List of references by topic

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This is a list of references by topics for journal articles and books pertaining to topics within the mathematics of reaction networks. The topics are organized alphabetically and the references are order chronologically within the topics. References may appear in more than one list.

Biochemistry

  • Eduardo Sontag, Structure and stability of certain chemical networks and applications to the kinetic proofreading model of t-cell receptor signal transduction, IEEE Trans. Automat. Control, 46(7):1028--1047, 2001.
  • Arjun Manrai and Jeremy Gunawardena, The geometry of multisite phosphorylation, Biophys. J., 95:5533--5543, 2009.
  • Dan Siegal-Gaskins, Erich Grotewold, and Gregory D. Smith, The capacity for multistability in small gene regulatory networks, BMC Syst. Biol., 3:96, 2009.
  • Matthew Thomson and Jeremy Gunawardena, The rational parameterisation theorem for multisite post-translational modification systems, J. Theor. Biol., 261(4):626--636, 2009.
  • Matthew Thomson and Jeremy Gunawardena, Unlimited multistability in multisite phosphorylation systems, Nature, 460(7252):274--277, 2009.
  • Guy Shinar and Martin Feinberg, Structural sources of robustness in biochemical reaction networks, Science, 327(5971):1389--1391, 2010.

Boundedness

  • David Angeli, Boundedness analysis for open chemical reaction networks with mass-action kinetics, Nat. Comput., 10(2):751--774, 2009.
  • David Anderson, Boundedness of trajectories for weakly reversible, single linkage class reaction systems, J. Math. Chem., 49(10):2275--2290, 2011.

Complex balanced systems

  • Fritz Horn and Roy Jackson, General mass action kinetics, Arch. Ration. Mech. Anal., 47:81--116, 1972.
  • Fritz Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Ration. Mech. Anal., 49:172--186, 1972.
  • Martin Feinberg, Complex balancing in general kinetic systems, Arch. Ration. Mech. Anal., 49:187--194, 1972.
  • Fritz Horn, Stability and complex balancing in mass-action systems with three complexes, Proc. Royal Soc. A, 334:331--342, 1973.
  • Fritz Horn, The dynamics of open reaction systems: mathematical aspects of chemical and biochemical problems and quantum chemistry, SIAM-AMS Proceedings, Vol. VIII, 125--137, 1974.
  • Einstein D. Averbukh, Complex balanced kinetic functions in inverse problems of chemical kinetics, Automation and Remote Control, 55(12):1723--1732, 1994.
  • Alain Bamberger and Emmanuel Billette, Quelques extensions d'un theoreme de horn et jackson. C. R. Acad. Sci. Paris S\'{e}r. I Math, 319(12):1257--1262, 1994.
  • David Siegel and Y. F. Chen, Global stability of deficiency zero chemical networks, Can. Appl. Math. Q., 2(3):413--434, 1994.
  • Mohamed Laydi, Mourad D. Zellaji, and Jean-Claude Miellou, Une nouvelle preuve d'une propriete thermodynamique de systemes equilbre complex, C. R. Acad. Sci. Paris Sér. I Math, 323(9):1009--1012, 1996.
  • David Siegel and Debra MacLean, Global stability of complex balanced mechanisms, J. Math. Chem., 27(1-2):89--110, 2000.
  • Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, and Bernd Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44(11):1551--1565, 2009.
  • Gabor Szederkenyi and Katalin Hangos, Finding complex balanced and detailed balanced realizations of chemical reaction networks, J. Math. Chem., 49:1163--1179, 2011.
  • Alicia Dickenstein and Mercedes Perez Millan, How far is complex balancing from detailed balancing? Bull. Math. Biol., 73:811--828, 2011.
  • Stefan Muller and George Regensburger, Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces, available on the arXiv at arXiv:1209.6488.

