Motifs, Control, and Stability

Abstract

Many of the detailed mechanisms by which bacteria express genes in response to various environmental signals are well-known. The molecular players underlying these responses are part of a bacterial transcriptional regulatory network (BTN). To explore the properties and evolution of such networks and to extract general principles, biologists have looked for common themes or motifs, and their interconnections, such as reciprocal links or feedback loops. A BTN motif can be thought of as a directed graph with regulatory interactions connecting transcription factors to their operon targets (the set of related bacterial genes that are transcribed together). For example, Figure 1A shows a BTN motif that describes a part of the transcriptional response to heat (and other) stressors. But biological networks are not just static physical constructs, and it is, in fact, their dynamical properties that determine their function. In this issue of PLoS Biology, Prill et al. [1] show that the relative abundance of small motifs in biological networks, including the BTN, may be explained by the stability of their dynamics across a wide range of cellular conditions. In a dynamical system, control engineers define "stability" as preservation of a specific behavior over time under some set of perturbations. The definitions of stability vary somewhat depending on the types of system, behavior, and perturbation specified [2]. For the BTN example, Prill et al. [1] study stability of gene expression levels, as modeled by a set of linear differential equations. Given interactions from a BTN motif, "structural stability" is robustness of stability to arbitrary signs and magnitudes of interactions. This is such a stringent notion of stability that it would be satisfied by few systems, yet Prill et al. [1] show that all BTN motifs are stable for all signs and magnitudes of interactions. For several other biological networks, they show a level of correlation between abundance and structural stability that is highly unlikely to occur at random. The significance of these results as well as those in recent related papers (see references in [1], particularly those of Alon and colleagues) can be better appreciated within the larger context of well-known concepts from biology and engineering, particularly control theory [3]. For additional mathematical details underlying the qualitative arguments presented here, see the online supplement (Text S1 and S2).

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