Modelling of circadian rhythms in Drosophila incorporating the interlocked PER/TIM and VRI/PDP1 feedback loops. (English) Zbl 1451.92039
Summary: Circadian rhythms of gene activity, metabolism, physiology and behaviour are observed in all the eukaryotes and some prokaryotes. In this study, we present a model to represent the transcriptional regulatory network essential for the circadian rhythmicity in Drosophila. The model incorporates the transcriptional feedback loops revealed so far in the network of the circadian clock (PER/TIM and VRI/PDP1 loops). Conventional Hill functions are not assumed to describe the regulation of genes, instead of the explicit reactions of binding and unbinding processes of transcription factors to promoters are modelled. The model simulates sustained circadian oscillations in mRNA and protein concentrations in constant darkness in agreement with experimental observations. It also simulates entrainment by light-dark cycles, disappearance of the rhythmicity in constant light and the shape of phase response curves resembling that of the experimental results. The model is robust over a wide range of parameter variations. In addition, the simulated E-box mutation, \(per^S\) and \(per^L\) mutants are similar to that observed in the experiments. The deficiency between the simulated mRNA levels and experimental observations in \(per^{01}\), \(tim^{01}\) and \(clk^{Jrk}\) mutants suggests some difference on the part of the model from reality.
Keywords:
computational biology; mathematical models; circadian rhythms; circadian clock; oscillationsReferences:
| [1] | Allada, R.; White, N. E., A mutant Drosophila homolog of mammalian clock disrupts circadian rhythms and transcription of period and timeless, Cell, 93, 5, 791-804 (1998) |
| [2] | Bae, K.; Lee, C., Circadian regulation of a Drosophila homolog of the mammalian Clock gene: PER and TIM function as positive regulators, Mol. Cell Biol., 18, 10, 6142-6151 (1998) |
| [3] | Bao, S.; Rihel, J., The Drosophila double-timeS mutation delays the nuclear accumulation of period protein and affects the feedback regulation of period mRNA, J. Neurosci., 21, 18, 7117-7126 (2001) |
| [4] | Blau, J.; Young, M. W., Cycling vrille expression is required for a functional Drosophila clock, Cell, 99, 6, 661-671 (1999) |
| [5] | Curtin, K. D.; Huang, Z. J., Temporally regulated nuclear entry of the Drosophila period protein contributes to the circadian clock, Neuron, 14, 2, 365-372 (1995) |
| [6] | Cyran, S. A.; Buchsbaum, A. M., vrille, Pdp1, and dClock form a second feedback loop in the Drosophila circadian clock, Cell, 112, 3, 329-341 (2003) |
| [7] | Dunlap, J. C., Molecular bases for circadian clocks, Cell, 96, 2, 271-290 (1999) |
| [8] | Edery, I.; L. Zwiebel, J., Temporal phosphorylation of the Drosophila period protein, Proc. Natl Acad. Sci. USA, 91, 6, 2260-2264 (1994) |
| [9] | Endy, D.; Brent, R., Modelling cellular behaviour, Nature, 409, 6818, 391-395 (2001) |
| [10] | Etchegaray, J.-P.; Lee, C., Rhythmic histone acetylation underlies transcription in the mammalian circadian clock, Nature, 421, 6919, 177-182 (2003) |
| [11] | Ewer, J.; Frisch, B., Expression of the period clock gene within different cell types in the brain of Drosophila adults and mosaic analysis of these cells’ influence on circadian behavioral rhythms, J. Neurosci., 12, 9, 3321-3349 (1992) |
| [12] | Forger, D. B.; Peskin, C. S., A detailed predictive model of the mammalian circadian clock, Proc. Natl Acad. Sci. USA, 100, 25, 14806-14811 (2003) |
