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Controlling Biological Time: Nonlinear Model Predictive Control for Populations of Circadian Oscillators

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Book cover Emerging Applications of Control and Systems Theory

Part of the book series: Lecture Notes in Control and Information Sciences - Proceedings ((LNCOINSPRO))

Abstract

In mammals, circadian regulation of gene expression is accomplished within each cell through a transcriptional oscillator commonly modeled by a limit cycle. There has been recent interest in regulating this oscillator by delivering doses of pharmaceuticals or light in a systematic manner. Generally, controller design for circadian manipulation has been formulated by considering the dynamics of a single oscillator representing the average dynamics of the population. We illustrate in this paper that such an approximation can result in desynchronization of circadian oscillators even if the mean dynamics attain desired behavior, due to the range of dynamic responses elicited among oscillators in a population with nonidentical phases. To address this issue, we present herein nonlinear MPC for control of phase and synchrony within a population of uncoupled circadian oscillators, by explicitly predicting the evolution of the phase probability density function. We then demonstrate in silico phase shifting of an example oscillator population while maintaining a high degree of synchrony. The MPC strategy formulated herein is a step toward a detailed, systems approach integrating population effects, pharmacokinetics and pharmacodynamics, and interactions between different oscillator populations.

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References

  1. Abel, J.H., Chakrabarty, A., Doyle III, F.J.: Nonlinear model predictive control for circadian entrainment using small-molecule pharmaceuticals. Proceedings of 20th IFAC World Congress. 9864–9870 (2017)

    Google Scholar 

  2. Abel, J.H., Doyle III, F.J.: A systems theoretic approach to analysis and control of mammalian circadian dynamics. Chem. Eng. Res. Des. 116, 48–60 (2016)

    Article  Google Scholar 

  3. Andersson, J., Akesson, J., Diehl, M.: Recent Advances in Algorithmic Differentiation, vol. 87. Springer, Berlin Heidelberg (2012)

    Book  Google Scholar 

  4. Bagheri, N., Stelling, J., Doyle III, F.J.: Circadian phase entrainment via nonlinear model predictive control. Int. J. Robust Nonlinear Control 17(May), 1555–1571 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bagheri, N., Taylor, S.R., Meeker, K., Petzold, L.R., Doyle III, F.J.: Synchrony and entrainment properties of robust circadian oscillators. J. R. Soc. Interface 5, S17–S28 (2008)

    Article  Google Scholar 

  6. Bass, J., Takahashi, J.S.: Circadian integration of metabolism and energetics. Science 330(6009), 1349–1354 (2010)

    Article  Google Scholar 

  7. Dunlap, J.C., Loros, J.J., DeCoursey, P.J.: Chronobiology. Sinauer Associates, Inc. (2004)

    Google Scholar 

  8. Glossop, N.R., Lyons, L.C., Hardin, P.E.: Interlocked feedback loops within the drosophila circadian oscillator. Science 286(5440), 766–768 (1999)

    Article  Google Scholar 

  9. Goodwin, B.C.: Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regul. 3, 425–437 (1965)

    Article  Google Scholar 

  10. Hirota, T., Lee, J.W., St. John, P.C., Sawa, M., Iwaisako, K., Noguchi, T., Pongsawakul, P.Y., Sonntag, T., Welsh, D.K., Brenner, D.A., Doyle III, F.J., Schultz, P.G., Kay, S.A.: Identification of small molecule activators of cryptochrome. Science 337(6098), 1094–1097 (2012)

    Article  Google Scholar 

  11. Huang, K.C., Meir, Y., Wingreen, N.S.: Dynamic structures in escherichia coli: Spontaneous formation of mine rings and mind polar zones. Proc. Natl. Acad. Sci. USA 100(22), 12724–12728 (2003)

    Article  Google Scholar 

  12. Ishiura, M., Kutsuna, S., Aoki, S., Iwasaki, H., Andersson, C.R., Tanabe, A., Golden, S.S., Johnson, C.H., Kondo, T.: Expression of a gene cluster kaiABC as a circadian feedback process in cyanobacteria. Science 281(5382), 1519–1523 (1998)

    Article  Google Scholar 

  13. Marquié, J.C., Tucker, P., Folkard, S., Gentil, C., Ansiau, D.: Chronic effects of shift work on cognition: findings from the visat longitudinal study. Occup. Environ. Med. 72(4), 258–264 (2015)

    Article  Google Scholar 

  14. Mirsky, H.P., Liu, A.C., Welsh, D.K., Kay, S.A., Doyle III, F.J.: A model of the cell-autonomous mammalian circadian clock. Proc. Natl. Acad. Sci. USA 106(27), 11107–11112 (2009)

    Article  MATH  Google Scholar 

  15. Mukherji, A., Kobiita, A., Damara, M., Misra, N., Meziane, H., Champy, M.F., Chambon, P.: Shifting eating to the circadian rest phase misaligns the peripheral clocks with the master scn clock and leads to a metabolic syndrome. Proc. Natl. Acad. Sci. USA 112(48), E6691–E6698 (2015)

