Bistable biological systems: A Characterization through local compact input-to-state stability

IEEE Transactions on Automatic Control

Volumn 53, Issue SPECIAL ISSUE, 2008, Pages 87-100

  Chaves, Madalena ^a   Eissing, Thomas ^b   Allgöwer, Frank ^b  

^a INRIA   (France)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Biological networks; Bistability; Compact input to state stability (ISS)

Indexed keywords

APOPTOSIS; BI-STABILITY; BIOLOGICAL NETWORKS; BIOLOGICAL VARIABILITY; BISTABLE SYSTEM; BISTABLES; COMPACT SETS; EXTERNAL INPUT; FIXED POINTS; INPUT-TO-STATE STABILITY; INVARIANT SET; KINETIC INTERACTIONS; LAC OPERON; STABLE MODES; STABLE STEADY STATE; STATE SPACE; FORWARD-INVARIANT SETS;

BIOLOGICAL SYSTEMS; CELL DEATH; POWDERS; BIOMEDICAL ENGINEERING; MATHEMATICAL MODELS; SET THEORY; STATE SPACE METHODS;

SYSTEM STABILITY; BIOLOGICAL SYSTEMS;

EID: 40049092380     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2007.911328     Document Type: Article

References (33)

1. F. Jacob and J. Monod, "Genetic regulatory mechanisms in the synthesis of proteins," J. Mol. Biol., vol.3, pp. 318-356, 1961.
2. E. Ozbudak, M. Thattai, H. Lim, B. Shraiman, and A. van Oudenaarden, "Multistability in the lactose utilization network of Escherichia coli," Nature, vol.427, pp. 737-740, 2004.
3. M. Ptashne, A Genetic Switch Phage λ and Higher Organisms. London, U.K.: Blackwell Science, 1992.
4. N. Danial and S. Korsmeyer, "Cell death Critical control points," Cell, vol.116, pp. 205-216, 2004.
5. A. Hoffmann, A. Levchenko, M. Scott, and D. Baltimore, "The dIkBNFkB signaling module Temporal control and selective gene activation," Science, vol.298, pp. 1241-1245, 2002.
6. T. Eissing, H. Conzelmann, E. Gilles, F. Allgöwer, E. Bullinger, and P. Scheurich, "Bistability analysis of a caspase activation model for receptor-induced apoptosis," J. Biol. Chem., vol.279, pp. 36892-36897, 2004.
7. J. Pomerening, E. Sontag, and J. E. Ferrell, Jr., "Building a cell cycle oscillator Hysteresis and bistability in the activation of Cdc2," Nat. Cell Biol., vol.5, pp. 346-351, 2003.
8. T. Eissing, F. Allgöwer, and E. Bullinger, "Robustness properties of apoptosis models with respect to parameter variations and stochastic influences," IEE Proc. Syst. Biol., vol.152, pp. 221-228, 2005.
9. D. Angeli, J. E. Ferrell, Jr., and E. Sontag, "Detection of multistability, bifurcations and hysteresis in a large class of biological positive-feedback systems," Proc. Natl. Acad. Sci. USA, vol.101, pp. 1822-1827, 2004.
10. J. Vilar, C. Guet, and S. Leibler, "Modeling network dynamics The lac operon, a case study," J. Cell Biol., vol.161, pp. 471-476, 2003.
11. A. Arkin, J. Ross, and H. McAdams, "Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected escherichia coli cells," Genetics, vol.149, pp. 1633-1648, 1998.
12. M. Khammash and H. El Samad, "Stochastic modeling and analysis of genetic networks," in Proc. 44th IEEE Conf. Decision and Control, Seville, Spain, 2005.
13. R. Thomas, "Boolean formalization of genetic control circuits," J. Theor. Biol., vol.42, pp. 563-585, 1973.
14. L. Sánchez and D. Thieffry, "A logical analysis of the drosophila gapgene system," J. Theor. Biol., vol.211, pp. 115-141, 2001.
15. R. Albert and H. Othmer, "The topology of the regulatory interactions predicts the expression pattern of the drosophila segment polarity genes," J. Theor. Biol., vol.223, pp. 1-18, 2003.