Computational approaches

  • Gabor Szederkenyi, Computing sparse and dense realizations of reaction kinetic systems, J. Math. Chem., 47:551--568, 2010.
  • Haixia Ji, Phillipp Ellison, Daniel Knight, and Martin Feinberg, The chemical reaction network toolbox, version 2.1. http://www.chbmeng.ohio-state.edu/~feinberg/crntwin/, 2011.
  • Gabor Szederkenyi and Katalin Hangos, Finding complex balanced and detailed balanced realizations of chemical reaction networks, J. Math. Chem., 49:1163--1179, 2011.
  • Gabor Szederkenyi, Katalin Hangos, and Tamas Peni, Maximal and minimal realizations of chemical kinetics systems: computation and properties.MATCH Commun. Math. Comput. Chem., 65:309--332, 2011.
  • Gabor Szederkenyi, Katalin Hangos, and Zsolt Tuza, Finding weakly reversible realizations of chemical reaction networks using optimization. MATCH Commun. Math. Comput. Chem., 67:193--212, 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks, J. Math. Chem., 50(1):274--288, 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods, to appear in MATCH Commun. Math. Comput. Chem., 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, Computing weakly reversible linearly conjugate chemical reaction Networks with minimal deficiency, to appear in Math. Biosci., 2012.

Deficiency theory

  • Fritz Horn, Necessary and sufficient conditions for complex balancing in chemical kinetics. Arch. Ration. Mech. Anal., 49:172--186, 1972.
  • Martin Feinberg, Complex balancing in general kinetic systems, Arch. Ration. Mech. Anal., 49:187--194, 1972.
  • Martin Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors: I. the deficiency zero and deficiency one theorems, Chem. Eng. Sci., 42(10):2229--2268, 1987.
  • Martin Feinberg, Chemical reaction network structure and the stability of complex isothermal reactors: II. multiple steady states for networks of deficiency one, Chem. Eng. Sci., 43(1):1--25, 1988.
  • Martin Feinberg, The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Ration. Mech. Anal., 132:311-370, 1995.
  • Martin Feinberg, Multiple steady states for chemical reaction networks of deficiency one, Arch. Ration. Mech. Anal., 132:371--406, 1995.
  • Phillipp Ellison, The advanced deficiency algorithm and its applications to mechanism discrimination, Ph.D. Thesis, University of Rochester, 1998.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency, to appear in Math. Biosci., 2012.

Detailed balanced systems

  • Frederick J. Krambeck, The mathematical structure of chemical kinetics in homogeneous single-phase systems, Arch. Rational Mech. Anal., 38:317--347, 1970.
  • Aizik I. Vol'pert and Sergei I. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Martinus Nijhoff Publishers, Dordrecht, Netherlands, 1985.
  • Martin Feinberg, Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity, Chem. Eng. Sci., 44(9):1819--1827, 1989.
  • Gabor Szederkenyi and Katalin Hangos, Finding complex balanced and detailed balanced realizations of chemical reaction networks, J. Math. Chem., 49:1163--1179, 2011.
  • A. N. Gorban and G. S. Yablonsky, Extended detailed balance for systems with irreversible reactions, Chem. Eng. Sci., 66:5388--5399, 2011.
  • Alicia Dickenstein and Mercedes~Perez Millan, How far is complex balancing from detailed balancing? Bull. Math. Biol., 73:811--828, 2011.

Dynamical equivalence

  • Frederick J. Krambeck, The mathematical structure of chemical kinetics in homogeneous single-phase systems, Arch. Rational Mech. Anal., 38:317--347, 1970.
  • Fritz Horn and Roy Jackson, General mass action kinetics, Arch. Ration. Mech. Anal., 47:81--116, 1972.
  • Einstein D. Averbukh, Some equivalent kinetic functions of macrodynamic equations, Automation and Remote Control, 55(11):1694--1698, 1994.
  • Einstein D. Averbukh, Complex balanced kinetic functions in inverse problems of chemical kinetics, Automation and Remote Control, 55(12):1723--1732, 1994.
  • Debra MacLean, Positivity and stability of chemical kinetics systems, Master's thesis, University of Waterloo, 1998.
  • Gabor Szederkenyi, Computing sparse and dense realizations of reaction kinetic systems, J. Math. Chem., 47:551--568, 2010.
  • Matthew D. Johnston and David Siegel, Linear conjugacy of chemical reaction networks, J. Math. Chem., 49(7):1263--1282, 2011.
  • Gabor Szederkenyi and Katalin Hangos, Finding complex balanced and detailed balanced realizations of chemical reaction networks, J. Math. Chem., 49:1163--1179, 2011.
  • Gabor Szederkenyi, Katalin Hangos, and Tamas Peni, Maximal and minimal realizations of chemical kinetics systems: computation and properties.MATCH Commun. Math. Comput. Chem., 65:309--332, 2011.
  • Gabor Szederkenyi, Katalin Hangos, and Zsolt Tuza, Finding weakly reversible realizations of chemical reaction networks using optimization. MATCH Commun. Math. Comput. Chem., 67:193--212, 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, A linear programming approach to weak reversibility and linear conjugacy of chemical reaction networks, J. Math. Chem., 50(1):274--288, 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, Dynamical equivalence and linear conjugacy of chemical reaction networks: New results and methods, to appear in MATCH Commun. Math. Comput. Chem., 2012.
  • Matthew D. Johnston, David Siegel, and Gabor Szederkenyi, Computing weakly reversible linearly conjugate chemical reaction networks with minimal deficiency, to appear in Math. Biosci., 2012.

