Advertisement

Hybrid Modeling and Simulation of Biomolecular Networks

  • Rajeev Alur
  • Calin Belta
  • Franjo Ivančić
  • Vijay Kumar
  • Max Mintz
  • George J. Pappas
  • Harvey Rubin
  • Jonathan Schug
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2034)

Abstract

In a biological cell, cellular functions and the genetic regula- tory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feed- back pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes a hybrid systems approach to modeling the intra-cellular network using continuous differ- ential equations to model the feedback mechanisms and mode-switching to describe the changes in the underlying dynamics. We use two case studies to illustrate a modular approach to modeling such networks and describe the architectural and behavioral hierarchy in the underlying models. We describe these models using Charon [2], a language that allows formal description of hybrid systems. We provide preliminary sim- ulation results that demonstrate how our approach can help biologists in their analysis of noisy genetic circuits. Finally we describe our agenda for future work that includes the development of models and simulation for stochastic hybrid systems.1

Keywords

Hybrid System Hybrid Automaton Protein Agent Biomolecular Network mRNA Decay Rate 
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, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The algorithmic analysis of hybrid systems. Theoretical Computer Science, 138:3–34, 1995.zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    R. Alur, R. Grosu, Y. Hur, V. Kumar, and I. Lee. Modular specifications of hybrid systems in Charon In Hybrid Systems: Computation and Control, Third International Workshop, volume LNCS 1790, pages 6–19, 2000.CrossRefGoogle Scholar
  3. 3.
    G. Booch, I. Jacobson, and J. Rumbaugh. Unified Modeling Language User Guide. Addison Wesley, 1997.Google Scholar
  4. 4.
    R. Brent. Genomic biology. Cell, 100(1):169–183, January 2000.CrossRefGoogle Scholar
  5. 5.
    H. de Jong, M. Page, C. Hernandez, H. Geiselmann, and S. Maza. Modeling and Simulation of Genetic Regulatory Networks. ERCIM News, 43, October 2000.Google Scholar
  6. 6.
    A. Deshpande, A. Göllu, and L. Semenzato. SHIFT programming language and run-time systems for dynamic networks of hybrid automata. Technical report, University of California at Berkeley, 1997.Google Scholar
  7. 7.
    M. Elowitz and S. Leibler. Asynthetic oscillatory network of transciptional regulators. Nature, 403:335–338, January 2000.CrossRefGoogle Scholar
  8. 8.
    D.T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 81:2340–2361, 1977.CrossRefGoogle Scholar
  9. 9.
    D. Harel. Statecharts: A visual formalism for complex systems. Science of Computer Programming, 8:231–274, 1987.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    L.H. Hartwell, J.J. Hopfield, S. Leibler, and A.W. Murray. From molecular to modular cell biology. Nature, 402((6761 Suppl)):C47–52, December 1999.CrossRefGoogle Scholar
  11. 11.
    D.J. Hassett, J.F. Ma, J.G. Elkins, T.R. McDermott, U.A. Ochsner, S.E. West, C.T. Huand, J. Fredericks, S. Burnett, P.S. Stewart, G. McFeters, L. Passador, and B.H. Iglewski. Quorum sensing in Pseudomonas aeruginosa controls expression of catalase and superoxide dismutase genes and mediates biofilm susceptibility to hydrogen peroxide. Mol Microbiol, 34(5):1082–1093, December 1999.CrossRefGoogle Scholar
  12. 12.
    C.A.R. Hoare. Communicating Sequential Processes. Prentice-Hall, 1985.Google Scholar
  13. 13.
    S. James, P. Nilson, G. James, S. Kjellenberg, and T. Fagerstrom. Luminescence control in the marine bacterium Vibrio fischeri: An analysis of the dynamics of lux regulation. J Mol Biol, 296(4):1127–1137, March 2000.CrossRefGoogle Scholar
  14. 14.
    D.E. Jr Koshland. The era of pathway quantification. Science, 280:852–853, 1998.CrossRefGoogle Scholar
  15. 15.
    N. Lynch, R. Segala, F. Vaandrager, and H. Weinberg. Hybrid I/O automata. In Hybrid Systems III: Verification and Control, LNCS 1066, pages 496–510, 1996.Google Scholar
  16. 16.
    H. H. McAdams and A. Arkin. Simulation of prokaryotic genetic circuits. Annu. Rev. Biophys. Biomol. Struct., 27:199–224, 1998.CrossRefGoogle Scholar
  17. 17.
    D.M. Sitnikov, J.B. Schineller and T.O. Baldwin. Transcriptional regulation of bioluminescence genes from Vibrio fischeri. Mol Microbiol, 17(5):801–812, September 1995.CrossRefGoogle Scholar
  18. 18.
    K.L. Visick, J. Foster, J. Doino, M. McFall-Ngai and E.G. Ruby. Vibrio fischeri lux genes play an important role in colonization and development of the host light organ. Bacteriol, 182(16):4578–4586, August 2000.CrossRefGoogle Scholar
  19. 19.
    G. von Dassow, E. Meir, E. M. Munro, and G. M. Odell. The segment polarity network is a robust development module. Nature, 406:188–192, July 2000.CrossRefGoogle Scholar
  20. 20.
    H. Yang, M. Matewish, I. Loubens, D.G. Storey, J.S. Lam, and S. Jin. migA, a quorum-responsive gene of Pseudomonas aeruginosa, is highly expressed in the cystic fibrosis lung environment and modifies low-molecular-mass lipopolysaccharide. Microbiology, 146((Pt 10)):2509–2519, October 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Rajeev Alur
  • Calin Belta
  • Franjo Ivančić
  • Vijay Kumar
  • Max Mintz
  • George J. Pappas
  • Harvey Rubin
  • Jonathan Schug

There are no affiliations available

Personalised recommendations

Cite paper

Buy options