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International Symposium on Automated Technology for Verification and Analysis

ATVA 2008: Automated Technology for Verification and Analysis pp 48–63Cite as

Computation Tree Regular Logic for Genetic Regulatory Networks

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5311))

Abstract

Model checking has proven to be a useful analysis technique not only for concurrent systems, but also for the genetic regulatory networks (Grns) that govern the functioning of living cells. The applications of model checking in systems biology have revealed that temporal logics should be able to capture both branching-time and fairness properties. At the same time, they should have a user-friendly syntax easy to employ by non-experts. In this paper, we define Ctrl (Computation Tree Regular Logic), an extension of Ctl with regular expressions and fairness operators that attempts to match these criteria. Ctrlsubsumes both Ctl and Ltl, and has a reduced set of temporal operators indexed by regular expressions, inspired from the modalities of Pdl (Propositional Dynamic Logic). We also develop a translation of Ctrl into HmlR (Hennessy-Milner Logic with Recursion), an equational variant of the modal μ-calculus. This has allowed us to obtain an on-the-fly model checker with diagnostic for Ctrl by directly reusing the verification technology available in the Cadp toolbox. We illustrate the application of the Ctrl model checker by analyzing the Grn controlling the carbon starvation response of Escherichia coli.

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References

  1. Fisher, J., Henzinger, T.A.: Executable cell biology. Nature Biotechnology 25(11), 1239–1250 (2007)

    Article  Google Scholar 

  2. Regev, A., Shapiro, E.: Cells as computation. Nature 419(6905), 343 (2002)

    Article  Google Scholar 

  3. de Jong, H.: Modeling and simulation of genetic regulatory systems: A literature review. J. of Computational Biology 9(1), 67–103 (2002)

    Article  Google Scholar 

  4. Antoniotti, M., Policriti, A., Ugel, N., Mishra, B.: Model building and model checking for biochemical processes. Cell Biochemistry and Biophysics 38(3), 271–286 (2003)

    Article  Google Scholar 

  5. Barnat, J., Brim, L., Cerná, I., Drazan, S., Safranek, D.: Parallel model checking large-scale genetic regulatory networks with DiVinE. In: FBTC 2007. ENTCS, vol. 194 (2008)

    Google Scholar 

  6. Batt, G., Ropers, D., de Jong, H., Geiselmann, J., Mateescu, R., Page, M., Schneider, D.: Validation of qualitative models of genetic regulatory networks by model checking: Analysis of the nutritional stress response in Escherichia coli. Bioinformatics 21 (Suppl. 1), i19–i28 (2005)

    Google Scholar 

  7. Bernot, G., Comet, J.-P., Richard, A., Guespin, J.: Application of formal methods to biological regulatory networks: Extending Thomas’ asynchronous logical approach with temporal logic. J. of Theoretical Biology 229(3), 339–348 (2004)

    Article  MathSciNet  Google Scholar 

  8. Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using the PRISM model checker. In: CMSB 2005, pp. 79–90 (2005)

    Google Scholar 

  9. Chabrier-Rivier, N., Chiaverini, M., Danos, V., Fages, F., Schächter, V.: Modeling and querying biomolecular interaction networks. TCS 325(1), 25–44 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fisher, J., Piterman, N., Hajnal, A., Henzinger, T.A.: Predictive modeling of signaling crosstalk during C. elegans vulval development. PLoS Computational Biology 3(5), e92 (2007)

    Article  Google Scholar 

  11. Batt, G., Bergamini, D., de Jong, H., Gavarel, H., Mateescu, R.: Model checking genetic regulatory networks using GNA and CADP. In: Graf, S., Mounier, L. (eds.) SPIN 2004. LNCS, vol. 2989, pp. 158–163. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Cimatti, A., Clarke, E., Giunchiglia, F., Roveri, M.: NuSMV: a new symbolic model checker. STTT 2(4), 410–425 (2000)

