Chemical Analog Computers for Clock Frequency Control Based on P Modules

  • Thomas Hinze
  • Christian Bodenstein
  • Benedict Schau
  • Ines Heiland
  • Stefan Schuster
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7184)


Living organisms comprise astonishing capabilities of information processing for efficient adaptation to environmental changes. Resulting chemical control loops and regulator circuits are expected to exhibit a high functional similarity to technical counterparts subsumed by analog computers. A fascinating example is given by circadian clocks providing an endogenous biological rhythm adapted to the daily variation of sunlight and darkness. Its underlying biochemical principle of operation suggests a general functional scheme corresponding to frequency control using phase-locked loops (PLL). From a systems biology point of view, clock systems can be decomposed into specific modules like low-pass filters, arithmetic signal comparators, and controllable core oscillators. Each of them processes analog chemical signals on the fly. We introduce P modules in order to capture structure, behaviour, and interface of pure chemical analog computer models in terms of building blocks along with two simulation case studies. The first one is focused on chemical analog computer components including a controllable Goodwin-type core oscillator while the second one evolves an entire PLL-based frequency control by means of a pure chemical circadian clock model.


External Stimulus Circadian Clock Period Length Frequency Control Module Topology 
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  1. 1.
    Aschoff, J.: A survey on biological rhythms. Biological Rhythms 4, 3–10 (1981)CrossRefGoogle Scholar
  2. 2.
    Bequette, B.W.: Process control: modeling, design, and simulation. Prentice-Hall (2003)Google Scholar
  3. 3.
    Best, R.E.: Phase-locked loops: design, simulation, and applications. McGraw-Hill (2007)Google Scholar
  4. 4.
    Bianco, L., Fontana, F., Manca, V.: P systems with reaction maps. International Journal of Foundations of Computer Science 17(1), 27–48 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Botti, B., Youan, C. (eds.): Chronopharmaceutics. Science and technology for biological rhythm guided therapy and prevention of diseases. John Wiley & Sons (2009)Google Scholar
  6. 6.
    Cao, H., Romero-Campero, F.J., Heeb, S., Camara, M., Krasnogor, N.: Evolving cell models for systems and synthetic biology. Systems and Synthetic Biology 4(1), 55–84 (2010)CrossRefGoogle Scholar
  7. 7.
    Connors, K.A.: Chemical Kinetics. VCH Publishers, Weinheim (1990)Google Scholar
  8. 8.
    Cory, S., Perkins, T.: Implementing arithmetic and other analytic operations by transcriptional regulation. PLoS Computational Biology 4(4) (2008)Google Scholar
  9. 9.
    Dittrich, P., Ziegler, J., Banzhaf, W.: Artificial Chemistries – A Review. Artificial Life 7(3), 225–275 (2001)CrossRefGoogle Scholar
  10. 10.
    Fontana, F., Manca, V.: Discrete solutions to differential equations by metabolic P systems. Theoretical Computer Science 372(2-3), 165–182 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Goodwin, B.C.: Oscillatory behaviour in enzymatic control processes. Advanced Enzyme Regulation 3, 425–438 (1965)CrossRefGoogle Scholar
  12. 12.
    Hawkins, B.A., Cornell, H.V. (eds.): Theoretical Approaches to Biological Control. Cambridge University Press (1999)Google Scholar
  13. 13.
    Heiland, I., Bodenstein, C., Schuster, S.: Temperature compensation and temperature entrainment – amity or enmity? In: FEBS-SystemsX-SysBio 2011, Innsbruck, Austria (2011)Google Scholar
  14. 14.
    Helmreich, E.J.: The biochemistry of cell signalling. Oxford University Press (2001)Google Scholar
  15. 15.
