Exact computation of amplification for a class of nonlinear systems arising from cellular signaling pathways

Automatica

Volumn 42, Issue 11, 2006, Pages 1987-1992

  Sontag, Eduardo D ^a   Chaves, Madalena ^b  

^a RUTGERS UNIVERSITY   (United States)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Gains; Nonlinear systems; Norms; Signaling pathways

Indexed keywords

AMPLIFICATION; COMPUTER SIMULATION; LINEARIZATION; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; NUMERICAL ANALYSIS;

BIOLOGICAL INTRACELLULAR SIGNALING CASCADES; NUMERICAL VALUE; SIGNALING PATHWAYS;

COMPUTATION THEORY;

EID: 33748938564     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.06.011     Document Type: Article

References (10)

1. Angeli D., Ferrell Jr. J.E., and Sontag E.D. Detection of multi-stability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proceedings of the National Academy of Sciences USA 101 (2004) 1822-1827
2. Angeli D., and Sontag E.D. Monotone control systems. IEEE Transactions on Automatic Control 48 (2003) 1684-1698
3. ∞ control for nonlinear systems with output feedback. IEEE Transactions on Automatic Control 38 (1993) 546-559
4. Chaves M., Sontag E.D., and Dinerstein R. Optimal length and signal amplification in weakly activated signal transduction cascades. Journal of Physical Chemistry B 108 (2004) 15311-15320
5. Doyle J., Francis B., and Tannenbaum A. Feedback control systems (1992), MacMillan Publishing Co, New York. http://www.control.utoronto.ca/-people/profs/francis/dft.html Also available on the web at: 〈http://www.control.utoronto.ca/-people/profs/francis/dft.html〉
6. Heinrich R., Neel B.G., and Rapoport T.A. Mathematical models of protein kinase signal transduction. Molecular Cell 9 (2002) 957-970
7. Lakshmikantham V., and Leela S. Differential and integral inequalities (1969), Academic Press, New York
8. Smith H.L. Monotone dynamical systems (1995), AMS, Providence
9. Sontag E.D. Mathematical control theory: Deterministic finite dimensional systems. 2nd ed. (1998), Springer, New York
10. ∞ control. IEEE Transactions on Automatic Control 37 (1992) 770-784