A compact model for the complex plant circadian clock

Frontiers in Plant Science

Volumn 7, Issue FEB2016, 2016, Pages

  De Caluwé, Joëlle ^a   Xiao, Qiying ^a   Hermans, Christian ^a   Verbruggen, Nathalie ^a   Leloup, Jean Christophe ^a   Gonze, Didier ^a  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

Author keywords

Arabidopsis thaliana; Circadian rhythms; Clock mutants; Entrainment by light dark cycles; Mathematical model

Indexed keywords

EID: 84958525162     PISSN: None     EISSN: 1664462X     Source Type: Journal    
DOI: 10.3389/fpls.2016.00074     Document Type: Article

References (88)

1. Akman, O. E., Watterson, S., Parton, A., Binns, N., Millar, A. J., and Ghazal, P. (2012). Digital clocks: simple Boolean models can quantitatively describe circadian systems. J. R. Soc. Interf. 9, 2365-2382. doi: 10.1098/rsif.2012.0080.
2. Alabadí, D., Oyama, T., Yanovsky, M. J., Harmon, F. G., Más, P., and Kay, S. A. (2001). Reciprocal regulation between TOC1 and LHY/CCA1 within the Arabidopsis circadian clock. Science 293, 880-883. doi: 10.1126/science.1061320.
3. Alabadí, D., Yanovsky, M. J., Más, P., Harmer, S. L., and Kay, S. A. (2002). Critical role for CCA1 and LHY in maintaining circadian rhythmicity in Arabidopsis. Curr. Biol. 12, 757-761. doi: 10.1016/S0960-9822(02)00815-1.
4. Anwer, M. U., Boikoglou, E., Herrero, E., Hallstein, M., Davis, A. M., Velikkakam James, G., et al. (2014). Natural variation reveals that intracellular distribution of ELF3 protein is associated with function in the circadian clock. eLife 3:e02206. doi: 10.7554/eLife.02206.
5. Barak, S., Tobin, E. M., Andronis, C., Sugano, S., and Green, R. M. (2000). All in good time: the Arabidopsis circadian clock. Trends Plant Sci. 5, 517-522. doi: 10.1016/S1360-1385(00)01785-4.
6. Bolouri Moghaddam, M. R., and Van den Ende, W. (2013). Sweet immunity in the plant circadian regulatory network. J. Exp. Bot. 64, 1439-1449. doi: 10.1093/jxb/ert046.
7. Corellou, F., Schwartz, C., Motta, J.-P., Djouani-Tahri, E. B., Sanchez, F., and Bouget, F.-Y. (2009). Clocks in the green lineage: comparative functional analysis of the circadian architecture of the picoeukaryote ostreococcus. Plant Cell 21, 3436-3449. doi: 10.1105/tpc.109.068825.
8. Dalchau, N. (2012). Understanding biological timing using mechanistic and black-box models. New Phytol. 193, 852-858. doi: 10.1111/j.1469-8137.2011.04004.x.
9. Dalchau, N., Baek, S.-J., Briggs, H. M., Robertson, F. C., Dodd, A. N., Gardner, M. J., et al. (2011). The circadian oscillator gene GIGANTEA mediates a long-term response of the Arabidopsis thaliana circadian clock to sucrose. Proc. Natl. Acad. Sci. U.S.A. 108, 5104-5109. doi: 10.1073/pnas.1015452108.
10. Dixon, L. E., Hodge, S. K., van Ooijen, G., Troein, C., Akman, O. E., and Millar, A. J. (2014). Light and circadian regulation of clock components aids flexible responses to environmental signals. New Phytol. 203, 568-577. doi: 10.1111/nph.12853.
11. Dixon, L. E., Knox, K., Kozma-Bognar, L., Southern, M. M., Pokhilko, A., and Millar, A. J. (2011). Temporal repression of core circadian genes is mediated through EARLY FLOWERING 3 in Arabidopsis. Curr. Biol. 21, 120-125. doi: 10.1016/j.cub.2010.12.013.
