Skip to main content
SpringerLink
Log in
Book cover

Applications of Membrane Computing in Systems and Synthetic Biology pp 133–173Cite as

Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for Applications in Chronobiology

Part of the Emergence, Complexity and Computation book series (ECC,volume 7)

Abstract

This chapter addresses three coordinated chronobiological studies demonstrating the convergence of experimental observations, fine-grained spatio-temporal modelling, and predictive simulation. Due to the discrete manner of molecular assembly in cell signalling and gene regulation, we define a framework of membrane systems equipped with discretised forms of reaction kinetics in concert with variable intramolecular structures. Our first study is dedicated to circadian clocks inducing daily biological rhythms. As an inspiring example, the KaiABC core oscillator reaches its functionality by cyclically varying protein structures. Within our second study, we present a meta-model of an entire circadian clockwork able to adapt its oscillation to an external stimulus in terms of a frequency control system acting in a phase-locked loop. Substrate concentration courses resulting from gene expression reflect its oscillatory behaviour utilised in a periodical trigger for subsequent processes. In this context, our third study cytometrically quantifies the dynamical behaviour of a bistable toggle switch resulting from mutual gene regulation.

Keywords

  • Circadian Clock
  • Gene Regulatory Network
  • Membrane System
  • Derivation Tree
  • Reaction Rule

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    See the BioNetGen Documentation. A BioNetGen tutorial can be found online at: http://bionetgen.org/index.php/BioNetGen_Tutorial

  2. 2.

    www.biosystemsanalysis.de

References

  1. B. Alberts, Essential Cell Biology (Garland Publishing, London, 2003)

    Google Scholar 

  2. U. Albrecht, The Circadian Clock (Springer Verlag, New York, 2010)

    CrossRef  Google Scholar 

  3. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman and Hall, Boca Raton, 2006)

    Google Scholar 

  4. A.P. Arkin, Synthetic cell biology. Curr. Opin. Biotechnol. 12(6), 638–644 (2011)

    CrossRef  Google Scholar 

  5. I.M. Axmann, S. Legewie, H. Herzel, A minimal circadian clock model. Genome Inf. 18, 54–64 (2007)

    Google Scholar 

  6. N. Barbacari, A. Profir, C. Zelinschi, Gene regulatory network modelling by means of membrane systems, in 7th International Workshop on Membrane Computing WMC 2006, ed. by H.J. Hoogeboom, G. Păun, G. Rozenberg, A. Salomaa, vol. 4361 (LNCS, 2006), pp. 162–178

    Google Scholar 

  7. J. Behre, S. Schuster, Modeling signal transduction in enzyme cascades with the concept of elementary flux modes. J. Comput. Biol. 16(6), 829–844 (2009)

    CrossRef  Google Scholar 

  8. B.W. Bequette, Process Control: Modeling, Design, and Simulation (Prentice Hall, Upper Saddle River, 2003)

    Google Scholar 

  9. F. Bernardini, V. Manca, Dynamical aspects of P systems. BioSystems 70, 85–93 (2003)

    CrossRef  Google Scholar 

  10. R.E. Best, Phase-Locked Loops: Design, Simulation, and Applications (McGraw-Hill, New York, 2007)

    Google Scholar 

  11. M.L. Blinov, J.R. Faeder, B. Goldstein, W.S. Hlavacek, BioNetGen: software for rule-based modeling of signal transduction based on the interactions of molecular domains. Bioinformatics 20, 3289–3292 (2004)

    CrossRef  Google Scholar 

  12. M.L. Blinov, J.R. Faeder, B. Goldstein, W.S. Hlavacek, A network model of early events in epidermal growth factor receptor signaling that accounts for combinatorial complexity. BioSystems 83, 136–151 (2006)

    CrossRef  Google Scholar 

  13. N. Busi, C. Zandron, Computing with genetic gates, proteins and membranes, in 7th International Workshop on Membrane Computing WMC 2006, ed. by H.J. Hoogeboom, G. Păun, G. Rozenberg, A. Salomaa, vol. 4361 (LNCS, 2006), pp. 213–228

    Google Scholar 

  14. K.A. Connors, Chemical Kinetics (VCH Publishers, New York, 1990)

    Google Scholar 

  15. P. Dittrich, J. Ziegler, W. Banzhaf, Artificial chemistries—a review. Artif. Life 7(3), 225–275 (2001)

    CrossRef  Google Scholar 

  16. F. Fontana, V. Manca, Discrete solutions to differential equations by metabolic P systems. Theor. Comput. Sci. 372(2–3), 165–182 (2007)

