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 2009-04, Vol.106 (16), p.6529-6534
Main Authors: Walczak, Aleksandra M, Mugler, Andrew, Wiggins, Chris H
Format: Article
Language:English
Subjects:
Approximation
Biology
Complex Systems: From Chemistry to Systems Biology Special Feature
Computational Biology - methods
Data transmission
death
Down-Regulation
equations
Gene expression
Gene Expression Regulation
genes
Information retrieval noise
Mathematical independent variables
Noise
Optimization
Physical Sciences
probability distribution
rev genes
Signal noise
Signal transduction
Signal Transduction - genetics
Spectral methods
Stochastic models
Stochastic Processes
transcription (genetics)
Transcription, Genetic
Transfer functions
Up-Regulation
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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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.0811999106