12. Dodd, A. N., Belbin, F. E., Frank, A., and Webb, A. A. R. (2015). Interactions between circadian clocks and photosynthesis for the temporal and spatial coordination of metabolism. Front. Plant Sci. 6:245. doi: 10.3389/fpls.2015.00245.
13. Dodd, A. N., Salathia, N., Hall, A., Kévei, E., Tóth, R., Nagy, F., et al. (2005). Plant circadian clocks increase photosynthesis, growth, survival, and competitive advantage. Science 309, 630-633. doi: 10.1126/science.1115581.
14. Doyle, M. R., Davis, S. J., Bastow, R. M., McWatters, H. G., Kozma-Bognár, L., Nagy, F., et al. (2002). The ELF4 gene controls circadian rhythms and flowering time inArabidopsis thaliana. Nature 419, 74-77. doi: 10.1038/nature00954.
15. Edwards, K. D., Akman, O. E., Knox, K., Lumsden, P. J., Thomson, A. W., Brown, P. E., et al. (2010). Quantitative analysis of regulatory flexibility under changing environmental conditions. Mol. Syst. Biol. 6:424. doi: 10.1038/msb.2010.81.
16. Ermentrout, B. (2002). Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students. Philadelphia: SIAM.
17. Farré, E. M., Harmer, S. L., Harmon, F. G., Yanovsky, M. J., and Kay, S. A. (2005). Overlapping and distinct roles of PRR7 and PRR9 in the Arabidopsis circadian clock.Curr. Biol. 15, 47-54. doi: 10.1016/j.cub.2004.12.067.
18. Farré, E. M., and Kay, S. A. (2007). PRR7 protein levels are regulated by light and the circadian clock in Arabidopsis. Plant J. 52, 548-560. doi: 10.1111/j.1365-313X.2007.03258.x.
19. Fogelmark, K., and Troein, C. (2014). Rethinking transcriptional activation in the Arabidopsis circadian clock. PLoS Comput. Biol. 10:e1003705. doi: 10.1371/journal.pcbi.1003705.
20. Fujiwara, S., Wang, L., Han, L., Suh, S.-S., Salomé, P. A., McClung, C. R., et al. (2008). Post-translational regulation of the Arabidopsis circadian clock through selective proteolysis and phosphorylation of pseudo-response regulator proteins. J. Biol. Chem. 283, 23073-23083. doi: 10.1074/jbc.M803471200.
21. Gendron, J. M., Pruneda-Paz, J. L., Doherty, C. J., Gross, A. M., Kang, S. E., and Kay, S. A. (2012). Arabidopsis circadian clock protein, TOC1, is a DNA-binding transcription factor. Proc. Natl. Acad. Sci. U.S.A. 109, 3167-3172. doi: 10.1073/pnas.1200355109.
22. Green, R. M., Tingay, S., Wang, Z.-Y., and Tobin, E. M. (2002). Circadian rhythms confer a higher level of fitness to Arabidopsis plants. Plant Physiol. 129, 576-584. doi: 10.1104/pp.004374.
23. Guerriero, M. L., Akman, O. E., and van Ooijen, G. (2014). Stochastic models of cellular circadian rhythms in plants help to understand the impact of noise on robustness and clock structure. Front. Plant Sci. 5:564. doi: 10.3389/fpls.2014.00564.
24. Guerriero, M. L., Pokhilko, A., Fernández, A. P., Halliday, K. J., Millar, A. J., and Hillston, J. (2012). Stochastic properties of the plant circadian clock. J. R. Soc. Interf. 9, 744-756. doi: 10.1098/rsif.2011.0378.
25. Haydon, M. J., Mielczarek, O., Robertson, F. C., Hubbard, K. E., and Webb, A. A. R. (2013). Photosynthetic entrainment of the Arabidopsis thaliana circadian clock.Nature 502, 689-692. doi: 10.1038/nature12603.