    Article  MATH  Google Scholar 

  13. Garavel, H., Lang, F., Mateescu, R., Serwe, W.: CADP 2006: A toolbox for the construction and analysis of distributed processes. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 158–163. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Thomas, R., Thieffry, D., Kaufman, M.: Dynamical behaviour of biological regulatory networks: I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bulletin of Mathematical Biology 57(2), 247–276 (1995)

    Article  MATH  Google Scholar 

  15. Manna, Z., Pnueli, A.: The Temporal Logic of Reactive and Concurrent Systems. Specification, vol. I. Springer, Heidelberg (1992)

    Book  MATH  Google Scholar 

  16. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  17. Emerson, E.A., Halpern, J.Y.: Sometimes and not never revisited: On branching versus linear time. In: POPL 1983, pp. 127–140 (January 1983)

    Google Scholar 

  18. Kozen, D.: Results on the propositional μ-calculus. TCS 27, 333–354 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  19. Beer, I., Ben-David, S., Landver, A.: On-the-fly model checking of RCTL formulas. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 184–194. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  20. Brázdil, T., Cerná, I.: Model checking of RegCTL. Computers and Artificial Intelligence 25(1) (2006)

    Google Scholar 

  21. Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. JCSS 18(2), 194–211 (1979)

    MathSciNet  MATH  Google Scholar 

  22. Streett, R.: Propositional dynamic logic of looping and converse. Information and Control (1982)

    Google Scholar 

  23. Larsen, K.G.: Proof systems for Hennessy-Milner logic with recursion. In: Dauchet, M., Nivat, M. (eds.) CAAP 1988. LNCS, vol. 299, pp. 215–230. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  24. Mateescu, R.: CÆSAR_SOLVE: A generic library for on-the-fly resolution of alternation-free boolean equation systems. STTT 8(1), 37–56 (2006)

    Article  Google Scholar 

  25. Mateescu, R., Monteiro, P.T., Dumas, E., Mateescu, R.: Computation tree regular logic for genetic regulatory networks. Research Report RR-6521, INRIA (2008)

    Google Scholar 

  26. Beer, I., Ben-David, S., Eisner, C., Fisman, D., Gringauze, A., Rodeh, Y.: The temporal logic Sugar. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 363–367. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  27. Holzmann, G.: The SPIN Model Checker – Primer and Reference Manual. Addison-Wesley, Reading (2003)

    Google Scholar 

  28. Wolper, P.: A translation from full branching time temporal logic to one letter propositional dynamic logic with looping (published manuscript, 1982)

    Google Scholar 

  29. Mateescu, R., Sighireanu, M.: Efficient on-the-fly model-checking for regular alternation-free mu-calculus. SCP 46(3), 255–281 (2003)

    MathSciNet  MATH  Google Scholar 

  30. Brzozowski, J.A.: Derivatives of regular expressions. JACM 11(4), 481–494 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  31. Aho, A.V., Sethi, R., Ullman, J.D.: Compilers: Principles, Techniques and Tools. Addison-Wesley, Reading (1986)

    MATH  Google Scholar 

  32. Cleaveland, R., Steffen, B.: A linear-time model-checking algorithm for the alternation-free modal mu-calculus. FMSD 2(2), 121–147 (1993)

    MATH  Google Scholar 

  33. Andersen, H.R.: Model checking and boolean graphs. TCS 126(1), 3–30 (1994)

    Article  MATH  Google Scholar 

  34. Vergauwen, B., Lewi, J.: Efficient local correctness checking for single and alternating boolean equation systems. In: Shamir, E., Abiteboul, S. (eds.) ICALP 1994. LNCS, vol. 820, pp. 304–315. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  35. Mateescu, R., Thivolle, D.: A model checking language for concurrent value-passing systems. In: Cuellar, J., Maibaum, T.S.E. (eds.) FM 2008. LNCS, vol. 5014, pp. 148–164. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  36. Arts, T., Earle, C.B., Derrick, J.: Development of a verified Erlang program for resource locking. STTT 5(2–3), 205–220 (2004)