    Article  Google Scholar 

  16. Panda, S., Antoch, M.P., Miller, B.H., Su, A.I., Schook, A.B., Straume, M., Schultz, P.G., Kay, S.A., Takahashi, J.S., Hogenesch, J.B.: Coordinated transcription of key pathways in the mouse by the circadian clock. Cell 109(3), 307–320 (2002)

    Article  Google Scholar 

  17. Ramkisoensing, A., Meijer, J.H.: Synchronization of biological clock neurons by light and peripheral feedback systems promotes circadian rhythms and health. Front. Neurol. 6(MAY) (2015)

    Google Scholar 

  18. Serkh, K., Forger, D.B.: Optimal schedules of light exposure for rapidly correcting circadian misalignment. PLoS Comput. Biol. 10(4), e1003,523 (2014)

    Google Scholar 

  19. Shaik, O., Sager, S., Slaby, O., Lebiedz, D.: Phase tracking and restoration of circadian rhythms by model-based optimal control. IET Syst. Biol. 2(1), 16–23 (2008)

    Article  Google Scholar 

  20. Slaby, O., Sager, S., Shaik, O.S., Kummer, U., Lebiedz, D.: Optimal control of self-organized dynamics in cellular signal transduction. Math. Comput. Model. Dyn. Syst. 13(5), 487–502 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  21. St. John, P.C., Hirota, T., Kay, S.A., Doyle III, F.J.: Spatiotemporal separation of per and cry posttranslational regulation in the mammalian circadian clock. Proc. Natl. Acad. Sci. USA 111(5), 2040–2045 (2014)

    Article  Google Scholar 

  22. St. John, P.C., Taylor, S.R., Abel, J.H., Doyle III, F.J.: Amplitude metrics for cellular circadian bioluminescence reporters. Biophys. J. 107(11), 2712–2722 (2014)

    Article  Google Scholar 

  23. Takahashi, J.S.: Transcriptional architecture of the mammalian circadian clock. Nat. Rev. Genet. (2016)

    Google Scholar 

  24. Taylor, S.R., Doyle III, F.J., Petzold, L.R.: Oscillator model reduction preserving the phase response: application to the circadian clock. Biophys. J. 95(4), 1658–1673 (2008)

    Article  Google Scholar 

  25. Ukai, H., Kobayashi, T.J., Nagano, M., Masumoto, K.H., Sujino, M., Kondo, T., Yagita, K., Shigeyoshi, Y., Ueda, H.R.: Melanopsin-dependent photo-perturbation reveals desynchronization underlying the singularity of mammalian circadian clocks singularity behaviour in circadian clocks. Nat. Cell Biol. 9(11), 1327–1334 (2007)

    Article  Google Scholar 

  26. Welsh, D.K., Takahashi, J.S., Kay, S.A.: Suprachiasmatic nucleus: cell autonomy and network properties. Annu. Rev. Physiol. 72, 551–577 (2010)

    Article  Google Scholar 

  27. Zhang, J., Qiao, W., Wen, J.T., Julius, A.: Light-based circadian rhythm control: entrainment and optimization. Automatica 68, 44–55 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhang, R., Lahens, N.F., Ballance, H.I., Hughes, M.E., Hogenesch, J.B.: A circadian gene expression atlas in mammals: Implications for biology and medicine. Proc. Natl. Acad. Sci. U. S. A. 111(45), 16219–16224 (2014)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Systems Biology, Harvard Medical School, Boston, MA, 02115, USA

    John H. Abel

  2. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Ankush Chakrabarty

  3. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, 02138, USA

    Francis J. Doyle III

  4. Division of Sleep Medicine, Harvard Medical School, Boston, MA, 02115, USA

    Francis J. Doyle III

Authors
  1. John H. Abel
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  2. Ankush Chakrabarty
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  3. Francis J. Doyle III
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Corresponding author

Correspondence to Francis J. Doyle III .

Editor information

Editors and Affiliations

  1. IEIIT—CNR, Politecnico di Torino, Turin, Italy

    Roberto Tempo

  2. Department of Systems Engineering, University of Texas at Dallas, Richardson, Texas, USA

    Stephen Yurkovich

  3. Russ Engineering Center, Wright State University, Dayton, Ohio, USA

    Pradeep Misra

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Abel, J.H., Chakrabarty, A., Doyle, F.J. (2018). Controlling Biological Time: Nonlinear Model Predictive Control for Populations of Circadian Oscillators. In: Tempo, R., Yurkovich, S., Misra, P. (eds) Emerging Applications of Control and Systems Theory. Lecture Notes in Control and Information Sciences - Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-67068-3_9

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  • DOI: https://doi.org/10.1007/978-3-319-67068-3_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67067-6

  • Online ISBN: 978-3-319-67068-3

  • eBook Packages: EngineeringEngineering (R0)

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