Extension of a genetic network model by iterative experimentation and mathematical analysis

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Abstract
Circadian clocks involve feedback loops that generate rhythmic expression of key genes. Molecular genetic studies in the higher plant Arabidopsis thaliana have revealed a complex clock network. The first part of the network to be identified, a transcriptional feedback loop comprising TIMING OF CAB EXPRESSION 1 (TOC1) , LATE ELONGATED HYPOCOTYL ( LHY ) and CIRCADIAN CLOCK ASSOCIATED 1 ( CCA1 ), fails to account for significant experimental data. We develop an extended model that is based upon a wider range of data and accurately predicts additional experimental results. The model comprises interlocking feedback loops comparable to those identified experimentally in other circadian systems. We propose that each loop receives input signals from light, and that each loop includes a hypothetical component that had not been explicitly identified. Analysis of the model predicted the properties of these components, including an acute light induction at dawn that is rapidly repressed by LHY and CCA1. We found this unexpected regulation in RNA levels of the evening‐expressed gene GIGANTEA ( GI ), supporting our proposed network and making GI a strong candidate for this component. ### Synopsis This study involves an iterative approach of mathematical modelling and experiment to develop an accurate mathematical model of the circadian clock in the higher plant Arabidopsis thaliana . Our approach is central to systems biology and should lead to a greater, quantitative understanding of the circadian clock, as well as being more widely relevant to research into genetic networks. The day–night cycle caused by the Earth's rotation affects most organisms, and has resulted in the evolution of the circadian clock. The circadian clock controls 24‐h rhythms in processes from metabolism to behaviour; in higher eukaryotes, the circadian clock controls the rhythmic expression of 5–10% of genes. In plants, the clock controls leaf and petal movements, the opening and closing of stomatal pores, the discharge of floral fragrances and many metabolic activities, especially those associated with photosynthesis. The relatively small number of components involved in the central circadian network makes it an ideal candidate for mathematical modelling of complex biological regulation. Genetic studies in a variety of model organisms have shown that the circadian rhythm is generated by a central network of between 6 and 12 genes. These genes form feedback loops generating a rhythm in mRNA production. One negative feedback loop in which a gene encodes a protein that, after several hours, turns off transcription is, in principle, capable of creating a circadian rhythm. However, real circadian clocks have proven to be more complicated than this, with interlocked feedback loops. Networks of this complexity are more easily understood through mathematical modelling. The clock mechanism in the model plant, A. thaliana , was first proposed to comprise a feedback loop in which two partially redundant genes, LATE ELONGATED HYPOCOTYL ( LHY ) and CIRCADIAN CLOCK ASSOCIATED 1 ( CCA1 ), repress the expression of their activator, TIMING OF CAB EXPRESSION 1 ( TOC1 ). We previously modelled this preliminary network and showed that it was not capable of recreating several important pieces of experimental data ([Locke et al , 2005][1]). Here, we extend the LHY/CCA1–TOC1 network in new mathematical models. To check the effects of each addition to the network, the outputs of the extended models are compared to published data and to new experiments. As is the case for most biological networks, the parameter values in our model, such as the translation rate of TOC1 protein, are unknown. We employ here an optimisation method, which works well with noisy and varied data and allows a global search of parameter space. This should ensure that the limitations we find in our networks are due to the network structure, and not to our parameter choices. Our final interlocked feedback loop model requires two hypothetical components, genes X and Y ([Figure 4][2]), but is the first Arabidopsis clock model to exhibit such a good correspondence with experimental data. The model simulates a residual short‐period oscillation in the cca1;lhy mutant, as characterised by our experiments. No single‐loop model is able to do this. Our model also matches experimental data under constant light (LL) conditions and correctly senses photoperiod. The model predicts an interlocked feedback loop structure similar to that seen in the circadian clock mechanisms of other organisms. The interlocked feedback loop model predicts a distinctive pattern of Y mRNA accumulation in the wild type (WT) and in the cca1;lhy double mutant, with Y mRNA levels increasing transiently at dawn. We designed an experiment to identify Y based on this prediction. GIGANTEA ( GI ) mRNA levels fit very well to our predicted profile for Y ([Figure 6][3]), identifying GI as a strong candidate for Y . The approach described here could act as a template for experimental biologists seeking to extend models of small genetic networks. Our results illustrate the usefulness of mathematical modelling in guiding experiments, even if the models are based on limited data. Our method provides a way of identifying suitable candidate networks and quantifying how these networks better describe a wide variety of experimental measurements. The characteristics of new putative genes are thereby obtained, facilitating the experimental search for new components. To facilitate future experimental design, we provide user‐friendly software that is specifically designed for numerical simulation of circadian experiments using models for several species ([Brown, 2004b][4]). *Footnote: Synopsis highlights were added on 5 July 2005. Mol Syst Biol. 1: 2005.0013 [1]: #ref-24 [2]: #F4 [3]: #F6 [4]: #ref-5