26. Haydon, M. J., Román, Á., and Arshad, W. (2015). Nutrient homeostasis within the plant circadian network. Front. Plant Sci. 6:299. doi: 10.3389/fpls.2015.00299.
27. Hazen, S. P., Schultz, T. F., Pruneda-Paz, J. L., Borevitz, J. O., Ecker, J. R., and Kay, S. A. (2005). LUX ARRHYTHMO encodes a Myb domain protein essential for circadian rhythms. Proc. Natl. Acad. Sci. U.S.A. 102, 10387-10392. doi: 10.1073/pnas.0503029102.
28. Helfer, A., Nusinow, D. A., Chow, B. Y., Gehrke, A. R., Bulyk, M. L., and Kay, S. A. (2011). LUX ARRHYTHMO encodes a nighttime repressor of circadian gene expression in the Arabidopsis core clock. Curr. Biol. 21, 126-133. doi: 10.1016/j.cub.2010.12.021.
29. Hermans, C., Vuylsteke, M., Coppens, F., Craciun, A., Inzé, D., and Verbruggen, N. (2010a). Early transcriptomic changes induced by magnesium deficiency inArabidopsis thaliana reveal the alteration of circadian clock gene expression in roots and the triggering of abscisic acid-responsive genes. New Phytol. 187, 119-131. doi: 10.1111/j.1469-8137.2010.03258.x.
30. Hermans, C., Vuylsteke, M., Coppens, F., Cristescu, S. M., Harren, F. J. M., Inzé, D., et al. (2010b). Systems analysis of the responses to long-term magnesium deficiency and restoration in Arabidopsis thaliana. New Phytol. 187, 132-144. doi: 10.1111/j.1469-8137.2010.03257.x.
31. Hicks, K. A., Albertson, T. M., and Wagner, D. R. (2001). EARLY FLOWERING 3 encodes a novel protein that regulates circadian clock function and flowering in Arabidopsis. Plant Cell 13, 1281-1292. doi: 10.1105/tpc.13.6.1281.
32. Hsu, P. Y., Devisetty, U. K., and Harmer, S. L. (2013). Accurate timekeeping is controlled by a cycling activator in Arabidopsis. eLife 2:e00473. doi: 10.7554/eLife.00473.
33. Huang, W., Pérez-García, P., Pokhilko, A., Millar, A. J., Antoshechkin, I., Riechmann, J. L., et al. (2012). Mapping the core of the Arabidopsis circadian clock defines the network structure of the oscillator. Science 336, 75-79. doi: 10.1126/science.1219075.
34. Imaizumi, T., Schultz, T. F., Harmon, F. G., Ho, L. A., and Kay, S. A. (2005). FKF1 F-Box protein mediates cyclic degradation of a repressor of CONSTANS in Arabidopsis.Science 309, 293-297. doi: 10.1126/science.1110586.
35. Ito, S., Nakamichi, N., Kiba, T., Yamashino, T., and Mizuno, T. (2007). Rhythmic and light-inducible appearance of clock-associated pseudo-response regulator protein PRR9 through programmed degradation in the dark in Arabidopsis thaliana. Plant Cell Physiol. 48, 1644-1651. doi: 10.1093/pcp/pcm122.
36. Ito, S., Niwa, Y., Nakamichi, N., Kawamura, H., Yamashino, T., and Mizuno, T. (2008). Insight into missing genetic links between two evening-expressed pseudo-response regulator genes TOC1 and PRR5 in the circadian clock-controlled circuitry in Arabidopsis thaliana. Plant Cell Physiol. 49, 201-213. doi: 10.1093/pcp/pcm178.
37. Johansson, M., and Staiger, D. (2015). Time to flower: interplay between photoperiod and the circadian clock. J. Exp. Bot. 66, 719-730. doi: 10.1093/jxb/eru441.
