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Biological clocks in theory and experiments Current: Megan Southern Laszlo Kozma-Bognar Kieron Edwards Vacancy ! Paul Brown James Locke Domingo Salazar Ozgur Akman Vacancy ! Past: Simon Thain Kamal Swarup Ruth Bastow Harriet McWatters Shigeru Hanano Seth Davis Mandy Dowson-Day Giovanni Murtas Neeraj Salathia Maria Eriksson Anthony Hall Alex Morton Boris Shulgin Nickiesha Bromley Victoria Hibberd www.amillar.org Collaborators IPCR Matthew Turner (Physics) David Rand (Maths) Bärbel Finkenstädt (Statistics) Mark Muldoon and David Broomhead (Manchester) Lorenz Wernisch (Birkbeck) Antony Dodd, Alex Webb, Julian Hibberd (Cambridge) Ferenc Nagy (Szeged) Eberhard Schäfer, Stefan Kircher (Freiburg) Mark Doyle, Scott Michaels, Rick Amasino (Madison) Graham King (HRI), Mike Kearsey (Birmingham) Funding: BBSRC, Gatsby, EPSRC, DTI Genome-wide circadian rhythms 0h Time in LL (h) 26 30 34 38 42 46 50 54 58 62 66 70 74 ~ 12% RNA transcripts rhythmic in white light ~ 3,000 genes of 22,000 on array • Functional clustering • 68% of rhythmic transcripts also stress-regulated, (Kreps et al. 2002) Edwards et al. unpublished Mutant plants identify genes in the clockwork ? Alabadi et al., 2001 • Negative regulation during the day - CCA1/LHY • Positive regulation at night • Mathematical model to test potential for regulation Luciferase (LUC) reporter CAB/ LHCB LUC protein code camera + • Luminescence reflects transcription rate of promoter • Unstable activity reports dynamic regulation • Spatial resolution, high throughput LUC: identifies mutants in clock genes elf3-1 WT elf3-7 1000 Photons/ seedling/ 25mins 800 EARLY-FLOWERING 3 (elf3): arhythmic in light CAB:LUC rhythm 600 Hicks et al, Science, 1996 McWatters et al., Nature, 2000 Reed et al., Plant Phys. 2000 400 200 0 0 24 48 72 96 120 30000 Time (hours) CCA1:LUC rhythm Counts/ sdlg/ 20000 second EARLY-FLOWERING 4 (elf4): arhythmic in all conditions, Fails to express CCA1 Doyle et al., Nature, 2000 WT 10000 elf4 0 0 12 24 36 Time (hours) 48 60 The circadian clock in Arabidopsis Acute light response cry1, 2 CAB TOC1 phyA, B, D + 3600 genes LHY CCA1 morphology Oscillator Input Overt Rhythms ELF3 zeitnehmer (PHY/CRY rhythms) Modelling Design principles Extension of network Projects in circadian rhythms - Current Data Data analysis Reporter genes RNA (PCR, arrays) Mutant plants Data preparation Rhythm detection Parameter estimation (MCMC, cost functions) Clock mechanism. Functions of interlocking loops, multiple light inputs Understanding Models Central loop: ODE, SDE, Simplified, etc. Predictions Software IRCs, Flexibility Model analysis dLHYm = dt vT TOCn4 kT + TOCn4 - vLCLHYm k1 + LHYm kd1 LHYm dLHYc = kLLHYm – kLCLHYc + kLPLHYn - vDCLHYc dt kLC + LHYc dLHYn = kLCLHYc – kLPLHYn + vDNLHYn dt kLN + LHYn dTOCm dt = vTOC kLHY + (LHYn)4 - vDTTOCm - kd TOCm kT + TOCm dTOCc = kTOCTOCm – kTCTOCc + kTPTOCn - vDTTOCc dt kTC + TOCc dTOCn = kTCTOCc – kTPTOCn + vDTPTOCn dt kTP + TOCn Single-loop network model Locke, Millar and Turner, J Theor Biol, 2005. Global parameter search. Random Sobol Interlocking loop model for Arabidopsis clock TOC1 cca1;lhy TOC1 Y Y Time (h) TOC1 mRNA LHY X WT TOC1 mRNA LHY LHY mRNA X LHY mRNA • Model- J. Locke • Hypothetical components X, Y • Cost function fit to WT and mutant behaviour • Predicts X and Y expression Experiments to identify Y turn up a good candidate • Prediction = dashed line WT • M. Southern tested candidate genes by qRTPCR. Data = crosses cca1;lhy • Unexpected light response of GIGANTEA RNA matches prediction • GI also matches other predictions for Y from literature Projects in circadian rhythms - Current Data Data analysis Data preparation Rhythm detection Parameter estimation (MCMC, cost functions) Understanding Models Central loop: ODE, SDE, Simplified, etc. Model analysis Data analysis: CAB:LUC in 16h L:8h D Morton, Finkenstadt raw prepared synthesis rate Parameter estimation: simple model for synthesis rate dY (t) Y (t) dt Model: sde version of p IT e %(t) a0 ak cos kt bk sin kt k 1 (t) %(T ) cIT e where T t d mod L Comparison of WT and elf3 mutant waveforms WT elf3 mutant clock effect • Quantify distinct features within the timeseries • Now apply to parameters of simple clock models Projects in circadian rhythms - Current Data Data analysis Reporter genes RNA (PCR, arrays) Mutant plants Data preparation Rhythm detection Parameter estimation (MCMC, cost functions) Clock mechanism. Functions of interlocking loops, multiple light inputs Understanding Models Central loop: ODE, SDE, Simplified, etc. Predictions Software IRCs, Flexibility Model analysis Projects in circadian rhythms – Future collaboration Data Data analysis Reduced/synthetic Fitting directly systems to multiple data types Protein data Network inference (2-D gels) Database (dynamic Bayes nets) Biochemistry (parameters) Models Photoreceptors, secondary loops Software Stochastic processes Noise (internal and external) Understanding Adding to model Inverse problem Model analysis