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Automated Abstraction Methodology for Genetic Regulatory Networks

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Transactions on Computational Systems Biology VI

Part of the book series: Lecture Notes in Computer Science ((TCSB,volume 4220))

Abstract

In order to efficiently analyze the complicated regulatory systems often encountered in biological settings, abstraction is essential. This paper presents an automated abstraction methodology that systematically reduces the small-scale complexity found in genetic regulatory network models, while broadly preserving the large-scale system behavior. Our method first reduces the number of reactions by using rapid equilibrium and quasi-steady-state approximations as well as a number of other stoichiometry-simplifying techniques, which together result in substantially shortened simulation time. To further reduce analysis time, our method can represent the molecular state of the system by a set of scaled Boolean (or n-ary) discrete levels. This results in a chemical master equation that is approximated by a Markov chain with a much smaller state space providing significant analysis time acceleration and computability gains. The genetic regulatory network for the phage λ lysis/lysogeny decision switch is used as an example throughout the paper to help illustrate the practical applications of our methodology.

This material is based upon work supported by the National Science Foundation under Grant No. 0331270.

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References

  1. Jong, H.D.: Modeling and simulation of genetic regulatory systems: A literature review. J. Comp. Biol. 9(1), 67–103 (2002)

    Article  Google Scholar 

  2. Baldi, P., Hatfield, G.W.: DNA Microarrays and Gene Expression. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  3. Arkin, A., Ross, J., McAdams, H.H.: Stochastic kinetic analysis of developmental pathway bifurcation in phage lambda-infected escherichia coli cells. Genetics 149, 1633–1648 (1998)

    Google Scholar 

  4. Elowitz, M.B., Levine, A.J., Siggia, E.D., Swain, P.S.: Stochastic gene expression in a single cell. Science 297, 1183–1186 (2002)

    Article  Google Scholar 

  5. Rao, C.V., Wolf, D.M., Arkin, A.P.: Control, exploitation and tolerance of intracellular noise. Nature 420, 231–238 (2002)

    Article  Google Scholar 

  6. Samoilov, M., Plyasunov, S., Arkin, A.P.: Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proceedings of the National Academy of Sciences US 102(7), 2310–2315 (2005)

    Article  Google Scholar 

  7. Raser, J.M., O’Shea, E.K.: Control of stochasticity in eukaryotic gene expression. Science 304, 1811–1814 (2004)

    Article  Google Scholar 

  8. Kierzek, A.M., Zaim, J., Zielenkiewicz, P.: The effect of transcription and translation initiation frequencies on the stochastic fluctuations in prokaryotic gene expression. J. Biol. Chem 276, 8165 (2001)

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Gillespie, D.T.: A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics 22, 403–434 (1976)

    Article  MathSciNet  Google Scholar 

  11. Turner, T.E., Schnell, S., Burrage, K.: Stochastic approaches for modelling in vivo reactions. Computational Biology 28 (2004)

    Google Scholar 

  12. Gibson, M.A., Bruck, J.: Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A 104, 1876–1889 (2000)

    Google Scholar 

  13. Gibson, M., Bruck, J.: An efficient algorithm for generating trajectories of stochastic gene regulation reactions. Technical report, California Institute of Technology (1998)

    Google Scholar 

  14. Gillespie, D.T.: Approximate accelerated stochastic simulation of chemically reacting systems. Journal of Chemical Physics 115(4), 1716–1733 (2001)

    Article  Google Scholar 

  15. Rathinam, M., Cao, Y., Petzold, L., Gillespie, D.: Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method. Journal of Chemical Physics 119, 12784–12794 (2003)

    Article  Google Scholar 

  16. Gillespie, D.T., Petzold, L.R.: Improved leap-size selection for accelerated stochastic simulation. Journal of Chemical Physics 119 (2003)

    Google Scholar 

  17. Cao, Y., Gillespie, D., Petzold, L.: Avoiding negative populations in explicit tau leaping. Journal of Chemical Physics 123 (2005)

    Google Scholar 

  18. Rao, C.V., Arkin, A.P.: Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the gillespie algorithm. J. Phys. Chem. 118(11) (2003)

    Google Scholar 

  19. Schnell, S., Maini, P.K.: A century of enzyme kinetics: Reliability of the k m and v max estimates. Comments on Theoretical Biology 8, 169–187 (2003)

    Article  Google Scholar 

  20. Myers, C.J., Belluomini, W., Killpack, K., Mercer, E., Peskin, E., Zheng, H.: Timed circuits: A new paradigm for high-speed design, pp. 335–340 (2001)

    Google Scholar 

  21. Berry, R.S., Rice, S.A., Ross, J.: Physical Chemistry, 2nd edn. Oxford University Press, New York (2000)

    Google Scholar 

  22. Systems Biology Workbench Development Group, http://www.sbw-sbml.org/

  23. BioSPICE, http://www.biospice.org/

  24. Schnell, S., Mendoza, C.: Enzyme kinetics of multiple alternative substrates. Journal of Mathematical Chemistry 27, 155–170 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  25. Ackers, G.K., Johnson, A.D., Shea, M.A.: Quantitative model for gene regulation by λ phage repressor. Proc. Natl. Acad. Sci. USA 79, 1129–1133 (1982)

    Article  Google Scholar 

  26. Santillán, M., Mackey, M.C.: Why the lysogenic state of phase λ is stable: A mathematical modeling approch. Biophysical Jounal 86 (2004)

    Google Scholar 

  27. Dacol, D.K., Rabitz, H.: Sensitivity analysis of stochastic kinetic models. J. Math. Phys. 25 (1984)

    Google Scholar 

  28. Gunawan, R., Cao, Y., Petzold, L., Doyle, F.J.: Sensitivity analysis of discrete stochastic systems. Biophysical Journal 88, 2530–2540 (2005)

    Article  Google Scholar 

  29. REB2SAC, http://www.async.ece.utah.edu/tools/

  30. Kourilsky, P.: Lysogenization by bacteriophage lambda: I. multiple infection and the lysogenic response. Mol. Gen. Genet. 122, 183–195 (1973)

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. Gillespie, D.T.: Markov Processes An Introduction for Physical Scientists. Academic Press, London (1992)

    MATH  Google Scholar 

  33. Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)

    MATH  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Kuwahara, H., Myers, C.J., Samoilov, M.S., Barker, N.A., Arkin, A.P. (2006). Automated Abstraction Methodology for Genetic Regulatory Networks. In: Priami, C., Plotkin, G. (eds) Transactions on Computational Systems Biology VI. Lecture Notes in Computer Science(), vol 4220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11880646_7

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  • DOI: https://doi.org/10.1007/11880646_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45779-4

  • Online ISBN: 978-3-540-46236-1

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