@article{10.1371/journal.pcbi.0020101, doi = {10.1371/journal.pcbi.0020101}, author = {Gianchandani, Erwin P AND Papin, Jason A AND Price, Nathan D AND Joyce, Andrew R AND Palsson, Bernhard O}, journal = {PLOS Computational Biology}, publisher = {Public Library of Science}, title = {Matrix Formalism to Describe Functional States of Transcriptional Regulatory Systems}, year = {2006}, month = {08}, volume = {2}, url = {https://doi.org/10.1371/journal.pcbi.0020101}, pages = {1-16}, 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.}, number = {8}, }