Skip to main content
SpringerLink
Log in

The Continuous π-Calculus: A Process Algebra for Biochemical Modelling

  • Conference paper
Computational Methods in Systems Biology (CMSB 2008)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 5307))

Included in the following conference series:

Abstract

We introduce the continuous π -calculus, a process algebra for modelling behaviour and variation in molecular systems. Key features of the language are: its expressive succinctness; support for diverse interaction between agents via a flexible network of molecular affinities; and operational semantics for a continuous space of processes. This compositional semantics also gives a modular way to generate conventional differential equations for system behaviour over time. We illustrate these features with a model of an existing biological system, a simple oscillatory pathway in cyanobacteria. We then discuss future research directions, in particular routes to applying the calculus in the study of evolutionary properties of biochemical pathways.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Priami, C., Regev, A., Shapiro, E., Silverman, W.: Application of a stochastic name-passing calculus to representation and simulation of molecular processes. Inf. Proc. Lett. 80 (2001)

    Google Scholar 

  2. Regev, A.: Computational Systems Biology: A Calculus for Biochemical Knowledge. PhD thesis, Tel Aviv University (2002)

    Google Scholar 

  3. Regev, A., Silverman, W., Shapiro, E.: Representation and simulation of biochemical processes using the pi-calculus process algebra. In: Pacific Symposium on Biocomputing (2001)

    Google Scholar 

  4. Kitano, H.: Biological robustness. Nature 5, 826–837 (2004)

    CAS  Google Scholar 

  5. Wagner, A.: Robustness and Evolvability in Living Systems. Princeton University Press, Princeton (2005)

    Google Scholar 

  6. Schuster, P., Fontana, W., Stadler, P., Hofacker, I.: From sequences to shapes and back: A case-study in RNA secondary structures. Proc. Royal Soc. Ser. B 255 (1994)

    Google Scholar 

  7. Tomita, J., Nakajima, M., Kondo, T., Iwasaki, H.: No transcription-translation feedback in circadian rhythm of KaiC phosphorylation. Science 307(5707), 251–254 (2005)

    Article  CAS  PubMed  Google Scholar 

  8. van Zon, J.S., Lubensky, D.K., Altena, P.R.H., ten Wolde, P.R.: An allosteric model of circadian KaiC phosphorylation. PNAS 104(18), 7420–7425 (2007)

    Article  PubMed  PubMed Central  Google Scholar 

  9. Milner, R.: The polyadic π-calculus: A tutorial. Technical Report ECS-LFCS-91-180, LFCS, University of Edinburgh (1991)

    Google Scholar 

  10. Milner, R.: Communicating and Mobile Systems: The π Calculus. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  11. Parrow, J.: An introduction to the π-calculus. In: Handbook of Process Algebra, pp. 479–543. Elsevier, Amsterdam (2001)

    Chapter  Google Scholar 

  12. Gillespie, D.T.: The chemical Langevin equation. J. Chem. Phys. 113(1), 297–306 (2000)

    Article  CAS  Google Scholar 

  13. Regev, A., Shapiro, E.: Cellular abstractions: Cells as computations. Nature 419 (2002)

    Google Scholar 

  14. Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: Bioambients: An abstraction for biological compartments. Theor. Comput. Sci. 325 (2004)

    Google Scholar 

  15. Hillston, J.: A Compositional Approach to Performance Modelling. Cambridge University Press, Cambridge (1996)

    Book  Google Scholar 

  16. Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. In: Proc. BioConcur. (2004)

    Google Scholar 

  17. Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. Theor. Comput. Sci. (2007)

    Google Scholar 

  18. Calder, M., Duguid, A., Gilmore, S., Hillston, J.: Stronger computational modelling of signalling pathways using both continuous and discrete-state methods. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 63–77. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  19. Kitano, H.: Towards system-level understanding of biological systems. In: Foundations of Systems Biology. MIT Press, Cambridge (2001)