Enzyme reactions

  • Leonor Michaelis and Maud Menten, Die kinetik der invertinwirkung, Biochem. Z., 49:333--369, 1913.
  • P. Arányi and Janos Tóth, A full stochastic description of the Michaelis-Menten reaction for small systems, Acta Biochimica et Biophysica Academiae Scientificarum Hungariae, 12(4), 375--388, 1977.
  • David Siegel and Yu Fang Chen, Global stability of deficiency zero chemical networks, Can. Appl. Math. Q., 2(3):413--434, 1994.
  • David Angeli and Eduardo Sontag, Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles. Nonlinear Analysis Series B: Real World Applications, 9:128--140, 2008.
  • Liming Wang and Eduardo Sontag, On the number of steady states in a multiple futile cycle, J. Math. Biol., 57(1):29--52, 2008.

Global attractor conjecture

See persistence.

Identifiability of rate constants

  • Frederick J. Krambeck, The mathematical structure of chemical kinetics in homogeneous single-phase systems, Arch. Rational Mech. Anal., 38:317--347, 1970.
  • Fritz Horn and Roy Jackson, General mass action kinetics, Arch. Ration. Mech. Anal., 47:187--194, 1972.
  • V. Hars and Janos Toth, On the inverse problem of reaction kinetics, Coll. Math. Soc. J. Bolyai, 30:363--379, 1981.
  • Einstein D. Averbukh, Some equivalent kinetic functions of macrodynamic equations, Automation and Remote Control, 55(11):1694--1698, 1994.
  • Einstein D. Averbukh, Complex balanced kinetic functions in inverse problems of chemical kinetics, Automation and Remote Control, 55(12):1723--1732, 1994.
  • Gheorghe Craciun and Casian Pantea, Identifiability of chemical reaction networks, J. Math Chem., 44(1):244--259, 2008.
  • Gabor Szederkenyi, Comment on "identifiability of chemical reaction networks" by G. Craciun and C. Pantea, J. Math. Chem., 45:1172--1174, 2009.
  • Gheorghe Craciun, Casian Pantea, and Grzegorz Rempala, Algebraic methods for inferring biochemical networks: a maximum likelihood approach, Compute. Biol. Chem., 33(5):361--367, 2009.
  • Gheorghe Craciun, Jaejik Kim, Casian Pantea, and Grzegorz A. Rempala, Statistical Model for Biochemical Networks Inference, to appear in Communications in Statistics: Simulation and Computation, 2012.

Injectivity

  • Gheorghe Craciun and Martin Feinberg, Multiple equilibria in complex chemical reaction networks: I. the injectivity property. SIAM J. Appl. Math, 65(5):1526--1546, 2005.
  • Gheorghe Craciun and Martin Feinberg, Multiple equilibria in complex chemical reaction networks: II. the species-reaction graph. SIAM J. Appl. Math, 66(4):1321--1338, 2006.
  • Murad Banaji, Pete Donnell and S. Baigent, P matrix properties, injectivity and stability in chemical reaction systems, SIAM J. Appl. Math., 67(6):1523-–1547, 2007
  • Murad Banaji, Graph-theoretic conditions for injectivity of functions on rectangular domains, J. Math. Anal. Appl., 370:302--311, 2010.
  • Murad Banaji and Gheorghe Craciun, Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements, Comm. Math. Sci., 7(4):867--900, 2009.

Kinetic schemes

  • Cato M. Guldberg and Peter Waage, Studies concerning affinity, C. M. Forhandlinger: Videnskabs-Selskabet i Chistiana, page 35, 1864.
  • Archibald Hill, The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves, J. Physiol., 40(4), 1910.
  • Leonor Michaelis and Maud Menten, Die kinetik der invertinwirkung, Biochem. Z., 49:333--369, 1913.
  • Gilbert N. Lewis, A new principle of equilibrium, Proc. Natn. Acad. Sci., 11:179--183, 1925.
  • Michael A. Savageau, Biochemical systems analysis II. the steady-state solutions for an n-pool system using a power-law approximation, J. Theoret. Biol., 25:370--379, 1969.
  • Michael A. Savageau and Eberhard O. Voit, Recasting nonlinear differential equations as S-systems: A canonical nonlinear form, Math. Biosci., 87:83--115, 1987.

