic spectral analysis of transcriptional regulatory cascades

The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here, we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS Vol. 106; no. 16; p. 6529
Main Authors: Walczak, Aleksandra M, Mugler, Andrew, Wiggins, Chris H
Format: Journal Article
Language:English
Published: United States 21.04.2009
Subjects:
Computational Biology - methods
Down-Regulation
Gene Expression Regulation
Signal Transduction - genetics
Stochastic Processes
Transcription, Genetic
Up-Regulation
ISSN:1091-6490, 1091-6490
Online Access:Get more information
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Summary:The past decade has seen great advances in our understanding of the role of noise in gene regulation and the physical limits to signaling in biological networks. Here, we introduce the spectral method for computation of the joint probability distribution over all species in a biological network. The spectral method exploits the natural eigenfunctions of the master equation of birth-death processes to solve for the joint distribution of modules within the network, which then inform each other and facilitate calculation of the entire joint distribution. We illustrate the method on a ubiquitous case in nature: linear regulatory cascades. The efficiency of the method makes possible numerical optimization of the input and regulatory parameters, revealing design properties of, e.g., the most informative cascades. We find, for threshold regulation, that a cascade of strong regulations converts a unimodal input to a bimodal output, that multimodal inputs are no more informative than bimodal inputs, and that a chain of up-regulations outperforms a chain of down-regulations. We anticipate that this numerical approach may be useful for modeling noise in a variety of small network topologies in biology.
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ISSN:1091-6490
1091-6490
DOI:10.1073/pnas.0811999106