38. Kawamura, M., Ito, S., Nakamichi, N., Yamashino, T., and Mizuno, T. (2008). The Function of the clock-associated transcriptional regulator CCA1 (CIRCADIAN CLOCK-ASSOCIATED 1) in Arabidopsis thaliana. Biosci. Biotechnol. Biochem. 72, 1307-1316. doi: 10.1271/bbb.70804.
39. Khanna, R., Shen, Y., Toledo-Ortiz, G., Kikis, E. A., Johannesson, H., Hwang, Y.-S., et al. (2006). Functional profiling reveals that only a small number of phytochrome-regulated early-response genes in Arabidopsis are necessary for optimal deetiolation.Plant Cell 18, 2157-2171. doi: 10.1105/tpc.106.042200.
40. Kiba, T., Henriques, R., Sakakibara, H., and Chua, N.-H. (2007). Targeted degradation of PSEUDO-RESPONSE REGULATOR5 by an SCFZTL complex regulates clock function and photomorphogenesis in Arabidopsis thaliana. Plant Cell 19, 2516-2530. doi: 10.1105/tpc.107.053033.
41. Kikis, E. A., Khanna, R., and Quail, P. H. (2005). ELF4 is a phytochrome-regulated component of a negative-feedback loop involving the central oscillator components CCA1 and LHY. Plant J. 44, 300-313. doi: 10.1111/j.1365-313X.2005.02531.x.
42. Kim, J.-Y., Song, H.-R., Taylor, B. L., and Carré, I. A. (2003). Light-regulated translation mediates gated induction of the Arabidopsis clock protein LHY. EMBO J. 22, 935-944. doi: 10.1093/emboj/cdg075.
43. Kim, T.-S., Kim, W. Y., Fujiwara, S., Kim, J., Cha, J.-Y., Park, J. H., et al. (2011). HSP90 functions in the circadian clock through stabilization of the client F-box protein ZEITLUPE. Proc. Natl. Acad. Sci. U.S.A. 108, 16843-16848. doi: 10.1073/pnas.1110406108.
44. Kim, W.-Y., Fujiwara, S., Suh, S.-S., Kim, J., Kim, Y., Han, L., et al. (2007). ZEITLUPE is a circadian photoreceptor stabilized by GIGANTEA in blue light. Nature 449, 356-360. doi: 10.1038/nature06132.
45. Kolmos, E., Herrero, E., Bujdoso, N., Millar, A. J., Tóth, R., Gyula, P., et al. (2011). A reduced-function allele reveals that EARLY FLOWERING3 repressive action on the circadian clock is modulated by phytochrome signals in Arabidopsis. Plant Cell 23, 3230-3246. doi: 10.1105/tpc.111.088195.
46. Li, G., Siddiqui, H., Teng, Y., Lin, R., Wan, X.-Y., Li, J., et al. (2011). Coordinated transcriptional regulation underlying the circadian clock in Arabidopsis. Nat. Cell Biol. 13, 616-622. doi: 10.1038/ncb2219.
47. Locke, J. C., Millar, A. J., and Turner, M. S. (2005a). Modelling genetic networks with noisy and varied experimental data: the circadian clock in Arabidopsis thaliana. J. Theor. Biol. 234, 383-393. doi: 10.1016/j.jtbi.2004.11.038.
48. Locke, J. C. W., Kozma-Bognár, L., Gould, P. D., Fehér, B., Kevei, E., Nagy, F., et al. (2006). Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Mol. Syst. Biol. 2:59. doi: 10.1038/msb4100102.
49. Locke, J. C. W., Southern, M. M., Kozma-Bognár, L., Hibberd, V., Brown, P. E., Turner, M. S., et al. (2005b). Extension of a genetic network model by iterative experimentation and mathematical analysis. Mol. Syst. Biol. 1:2005.0013. doi: 10.1038/msb4100018.
