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XS-systems: eXtended S-Systems and Algebraic Differential Automata for Modeling Cellular Behavior

  • Marco Antoniotti
  • Alberto Policriti
  • Nadia Ugel
  • Bud Mishra
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2552)

Abstract

Several biological and biochemical mechanisms can be modeled with relativelysimp le sets of differential algebraic equations (DAE). The numerical solution to these differential equations provide the main investigative tool for biologists and biochemists. However, the set of numerical traces of verycomp lex systems become unwieldyt o wade through when several variables are involved. To address this problem, we propose a novel wayto querylarge sets of numerical traces bycom bining in a new wayw ell known tools from numerical analysis, temporal logic and verification, and visualization.

In this paper we describe XS-systems: computational models whose aim is to provide the users of S-systems with the extra tool of an automaton modeling the temporal evolution of complex biochemical reactions. The automaton construction is described starting from both numerical and analytic solutions of the differential equations involved, and parameter determination and tuning are also considered. A temporal logic language for expressing and verifying properties of XS-systems is introduced and a prototype implementation is presented.

Keywords

Temporal Logic Differential Algebraic Equation Genetic Regulatory Network Algebraic Constraint Qualitative Simulation 
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.

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References

  1. [1]
    R. Alur, C. Belta, F. Ivančić, V. Kumar, M. Mintz, G. Pappas, H. Rubin, and J. Schug. Hybrid modeling and simulation of biological systems. In Proc. of the Fourth International Workshop on Hybrid Systems: Computation and Control, LNCS 2034, pages 19–32, Berlin, 2001. Springer-Verlag. 435CrossRefGoogle Scholar
  2. [2]
    R. Alur, C. Courcoubetis, N. Halbwachs, T.A. Henzinger, P.-H. Ho, X. Nicollin, A. Olivero, J. Sifakis, and S. Yovine. The Algorithmic Analysis of Hybrid Systems. Theoretical Computer Science, 138:3–34, 1995. 432, 441zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    U. S. Bhalla and R. Iyengar. Emergent properties of networks of biological signaling pathways. SCIENCE, 283:381–387, 15 January1999. 435Google Scholar
  4. [4]
    R.W. Brockett. Dynamical systems and their associated automata. In U. Helmke, R. Mennicken, and J. Saurer, eds., Systems and Networks: Mathematical Theory and Applications—Proceedings of the 1993 MTNS, volume 77, pages 49–69, Berlin, 1994. Akademie-Verlag. 435, 441Google Scholar
  5. [5]
    A. Cornish-Bowden. Fundamentals of Enzyme Kinetics. Portland Press, London, second revised edition, 1999. 433Google Scholar
  6. [6]
    H. de-Jong, M. Page, C. Hernandez, and J. Geiselmann. Qualitative simulation of genetic regulatoryne tworks: methods and applications. In B. Nebel, ed., Proc. of the 17th Int. Joint Conf. on Art. Int., San Mateo, CA, 2001. Morgan Kaufmann. 434Google Scholar
  7. [7]
    M. Elowitz and S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature, 403:335–338, 2000. 434, 435, 440, 441CrossRefGoogle Scholar
  8. [8]
    E.A. Emerson. Temporal and Modal Logic. In J. van Leeuwen, ed., Handbook of Theoretical Computer Science, volume B, chapter 16, pages 995–1072. MIT Press, 1990. 439Google Scholar
  9. [9]
    D. Endy and R. Brent. Modeling cellular behavior. Nature, 409(18):391–395, January 2001. 435CrossRefGoogle Scholar
  10. [10]
    R. Hofestädt and U. Scholz. Information processing for the analysis of metabolic pathways and inborn errors. BioSystems, 47:91–102, 1998.CrossRefGoogle Scholar
  11. [11]
    D.H. Irvine and M.A. Savageau. Efficient solution of nonlinear ordinary differential equations expressed in S-System canonical form. SIAM Journal on Numerical Analysis, 27(3):704–735, 1990. 434zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    B. Kuipers. Qualitative Reasoning. MIT Press, 1994. 435Google Scholar
  13. [13]
    B. E. Shapiro and E.D. Mjolsness. Developmental simulation with cellerator. In Proc. of the Second International Conference on Systems Biology (ICSB), Pasadena, CA, November 2001. 435Google Scholar
  14. [14]
    B. Shults and B. J. Kuipers. Proving properties of continuous systmes: qualitative simulation and temporal logic. Artificial Intelligence Journal, 92(1-2), 1997. 435Google Scholar
  15. [15]
    E.O. Voit. Canonical Nonlinear Modeling, S-system Approach to Understanding Complexity. Van Nostrand Reinhold, New York, 1991. 432, 433Google Scholar
  16. [16]
    E.O. Voit. Computational Analysis of Biochemical Systems A Practical Guide for Biochemists and Molecular Biologists. Cambridge University Press, 2000. 432, 433Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Marco Antoniotti
    • 1
  • Alberto Policriti
    • 2
  • Nadia Ugel
    • 1
  • Bud Mishra
    • 3
  1. 1.Courant Institute of Mathematical SciencesNYU New YorkUSA
  2. 2.Università di UdineUdineItaly
  3. 3.Watson School of Biological Sciences Cold Spring HarborUSA

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