16. M. Chaves, R. Albert, and E. Sontag, "Robustness and fragility of boolean models for genetic regulatory networks," J. Theor. Biol., vol.235, pp. 431-449, 2005.
17. R. Ghosh and C. Tomlin, "Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modeling Delta-notch protein signaling," IEE Trans. Syst. Biol., vol.1, pp. 170-183, 2004.
18. L. Glass and S. Kauffman, "The logical analysis of continuous, nonlinear biochemical control networks," J. Theor. Biol., vol.39, pp. 103-129, 1973.
19. H. de Jong, J. Gouzé, C. Hernandez, M. Page, T. Sari, and J. Geiselmann, "Qualitative simulation of genetic regulatory networks using piecewise-linear models," Bull. Math. Biol., vol.66, pp. 301-340, 2004.
20. R. Casey, H. de Jong, and J. S., "Piecewise-linear models of genetic regulatory networks Equilibria and their stability," J. Math. Biol., vol.52, pp. 27-56, 2006. (Pubitemid 41830874)
21. E. Farcot, "Geometric properties of a class of piecewise affine biological network models," J. Math. Biol., vol.52, pp. 373-418, 2006.
22. M. Chaves, E. Sontag, and R. Albert, "Methods of robustness analysis for boolean models of gene control networks," IEE Proc. Syst. Biol., vol.153, pp. 154-167, 2006.
23. H. de Jong and D. Thieffry, "Modélisation, analyse et simulation des réseaux génétiques," Medecine/Sciences, vol.18, pp. 492-502, 2002.
24. E. Sontag and Y.Wang, "On characterizations of the input-to-state stability property with respect to compact sets," in Proc. IFAC Nonlinear Control Symposium (NOLCOS95), Tahoe City, CA, 1995.
25. E. Sontag, "Smooth stabilization implies coprime factorization," IEEE Trans. Automat. Control, vol.34, pp. 435-443, 1989.
26. E. Sontag and Y.Wang, "On characterizations of the input-to-state stability property," Systems Control Lett., vol.24, pp. 351-359, 1995.
27. M. Chaves and E. Sontag, "State-estimators for chemical reaction networks of Feinberg-Horn-Jackson zero-deficiency type," Eur. J. Control, vol.8, pp. 343-359, 2002.
28. M. Chaves, "Input-to-state stability of rate-controlled biochemical networks," SIAM J. Control Optim., vol.44, pp. 704-727, 2005.
29. M. Chaves, T. Eissing, and F. Allgöwer, "Identifying mechanisms for bistability in an apoptosis network," in Réseaux d'interactions Analyse, modélisation et simulation, Lyon, France, 2006, ser. tegrative Post-Genomics.
30. M. Krichman, E. Sontag, and Y. Wang, "Input-output-to-state stability," SIAM J. Control Optim., vol.39, pp. 1874-1928, 2001.
31. M. Arcak, D. Angeli, and E. Sontag, "Aunifying integral iss framework for stability of nonlinear cascades," SIAM J. Control Optim., vol.40, pp. 1888-1904, 2002.
32. M. Schliemann, T. Eissing, P. Scheurich, and E. Bullinger, "Mathematical modelling of TNF-α induced apoptotic and anti-apoptotic signalling pathways in mammalian cells based on dynamic and quantitative experiments," in 2nd Foundations of Systems Biology in Engineering (FOSBE), Stuttgart, Germany, 2007, in press.
33. T. Eissing, S. Waldherr, E. Bullinger, C. Gondro, O. Sawodny, F. Allgöwer, P. Scheurich, and T. Sauter, "Sensitivity analysis of programmed cell death and implications for crosstalk phenomena during tumor necrosis factor stimulation," in Proc. IEEE Conf. Control Applications (CCA), Munich, Germany, 2006, pp. 1746-1752.