Matrix formalism to describe functional states of transcriptional regulatory systems

Erwin P. Gianchandani, Jason A. Papin, Nathan D. Price, Andrew R. Joyce, Bernhard O. Palsson

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)902-917
Number of pages16
JournalPLoS computational biology
Volume2
Issue number8
DOIs
StatePublished - 2006
Externally publishedYes

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Modeling and Simulation
  • Ecology
  • Molecular Biology
  • Genetics
  • Cellular and Molecular Neuroscience
  • Computational Theory and Mathematics

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