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Original Articles

A network dynamics approach to chemical reaction networks

, &
Pages 731-745 | Received 01 Feb 2015, Accepted 13 Sep 2015, Published online: 15 Oct 2015

References

  • Anderson, D.F. (2011). A proof of the global attractor conjecture in the single linkage class case. SIAM Journal on Applied Mathematics, 71(4), 1487–1508.
  • Angeli, D. (2009). A tutorial on chemical reaction network dynamics. European Journal of Control, 15(3–4), 398–406.
  • Angeli, D. (2011). Boundedness analysis for open chemical reaction networks with mass-action kinetics. Natural Computing, 10, 751–774.
  • Angeli, D., De Leenheer, P., & Sontag, E.D. (2009). Chemical networks with inflows and outflows: A positive linear differential inclusions approach. Biotechnology Progress, 25(3), 632–642.
  • Angeli, D., De Leenheer, P., & Sontag, E.D. (2011). Persistence results for chemical reaction networks with time-dependent kinetics and no global conservation laws. SIAM Journal on Applied Mathematics, 71, 128–146.
  • Bollobas, B. (1998). Modern graph theory. New York, NY: Springer.
  • Chapman, A., & Mesbahi, M. (2011). Advection on graphs. In 50th IEEE Conference on Decision and Control and European Control Conference (pp. 1461–1466). Orlando, FL.
  • Chaves, M. (2005). Input-to-state stability of rate-controlled biochemical networks. SIAM Journal on Control and Optimization, 44(2), 704–727.
  • Cherukuri, A., & Cortés, J. (2015). Distributed generator coordination for initialization and anytime optimization in economic dispatch. IEEE Transactions on Control of Network Systems, 2(3), 226–237.
  • Cortés, J. (2008). Distributed algorithms for reaching consensus on general functions. Automatica, 44, 726–737.
  • Craciun, G., & Feinberg, M. (2010). Multiple equilibria in comples chemical reaction networks: Semi-open mass action systems. SIAM Journal on Applied Mathematics, 70(6), 1859–1877.
  • De Persis, C., & Jayawardhana, B. (2012). On the internal model principle in formation control and in output synchronization of nonlinear systems. In Proceedings of the 51st IEEE Annual Conference on Decision and Control (CDC) (pp. 4894–4899). Maui, HI.
  • Dickenstein, A., & Perez Millan, M. (2011). How far is complex balancing from detailed balancing? Bulletin of Mathematical Biology, 73, 811–828.
  • Ederer, M., & Gilles, E.D. (2007). Thermodynamically feasible kinetic models of reaction networks. Biophysical Journal, 92, 1846–1857.
  • Feinberg, M. (1972). Complex balancing in chemical kinetics. Archive for Rational Mechanics and Analysis, 49, 187–194.
  • Feinberg, M. (1989). Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity. Chemical Engineering Science, 44(9), 1819–1827.
  • Feinberg, M. (1995). The existence and uniqueness of steady states for a class of chemical reaction networks. Archive for Rational Mechanics and Analysis, 132, 311–370.
  • Feinberg, M., & Horn, F.J.M. (1974). Dynamics of open chemical systems and the algebraic structure of the underlying reaction network. Chemical Engineering Science, 29, 775–787.
  • Flach, E.H., & Schnell, S. (2010). Stability of open pathways. Mathematical Biosciences, 228(2), 147–152.
  • Gatermann, K. (2002). Chemical reactions stoichiometric network analysis. Berlin: Seminar Freien Universität Berlin.
  • Godsil, C., & Royle, G.F. (2001). Algebraic graph theory. New York, NY: Springer.
  • Gunawardena, J. (2014). Time-scale separation - Michaelis and Menten's old idea, still bearing fruit. FEBS Journal 281(2), 473–488.
  • Hangos, K.M., & Cameron, I.T. (2001). Process modelling and model analysis. London: Academic Press.
  • Horn, F., & Jackson, R. (1972). General mass action kinetics. Archive for Rational Mechanics and Analysis, 47, 81–116.
  • Horn, F.J.M. (1972). Necessary and sufficient conditions for complex balancing in chemical kinetics. Archive for Rational Mechanics and Analysis, 49, 172–186.
  • Jayawardhana, B., Rao, S., & van der Schaft, A.J. (2012). Balanced chemical reaction networks governed by general kinetics. In 20th International Symposium on Mathematical Theory of Networks and Systems. Melbourne.