    Hinze, T., Fassler, R., Lenser, T., Dittrich, P.: Register Machine Computations on Binary Numbers by Oscillating and Catalytic Chemical Reactions Modelled using Mass-Action Kinetics. International Journal of Foundations of Computer Science 20(3), 411–426 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Hinze, T., Lenser, T., Dittrich, P.: A Protein Substructure Based P System for Description and Analysis of Cell Signalling Networks. In: Hoogeboom, H.J., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2006. LNCS, vol. 4361, pp. 409–423. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Hinze, T., Lenser, T., Escuela, G., Heiland, I., Schuster, S.: Modelling Signalling Networks with Incomplete Information about Protein Activation States: A P System Framework of the KaiABC Oscillator. In: Păun, G., Pérez-Jiménez, M.J., Riscos-Núñez, A., Rozenberg, G., Salomaa, A. (eds.) WMC 2009. LNCS, vol. 5957, pp. 316–334. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  18. 18.
    Kuramoto, Y.: Chemical Oscillations, Waves, and Turbulences. Springer, Heidelberg (1984)CrossRefzbMATHGoogle Scholar
  19. 19.
    Lenser, T., Hinze, T., Ibrahim, B., Dittrich, P.: Towards Evolutionary Network Reconstruction Tools for Systems Biology. In: Marchiori, E., Moore, J.H., Rajapakse, J.C. (eds.) EvoBIO 2007. LNCS, vol. 4447, pp. 132–142. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  20. 20.
    Lewis, R.D.: Control systems models for the circadian clock of the New Zealand Weta. Hemideina thoracia. Journal of Biological Rhythms 14, 480–485 (1999)CrossRefGoogle Scholar
  21. 21.
    Manca, V.: Metabolic P Systems for Biochemical Dynamics. Progress in Natural Sciences 17(4), 384–391 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Marhl, M., Perc, M., Schuster, S.: Selective regulation of cellular processes via protein cascades acting as band-pass filters for time-limited oscillations. FEBS Letters 579(25), 5461–5465 (2005)CrossRefGoogle Scholar
  23. 23.
    Mori, T., Williams, D.R., Byrne, M.O., Qin, X., Egli, M., Mchaourab, H.S., Stewart, P.L., Johnson, C.H.: Elucidating the ticking of an in vitro circadian clockwork. PLoS Biology 5(4), 841–853 (2007)CrossRefGoogle Scholar
  24. 24.
    Polderman, J.W., Willems, J.C.: Introduction to Mathematical Systems Theory. A Behavioral Approach. Springer, Heidelberg (1998)CrossRefzbMATHGoogle Scholar
  25. 25.
    Păun, G., Rozenberg, G., Salomaa, A.: DNA Computing. Springer, Heidelberg (1998)CrossRefzbMATHGoogle Scholar
  26. 26.
    Ruoff, P., Vinsjevik, M., Monnerjahn, C., Rensing, L.: The Goodwin Oscillator: On the Importance of Degradation Reactions in the Circadian Clock. Journal of Biological Rhythms 14(6), 469–479 (1999)CrossRefGoogle Scholar
  27. 27.
    Samoilov, M., Arkin, A., Ross, J.: Signal Processing by Simple Chemical Systems. J. Phys. Chem. A 106(43), 10205–10221 (2002)CrossRefGoogle Scholar
  28. 28.
    Sharma, V.K., Joshi, A.: Clocks, genes, and evolution. The evolution of circadian organization. In: Kumar, V. (ed.) Biological Rhythms, pp. 5–23. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  29. 29.
    Wilhelm, T.: The smallest chemical reaction system with bistability. BMC Systems Biology 3, 90 (2009)CrossRefGoogle Scholar
  30. 30.
    Wolkenhauer, O., Sreenath, S.N., Wellstead, P., Ullah, M., Cho, K.H.: A systems and signal-oriented approach to intracellular dynamics. Biochemical Society Transactions 33, 507–515 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas Hinze
    • 1
  • Christian Bodenstein
    • 1
  • Benedict Schau
    • 1
  • Ines Heiland
    • 1
  • Stefan Schuster
    • 1
  1. 1.School of Biology and Pharmacy, Department of BioinformaticsFriedrich Schiller University JenaJenaGermany

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