| [13] | Funahashi, A.; Tanimura, N.; Morohashi, M.; Kitano, H., CellDesigner: a process diagram editor for gene-regulatory and biochemical networks, Biosilico, 1, 159-162 (2003) |
| [14] | Glossop, N. R.; Lyons, L. C., Interlocked feedback loops within the Drosophila circadian oscillator, Science, 286, 5440, 766-768 (1999) |
| [15] | Glossop, N. R.J.; Houl, J. H., Vrille feeds back to control circadian transcription of Clock in the Drosophila circadian oscillator, Neuron, 37, 2, 249-261 (2003) |
| [16] | Goldbeter, A., A model for circadian oscillations in the Drosophila period protein (PER), Proc. R. Soc. London B, 261, 1362, 319-324 (1995) |
| [17] | Goldbeter, A., Computational approaches to cellular rhythms, Nature, 420, 6912, 238-245 (2002) |
| [18] | Hardin, P. E., The circadian timekeeping system of Drosophila, Curr. Biol., 15, 17, R714-R722 (2005) |
| [19] | Hardin, P. E.; Hall, J. C., Feedback of the Drosophila period gene product on circadian cycling of its messenger RNA levels, Nature, 343, 6258, 536-540 (1990) |
| [20] | Hida, A.; Koike, N., The human and mouse Period1 genes: five well-conserved E-boxes additively contribute to the enhancement of mPer1 transcription, Genomics, 65, 3, 224-233 (2000) |
| [21] | Hill, A. V., The possible effects of the aggregation of the molecules of haemoglobin on its oxygen dissociation curve, J. Physiol., 40, 4-7 (1910) |
| [22] | Kitano, H., Systems biology: a brief overview, Science, 295, 5560, 1662-1664 (2002) |
| [23] | Konopka, R. J.; Benzer, S., Clock mutants of Drosophila melanogaster, Proc. Natl Acad. Sci. USA, 68, 9, 2112-2116 (1971) |
| [24] | Konopka, R. J.; Smith, R., Characterization of Andante, a new Drosophila clock mutant, and its interactions with other clock mutants, J. Neurogenet., 7, 2-3, 103-114 (1991) |
| [25] | Kurosawa, G.; Mochizuki, A., Comparative study of circadian clock models, in search of processes promoting oscillation, J. Theor. Biol., 216, 2, 193-208 (2002) |
| [26] | Lee, C.; Bae, K., The Drosophila CLOCK protein undergoes daily rhythms in abundance, phosphorylation, and interactions with the PER-TIM complex, Neuron, 21, 4, 857-867 (1998) |
| [27] | Lee, C.; Parikh, V., Resetting the Drosophila clock by photic regulation of PER and a PER-TIM complex, Science, 271, 5256, 1740-1744 (1996) |
| [28] | Leloup, J. C.; Goldbeter, A., A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins, J. Biol. Rhythms, 13, 1, 70-87 (1998) |
| [29] | Leloup, J.-C.; Goldbeter, A., Toward a detailed computational model for the mammalian circadian clock, Proc. Natl Acad. Sci., 100, 12, 7051-7056 (2003) |
| [30] | Leloup, J. C.; Gonze, D., Limit cycle models for circadian rhythms based on transcriptional regulation in Drosophila and Neurospora, J. Biol. Rhythms, 14, 6, 433-448 (1999) |
| [31] | Lema, M. A.; Golombek, D. A., Delay model of the circadian pacemaker, J. Theor. Biol., 204, 4, 565-573 (2000) |
| [32] | Levine, J. D.; Funes, P., Signal analysis of behavioral and molecular cycles, BMC Neurosci., 3, 1 (2002) |
| [33] | McDonald, M. J.; Rosbash, M., Microarray analysis and organization of circadian gene expression in Drosophila, Cell, 107, 5, 567-578 (2001) |
| [34] | Murray, J. D., Mathematical biology (2002), Springer: Springer New York · Zbl 1006.92001 |
| [35] | Pittendrigh, C. S., Temporal organization: reflections of a Darwinian clock-watcher, Annu. Rev. Physiol., 55, 16-54 (1993) |
| [36] | Price, J. L.; Dembinska, M. E., Suppression of PERIOD protein abundance and circadian cycling by the Drosophila clock mutation timeless, EMBO J., 14, 16, 4044-4049 (1995) |
| [37] | Price, J. L.; Blau, J., double-time is a novel Drosophila Clock gene that regulates PERIOD protein accumulation, Cell, 94, 1, 83-95 (1998) |
