title: Matrix formalism to describe functional states of transcriptional regulatory systems.
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.
authors.affiliation: Department of Biomedical Engineering, University of Virginia, Charlottesville, Virginia, USA.
authors.forename: Erwin P
authors.initials: EP
authors.lastname: Gianchandani
authors.forename: Jason A
authors.initials: JA
authors.lastname: Papin
authors.forename: Nathan D
authors.initials: ND
authors.lastname: Price
authors.forename: Andrew R
authors.initials: AR
authors.lastname: Joyce
authors.forename: Bernhard O
authors.initials: BO
authors.lastname: Palsson
mesh_terms: D019295:Computational Biology / Q000379:methods*; D004926:Escherichia coli / Q000235:genetics; D005786:Gene Expression Regulation; D016678:Genome / Q000235:genetics*; D023281:Genomics; D007763:Lac Operon / Q000235:genetics; D008957:Models, Genetic; D014158:Transcription, Genetic / Q000235:genetics*