Concordant chemical reaction networks

Mathematical Biosciences

Volumn 240, Issue 2, 2012, Pages 92-113

  Shinar, Guy ^a,c   Feinberg, Martin ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b Ohio State University   (United States)

^c NONE   (Israel)

Author keywords

Bistability; Concordant; Multistability; Network; Persistence; Reaction network

Indexed keywords

MATHEMATICAL TECHNIQUES; NETWORKS (CIRCUITS); OPTICAL BISTABILITY; STATISTICS;

BIOCHEMICAL NETWORK; CHEMICAL REACTION NETWORKS; CONCORDANT; DEGRADATION REACTION; MULTI STABILITIES; PERSISTENCE; POSITIVE STEADY STATE; REACTION NETWORK;

BIODEGRADATION;

BIOCHEMISTRY; CHEMICAL REACTION; DEGRADATION; REACTION KINETICS;

ARTICLE; CHEMICAL REACTION; COMPUTER NETWORK; CONCORDANT CHEMICAL REACTION NETWORK; DEGRADATION; KINETICS; MATHEMATICAL ANALYSIS; STEADY STATE;

EID: 84867854824     PISSN: 00255564     EISSN: 18793134     Source Type: Journal    
DOI: 10.1016/j.mbs.2012.05.004     Document Type: Article

References (39)

1. H. Ji, P. Ellison, D. Knight, M. Feinberg, The chemical reaction network toolbox, version 2.1, 2011. Available at http://www.chbmeng.ohio-state.edu/~feinberg/crntwin/.
2. H. Ji, Uniqueness of equilibria for complex chemical reaction networks, Ph.D. thesis, Department of Mathematics, The Ohio State University, 2011.
3. G. Shinar, M. Feinberg, Concordant reaction networks and the species-reaction graph, arXiv:1203.6560v2 [q-bio.MN] (2012). Available at Submitted to Mathematical Biosciences. http://arxiv.org/pdf/1203.6560v2.pdf.
4. Craciun G., Feinberg M. Multiple equilibria in complex chemical reaction networks II. The species-reaction graph. SIAM Journal on Applied Mathematics 2006, 66:1321.
5. Banaji M., Craciun G. Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems. Advances in Applied Mathematics 2010, 44:168.
6. Craciun G., Tang Y., Feinberg M. Understanding bistability in complex enzyme-driven reaction networks. Proceedings of the National Academy of Sciences 2006, 103:8697.
7. Banaji M., Craciun G. Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements. Communications in Mathematical Sciences 2009, 7:867.
8. Feinberg M. Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems. Chemical Engineering Science 1987, 42:2229.
9. Feinberg M. Chemical reaction network structure and the stability of complex isothermal reactors II. Multiple steady states for networks of deficiency one. Chemical Engineering Science 1988, 43:1.
10. M. Feinberg, Lectures on chemical reaction networks, 1979. Written version of lectures given at the Mathematical Research Center, University of Wisconsin, Madison, WI Available at http://www.chbmeng.ohio-state.edu/~feinberg/LecturesOnReactionNetworks.
11. Feinberg M. The existence and uniqueness of steady states for a class of chemical reaction networks. Archive for Rational Mechanics and Analysis 1995, 132:311.
12. Feinberg M. Multiple steady states for chemical reaction networks of deficiency one. Archive for Rational Mechanics and Analysis 1995, 132:371.
13. Ellison P., Feinberg M. How catalytic mechanisms reveal themselves in multiple steady-state data: I. Basic principles. Journal of Molecular Catalysis. A, Chemical 2000, 154:155.
14. Schlosser P.M., Feinberg M. A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions. Chemical Engineering Science 1994, 49:1749.
15. P.M. Schlosser, A graphical determination of the possibility of multiple steady states in complex isothermal CFSTRs, Ph.D. thesis, University of Rochester, 1988.
16. Craciun G., Feinberg M. Multiple equilibria in complex chemical reaction networks I. The injectivity property. SIAM Journal on Applied Mathematics 2005, 65:1526.
17. Banaji M., Donnell P., Baigent S. P-matrix properties, injectivity, and stability in chemical reaction systems. SIAM Journal on Applied Mathematics 2007, 67:1523.
18. Gale D., Nikaido H. The jacobian matrix and global univalence of mappings. Mathematische Annalen 1965, 159:81.
19. Craciun G., Feinberg M. Multiple equilibria in complex chemical reaction networks: extensions to entrapped species models. IEE Proc. Syst. Biol 2006, 153:179.
20. Craciun G., Feinberg M. Multiple equilibria in complex chemical reaction networks: semiopen mass action systems. SIAM Journal on Applied Mathematics 2010, 70:1859.
21. Biggs N. Algebraic Graph Theory 1993, Cambridge University Press. second ed.
22. Horn F., Jackson R. General mass action kinetics. Archive for Rational Mechanics and Analysis 1972, 47:81.
23. Reidl J., Borowski P., Sensse A., Starke J., Zapotocky M., Eiswirth M. Model of calcium oscillations due to negative feedback in olfactory cilia. Biophysical Journal 2006, 90:1147.
24. Shinar G., Milo R., Rodriguez-Martinez M., Alon U. Input output robustness in simple bacterial signaling systems. Proceedings of the National Academy of Sciences 2007, 104:19931.
25. Shinar G., Feinberg M. Structural sources of robustness in biochemical reaction networks. Science 2010, 327:1389.
26. Shinar G., Feinberg M. Design principles for robust biochemical reaction networks: what works, what cannot work, and what might almost work. Mathematical Biosciences 2011, 231:39.
27. G. Craciun, Systems of nonlinear differential equations deriving from complex chemical reaction networks, Ph.D. thesis, The Ohio State University, 2002.
28. Anderson D.F. Global asymptotic stability for a class of nonlinear chemical equations. SIAM Journal on Applied Mathematics 2008, 68:1464.
29. Angeli D., Leenheer P.D., Sontag E.D. Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws. SIAM Journal on Applied Mathematics 2011, 71:128.
30. Gnacadja G. Reachability, persistence, and constructive chemical reaction networks (part I): reachability approach to the persistence of chemical reaction networks. Journal of Mathematical Chemistry 2011, 49:2117.
31. Gnacadja G. Reachability, persistence, and constructive chemical reaction networks (part II): a formalism for species composition in chemical reaction network theory and application to persistence. Journal of Mathematical Chemistry 2011, 49:2137.
32. Gnacadja G. Reachability, persistence, and constructive chemical reaction networks (part III): a mathematical formalism for binary enzymatic networks and application to persistence. Journal of Mathematical Chemistry 2011, 49:2158.
33. Vol'pert A., Hudjaev S. Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics 1985, Springer.
34. Siegel D., MacLean D. Global stability of complex balanced mechanisms. Journal of Mathematical Chemistry 2000, 27:89.
35. J. Deng, M. Feinberg, C.K.R.T. Jones, A. Nachman, On the steady states of weakly reversible chemical reaction networks, 2011. ArXiv:1111.2386v2 [q-bio.QM] available at http://arxiv.org/pdf/1111.2386.pdf.
36. Browder F.E. A new generalization of the Schauder fixed point theorem. Mathematische Annalen 1967, 174:285.
37. Horn F. Necessary and sufficient conditions for complex balancing in chemical kinetics. Archive for Rational Mechanics and Analysis 1972, 49:172.
38. Segel I.H. Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems 1993, Wiley-Interscience.
39. Kato T. A Short Introduction to Perturbation Theory for Linear Operators 1982, Springer-Verlag.