Finite state abstraction of a stochastic model of the lactose regulation system of Escherichia coli

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 19-24

  Julius, A Agung ^a   Halasz, Adam ^a   Kumar, Vijay ^a   Pappas, George J ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ESCHERICHIA COLI; FEEDBACK CONTROL; MARKOV PROCESSES; NONLINEAR SYSTEMS; STOCHASTIC MODELS;

DETERMINISTIC MODELS; NONLINEAR DYNAMICAL SYSTEM;

FINITE AUTOMATA;

EID: 39649099594     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.376739     Document Type: Conference Paper

References (35)

1. G. A. Enciso, H. L. Smith, and E. D. Sontag, "Non-monotone systems decomposable into monotone systems with negative feedback," J. of Differential Equations, no. 224, pp. 205-227, 2006.
2. H. El-Samad, H. Kurata, J. Doyle, C. Gross, and M. Khammash, "Surviving heat shock: control strategies for robustness and performance," PNAS, vol. 102, no. 8, pp. 2736-2741, 2005.
3. R. Ghosh and C. Tomlin, "Lateral inhibition through delta-notch signaling: A piecewise affine hybrid model," in Hybrid Systems: Computation and Control, ser. LNCS, vol. 2034. Springer, 2001, pp. 232-246.
4. G. Batt, D. Ropers, H. de Jong, J. Geiselmann, M. Page, and D. Schneider, "Qualitative analysis and verification of hybrid models of genetic regulatory networks: nutritional stress response," in Hybrid Systems: Computation and Control, ser. LNCS. Springer, 2005, pp. 134-150.
5. C. Belta, P. Finin, L. Habets, Á. Halász, M. Imielinski, V. Kumar, and H. Rubin, "Understanding the bacterial stringent response using reachability analysis of hybrid systems," in Hybrid Systems: Computation and Control, ser. LNCS, vol. 2993. Springer, 2004, pp. 111-125.
6. A. Singh and J. Hespanha, "Models for gene regulatory networks using polynomial stochastic hybrid systems," in Proceedings of the 44th Conference on Decision and Control, Seville, Spain, December 2005.
7. K. Amonlirdviman, N. A. Khare, D. R. Tree, W. S. Chen, J. D. Axelrod, and C. J. Tomlin, "Mathematical modeling of planar cell polarity to understand domineering nonautonomy," Science, vol. 307, pp. 423-426, 2005.
8. J. Beckwith, The lactose operon. American Society for Microbiology, 1987, ch. 4, pp. 1444-1452.
9. J. Monod and A. M. Pappenheimer, 'The kinetics of the biosynthesis of beta-galactosidase in escherichia coli as a function of growth," Biochim. et Biophys. Acta, vol. 9, p. 648, 1952.
10. A. Novick and M. Weiner, "Enzyme induction as an all-or-none phenomenon," Proc. Natl. Acad. Sci. USA, vol. 43, pp. 553-566, 1957.
11. W. A. Knorre, "Oscillation of the rate of synthesis of betagalactosidase in escherichia coli ml 30 and ml 308," Biochem. Biophys. Res. Commun, 1968.
12. N. P. Pih and P. Dhurjati, "Oscillatory behavior of beta-galactosidase enzyme activity in escherichia coli during perturbed batch experiments," Biotech. Bioeng., vol. 29, pp. 292-296, 1987.
13. J. M. Mahaffy and E. Simeonov, "Stability analysis for a mathematical model of the lac operon," Q. Appl. Math., vol. 57, pp. 37-53, 1999.
14. N. Yildirim and M. C. Mackey, "Feedback regulation in the lactose operon: A mathematical modeling study and comparison with experimental data," Biophys. J., pp. 2841-2851, 2003.
15. D. T. Gillespie, "A general method for numerically simulating the stochastic time evolution of coupled chemical reactions," Journal of Computational Physics, vol. 22, pp. 403-434, 1976.