    CrossRef  MATH  MathSciNet  Google Scholar 

  17. P. Frisco, Computing with Cells. Advances in Membrane Computing (Oxford University Press, Oxford, 2009)

    CrossRef  MATH  Google Scholar 

  18. T.S. Gardner, C.R. Cantor, J.J. Collins, Construction of a genetic toggle switch in Escherichia coli. Nature 403, 339–342 (2000)

    CrossRef  Google Scholar 

  19. D.T. Gillespie, Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)

    CrossRef  Google Scholar 

  20. D.T. Gillespie, A rigorous derivation of the chemical master equation. Physica A 188(1–3), 404–425 (1992)

    CrossRef  MathSciNet  Google Scholar 

  21. S.S. Golden, V.M. Cassone, A. LiWang, Shifting nanoscopic clock gears. Nat. Struct. Mol. Biol. 14, 362–363 (2007)

    CrossRef  Google Scholar 

  22. B.C. Goodwin, Oscillatory behaviour in enzymatic control processes. Adv. Enzyme Regul. 3, 425–438 (1965)

    CrossRef  Google Scholar 

  23. G. Gruenert, B. Ibrahim, T. Lenser, M. Lohel, T. Hinze, P. Dittrich, Rule-based spatial modeling with diffusing, geometrically constrained molecules. BMC Bioinform. 11, 307 (2010)

    CrossRef  Google Scholar 

  24. G. Gruenert, P. Dittrich, Using the SRSim software for spatial and rule-based modelling of combinatorially complex biochemical reaction systems, in 11th International Conference on Membrane Computing CMC 2010, ed. by M. Gheorghe, T. Hinze, G. Păun, G. Rozenberg, A. Salomaa, vol. 6501 (LNCS, 2010), pp. 240–256

    Google Scholar 

  25. J. Hastings, K.H. Nealson, Bacterial bioluminescence. Ann. Rev. Microbiol. 31, 549–595 (1977)

    CrossRef  Google Scholar 

  26. B.A. Hawkins, H.V. Cornell, Theoretical Approaches to Biological Control (Cambridge University Press, Cambridge, 1999)

    CrossRef  MATH  Google Scholar 

  27. S. Hayat, K. Ostermann, L. Brusch, W. Pompe, G. Rödel, Towards in vivo computing: quantitative analysis of an artificial gene regulatory network behaving as an RS flip-flop, in 1st International Conference on Bio Inspired Models of Network, Information and Computing Systems BIONETICS 06, ed. by T. Suda, C. Tschudin (ACM, 2006)

    Google Scholar 

  28. R. Heinrich, S. Schuster, The Regulation of Cellular Systems (Springer-Verlag, 2006)

    Google Scholar 

  29. T. Hinze, T. Lenser, P. Dittrich, A protein substructure based P system for description and analysis of cell signalling networks, in 7th International Workshop on Membrane Computing WMC 2006, ed. by H.J. Hoogeboom, G. Păun, G. Rozenberg, A. Salomaa, vol. 4361 (LNCS, 2006), pp. 409–423

    Google Scholar 

  30. T. Hinze, S. Hayat, T. Lenser, N. Matsumaru, P. Dittrich, Hill kinetics meets P systems, in 8th International Workshop on Membrane Computing WMC 2007, ed. by G. Eleftherakis, P. Kefalas, G. Păun, G. Rozenberg, A. Salomaa, vol. 4860 (LNCS, 2007), pp. 320–335

    Google Scholar 

  31. T. Hinze, R. Fassler, T. Lenser, P. Dittrich, Register machine computations on binary numbers by oscillating and catalytic chemical reactions modelled using mass-action kinetics. Int. J. Found. Comput. Sci. 20(3), 411–426 (2009)

    CrossRef  MATH  MathSciNet  Google Scholar 

  32. T. Hinze, T. Lenser, G. Escuela, I. Heiland, S. Schuster, Modelling signalling networks with incomplete information about protein activation states: a P system framework of the KaiABC oscillator, in 10th International Workshop on Membrane Computing WMC 2009, ed. by G. Păun, M.J. Perez-Jimenez, A. Riscos-Nunez, G. Rozenberg, A. Salomaa, vol. 5957 (LNCS, 2010), pp. 316–334

    Google Scholar 

  33. T. Hinze, C. Bodenstein, B. Schau, I. Heiland, S. Schuster, Chemical analog computers for clock frequency control based on P modules, in 12th International Conference on Membrane Computing CMC 2011, ed. by M. Gheorghe, G. Păun, G. Rozenberg, A. Salomaa, S. Verlan, vol. 7184 (LNCS, 2012), pp. 182–202

