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Semi-algebraic optimization of temperature compensation in a general switch-type negative feedback model of circadian clocks

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Abstract

Temperature compensation is an essential property of circadian oscillators which enables them to act as physiological clocks. We have analyzed the temperature compensating behavior of a generalized transcriptional–translational negative feedback oscillator with a hard hysteretic switch and rate constants with an Arrhenius-type temperature dependence. These oscillations can be considered as the result of a lowpass filtering operator acting on a train of rectangular pulses. Such a signal-processing viewpoint makes it possible to express, in a semi-algebraic manner, the period length, the oscillator’s control (sensitivity) coefficients, and the first and second-order derivatives of the period–temperature relationship. We have used the semi-algebraic approach to investigate a 3-dimensional Goodwin-type representation of the oscillator, where local optimization for temperature compensation has been considered. In the local optimization, activation energies are found, which lead to a zero first order derivative and to a closest-to-zero second order derivative at a given reference temperature. We find that the major contribution to temperature compensation over an extended temperature range is given by the (local) zero first order derivative, while only minor contributions to temperature compensation are given by an optimized second order derivative. In biological terms this could be interpreted to relate to a circadian clock mechanism which during evolution is being optimized for a certain but relative narrow (habitat) temperature range.

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References

  1. Apostol T.M. (1969). Calculus, vol II. Xerox College Publishing, Waltham

    MATH  Google Scholar 

  2. Aronson B.D., Johnson K.A., Loros J.J. and Dunlap J.C. (1994). Negative feedback defining a circadian clock: autoregulation of the clock gene frequency. Science 263(5153): 1578–1584

    Article  Google Scholar 

  3. Bünning E. (1963). The Physiological Clock. Springer-Verlag, Berlin

    Google Scholar 

  4. Dunlap J.C. (1999). Molecular bases for circadian clocks. Cell 96(2): 271–290

    Article  Google Scholar 

  5. Dunlap J.C. and Loros J.J. (2004). The Neurospora circadian system. J. Biol. Rhythms. 19(5): 414–424

    Article  Google Scholar 

  6. Dunlap J.C., Loros J.J, DeCoursey P.J. (eds) (2004). Chronobiology. Biological Timekeeping. Sinauer Associates, Inc. Publishers, Sunderland

    Google Scholar 

  7. Edmunds L.N. (1988). Cellular and Molecular Bases of Biological Clocks. Springer-Verlag, New York

    Google Scholar 

  8. Fell D. (1997). Understanding the Control of Metabolism. Portland Press, London and Miami

    Google Scholar 

  9. Gardner G.F. and Feldman J.F. (1981). Temperature compensation of circadian periodicity in clock mutants of neurospora crassa. Plant Physiol. 68: 1244–1248

    Article  Google Scholar 

  10. Goldbeter A. (2002). Computational approaches to cellular rhythms. Nature 420(6912): 238–245

    Article  Google Scholar 

  11. Goodwin B.C. (1965). Oscillatory behavior in enzymatic control processes. Adv. Enzyme Regulat. 3: 425–438

    Article  Google Scholar 

  12. Gould P.D., Locke J.C., Larue C., Southern M.M., Davis S.J., Hanano S., Moyle R., Milich R., Putterill J., Millar A.J. and Hall A. (2006). The molecular basis of temperature compensation in the Arabidopsis circadian clock. Plant Cell 18(5): 1177–1187

    Article  Google Scholar 

  13. Hastings J.W. and Sweeney B.M. (1957). On the mechanism of temperature independence in a biological clock. Proc. Natl. Acad. Sci. USA 43: 804–811

    Article  Google Scholar 

  14. Heinrich R. and Schuster S. (1996). The Regulation of Cellular Systems. Chapman and Hall, New York

    MATH  Google Scholar 

  15. Hong C.I., Conrad E.D. and Tyson J.J. (2007). A proposal for robust temperature compensation of circadian rhythms. Proc. Natl. Acad. Sci. USA 104(4): 1195–1200

    Article  Google Scholar 

  16. Kurosawa G. and Iwasa Y. (2005). Temperature compensation in circadian clock models. J. Theor. Biol. 233(4): 453–468

    Article  Google Scholar 

  17. Lakin-Thomas P.L., Brody S. and Cote G.G. (1991). Amplitude model for the effects of mutations and temperature on period and phase resetting of the neurospora circadian oscillator. J. Biol. Rhythms 6(4): 281–297

    Article  Google Scholar 

  18. Leloup J.C. and Goldbeter A. (1997). Temperature compensation of circadian rhythms: control of the period in a model for circadian oscillations of the per protein in Drosophila. Chronobiol. Int. 14(5): 511–520

    Google Scholar 

  19. Pittendrigh C.S. and Caldarola P.C. (1973). General homeostasis of the frequency of circadian oscillations. Proc. Natl. Acad. Sci. USA 70(9): 2697–2701

    Article  Google Scholar 

  20. Radhakrishnan, K., Hindmarsh, A.C.: Description and use of LSODE, the Livermore Solver for Ordinary Differential Equations. Tech. Rep. NASA Reference Publication 1327, National Aeronautics and Space Administration, Lewis Research Center (1993)

  21. Ruoff P. (1992). Introducing temperature-compensation in any reaction kinetic oscillator model. J. Interdiscipl. Cycle Res. 23: 92–99

    Google Scholar 

  22. Ruoff P., Behzadi A., Hauglid M., Vinsjevik M. and Havås H. (2000). pH homeostasis of the circadian sporulation rhythm in clock mutants of Neurospora crassa. Chronobiol. Int. 17(6): 733–750

    Article  Google Scholar 

  23. Ruoff, P., Loros, J.J., Dunlap, J.C.: The relationship between FRQ protein stability and temperature compensation in the Neurospora circadian clock. Proc. Natl. Acad. Sci. USA 102(49), 17,681–17,686

  24. Ruoff P. and Noyes R.M. (1988). Phase response behaviors of different oscillatory states in the Belousov–Zhabotinsky reaction. J. Chem. Phys. 89: 6247–6254

    Article  Google Scholar 

  25. Ruoff P. and Rensing L. (1996). The temperature-compensated Goodwin model simulates many circadian clock properties. J. Theor. Biol. 179: 275–285

    Article  Google Scholar 

  26. Ruoff P., Vinsjevik M. and Rensing L. (2000). Temperature compensation in biological oscillators: A challenge for joint experimental and theoretical analysis. Comments Theor. Biol. 5: 361–382

    Google Scholar 

  27. Valeur K.R. and degli Agosti R. (2002). Simulations of temperature sensitivity of the peroxidase-oxidase oscillator. Biophys. Chem. 99(3): 259–270

    Article  Google Scholar 

  28. Winfree A.T. (2000). The geometry of biological time. 2, Springer-Verlag, New York

    Google Scholar 

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Stavanger, 4036, Stavanger, Norway

    Sven Ole Aase

  2. Department of Mathematics and Natural Sciences, University of Stavanger, 4036, Stavanger, Norway

    Peter Ruoff

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  1. Sven Ole Aase
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  2. Peter Ruoff
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Correspondence to Sven Ole Aase.

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Aase, S.O., Ruoff, P. Semi-algebraic optimization of temperature compensation in a general switch-type negative feedback model of circadian clocks. J. Math. Biol. 56, 279–292 (2008). https://doi.org/10.1007/s00285-007-0115-5

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  • DOI: https://doi.org/10.1007/s00285-007-0115-5

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