    Article  Google Scholar 

  37. Garavel, H.: OPEN/CÆSAR: An open software architecture for verification, simulation, and testing. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 68–84. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  38. Garavel, H., Lang, F., Mateescu, R.: Compiler construction using LOTOS NT. In: Horspool, R.N. (ed.) CC 2002. LNCS, vol. 2304, pp. 9–13. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  39. Glass, L., Kauffman, S.A.: The logical analysis of continuous non-linear biochemical control networks. J. of Theoretical Biology 39(1), 103–129 (1973)

    Article  Google Scholar 

  40. Batt, G., de Jong, H., Page, M., Geiselmann, J.: Symbolic reachability analysis of genetic regulatory networks using discrete abstractions. Automatica 44(4), 982–989 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  41. de Jong, H., Gouzé, J.-L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bulletin of Mathematical Biology 66(2), 301–340 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  42. Ropers, D., de Jong, H., Page, M., Schneider, D., Geiselmann, J.: Qualitative simulation of the carbon starvation response in Escherichia coli. Biosystems 84(2), 124–152 (2006)

    Article  Google Scholar 

  43. Joubert, C., Mateescu, R.: Distributed local resolution of boolean equation systems. In: PDP 2005. IEEE Computer Society, Los Alamitos (2005)

    Google Scholar 

  44. Joubert, C., Mateescu, R.: Distributed on-the-fly model checking and test case generation. In: Valmari, A. (ed.) SPIN 2006. LNCS, vol. 3925, pp. 126–145. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  45. Monteiro, P.T., Ropers, D., Mateescu, R., Freitas, A.T., de Jong, H.: Temporal logic patterns for querying dynamic models of cellular interaction networks. Bioinformatics (in press, 2008)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Inria Rhône-Alpes, 655 Av. de l’Europe, F-38330, Montbonnot St Martin, France

    Radu Mateescu, Pedro T. Monteiro, Estelle Dumas & Hidde de Jong

  2. Inesc-Id/Ist, Rua Alves Redol 9, 1000-029, Lisboa, Portugal

    Pedro T. Monteiro

Authors
  1. Radu Mateescu
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  2. Pedro T. Monteiro
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  3. Estelle Dumas
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  4. Hidde de Jong
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Editor information

Editors and Affiliations

  1. College of Information & Communication, Division of Computer and Communication Engineering, Korea University, Anam-Dong, Seongbuk-Gu, 136-701, Seoul, South Korea

    Sungdeok (Steve) Cha

  2. Departmnet of Computer Science and Engineering, Korea University, Anam-Dong, Seongbuk-Gu, 136-702, Seoul, South Korea

    Jin-Young Choi

  3. KAIST, Department of Computer Science, Guseong-Dong, Yuseong-Gu, 305-701, Daejon, South Korea

    Moonzoo Kim

  4. School of Engineering and Applied Science, Department of Computer and Information Science,, University of Pennsylvania, Levine Hall, Room 602, 3330 Walnut Street, PA 19104-6389, Philadelphia, USA

    Insup Lee

  5. Thomas M. Siebel Center , University of Illinois at Urbana-Champaign, 201 N. Goodwin Avenue, IL 61801-2302, Urbana, USA

    Mahesh Viswanathan

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© 2008 Springer-Verlag Berlin Heidelberg

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Mateescu, R., Monteiro, P.T., Dumas, E., de Jong, H. (2008). Computation Tree Regular Logic for Genetic Regulatory Networks. In: Cha, S.(., Choi, JY., Kim, M., Lee, I., Viswanathan, M. (eds) Automated Technology for Verification and Analysis. ATVA 2008. Lecture Notes in Computer Science, vol 5311. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88387-6_6

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  • DOI: https://doi.org/10.1007/978-3-540-88387-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88386-9

  • Online ISBN: 978-3-540-88387-6

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