Simplifying the jacobian criterion for precluding multistationarity in chemical reaction networks

SIAM Journal on Applied Mathematics

Volumn 72, Issue 3, 2012, Pages 857-876

  Joshi, Badal ^a   Shiu, Anne ^b  

^a DUKE UNIVERSITY   (United States)

^b UNIVERSITY OF CHICAGO   (United States)

Author keywords

Chemical reaction networks; Injectivity; Jacobian criterion; Mass action kinetics; Multiple steady states; Species reaction graph

Indexed keywords

CHEMICAL REACTION NETWORKS; INJECTIVITY; JACOBIANS; MASS ACTION KINETICS; MULTIPLE STEADY STATE; SPECIES-REACTION GRAPH;

DYNAMICAL SYSTEMS; JACOBIAN MATRICES; POLYNOMIALS;

REACTION KINETICS;

EID: 84865683792     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/110837206     Document Type: Article

References (26)

1. M. Banaji and G. Craciun, Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements, Commun. Math. Sci., 7 (2009), pp. 867-900.
2. M. Banaji and G. Craciun, Graph-theoretic criteria for injectivity and unique equilibria in general chemical reaction systems, Adv. Appl. Math., 44 (2010), pp. 168-184.
3. M. Banaji, P. Donnell, and S. Baigent, P matrix properties, injectivity, and stability in chemical reaction systems, SIAM J. Appl. Math., 67 (2007), pp. 1523-1547.
4. C. Conradi, D. Flockerzi, J. Raisch, and J. Stelling, Subnetwork analysis reveals dynamic features of complex (bio)chemical networks, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 19175-19180.
5. G. Craciun and M. Feinberg, Multiple equilibria in complex chemical reaction networks. I. The injectivity property, SIAM J. Appl. Math., 65 (2005), pp. 1526-1546. (Pubitemid 41639786)
6. G. Craciun and M. Feinberg, Multiple equilibria in complex chemical reaction networks: Extensions to entrapped species models, Syst. Biol., 153 (2006), pp. 179-186. (Pubitemid 44151478)
7. G. Craciun and M. Feinberg, Multiple equilibria in complex chemical reaction networks: II. The species-reaction graph, SIAM J. Appl. Math., 66 (2006), pp. 1321-1338. (Pubitemid 44231192)
8. G. Craciun and M. Feinberg, Multiple equilibria in complex chemical reaction networks: Semiopen mass action systems, SIAM J. Appl. Math., 70 (2010), pp. 1859-1877.
9. G. Craciun, J. W. Helton, and R. J. Williams, Homotopy methods for counting reaction network equilibria, Math. Biosci., 216 (2008), pp. 140-149.
10. G. Craciun, Y. Tang, and M. Feinberg, Understanding bistability in complex enzyme-driven reaction networks, Proc. Natl. Acad. Sci. USA, 103 (2006), pp. 8697-8702. (Pubitemid 43878082)
11. A. C. Deckard, F. T. Bergmann, and H. M. Sauro, Enumeration and Online Library of Mass-Action Reaction Networks, preprint, 2009, available at arXiv/0901.3067.
12. P. Ellison, The Advanced Deficiency Algorithm and Its Applications to Mechanism Discrimination, Ph.D. thesis, Chemical Engineering, University of Rochester, Rochester, NY, 1998.
13. P. Ellison, M. Feinberg, and H. Ji, Chemical Reaction Network Toolbox, 2011, available online at http://www.che.eng.ohio-state.edu/~feinberg/crnt/.
14. M. Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors I. The deficiency zero and deficiency one theorems, Chem. Eng. Sci., 42 (1987), pp. 2229-2268. (Pubitemid 18529434)
15. E. Feliu and C. Wiuf, Preclusion of Switch Behavior in Reaction Networks with Mass-Action Kinetics, preprint, 2011, available at arXiv/1109.5149.
16. G. Gnacadja, A. Shoshitaishvili, M. J. Gresser, B. Varnum, D. Balaban, M. Durst, C. Vezina, and Y. Li, Monotonicity of interleukin-1 receptor-ligand binding with respect to antagonist in the presence of decoy receptor, J. Theoret. Biol., 244 (2007), pp. 478-488. (Pubitemid 46027143)
17. J. W. Helton, I. Klep, and R. Gomez, Determinant expansions of signed matrices and of certain Jacobians, SIAM J. Matrix Anal. Appl., 31 (2009), pp. 732-754.
18. F. Horn and R. Jackson, General mass action kinetics, Arch. Ration. Mech. Anal., 47 (1972), pp. 81-116.
19. H. Ji, Uniqueness of Equilibria for Complex Chemical Reaction Networks, Ph.D. thesis, Mathematics, Ohio State University, Columbus, OH, 2011.
20. B. Joshi and A. Shiu, Atoms of Multistationarity in Chemical Reaction Networks, preprint, 2011, available at arXiv:1108.5238.
21. I. Klep, K. Fredrickson, and B. Helton, Chemical Reaction Network Software (under Mathematica), 2008, available online at http://www.math.ucsd. edu/~chemcomp/.
22. C. Pantea, BioNetX, software, 2010, available online at http://www.math.wisc.edu/~pantea/.
23. C. Pantea and G. Craciun, Computational methods for analyzing bistability in biochemical reaction networks, in Proceedings of the 2010 IEEE International Symposium on Circuits and Systems (ISCAS), IEEE, Piscataway, NJ, 2010, pp. 549-552.
24. M. P'erez Mill'an, A. Dickenstein, A. Shiu, and C. Conradi, Chemical reaction systems with toric steady states, Bull. Math. Biol., 74 (2012), pp. 1027-1065.
25. P. M. Schlosser and M. Feinberg, A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions, Chem. Eng. Sci., 49 (1994), pp. 1749-1767.
26. G. Shinar, A. Mayo, H. Ji, and M. Feinberg, Constraints on reciprocal flux sensitivities in biochemical reaction networks, Biophys. J., 100 (2011), pp. 1383-1391.