    Google Scholar 

  20. Stadler, B.M.R., Stadler, P.F., Wagner, G., Fontana, W.: The topology of the possible: Formal spaces underlying patterns of evolutionary change. J. Theor. Biol. 213 (2001)

    Google Scholar 

  21. Soyer, O., Salathe, M., Bonhoeffer, S.: Signal transduction networks: Topology, response, and biochemical reactions. J. Theor. Biol. 238 (2006)

    Google Scholar 

  22. Plotkin, G.D.: A structural approach to operational semantics. J. Log. Algeb. Progr. 60–61, 17–139 (2004)

    Google Scholar 

  23. 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  CAS  PubMed  Google Scholar 

  24. Golden, S.S., Johnson, C.H., Kondo, T.: The cyanobacterial circadian system: A clock apart. Current Opinion in Microbiology 1(6), 669–673 (1998)

    Article  CAS  PubMed  Google Scholar 

  25. van Zon, J.S., Lubensky, D.K., Altena, P.R.H., ten Wolde, P.R.: An allosteric model of circadian KaiC phosphorylation: Supporting information (2007), http://www.pnas.org/cgi/content/full/0608665104/DC1

  26. Haskell, http://www.haskell.org/

  27. Peyton Jones, S. (ed.): Haskell 98 Language and Libraries: The Revised Report. Cambridge University Press, Cambridge (April 2003)

    Google Scholar 

  28. Octave, http://www.gnu.org/software/octave/

  29. Eaton, J.W.: GNU Octave Manual. Network Theory (2002)

    Google Scholar 

  30. van Zon, J.S.: A detail of the KaiABC model. Personal communication (2008)

    Google Scholar 

  31. Calder, M., Gilmore, S., Hillston, J.: Automatically deriving ODEs from process algebra models of signalling pathways. In: Proc. CMSB (2005)

    Google Scholar 

  32. Meyer, R., Khomenko, V., Strazny, T.: A practical approach to verification of mobile systems using net unfoldings. In: Application and Theory of Petri Nets: Proc. ATPN (to appear, 2008)

    Google Scholar 

  33. Demate, L., Priami, C., Romanel, A., Soyer, O.: A formal and integrated framework to simulate evolution of biological pathways. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 106–120. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  34. Priami, C., Quaglia, P.: Beta binders for biological interactions. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 20–33. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  35. Bortolussi, L., Policriti, A.: Connecting process algebras and differential equations for systems biology. In: Process Algebra and Stochastically Timed Activities: Proc. 6th PASTA workshop (2006)

    Google Scholar 

  36. Segala, R., Vaandrager, F., Lynch, N.: Hybrid I/O automata. Inf. & Comput. 185(1) (2003)

    Google Scholar 

  37. Bergstra, J.A., Middleburg, C.A.: Process algebra for hybrid systems. Theor. Comput. Sci. 335 (2005)

    Google Scholar 

  38. Vilar, J.M.G., Guet, C.G., Leibler, S.: Modeling network dynamics: The lac operon, a case study. J. Cell Biol. 161 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Foundations of Computer Science School of Informatics, The University of Edinburgh, Scotland

    Marek Kwiatkowski & Ian Stark

Authors
  1. Marek Kwiatkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ian Stark
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Brandenburg University of Technology, Postbox 10 13 44, 03013, Cottbus, Germany

    Monika Heiner

  2. University of Rostock, Albert-Einstein-Str. 21, D-18059, Rostock, Germany

    Adelinde M. Uhrmacher

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kwiatkowski, M., Stark, I. (2008). The Continuous π-Calculus: A Process Algebra for Biochemical Modelling. In: Heiner, M., Uhrmacher, A.M. (eds) Computational Methods in Systems Biology. CMSB 2008. Lecture Notes in Computer Science(), vol 5307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88562-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88562-7_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88561-0

  • Online ISBN: 978-3-540-88562-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation