Smooth bistable S-systems

IEE Proceedings Systems Biology

Volumn 152, Issue 4, 2005, Pages 207-213

  Voit, Eberhard O ^a  

^a Emory University   (United States)

Author keywords

Biochemical systems; Biochemistry; Bistability; Cell cycle phenomena; Cellular biophysics; Differentiable nonlinearity; Gene expression; Genetics; Linear equations; Physiological models; Recasting; Signal transduction; Smooth bistable S systems; Switching phenomena

Indexed keywords

APPROXIMATION THEORY; CELLS; COMPUTER SIMULATION; GENES; LINEAR ALGEBRA; LINEAR EQUATIONS; MATHEMATICAL MODELS; SENSITIVITY ANALYSIS; STABILITY;

BIOCHEMICAL SYSTEMS; PATHWAY MODEL; S-SYSTEMS;

BIOLOGY;

ANALYTIC METHOD; ARTICLE; CELL CYCLE; FEEDBACK SYSTEM; GENE EXPRESSION; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOLECULAR BIOLOGY; SIGNAL TRANSDUCTION; SIMULATION; STEADY STATE;

CELL PHYSIOLOGY; COMPUTER SIMULATION; GENE EXPRESSION REGULATION; MODELS, BIOLOGICAL; MODELS, STATISTICAL; SIGNAL TRANSDUCTION; TRANSCRIPTION FACTORS;

EID: 31144466208     PISSN: 17412471     EISSN: None     Source Type: Journal    
DOI: 10.1049/ip-syb:20050063     Document Type: Article

References (31)

1. Savageau, M.A.: 'Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions 'J. Theor. Biol., 1969, 25, (3), p. 365-369
2. Savageau, M.A.: 'Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation', J. Theor. Biol., 1969, 25, (3), p. 370-379
3. Savageau, M.A.: 'BiochemiAal systems analysis: a study of function and design in molecular biology', (Addison-Wesley, Reading, MA 1976), p. xvii, 379 Advanced Book Program
4. Voit, E.O.: 'Canonical nonlinear modeling: S-system approach to understanding complexity '(Van Nostrand Reinhold, New York 1991), p. xii, 365
5. Voit, E.O.: 'Computational analysis of biochemical systems: A practical guide for biochemists and molecular biologists', (Cambridge University Press, New York 2000)
6. Torres, N.V., and Voit, E.O.: 'Pathway analysis and optimization in metabolic engineering', (Cambridge University Press, New York 2002), p. xiv, 305
7. Schwacke, J.H., and Voit, E.O.: 'BSTLab: A Matlab toolbox for biochemical systems theory'.', Eleventh International Conference on Intelligent Systems for Molecular Biology, Brisbane, Australia 2003)
8. Schwacke, J.H.: (BSTLab), https://bioinformatics.musc.edu/bstlab/
9. Savageau, M.A.: 'A theory of alternative designs for biochemical control systems', Biomed. Biochim. Acta, 1985, 44, (6), p. 875-880
10. Irvine, D.H., and Savageau, M.A.: 'Network regulation of the immune response: Alternative control points for suppressor modulation of effector lymphocytes', J. Immunol., 1985, 134, (4), p. 2100-2116
11. Hlavacek, W.S., and Savageau, M.A.: 'Completely uncoupled and perfectly coupled gene expression in repressible systems', J. Mol. Biol., 1997, 266, (3), p. 538-558
12. Alves, R., and Savageau, M.A.: 'Comparing systemic properties of ensembles of biological networks by graphical and statistical methods', Bioinformatics, 2000, 16, (6), p. 527-533
13. Schwacke, J.H., and Voit, E.O.: 'Improved methods for the mathematically controlled comparison of biochemical systems', Biol. and Med. Model., 1, (1), p. 2004
14. Savageau, M.A., and Voit, E.O.: 'Recasting nonlinear differential equations as S-systems: A canonical nonlinear form', Mathem. Biosci., 1987, 87, p. 83-115
15. Savageau, M.A.: 'Design principles for elementary gene circuits: Elements, methods, and examples', Chaos, 2001, 11, (1), p. 142-159 10.1063/1.1349892 1054-1500
16. Savageau, M.A.: 'Alternative designs Aor a genetic switch: analysis of switching times using the piecewise power-law representation', Math. Biosci., 2002, 180, p. 237-253 0025-5564
17. Sorribas, A., Vilaprinyo, E., and Hernandez-Bermejo, B.: 'Insights on the extension of the power-law formalism to deal with saturation and cooperativity', International Conference on Molecular Systems Biology (ICMSB '04), Tahoe City, CA 2004
18. Irvine, D.H., and Savageau, M.A.: 'Efficient solution of nonlinear ordinary differential equations expressed in S-system canonical form', SIAM J. Numer. Anal., 1990, 27, p. 704-735 0036-1429
19. Voit, E.O.: 'Recasting nonlinear models as S-systems', Math. Comput. Model., 1988, 11, p. 140-145 10.1016/0895-7177(88)90469-4 0895-7177
20. Angeli, D., Ferrell, J.E., and Sontag, E.D.: 'Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems', Proc. Natl. Acad. Sci. USA, 2004, 101, (7), p. 1822-1827 0027-8424
21. Ferreira, A.: 'Power law analysis and simulation',, http://www.dqb.fc.ul.pt/docentes/aferreira/plas.html
22. Kacser, H., and Burns, J.A.: 'The control of flux', Symp. Soc. Exp. Biol., 1973, 27, p. 65-104
23. Heinrich, R., and Rapoport, T.A.: 'A linear steady-state treatment of enzymatic chains: General properties, control and effector strength', Eur. J. Biochem., 1974, 42, (1), p. 89-95
24. Fell, D.: 'Understanding the control of metabolism', (Portland Press, London 1997)
25. Hatzimanikatis, V., and Bailey, J.E.: 'MCA has more to say', J. Theor. Biol., 1996, 182, p. 233-242
26. Hill, C.M., Waight, R.D., and Bardsley, W.G.: 'Does any enzyme follow the Michaelis-Menten equation?', Mol. Cell Biochem., 1977, 15 (3), p. 173-178
27. Savageau, M.A.: 'Critique of the enzymologist's test tube', Bittar, E.E., Fundamentals of medical cell biology: A multi-volume work, (JAI Press, Greenwich 1991), p. 45-108
28. Goldbeter, A.: 'Biochemical oscillations and cellular rhythms', (Cambridge University Press, Cambridge p. xxiv, 605
29. Bhalla, U.S., and Iyengar, R.: 'Functional modules in biological signalling networks', Novartis Found. Symp., 2001, 239, p. 4-13 [discussion 13-5, 45-51]
30. Ferrell, J.E.: 'Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability', Curr. Opin. Cell Biol., 2002, 14, (2), p. 140-148
31. Papachristodoulou, A., and Prajna, S.: 'Analysis of non-polynomial systems using the sum of squares decomposition', Positive polynomials in control, (Springer-Verlag, New York in press