Lumping

  • James Wei and James C. W. Kuo, A lumping analysis in monomolecular reaction systems, Ind. Eng. Chem. Fundamentals, 8:114--133, 1969.
  • Genyuan Li and Hershel Rabitz, A general analysis of exact lumping in chemical kinetics, Chem. Eng. Sci., 44(6):1413--1430, 1989.
  • Genyuan Li and Hershel Rabitz, A general analysis of approximate lumping in chemical kinetics, Chem. Eng. Sci., 45(4):977--1002, 1990.
  • Genyuan Li and Hershel Rabitz, A general analysis of exact nonlinear lumping in chemical kinetics, Chem. Eng. Sci., 49(3):343--361, 1994.
  • Alison S. Tomlin, Genyuan Li, Hershel Rabitz, and Janos Toth, A general analysis of approximate nonlinear lumping in chemical kinetics. I. unconstrained lumping, J. Chem. Phys., 101(2):1172--1187, 1994.
  • Alison S. Tomlin, Genyuan Li, Hershel Rabitz, and Janos Toth, A general analysis of approximate nonlinear lumping in chemical kinetics. II. constrained lumping, J. Chem. Phys., 101(2):1188--1201, 1994.
  • Janos Toth, Genyuan Li, Herschel Rabitz, and Alison S. Tomlin, The effect of lumping and expanding on kinetic differential equations, SIAM J. Appl. Math., 57(6):1531--1556, 1997.
  • Gyula Farkas, Kinetic lumping schemes, Chem. Eng. Sci., 54:3909--3915, 1999.

Miscellaneous

  • Fritz Horn and Martin Feinberg, Chemical mechanism structure and the coincidence of the stoichiometric and kinetic subspaces. Arch. Rational Mech. Anal., 66:83--97, 1977.
  • Bruce L. Clarke, Stoichiometric network analysis, Cell Biophys 12: 237–253, 1988.
  • David Siegel and Y. F. Chen, The S-C-L graph in chemical kinetics, Rocky Mountain J. Math., 25(1):479--489, 1995.
  • Thomas Wilhelm and Reinhart Heinrich, Smallest chemical reaction system with Hopf bifurcation, J. Math. Chem., 17(1):1--14, 1995.
  • Thomas Wilhelm and Reinhart Heinrich, Mathematical analysis of the smallest chemical reaction system with Hopf bifurcation, J. Math. Chem., 19(2):111--130, 1996.
  • Guy Shinar and Martin Feinberg, Concordance chemical reaction networks, to appear in Math. Biosci., 2012.

Model Reduction

  • Leonor Michaelis and Maud Menten, Die kinetik der invertinwirkung, Biochem. Z., 49:333--369, 1913.

Monotonicity

  • Herb Kunze and David Siegel, Monotonicity properties of chemical reactions with a single initial bimolecular step, J. Math. Chem., 31(4):339--344, 2002
  • David Angeli and Eduardo Sontag, Translation-invariant monotone systems, and a global convergence result for enzymatic futile cycles. Nonlinear Analysis Series B: Real World Applications, 9:128--140, 2008.
  • Murad Banaji, Monotonicity in chemical reaction systems, Dyn. Syst., 24(1):1--30, 2009.
  • Murad Banaji and David Angeli, Convergence in strongly monotone systems with an increasing first integral, SIAM J. Math. Anal., 42(1):334--353, 2010.