  • Kirchhoff, G. (1847). Über die Auflösung der Gleichungen, auf welche man bei der Untersuchung der Linearen Verteilung galvanischer Ströme geführt wird [About the solving of equations to which one is led in the study of the linear distribution of galvanic currents]. Annals Physical Chemistry, 72, pp. 497–508.
  • Kron, G. (1939). Tensor analysis of networks. New York, NY: Wiley.
  • Mirzaev, I., & Gunawardena, J. (2013). Laplacian dynamics on general graphs. Bulletin of Mathematical Biology, 75, 2118–2149.
  • Mitchell, S., & Mendes, P. (2013). A computational model of liver iron metabolism. PLoS Computational Biology, 9(11), e1003299.
  • Oster, J.F., & Perelson, A.S. (1974). Chemical reaction dynamics, Part I: Geometrical structure. Archive for Rational Mechanics and Analysis, 55, 230–273.
  • Oster, J.F., Perelson, A.S., & Katchalsky, A. (1973). Network dynamics: Dynamic modeling of biophysical systems. Quarterly Reviews of Biophysics, 6(1), 1–134.
  • Rao, S., van der Schaft, A.J., & Jayawardhana, B. (2013a). A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks. Journal of Mathematical Chemistry, 51(9), 2401–2422.
  • Rao, S., van der Schaft, A.J., & Jayawardhana, B. (2013b). Stability analysis of chemical reaction networks with fixed boundary concentrations. In Proceedings of the 52nd IEEE Conference on Decision and Control (pp. 3403–3408). Florence: IEEE.
  • Rao, S., van der Schaft, A.J., van Eunen, K., Bakker, B.M., & Jayawardhana, B. (2014). Model reduction of biochemical reaction networks. BMC Systems Biology, 8, 52.
  • Schuster, S., & Schuster, R. (1989). A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation. Journal of Mathematical Chemistry, 3, 25–42.
  • Siegel, D., & MacLean, D. (2000). Global stability of complex balanced mechanisms. Journal of Mathematical Chemistry, 27, 89–110.
  • Sontag, E.D. (2001). Structure and stability of certain chemical networks and applications to the kinetic proofreading model of T-cell receptor signal transduction. IEEE Transactions on Automatic Control, 46(7), 1028–1047.
  • Uhlendorf, J. et al. (2012). Long-term model predictive control of gene expression at the population and single-cell levels. Proceedings of the National Academy of Sciences, 109(35), 14271–14276.
  • van der Schaft, A.J. (2000). L2-gain and passivity techniques in nonlinear control (2nd revised and enlarged edition). London: Springer-Verlag.
  • van der Schaft, A.J. (2010). Characterization and partial synthesis of the behavior of resistive circuits at their terminals. Systems & Control Letters, 59, 423–428.
  • van der Schaft, A.J., & Jeltsema, D. (2014). Port-Hamiltonian systems theory: An introductory overview. Foundations and Trends in Systems and Control, 1(2/3), 173–378.
  • van der Schaft, A.J., & Maschke, B. (2013). Port-Hamiltonian systems on graphs. SIAM Journal on Control and Optimization, 51(2), 906–937.
  • van der Schaft, A.J., & Maschke, B.M. (1995). The Hamiltonian formulation of energy conserving physical systems with external ports. Archiv für Elektronik und Übertragungstechnik, 49, 362–371.
  • van der Schaft, A.J., Rao, S., & Jayawardhana, B. (2013a). On the mathematical structure of balanced chemical reaction networks governed by mass action kinetics. SIAM Journal on Applied Mathematics, 73(2), 953–973.
  • van der Schaft, A.J., Rao, S., & Jayawardhana, B. (2013b). On the network thermodynamics of mass action chemical reaction networks. In Proceedings of 1st IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory (pp. 24–29). Lyon: IFAC.
  • van der Schaft, A.J., Rao, S., & Jayawardhana, B. (2015). Complex balancing for chemical reaction networks revisited. Journal of Mathematical Chemistry, 53(6), 1445–1458.
  • van Eunen, K., Kiewiet, J.A.L, Westerhoff, H.V., & Bakker, B.M. (2012). Testing biochemistry revisited: How in vivo metabolism can be understood from in vitro enzyme kinetics. PLOS Computational Biology, 8(4), e1002483.
  • van Eunen, K., Simons, S.M., Gerding, A., Bleeker, A., den Besten, G., Touw, C.M., … Bakker, B.M. (2013). Biochemical competition makes fatty-acid β-oxidation vulnerable to substrate overload. PLOS Computational Biology, 9(8), e1003186.

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