50. Makino, S., Kiba, T., Imamura, A., Hanaki, N., Nakamura, A., Suzuki, T., et al. (2000). Genes encoding pseudo-response regulators: insight into His-to-Asp phosphorelay and circadian rhythm in Arabidopsis thaliana. Plant Cell Physiol. 41, 791-803. doi: 10.1093/pcp/41.6.791.
51. Martinez-García, J. F., Huq, E., and Quail, P. H. (2000). Direct targeting of light signals to a promoter element-bound transcription factor. Science 288, 859-863. doi: 10.1126/science.288.5467.859.
52. Más, P., Kim, W.-Y., Somers, D. E., and Kay, S. A. (2003). Targeted degradation of TOC1 by ZTL modulates circadian function in Arabidopsis thaliana. Nature 426, 567-570. doi: 10.1038/nature02163.
53. Matsushika, A., Imamura, A., Yamashino, T., and Mizuno, T. (2002). Aberrant expression of the light-inducible and circadian-regulated APRR9 gene belonging to the circadian-associated APRR1/TOC1 quintet results in the phenotype of early flowering in Arabidopsis thaliana. Plant Cell Physiol. 43, 833-843. doi: 10.1093/pcp/pcf118.
54. Matsushika, A., Makino, S., Kojima, M., and Mizuno, T. (2000). Circadian waves of expression of the APRR1/TOC1 family of pseudo-response regulators in Arabidopsis thaliana: insight into the plant circadian clock. Plant Cell Physiol. 41, 1002-1012. doi: 10.1093/pcp/pcd043.
55. Matsushika, A., Murakami, M., Ito, S., Nakamichi, N., Yamashino, T., and Mizuno, T. (2007). Characterization of circadian-associated pseudo-response regulators: I. Comparative studies on a series of transgenic lines misexpressing five distinctive PRR genes in Arabidopsis thaliana. Biosci. Biotechnol. Biochem. 71, 527-534. doi: 10.1271/bbb.60583.
56. McWatters, H. G., Kolmos, E., Hall, A., Doyle, M. R., Amasino, R. M., Gyula, P., et al. (2007). ELF4 is required for oscillatory properties of the circadian clock. Plant Physiol. 144, 391-401. doi: 10.1104/pp.107.096206.
57. Mizoguchi, T., Wheatley, K., Hanzawa, Y., Wright, L., Mizoguchi, M., Song, H.-R., et al. (2002). LHY and CCA1 are partially redundant genes required to maintain circadian rhythms in Arabidopsis. Dev. Cell 2, 629-641. doi: 10.1016/S1534-5807(02)00170-3.
58. Mizuno, T., Kitayama, M., Oka, H., Tsubouchi, M., Takayama, C., Nomoto, Y., et al. (2014a). The EC night-time repressor plays a crucial role in modulating circadian clock transcriptional circuitry by conservatively double-checking both warm-night and night-time-light signals in a synergistic manner in Arabidopsis thaliana. Plant Cell Physiol. 55, 2139-2151. doi: 10.1093/pcp/pcu144.
59. Mizuno, T., Nomoto, Y., Oka, H., Kitayama, M., Takeuchi, A., Tsubouchi, M., et al. (2014b). Ambient temperature signal feeds into the circadian clock transcriptional circuitry through the EC night-time repressor in Arabidopsis thaliana. Plant Cell Physiol. 55, 958-976. doi: 10.1093/pcp/pcu030.
60. Mockler, T. C., Michael, T. P., Priest, H. D., Shen, R., Sullivan, C. M., Givan, S. A., et al. (2007). The Diurnal project: diurnal and circadian expression profiling, model-based pattern matching, and promoter analysis. Cold Spring Harb. Symp. Quant. Biol. 72, 353-363. doi: 10.1101/sqb.2007.72.006.
61. Nagel, D. H., and Kay, S. A. (2012). Complexity in the wiring and regulation of plant circadian networks. Curr. Biol. 22, R648-R657. doi: 10.1016/j.cub.2012.07.025.
