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Biophysical Journal 86:1922-1945 (2004)
© 2004 The Biophysical Society

A Nonlinear Discrete Dynamical Model for Transcriptional Regulation: Construction and Properties

John Goutsias * and Seungchan Kim {dagger}

* The Whitaker Biomedical Engineering Institute, The Johns Hopkins University, Baltimore, Maryland 21218; and {dagger} Translational Genomics Research Institute, Phoenix, Arizona 85004

Correspondence: Address reprint requests to John Goutsias, E-mail: goutsias{at}jhu.edu.

Transcriptional regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties, by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this article, we revisit the problem of mathematically modeling transcriptional regulation. First, we adopt a biologically motivated continuous model for gene transcription and mRNA translation, based on first-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. Then, we view the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, motivates us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics allow us to specify the nonlinearities underlying cis-regulation and to include both activators and repressors as well as the notion of regulatory modules in our formulation. We show that the steady-state behavior of the proposed discrete dynamical system is identical to that of the continuous model. We discuss several aspects of our model, related to homeostatic and epigenetic regulation as well as to Boolean networks, and elaborate on their significance. Simulations of transcriptional regulation of a hypothetical metabolic pathway illustrate several properties of our model, and demonstrate that a nonlinear discrete dynamical system may be effectively used to model transcriptional regulation in a biologically relevant way.




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