Over 50 years ago, Monod and Jacob argued that the mechanisms controlling expression of individual genes in bacteria could be interconnected to generate genetic regulatory circuits that would underlie vital functions including oscillation and differentiation.1 The basic idea was that a diffusible protein, called a transcription factor, which is coded by one gene, could bind to the DNA molecule to modulate the rate of production of itself or other genes. Thus, the DNA combined with the transcription factors generated networks where the nodes of the network were the genes, and the transcription factors led to interactions between the genes. Although Jacob and Monod did not provide mathematical analyses, their prescient suggestions provided a basis for theoretical models of genetic control in terms of logical switching networks in which the logical states of genes updated following specific delays4,5,6 or in which there was synchronous updating of all variables.7 Alternatively, the logical structure and relationships could be embedded in differential equations8 as either discontinuous switching functions or sigmoidal functions.
Subsequent to these early papers, there has been a continuing research in theoretical models of genetic networks.9,10 However, sparked by advances in molecular biology and synthetic biology,11,12 there has been an accelerating interest in these theoretical models. This Focus issue gives an overview of many of the important advances and current research directions. In Sec. 2, we summarize the theoretical approaches to the analysis of models of genetic networks that are of particular interest to the nonlinear dynamics community. We discuss the applications of theoretical approaches to analysis of naturally occurring biological systems in Sec. 3 and to synthetic biology in Sec. 4.
Introduction to Focus Issue: Quantitative Approaches to Genetic Networks
Réka Albert, James J. Collins, Leon Glass
Chaos 23, 025001 (2013)