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Matrix Formalism to Describe Functional States of Transcriptional Regulatory Systems

Authors
Journal
PLoS Computational Biology
1553-734X
Publisher
Public Library of Science
Publication Date
Volume
2
Issue
8
Identifiers
DOI: 10.1371/journal.pcbi.0020101
Keywords
  • Research Article
  • Bioinformatics - Computational Biology
  • Biotechnology
  • Genetics/Genomics
  • Microbiology
  • Systems Biology
  • Eubacteria
  • Escherichia Coli
  • Lac Operon
Disciplines
  • Design
  • Ecology
  • Geography
  • Mathematics

Abstract

Complex regulatory networks control the transcription state of a genome. These transcriptional regulatory networks (TRNs) have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals. The Boolean formalism results in a series of regulatory rules for the individual genes of a TRN that in turn can be used to link environmental cues to the transcription state of a genome, thereby forming a complete transcriptional regulatory system (TRS). Herein, we develop a formalism that represents such a set of regulatory rules in a matrix form. Matrix formalism allows for the systemic characterization of the properties of a TRS and facilitates the computation of the transcriptional state of the genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a TRS as it becomes available. In this study, the regulatory network matrix, R, for a prototypic TRS is characterized and the fundamental subspaces of this matrix are described. We illustrate how the matrix representation of a TRS coupled with its environment (R*) allows for a sampling of all possible expression states of a given network, and furthermore, how the fundamental subspaces of the matrix provide a way to study key TRS features and may assist in experimental design.

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