Siphons in chemical reaction networks

Bulletin of Mathematical Biology

Volumn 72, Issue 6, 2010, Pages 1448-1463

  Shiu, Anne ^a   Sturmfels, Bernd ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Binomial ideal; Chemical reaction systems; Monomial ideal; Primary decomposition; Siphon; Steady state

Indexed keywords

ARTICLE; BINOMIAL DISTRIBUTION; CHEMICAL MODEL; COMPUTER PROGRAM; COMPUTER SIMULATION; METABOLISM; METHODOLOGY; SYSTEMS BIOLOGY;

BINOMIAL DISTRIBUTION; COMPUTER SIMULATION; METABOLIC NETWORKS AND PATHWAYS; MODELS, CHEMICAL; SOFTWARE; SYSTEMS BIOLOGY;

EID: 77955170883     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9502-y     Document Type: Article

References (20)

1. Adleman, L., Gopalkrishnan, M., Huang, M.-D., Moisset, P., Reishus, D., 2008. On the mathematics of the law of mass action. arXiv: 0810. 1108.
2. Anderson, D., 2008. Global asymptotic stability for a class of nonlinear chemical equations. SIAM J. Appl. Math. 68, 1464-1476.
3. Anderson, D., Shiu, A., 2010. Persistence of deterministic population processes and the global attractor conjecture. SIAM J. Appl. Math. (to appear). arXiv: 0903. 0901.
4. Angeli, D., Sontag, E., 2006. Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles. Nonlinear Anal. Ser. B: Real World Appl. 9, 128-140.
5. Angeli, D., De Leenheer, P., Sontag, E., 2007. A Petri net approach to persistence analysis in chemical reaction networks. In: Queinnec, I., Tarbouriech, S., Garcia, G., Niculescu, S.-I. (Eds.), Biology and Control Theory: Current Challenges, Lecture Notes in Control and Information Sciences, vol. 357, pp. 181-216. Springer, Berlin.
6. Chavez, M., 2003. Observer design for a class of nonlinear systems, with applications to chemical and biological networks. Ph. D. Thesis, Rutgers University.
7. Cordone, R., Ferrarini, L., Piroddi, L., 2005. Enumeration algorithms for minimal siphons in Petri nets based on place constraints. IEEE Trans. Syst. Man Cybern. Part A 35(6), 844-854.
8. Cox, D., Little, J., O'Shea, D., 2007. Ideals, Varieties and Algorithms, 3rd edn., Undergraduate Texts in Mathematics. Springer, New York.
9. Craciun, G., Dickenstein, A., Shiu, A., Sturmfels, B., 2009. Toric dynamical systems. J. Symb. Comput. 44(11), 1551-1565.
10. Craciun, G., Pantea, C., Rempala, G., 2009. Algebraic methods for inferring biochemical networks: a maximum likelihood approach. Comput. Biol. Chem. 33(5), 361-367.
11. Diaconis, P., Eisenbud, D., Sturmfels, B., 1998. Lattice walks and primary decomposition. In: Sagan, B. E., Stanley, R. P. (Eds.), Mathematical Essays in Honor of Gian-Carlo Rota, pp. 173-193. Birkhäuser, Basel.
12. Dickenstein, A., Matusevich, L., Miller, E., 2010. Combinatorics of binomial primary decomposition. Math. Z. (to appear). arXiv: 0803. 3846.
13. Eisenbud, D., Sturmfels, B., 1996. Binomial ideals. Duke Math. J. 84, 1-45.
14. Gawrilow, E., Joswig, M., 2000. Polymake: a framework for analyzing convex polytopes. In: Polytopes-Combinatorics and Computation, Oberwolfach, 1997, DMV Sem., vol. 29, pp. 43-73. Birkhäuser, Basel.
15. Grayson, D., Stillman, M. Macaulay 2, a software system for research in algebraic geometry, www. math. uiuc. edu/Macaulay2/.
16. Kahle, T., 2009. Decompositions of binomial ideals. arXiv: 0906. 4873.
17. Manrai, A., Gunawardena, J., 2008. The geometry of multisite phosphorylation. Biophys. J. 95, 5533-5543.
18. Miller, E., Sturmfels, B., 2005. Combinatorial Commutative Algebra, Graduate Texts in Mathematics. Springer, New York.
19. Roune, B., 2009. The slice algorithm for irreducible decomposition of monomial ideals. J. Symb. Comput. 44(4), 358-381.
20. Siegel, D., MacLean, D., 2004. Global stability of complex balanced mechanisms. J. Math. Biol. 27, 89-110.