Multistability

  • Barry B. Edelstein, A biochemical model with multiple steady states and hysteresis, J. Theor. Biol., 29:57--62, 1970.
  • Paul Schlosser and Martin Feinberg, A theory of multiple steady states in isothermal homogeneous CFSTRs with many reactions, Chem. Eng. Sci., 49(11):1749--1767, 1994.
  • Martin Feinberg, The existence and uniqueness of steady states for a class of chemical reaction networks, Arch. Ration. Mech. Anal., 132:311--370, 1995.
  • Martin Feinberg, Multiple steady states for chemical reaction networks of deficiency one, Arch. Rational Mech. Anal., 132:371--406, 1995.
  • Phillipp Ellison and Martin Feinberg, How catalytic mechanisms reveal themselves in multiple steady state data. I. basic principles. J. Mol. Catal. A - Chemical, 154:155--167, 2000.
  • Gheorghe Craciun and Martin Feinberg, Multiple equilibria in complex chemical reaction networks: I. the injectivity property. SIAM J. Appl. Math, 65(5):1526--1546, 2005.
  • Gheorghe Craciun and Martin Feinberg, Multiple equilibria in complex chemical reaction networks: II. the species-reaction graph. SIAM J. Appl. Math, 66(4):1321--1338, 2006.
  • Gheorghe Craciun, Martin Feinberg, and Yangzhong Tang, Understanding bistability in complex enzyme-driven reaction networks, Proc. Natl. Acad. Sci. USA, 103(23):8697--8702, 2006.
  • Dietrich Flockerzi and Carsten Conradi, Subnetwork analysis for multistationarity in mass-action kinetics, J. Phys. Conf. Ser. 138(1):012006, 2008.
  • Carsten Conradi, Dietrich Flockerzi, and Jorge Raisch, Multistationarity in the activation of a MAPK: Parametrizing the relevant region in parameter space, Math. Bio., 211:105--131, 2008.
  • Gheorghe Craciun, J. William Helton, and Ruth J. Williams, Homotopy methods for counting reaction network equilibria, Math. Biosci., 216(2):140--149, 2008.
  • Carsten Conradi, Multistationarity in (bio)chemical reaction networks with mass action kinetics: model discrimination, robustness and beyond, Ph.D. Thesis, Technische Universitat Berlin, 2008.
  • Liming Wang and Eduardo Sontag, On the number of steady states in a multiple futile cycle, J. Math. Biol., 57(1):29--52, 2008.
  • Murad Banaji and Gheorghe Craciun, Graph-theoretic approaches to injectivity and multiple equilibria in systems of interacting elements, Comm. Math. Sci., 7(4):867--900, 2009.
  • Dan Siegal-Gaskins, Erich Grotewold, and Gregory D. Smith, The capacity for multistability in small gene regulatory networks, BMC Syst. Biol., 3:96, 2009.
  • Matthew Thomson and Jeremy Gunawardena, Unlimited multistability in multisite phosphorylation systems, Nature, 460(7252):274--277, 2009.
  • M. Domijan and M. Kirkilionis, Bistability and oscillations in chemical reaction networks, J. Math. Biol., 59(4):467--501, 2009.
  • Thomas Wilhelm, The smallest chemical reaction system with bistability, BMC Syst. Biol., 3:90, 2009.
  • Gheorghe Craciun and Martin Feinberg, Multiple equilibria in complex chemical reaction networks: semiopen mass action systems, SIAM J. Appl. Math., 70(6):1859--1877, 2010.
  • Mercedes Perez Millan, Alicia Dickenstein, Anne Shiu, and Carsten Conradi, Chemical reaction systems with toric steady states, Bull. Math. Biol., 2011.
  • H. Ji, Uniqueness of equilibria for complex chemical reaction networks, Ph.D. Thesis, Ohio State University, 2011.

Persistence

  • David Siegel and Y. F. Chen, Global stability of deficiency zero chemical networks, Can. Appl. Math. Q., 2(3):413--434, 1994.
  • David Siegel and Debra MacLean, Global stability of complex balanced mechanisms, J. Math. Chem., 27(1-2):89--110, 2000.
  • David Angeli, Patrick Leenheer, and Eduardo Sontag, A petri net approach to the study of persistence in chemical reaction networks. Math. Biosci., 210(2):598--618, 2007.
  • David Anderson, Global asymptotic stability for a class of nonlinear chemical equations, SIAM J. Appl. Math., 68(5):1464--1476, 2008.
  • Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, and Bernd Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44(11):1551--1565, 2009.
  • David Anderson and Anne Shiu, The dynamics of weakly reversible population processes near facets, SIAM J. Appl. Math., 70(6):1840--1858, 2010.
  • Anne Shiu and Bernd Sturmfels, Siphons in chemical reaction networks, B. Math. Biol., 72(6):1448--1463, 2010.
  • David Angeli, Patrick Leenheer, and Eduardo Sontag, Persistence results for chemical reaction networks with time-dependent kinetics and noglobal conservation laws, SIAM Appl. Math., 71(1):128--146, 2011.
  • David Siegel and Matthew D. Johnston, A stratum approach to global stability of complex balanced systems, Dyn. Syst., 26(2):125--146, 2011.
  • Matthew D. Johnston and David Siegel, Weak dynamic non-emptiability and persistence of chemical kinetics systems, SIAM J. Appl. Math., 71(4):1263--1279, 2011.
  • David Anderson, A proof of the global attractor conjecture in the single linkage class case, SIAM J. Appl. Math., 71(4):1487--1508, 2011.
  • Gheorghe Craciun, Casian Pantea, and Fedor Nazarov, Persistence and permanence of mass-action and power-law dynamical systems, to appear SIAM J. Appl. Math., 2012.
  • Casian Pantea, On the persistence and global stability of mass-action systems, SIAM J. Math. Anal., 44(3), 2012.

