STABILITY ANALYSIS FOR BACTERIAL LINEAR METABOLIC PATHWAYS WITH MONOTONE CONTROL SYSTEM THEORY

Nacim Meslem, Vincent Fromion, Anne Goelzer, Laurent Tournier

2010

Abstract

In this work we give technical conditions which guarantee the global attractivity of bacterial linear metabolic pathways (reversible and irreversible structures) where both genetic and enzymatic controls involve the end product through metabolic effectors. To reach this goal, we use the negative feedback theorem of the monotone control systems theory, and we represent all conditions needed to apply the negative feedback theorem to the bacterial linear metabolic pathways in convenient deduced forms.

References

  1. Angeli, D. and Sontag, E. D. (2003). Monotone control systems. IEEE transactions on automatic control, 48:1684-1698.
  2. Angeli, D. and Sontag, E. D. (2004). Multi-stability in monotone input/output systems. Systems and Control Letters, 51:185-202.
  3. Angeli, D. and Sontag, E. D. (2008). Oscillations in i/o monotone systems under negative feedback. IEEE transactions on automatic control, 55:166-176.
  4. Arcak, M. and Sontag, E. D. (2006). Diagonal stability of a class of cyclic systems and its connection with the secant criterion. Automatica, 42:1531-1537.
  5. Berman, A. and Plemmons, R. (1994). Nonnegative Matrices in the Mathematical Sciences. Society for Industrial and applied Mathematics, Philadelphia.
  6. Enciso, G. A. and Sontag, E. D. (2006). Global attractivity, i/o monotone small-gain theorems, and biological delay systems. Discrete and Continuous Dynamical Systems, 14:549-578.
  7. Goelzer, A., Bekkal-Brikci, F., Martin-Verstraete, I., Noirot, P., Bessiéres, P., Aymerich, S., and Fromion, V. (2008). Reconstruction and analysis of the genetic and metabolic regulatory networks of the central metabolism of bacillus subtilis. BMC Systems Biology, doi:10.1186/1752-0509-2-20.
  8. Gollnick, P., Babitzke, P., Antson, A., and CA, C. (2005). Complexity in regulation of tryptophan biosynthesis in bacillus subtilis. Annual review of genetics, 39:47- 68.
  9. Grundy, F., Lehman, S., and Henkin, T. (2003). The l box regulon: lysine sensing by leader rnas of bacterial lysine biosynthesis genes. PNAS, 100(21):12057- 12062.
  10. Sanchez, L. (2009). Global asymptotic stability of the goodwin system with repression. Nonlinear analysis : real world applications, 10(4):2151-2156.
  11. Smith, H. L. (1995). Monotone dynamical systems: An Introduction to the theory of competitive and cooperative systems. Mathematical Surveys and Monographs Vol. 41, AMS, Providence, RI.
  12. Tyson, J. and Othmer, H. (1978). The dynamics of feedback control circuits in biological pathways. In R. Rosen, and F.M. Snell (Eds.), Progress in theoretical biology (Vol. 5), pages 1-62, New York: Academic Press.
  13. Wang, L., de Leenheer, P., and Sontag, E. (2008). Global stability for monotone tridiagonal systems with negative feedback. In Proc. IEEE Conf. Decision and Control CDC, pages 4091-4096, Cancun,Mexico.
Download


Paper Citation


in Harvard Style

Meslem N., Fromion V., Goelzer A. and Tournier L. (2010). STABILITY ANALYSIS FOR BACTERIAL LINEAR METABOLIC PATHWAYS WITH MONOTONE CONTROL SYSTEM THEORY . In Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO, ISBN 978-989-8425-02-7, pages 22-29. DOI: 10.5220/0002944900220029


in Bibtex Style

@conference{icinco10,
author={Nacim Meslem and Vincent Fromion and Anne Goelzer and Laurent Tournier},
title={STABILITY ANALYSIS FOR BACTERIAL LINEAR METABOLIC PATHWAYS WITH MONOTONE CONTROL SYSTEM THEORY},
booktitle={Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},
year={2010},
pages={22-29},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002944900220029},
isbn={978-989-8425-02-7},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 7th International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,
TI - STABILITY ANALYSIS FOR BACTERIAL LINEAR METABOLIC PATHWAYS WITH MONOTONE CONTROL SYSTEM THEORY
SN - 978-989-8425-02-7
AU - Meslem N.
AU - Fromion V.
AU - Goelzer A.
AU - Tournier L.
PY - 2010
SP - 22
EP - 29
DO - 10.5220/0002944900220029