16. _, "Approximate accelerated stochastic simulation of chemically reacting systems," J. Chem. Phys., vol. 115, no. 4, p. 1716, 2001.
17. D. Gillespie and L. Petzold, "Improved leap-size selection for accelerated stochastic simulation," J. Chemical Physics, vol. 119, pp. 8229-8234, 2003.
18. T. B. Kepler and T. C. Elston, "Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations," Biophys. J., vol. 81, pp. 3116-3136, 2001.
19. A. Arkin, J. Ross, and H. H. McAdams, "Stochastic kinetic analysis of developmental pathway bifurcation on phage lambda-infected escherichia coli cells," Genetics, vol. 149, pp. 1633-1648, 1998.
20. N. Q. Balaban, J. Merrin, R. Chait, L. Kowalik, and S. Leibler, "Bacterial persistence as a phenotypic switch," Science, vol. 305, pp. 1622-1625, 2004.
21. E. Kussell and S. Leibler, "Phenotypic diversity, population growth, and information in fluctuating environments," Science, vol. 309, p. 2075, 2005.
22. E. M. Ozbudak, M. Thattai, H. N. Lim, B. I. Shraiman, and A. van Oudenarden, "Multistability in the lactose utilization network of escherichia coli," Nature, vol. 427, pp. 737-740, 2004.
23. N. A. Neogi, "Dynamic partitioning of large discrete event biological systems for hybrid simulation and analysis," in Hybrid Systems: Computation and Control, ser. LNCS, vol. 2993. Springer, 2004, pp. 463 - 476.
24. C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Systems. Kluwer, 1999.
25. N. Yildirim and M. C. Mackey, "Feedback regulation in the lactose operon: a mathematical modeling study and comparison with experimental data," Biophysical Journal, vol. 84, pp. 2841 - 2851, May 2003.
26. S. Pestka, B. L. Daugherty, V. Jung, K. Hotta, and R. K. Pestka, "Antimrna: Specific inhibition of translation of single mrna molecules," Proc. Natl. Acad. Sci. USA, vol. 81, pp. 7525-7528, 1984.
27. M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, "Stochastic gene expression in a single cell," Science, vol. 297, pp. 1183-1186, 2002.
28. R. A. Cox, "Quantitative relationships for specific growth rates and macromolecular compositions of mycobacterium tuberculosis, streptomyces coelicolor a3(2) and escherichia coli b/r: an intergrative theoretical approach," Microbiology, vol. 150, pp. 1413-1426, 2004.
29. T. B. Kepler and T. C. Elston, "Stochasticity in transcriptional regulation: origins, consequences, and mathematical representations," Biophysical Journal, vol. 81, pp. 3116 - 3136, December 2001.
30. T. Tian and K. Burrage, "Stochastic models for regulatory networks of the genetic toggle switch," Proc. National Academy of Science, vol. 103, no. 22, pp. 8372 - 8377, 2006.
31. J. M. G. Vilar, C. C. Guet, and S. Leibler, "Modeling network dynamics: the lac operon, a case study," J. Cell Biology, vol. 161, no. 3, pp. 471-476, 2003.
32. Y. Cao, D. Gillespie, and L.Petzold, "Avoiding negative populations in explicit Poisson tau-leaping," Journal of Chemical Physics, vol. 123, pp. 054 104-054 112, 2005.
33. A. A. Julius, "Approximate abstraction of stochastic hybrid automata," in Hybrid Systems: Computation and Control, ser. LNCS, vol. 3927. Springer Verlag, 2006, pp. 318-332.
34. J. T. Mettetal, D. Muzzey, J. M. Pedraza, E. M. Ozbudak, and A. van Oudenaarden, "Predicting stochastic gene expression dynamics in single cells," Proc. National Academy of Science, vol. 103, pp. 7304-7309, 2006.
35. S. Berman, A. Halasz, V. Kumar, and S. Pratt, "Algorithms for the analysis and synthesis of a bio-inspired swarm robotic system," Rome, 2006, submitted to the SAB'06 Swarms Robotics Workshop.