    Google Scholar 

  34. W.S. Hlavacek, J.R. Faeder, M.L. Blinov, R.G. Posner, M. Hucka, W. Fontana, Rules for modeling signal-transduction systems. Sci. STKE 344, re6 (2006)

    Google Scholar 

  35. P. Hofstedt, Multiparadigm Constraint Programming Languages. Series Cognitive Technologies (Springer, New York, 2011)

    CrossRef  Google Scholar 

  36. W.L. Koukkari, R.B. Sothern, Introducing Biological Rhythms (Springer Verlag, Berlin, 2006)

    Google Scholar 

  37. N. Krasnogor, M. Gheorghe, G. Terrazas, S. Diggle, P. Williams, M. Camara, An appealing computational mechanism drawn from bacterial quorum sensing. Bull. EATCS 85, 135–148 (2005)

    MATH  MathSciNet  Google Scholar 

  38. G. Krauss, Biochemistry of Signal Transduction and Regulation (Wiley-VCH, Weinheim, 2003)

    CrossRef  Google Scholar 

  39. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulences (Springer Verlag, Berlin, 1984)

    CrossRef  Google Scholar 

  40. T. Lenser, T. Hinze, B. Ibrahim, P. Dittrich, Towards evolutionary network reconstruction tools for systems biology, in 5th European Conference on Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics EvoBIO2007, ed. by E. Marchiori, J.H. Moore, J.C. Rajapakse, vol. 4447 (LNCS, 2007), pp. 132–142

    Google Scholar 

  41. R.D. Lewis, Control systems models for the circadian clock of the New Zealand Weta Hemideina thoracia. J. Biol. Rhythms 14, 480–485 (1999)

    CrossRef  Google Scholar 

  42. M.O. Magnasco, Chemical kinetics is turing universal. Phys. Rev. Lett. 78(6), 1190–1193 (1997)

    CrossRef  Google Scholar 

  43. V. Manca, L. Bianco, F. Fontana, Evolution and oscillation in P systems: applications to biological phenomena, in 5th International Workshop on Membrane Computing WMC 2004, vol. 3365 (LNCS, 2005), pp. 63–84

    Google Scholar 

  44. M. Marhl, M. Perc, S. Schuster, Selective regulation of cellular processes via protein cascades acting as band-pass filters for time-limited oscillations. FEBS Lett. 579(25), 5461–5465 (2005)

    CrossRef  Google Scholar 

  45. M.B. Miller, B.L. Bassler, Quorum sensing in bacteria. Ann. Rev. Microbiol. 55, 165–199 (2001)

    CrossRef  Google Scholar 

  46. T. Mori, D.R. Williams, M.O. Byrne, X. Qin, M. Egli, H.S. Mchaourab, P.L. Stewart, C.H. Johnson, Elucidating the ticking of an in vitro circadian clockwork. PLoS Biol. 5(4), 841–853 (2007)

    Google Scholar 

  47. M. Nakajima, K. Imai, H. Ito, T. Nishiwaki, Y. Murayama, Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro. Science 308, 414–415 (2005)

    CrossRef  Google Scholar 

  48. J. O’Neill, G. Ooijen, L.E. Dixon, C. Troein, F. Corellou, F.Y. Bouget, A.B. Reddy, A.J. Millar, Circadian rhythms persist without transcription in a eukaryote. Nature 469, 554–558 (2011)

    CrossRef  Google Scholar 

  49. T. Nishiwaki, Y. Satomi, Y. Kitayama, K. Terauchi, R. Kiyohara, T. Takao, T. Kondo, A sequential program of dual phosphorylation of KaiC as a basis for circadian rhythm in cyanobacteria. EMBO J. 26, 4029–4037 (2007)

    CrossRef  Google Scholar 

  50. D.A. Paranjpe, V.K. Sharma, Evolution of temporal order in living organisms. J. Circadian Rhythms 3, 7 (2007)

    CrossRef  Google Scholar 

  51. G. Păun, Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)

    CrossRef  MATH  MathSciNet  Google Scholar 

  52. G. Păun, Membrane Computing (Springer Verlag, Berlin, 2002)

    Google Scholar 

  53. T. Pavlidis, Biological Oscillators: Their Mathematical Analysis (Academic Press, New York, 1974)

    Google Scholar 

  54. S.J. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995)

    CrossRef  MATH  Google Scholar 

  55. F. Ponten, K. Jirström, M. Uhlen, The human protein atlas: a tool for pathology. J. Pathol. 216(4), 387–393 (2008)

    CrossRef  Google Scholar 

  56. F.J. Romero-Campero, M.J. Perez-Jimenez, Modelling gene expression control using P systems: the Lac Operon, a case study. Biosystems 91(3), 438–457 (2008)

