Extension of a genetic network model by iterative experimentation and mathematical analysis
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James C W Locke1,2,3, Megan M Southern1, László Kozma-Bognár1,4, Victoria Hibberd1, Paul E Brown1,3,4, Matthew S Turner2,3 & Andrew J Millar1,3,4
- Department of Biological Sciences, University of Warwick, Coventry, UK
- Department of Physics, University of Warwick, Coventry, UK
- Interdisciplinary Programme for Cellular Regulation, University of Warwick, Coventry, UK
- Present address: Institute of Molecular Plant Sciences, University of Edinburgh, Rutherford Building, Mayfield Road, Edinburgh EH9 3JH, UK
Correspondence to: Andrew J Millar1,3,4 Institute of Molecular Plant Sciences, University of Edinburgh, Rutherford Building, Mayfield Road, Edinburgh EH9 3JH, UK. Tel.: +44 1316513325; Fax: +44 1316505392; E-mail: Email: andrew.millar@ed.ac.uk
Received 5 April 2005; Accepted 7 June 2005; Published online 28 June 2005
Article highlights
- We extend the current model of the plant circadian clock, in order to accommodate new and published data. Throughout our model development we use a global parameter search to ensure that any limitations we find are due to the network architecture and not to our selection of the parameter values, which have not been determined experimentally. Our final model includes two, interlocked loops of gene regulation and is reminiscent of the circuit structures previously identified by experiments on insect and fungal clocks. It is the first Arabidopsis clock model to show such good correspondence to experimental data.
- Our interlocked feedback loop model predicts the regulation of two unknown components. Experiments motivated by these predictions identify the GIGANTEA gene as a strong candidate for one component, with an unexpected pattern of light regulation.*
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). 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), 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.
Figure 4
The interlocked feedback loop network. Left panel: Network diagram. Compared to Figure 1, TOC1 is activated by light indirectly via hypothetical gene Y. Y activates TOC1 transcription and both LHY and TOC1 repress Y transcription, forming a second feedback loop. Right panel: Simulation of LHY (dashed line) and TOC1 (solid line) mRNA levels for the optimal parameter set, representing WT (top) and cca1;lhy double mutant (bottom) in DD. Translation rate of LHY mRNA in simulated mutant is 1/1000 WT value. Period of WT in DD is 26 h and period of mutant is 17 h.
Figure 1
The single-loop LHY/CCA1–TOC1-X network. Left panel: Network diagram. LHY and CCA1 are modelled as a single gene, LHY (genes are boxed). Nuclear and cytoplasmic protein levels are grouped for clarity (shown encircled) and degradation is not shown. Light acutely activates LHY transcription at dawn and activates TOC1 transcription throughout the day. TOC1 activates a putative gene X, which in turn activates LHY. Nuclear LHY protein represses TOC1 transcription. Right panel: Simulation of mRNA levels for the optimal parameter set. In all figures, filled box above the panel represent dark interval and open or no box represent light interval. LHY mRNA (dotted line) peaks at dawn in LD12:12 and TOC1 (solid line) falls after dusk, due to the loss of light activation.
Full figure and legend (26K)Figures & Tables indexFull figure and legend (43K)Figures & Tables index
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), identifying GI as a strong candidate for Y.
Figure 6
GI is a candidate gene for Y. Simulated Y mRNA levels under LD12:12 and LL (dashed line). Data for GI mRNA levels (crosses), assayed by quantitative RT–PCR relative to the ACT2 control, from samples harvested at the times indicated. Left panel, WT; right panel, cca1;lhy. Highest value of data and simulation is set to 1, for each panel.
Full figure and legend (26K)Figures & Tables indexThe 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).
*Footnote: Synopsis highlights were added on 5 July 2005.
Acknowledgements
We are grateful to OE Biringen-Akman, D Salazar, JA Langdale, CD Westbrook and DA Rand for useful discussions, and to N Shariff for technical assistance. JCWL was supported by a postgraduate studentship from the Gatsby Charitable Foundation; MMS was supported by a postgraduate studentship from BBSRC; LKB was supported by an EMBO postdoctoral fellowship; experimental work was funded by grants G15231 and G19886 from BBSRC to AJM. Computer facilities were provided by the Centre for Scientific Computing at the University of Warwick.
References
- BrownPE (2004b) Circadian Modellinghttp://www.amillar.org/Downloads.html
- LockeJCW, MillarAJ, TurnerMS (2005) Modelling genetic networks with noisy and varied experimental data: the circadian clock in Arabidopsis thaliana. J Theor Biol234: 383–393 | Article | PubMed | ISI | ChemPort |