62. Nakamichi, N., Kiba, T., Henriques, R., Mizuno, T., Chua, N.-H., and Sakakibara, H. (2010). PSEUDO-RESPONSE REGULATORS 9, 7, and 5 are transcriptional repressors in the Arabidopsis circadian clock. Plant Cell 22, 594-605. doi: 10.1105/tpc.109.072892.
63. Nakamichi, N., Kita, M., Ito, S., Yamashino, T., and Mizuno, T. (2005). PSEUDO-RESPONSE REGULATORS, PRR9, PRR7 and PRR5, together play essential roles close to the circadian clock of Arabidopsis thaliana. Plant Cell Physiol. 46, 686-698. doi: 10.1093/pcp/pci086.
64. Niwa, Y., Yamashino, T., and Mizuno, T. (2009). The circadian clock regulates the photoperiodic response of hypocotyl elongation through a coincidence mechanism inArabidopsis thaliana. Plant Cell Physiol. 50, 838-854. doi: 10.1093/pcp/pcp028.
65. Nozue, K., Covington, M. F., Duek, P. D., Lorrain, S., Fankhauser, C., Harmer, S. L., et al. (2007). Rhythmic growth explained by coincidence between internal and external cues. Nature 448, 358-361. doi: 10.1038/nature05946.
66. Nusinow, D. A., Helfer, A., Hamilton, E. E., King, J. J., Imaizumi, T., Schultz, T. F., et al. (2011). The ELF4-ELF3-LUX complex links the circadian clock to diurnal control of hypocotyl growth. Nature 475, 398-402. doi: 10.1038/nature10182.
67. Ohara, T., Fukuda, H., and Tokuda, I. T. (2015). An extended mathematical model for reproducing the phase response of Arabidopsis thaliana under various light conditions. J. Theor. Biol. 382, 337-344. doi: 10.1016/j.jtbi.2015.07.016.
68. Onai, K., and Ishiura, M. (2005). PHYTOCLOCK 1 encoding a novel GARP protein essential for the Arabidopsis circadian clock. Genes Cells 10, 963-972. doi: 10.1111/j.1365-2443.2005.00892.x.
69. Para, A., Farré, E. M., Imaizumi, T., Pruneda-Paz, J. L., Harmon, F. G., and Kay, S. A. (2007). PRR3 Is a vascular regulator of TOC1 stability in the Arabidopsis circadian clock. Plant Cell 19, 3462-3473. doi: 10.1105/tpc.107.054775.
70. Pokhilko, A., Fernández, A. P. N., Edwards, K. D., Southern, M. M., Halliday, K. J., and Millar, A. J. (2012). The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops. Mol. Syst. Biol. 8:574. doi: 10.1038/msb.2012.6.
71. Pokhilko, A., Hodge, S. K., Stratford, K., Knox, K., Edwards, K. D., Thomson, A. W., et al. (2010). Data assimilation constrains new connections and components in a complex, eukaryotic circadian clock model. Mol. Syst. Biol. 6:416. doi: 10.1038/msb.2010.69.
72. Pokhilko, A., Mas, P., and Millar, A. J. (2013). Modelling the widespread effects of TOC1 signalling on the plant circadian clock and its outputs. BMC Syst. Biol. 7:23. doi: 10.1186/1752-0509-7-23.
73. Rawat, R., Takahashi, N., Hsu, P. Y., Jones, M. A., Schwartz, J., Salemi, M. R., et al. (2011). REVEILLE8 and PSEUDO-REPONSE REGULATOR5 form a negative feedback loop within the Arabidopsis circadian clock. PLoS Genet. 7:e1001350. doi: 10.1371/journal.pgen.1001350.
74. Salomé, P. A., and McClung, C. R. (2005). PSEUDO-RESPONSE REGULATOR 7 and 9 are partially redundant genes essential for the temperature responsiveness of the Arabidopsis circadian clock. Plant Cell 17, 791-803. doi: 10.1105/tpc.104.029504.