    CrossRef  Google Scholar 

  57. F.J. Romero-Campero, M.J. Perez-Jimenez, A model of the quorum sensing system in Vibrio fischeri using P systems. Artif. Life 14(1), 95–109 (2008)

    CrossRef  Google Scholar 

  58. E. Rosato, Circadian Rhythms: Methods and Protocols (Springer-Verlag, New York, 2007)

    CrossRef  Google Scholar 

  59. F. Rossi, P. van Beek, T. Walsh, Handbook of Constraint Programming (Elsevier Science, Amsterdam, 2006)

    MATH  Google Scholar 

  60. M.R. Roussel, D. Gonze, A. Goldbeter, Modeling the differential fitness of cyanobacterial strains whose circadian oscillators have different free-running periods. J. Theor. Biol. 205(2), 321–340 (2000)

    CrossRef  Google Scholar 

  61. P. Ruoff, M. Vinsjevik, C. Monnerjahn, L. Rensing, The Goodwin oscillator: on the importance of degradation reactions in the circadian clock. J. Biol. Rhythms 14(6), 469–479 (1999)

    CrossRef  Google Scholar 

  62. M. Samoilov, A. Arkin, J. Ross, Signal processing by simple chemical systems. J. Phys. Chem. A 106(43), 10205–10221 (2002)

    CrossRef  Google Scholar 

  63. J. Smaldon, N. Krasnogor, C. Alexander, M. Gheorghe, Liposome logic, in 11th Annual Conference on Genetic and Evolutionary Computation GECCO 2009, ed. by F. Rothlauf (ACM, 2009), pp. 161–168

    Google Scholar 

  64. J. Tomita, M. Nakajima, T. Kondo, H. Iwasaki, No transcription-translation feedback in circadian rhythm of KaiC phosphorylation. Science 307, 251–254 (2005)

    CrossRef  Google Scholar 

  65. O. Wolkenhauer, S.N. Sreenath, P. Wellstead, M. Ullah, K.H. Cho, A systems and signal-oriented approach to intracellular dynamics. Biochem. Soc. Trans. 33, 507–515 (2005)

    CrossRef  Google Scholar 

  66. SRSim web site. http://www.biosys.uni-jena.de/Members/Gerd+Gruenert/SRSim.html

  67. Model repository and download area. http://www.molecular-computing.de via menu item Veröffentlichungen/Publications

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science and Information and Media Technology, Brandenburg University of Technology, Postfach 10 13 44, 03013, Cottbus, Germany

    Thomas Hinze, Petra Hofstedt & Peter Sauer

  2. School of Biology and Pharmacy, Department of Bioinformatics, Friedrich Schiller University of Jena, Ernst-Abbe-Platz 1–4, 07743, Jena, Germany

    Thomas Hinze, Christian Bodenstein, Gabi Escuela, Gerd Grünert & Peter Dittrich

  3. Theoretical Systems Biology Group, Institute of Food Research, Norwich Research Park, Colney, Norwich, NR4 7UA, UK

    Jörn Behre

  4. Department of Biochemistry and Biophysics, University of Stockholm, Svante Arrhenius väg 16C, SE-106 91, Stockholm, Sweden

    Sikander Hayat

Authors
  1. Thomas Hinze
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jörn Behre
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christian Bodenstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gabi Escuela
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Gerd Grünert
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Petra Hofstedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Peter Sauer
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Sikander Hayat
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Peter Dittrich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thomas Hinze .

Editor information

Editors and Affiliations

  1. The School of Mathematical and Computer Sciences, Heriot-Watt University, Eindhoven, United Kingdom

    Pierluigi Frisco

  2. The Department of Computer Science, University of Sheffield, Sheffield, United Kingdom

    Marian Gheorghe

  3. Department of Computer Science and Artificial Intelligence, University of Sevilla, Sevilla, Spain

    Mario J. Pérez-Jiménez

Rights and permissions

Reprints and Permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Hinze, T. et al. (2014). Membrane Systems and Tools Combining Dynamical Structures with Reaction Kinetics for Applications in Chronobiology. In: Frisco, P., Gheorghe, M., Pérez-Jiménez, M. (eds) Applications of Membrane Computing in Systems and Synthetic Biology. Emergence, Complexity and Computation, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-03191-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03191-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03190-3

  • Online ISBN: 978-3-319-03191-0

  • eBook Packages: EngineeringEngineering (R0)

search

Navigation