| [38] | Ruoff, P.; Christensen, M. K., PER/TIM-mediated amplification, gene dosage effects and temperature compensation in an interlocking-feedback loop model of the Drosophila circadian clock, J. Theor. Biol., 237, 1, 41-57 (2005) · Zbl 1445.92016 |
| [39] | Ruoff, P.; Rensing, L., The temperature-compensated Goodwin model simulates many circadian clock properties, J. Theor. Biol., 179, 4, 275-285 (1996) |
| [40] | Scheper, T.; Klinkenberg, D., A mathematical model for the intracellular circadian rhythm generator, J. Neurosci., 19, 1, 40-47 (1999) |
| [41] | Schmidt, H.; Jirstrand, M., Systems Biology Toolbox for MATLAB: a computational platform for research in Systems Biology, Bioinformatics, 799 (2005) |
| [42] | Schoning, J. C.; Staiger, D., At the pulse of time: protein interactions determine the pace of circadian clocks, FEBS Lett., 579, 15, 3246-3252 (2005) |
| [43] | Segel, I. H., Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady State Enzyme Systems (1993), Wiley: Wiley New York |
| [44] | Shafer, O. T.; Rosbash, M., Sequential nuclear accumulation of the clock proteins period and timeless in the pacemaker neurons of Drosophila melanogaster, J. Neurosci., 22, 14, 5946-5954 (2002) |
| [45] | Shu, Y.; Hong-Hui, L., Transcription, translation, degradation, and circadian clock, Biochem. Biophys. Res. Commun., 321, 1, 1-6 (2004) |
| [46] | Smolen, P.; Baxter, D. A., Modeling circadian oscillations with interlocking positive and negative feedback loops, J. Neurosci., 21, 17, 6644-6656 (2001) |
| [47] | Smolen, P.; Hardin, P. E., Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK, Biophys. J., 86, 5, 2786-2802 (2004) |
| [48] | So, W. V.; Rosbash, M., Post-transcriptional regulation contributes to Drosophila clock gene mRNA cycling, EMBO J., 16, 23, 7146-7155 (1997) |
| [49] | Tyson, J. J.; Hong, C. I., A simple model of circadian rhythms based on dimerization and proteolysis of PER and TIM, Biophys. J., 77, 5, 2411-2417 (1999) |
| [50] | Ueda, H.; Hirose, K., Intercellular coupling mechanism for synchronized and noise-resistant circadian oscillators, J. Theor. Biol., 216, 4, 501-512 (2002) |
| [51] | Ueda, H. R.; Hagiwara, M., Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm, J. Theor. Biol., 210, 4, 401-406 (2001) |
| [52] | Van Gelder, R. N.; Herzog, E. D., Circadian rhythms: in the loop at last, Science, 300, 5625, 1534-1535 (2003) |
| [53] | Vilar, J. M.; Kueh, H. Y., Mechanisms of noise-resistance in genetic oscillators, Proc. Natl Acad. Sci. USA, 99, 9, 5988-5992 (2002) |
| [54] | Vosshall, L. B.; Price, J. L., Block in nuclear localization of period protein by a second clock mutation, timeless, Science, 263, 5153, 1606-1609 (1994) |
| [55] | Yamaguchi, S.; Mitsui, S., The 5′ upstream region of mPer1 gene contains two promoters and is responsible for circadian oscillation, Curr. Biol., 10, 14, 873-876 (2000) |
| [56] | Young, M. W.; Kay, S. A., Time zones: a comparative genetics of circadian clocks, Nat. Rev. Genet., 2, 9, 702-715 (2001) |
| [57] | Yu, W.; Zheng, H., PER-dependent rhythms in CLK phosphorylation and E-box binding regulate circadian transcription, Genes Dev., 20, 6, 723-733 (2006) |
| [58] | Zeng, H.; Qian, Z., A light-entrainment mechanism for the Drosophila circadian clock, Nature, 380, 6570, 129-135 (1996) |
| [59] | Zerr, D. M.; Hall, J. C., Circadian fluctuations of period protein immunoreactivity in the CNS and the visual system of Drosophila, J. Neurosci., 10, 8, 2749-2762 (1990) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