75. Salomé, P. A., Weigel, D., and McClung, C. R. (2010). The role of the Arabidopsis morning loop components CCA1, LHY, PRR7, and PRR9 in temperature compensation. Plant Cell 22, 3650-3661. doi: 10.1105/tpc.110.079087.
76. Schaffer, R., Ramsay, N., Samach, A., Corden, S., Putterill, J., Carré, I. A., et al. (1998). The late elongated hypocotyl mutation of Arabidopsis disrupts circadian rhythms and the photoperiodic control of flowering. Cell 93, 1219-1229. doi: 10.1016/S0092-8674(00)81465-8.
77. Schmal, C., Leloup, J.-C., and Gonze, D. (2014). Modeling and simulating theArabidopsis thaliana circadian clock using XPP-AUTO. Methods Mol. Biol. 1158, 337-358. doi: 10.1007/978-1-4939-0700-7_23.
78. Schmal, C., Myung, J., Herzel, H., and Bordyugov, G. (2015). A theoretical study on seasonality. Front. Neurol. 6:94. doi: 10.3389/fneur.2015.00094.
79. Schmal, C., Reimann, P., and Staiger, D. (2013). A circadian clock-regulated toggle switch explains AtGRP7 and AtGRP8 oscillations in Arabidopsis thaliana. PLoS Comput. Biol. 9:e1002986. doi: 10.1371/journal.pcbi.1002986.
80. Schmidt, H., and Jirstrand, M. (2006). Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22, 514-515. doi: 10.1093/bioinformatics/bti799.
81. Seaton, D. D., Smith, R. W., Song, Y. H., MacGregor, D. R., Stewart, K., Steel, G., et al. (2015). Linked circadian outputs control elongation growth and flowering in response to photoperiod and temperature. Mol. Syst. Biol. 11:776. doi: 10.15252/msb.20145766.
82. Thommen, Q., Pfeuty, B., Schatt, P., Bijoux, A., Bouget, F. Y., and Lefranc, M. (2015). Probing entrainment of Ostreococcus tauri circadian clock by green and blue light through a mathematical modeling approach. Front. Genet. 6:65. doi: 10.3389/fgene.2015.00065.
83. Troein, C., Corellou, F., Dixon, L. E., van Ooijen, G., O'Neill, J. S., Bouget, F.-Y., et al. (2011). Multiple light inputs to a simple clock circuit allow complex biological rhythms. Plant J. 66, 375-385.
84. Wang, L., Fujiwara, S., and Somers, D. E. (2010). PRR5 regulates phosphorylation, nuclear import and subnuclear localization of TOC1 in the Arabidopsis circadian clock. EMBO J. 29, 1903-1915. doi: 10.1038/emboj.2010.76.
85. Wang, Z. Y., and Tobin, E. M. (1998). Constitutive expression of the CIRCADIAN CLOCK ASSOCIATED 1 (CCA1) gene disrupts circadian rhythms and suppresses its own expression. Cell 93, 1207-1217. doi: 10.1016/S0092-8674(00)81464-6.
86. Webb, A. A. R., and Satake, A. (2015). Understanding circadian regulation of carbohydrate metabolism in Arabidopsis using mathematical models. Plant Cell Physiol. 56, 586-593. doi: 10.1093/pcp/pcv033.
87. Yazdanbakhsh, N., Sulpice, R., Graf, A., Stitt, M., and Fisahn, J. (2011). Circadian control of root elongation and C partitioning in Arabidopsis thaliana. Plant Cell Environ. 34, 877-894. doi: 10.1111/j.1365-3040.2011.02286.x.
88. Zeilinger, M. N., Farré, E. M., Taylor, S. R., Kay, S. A., and Doyle, F. J. (2006). A novel computational model of the circadian clock in Arabidopsis that incorporates PRR7 and PRR9. Mol. Syst. Biol. 2:58. doi: 10.1038/msb4100101.