Mathematical modeling of an oscillating gene circuit to unravel the circadian clock network of Arabidopsis thaliana

Abstract

The Arabidopsis thaliana circadian clock is an interconnected network highly tractable to systems approaches. Most elements in the transcriptional-translational oscillator were identified by genetic means and the expression of clock genes in various mutants led to the founding hypothesis of a positive-negative feedback loop being the core clock. The identification of additional clock genes beyond those defined in the core led to the use of systems approaches to decipher this angiosperm oscillator circuit. Kinetic modeling was first used to explain periodicity effects of various circadian mutants. This conformed in a flexible way to experimental details. Such observations allowed a recursive use of hypothesis generating from modeling, followed by experimental corroboration. More recently, the biochemical finding of new description of a DNA-binding activity for one class of clock components directed improvements in feature generation, one of which revealed that the core of the oscillator is a negative-negative feedback loop. The recursive use of modeling and experimental validation has thus revealed many essential transcriptional components that drive negative arms in the circadian oscillator. What awaits is to more fully describe the positive arms and an understanding of how additional pathways converge on the clock.

Keywords: Arabidopsis thaliana; circadian clock; hormone signal integration; light signal transduction; mathematical modeling; metabolic signal integration; stress signal integration; temperature acclimation.

FIGURE 1

Graphical outline of the mathematical A. thaliana clock models in historical order, showing the development from a simple positive–negative feedback model (Locke et al., 2005a) toward more complicated interconnected feedback loops (Locke et al., 2005b, 2006; Zeilinger et al., 2006; Pokhilko et al., 2010). The oscillator expands with he subsequent placement of an evening complex element (Kolmos et al., 2009). Recent experiments could prove the existence of an evening complex working directly on the morning loop (Herrero et al., 2012; Pokhilko et al., 2012). Activation elements are defined by a green positive arrow and a red negative arrow indicates repression, respectively. All models are centered at the CCA1/LHY hub to illustrate the directional movement of the models over publication time. Each model is described in the text and the models are named after the primary author and publication year. Note that two models define the 2006 efforts, and are the predominant models that has driven most recent circadian work.