Reaction-diffusion models

  • Maya Mincheva and David Siegel, Nonnegativity and positiveness of solutions to mass action reaction-diffusion systems, J. Math. Chem., 42:1135--1145, 2007.

Stochastic models

  • Tom Kurtz, The relationship between stochastic and deterministic models for chemical reactions, J. Chem. Phys., 57(7):2976--2978, 1972.
  • Daniel Gillespie, A general method for numerically simulating the stochastic time evolution of coupled chemical reactions, J. Comput. Phys., 22(4):403--434, 1976.
  • P. Arányi and Janos Tóth, A full stochastic description of the Michaelis-Menten reaction for small systems, Acta Biochimica et Biophysica Academiae Scientificarum Hungariae, 12(4), 375--388, 1977.
  • Daniel Gillespie, Exact stochastic simulation of coupled chemical reactions, J. Phys. Chem., 81:2340--2361, 1977.
  • Daniel Gillespie, A rigorous derivation of the chemical master equation, Physica A 188: 404--425, 1992.
  • Karen Ball, Thomas Kurtz, Lea Popovic, and Greg Rempala, Asymptotic analysis of multiscale approximations to reaction networks, Ann. Appl. Probab., 16(4):1925-1961, 2006.
  • Darren Wilkinson, Stochastic modelling for systems biology, Chapman & Hall / CRC, London, 2006.
  • David Anderson, Gheorghe Craciun, and Tom Kurtz, Product-form stationary distributions for deficiency zero chemical reaction networks, Bull. Math. Biol. 72, 1947--1970, 2011.

Summary works

  • Martin Feinberg, Lectures on chemical reaction networks, Unpublished written versions of lectures given at the Mathematics Research Center, University of Wisconsin, 1979. (Available here)
  • Bruce L. Clarke, Stability of complex reaction networks, Advances In Chemical Physics, 43: 1–-215, 1980.
  • Aizik I. Vol'pert and Sergei I. Hudjaev, Analysis in Classes of Discontinuous Functions and Equations of Mathematical Physics, Martinus Nijhoff Publishers, Dordrecht, Netherlands, 1985.
  • Peter Erdi and Janos Toth, Mathematical models of Chemical Reactions, Princeton University Press, 1989.
  • Jeremy Gunawardena, Chemical reaction network theory for in-silico biologists, 2003. (Available here)
  • Darren J. Wilkinson, Stochastic modelling for systems biology, Chapman & Hall / CRC, London, 2006.
  • Matthew D. Johnston, Topics in chemical reaction network theory, Ph.D. Thesis, University of Waterloo, 2011. (Available here)

Toric dynamical systems

  • Karin Gatermann and Birkett Huber, A family of sparse polynomial systems arising in chemical reaction systems, J. Symbolic Comput., 33(3):275--305, 2002.
  • Karin Gatermann and Matthias Wolfrum, Bernstein's second theorem and Viro's method for sparse polynomial systems in chemistry, Advanced in Applied Mathematics, 34(2): 252--294, 2005.
  • Karin Gatermann, Markus Eiswirth, and Anke Sensse, Toric ideals and graph theory to analyze Hopf bifurcations in mass action systems, J. Symb. Comput. 40(6): 1361--1382, 2005.
  • Gheorghe Craciun, Alicia Dickenstein, Anne Shiu, and Bernd Sturmfels, Toric dynamical systems, J. Symbolic Comput., 44(11):1551--1565, 2009.
  • Mercedes Perez Millan, Alicia Dickenstein, Anne Shiu, and Carsten Conradi, Chemical reaction systems with toric steady states, Bull. Math. Biol., 2011.