ReactionKinetics—A Mathematica package with applications

Requirements are formulated for a reaction kinetics program package to be useful for an as wide as possible circle of users and they are illustrated with examples using ReactionKinetics, a Mathematica based package currently being developed by the authors. Treating a realistic problem in any field of reaction kinetics raises a series of problems, both mathematical and computational: we illustrate a number of these also with examples using our package.

[1]  M. P. Barnett,et al.  Symbolic calculation in chemistry: Selected examples , 2004 .

[2]  Vladimir Gol'dshtein,et al.  Simple global reduction technique based on decomposition approach , 2008 .

[3]  D Garfinkel,et al.  Computer applications to biochemical kinetics. , 1970, Annual review of biochemistry.

[4]  INVARIANTS OF KINETIC DIFFERENTIAL EQUATIONS , 2003 .

[5]  J. Tóth,et al.  Specification of oscillating chemical models starting from a given linearized form , 1986 .

[6]  Béla Barabás,et al.  Stochastic aspects of asymmetric autocatalysis and absolute asymmetric synthesis , 2010 .

[7]  Muruhan Rathinam,et al.  Stiffness in stochastic chemically reacting systems: The implicit tau-leaping method , 2003 .

[8]  John C. Butcher,et al.  Towards efficient Runge-Kutta methods for stiff systems , 1990 .

[9]  Jean-Pierre Rospars,et al.  Dynamic modeling of biochemical reactions with application to signal transduction: principles and tools using Mathematica. , 2005, Bio Systems.

[10]  G. Szederkényi,et al.  Finding complex balanced and detailed balanced realizations of chemical reaction networks , 2010, 1010.4477.

[11]  Manuel Silva,et al.  A Simple and Fast Algorithm to Obtain All Invariants of a Generalized Petri Net , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[12]  Rongling Wu,et al.  Modeling with Compartments , 2002 .

[13]  B. Vizvári,et al.  Effective solution of linear Diophantine equation systems with an application in chemistry , 2006 .

[14]  Péter Érdi,et al.  Stochastic simulation of chemical reactions by digital computer, II. Applications , 1974 .

[15]  C. W. Gear,et al.  Invariants and numerical methods for ODEs , 1992 .

[16]  Ewart Carson,et al.  Introduction to modeling in physiology and medicine , 2007 .

[17]  Guy Marin,et al.  Coincidences in chemical kinetics: Surprising news about simple reactions , 2010 .

[18]  E. A. Milne,et al.  A Note on the Principle of Detailed Balancing. , 1925, Proceedings of the National Academy of Sciences of the United States of America.

[19]  Iliya V. Karlin,et al.  Method of invariant manifold for chemical kinetics , 2003 .

[20]  Martin Feinberg,et al.  Necessary and sufficient conditions for detailed balancing in mass action systems of arbitrary complexity , 1989 .

[21]  J. Tóth,et al.  Detailed balance in ion channels: Application of Feinberg’s theorem , 2009 .

[22]  Péter Érdi,et al.  Mathematical models of chemical reactions , 1989 .

[23]  Thomas Wilhelm,et al.  The smallest chemical reaction system with bistability , 2009, BMC Systems Biology.

[24]  D. Gillespie,et al.  Avoiding negative populations in explicit Poisson tau-leaping. , 2005, The Journal of chemical physics.

[25]  F. Horn,et al.  On the possibility of sustained oscillations, multiple steady states, and asymmetric steady states in multicell reaction systems , 1979 .

[26]  János Tóth,et al.  Orthogonal transforms of the Lorenz- and Rössler-equation , 1986 .

[27]  Rud. Wegscheider.  Über simultane Gleichgewichte und die Beziehungen zwischen Thermodynamik und Reaktionskinetik homogener Systeme , 1902 .

[28]  Eric W. Weisstein.  Hundred-Dollar, Hundred-Digit Challenge Problems , 2002 .

[29]  M. Feinberg,et al.  Structural Sources of Robustness in Biochemical Reaction Networks , 2010, Science.

[30]  Marc R. Roussel,et al.  Invariant manifold methods for metabolic model reduction. , 2001, Chaos.

[31]  J. Tóth,et al.  A full stochastic description of the Michaelis-Menten reaction for small systems. , 1977, Acta biochimica et biophysica; Academiae Scientiarum Hungaricae.

[32]  J. Ross.  Determination of complex reaction mechanisms. Analysis of chemical, biological and genetic networks. , 2005, The journal of physical chemistry. A.

[33]  G. Szederkényi.  Computing sparse and dense realizations of reaction kinetic systems , 2010 .

[34]  Herschel Rabitz,et al.  The Effect of Lumping and Expanding on Kinetic Differential Equations , 1997, SIAM J. Appl. Math..

[35]  Bruce L. Clarke.  Stoichiometric network analysis of the oxalate–persulfate–silver oscillator , 1992 .

[36]  Tamás Turányi,et al.  Chapter 4 Mathematical tools for the construction, investigation and reduction of combustion mechanisms , 1997 .

[37]  Michael A. Gibson,et al.  Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels , 2000 .

[38]  Tom Lenaerts,et al.  Information theoretical quantification of cooperativity in signalling complexes , 2009, BMC Systems Biology.

[39]  B. Vizvári,et al.  Decomposition of the permanganate/oxalic acid overall reaction to elementary steps based on integer programming theory , 2004 .

[40]  R. Graham,et al.  Handbook of Combinatorics , 1995 .

[41]  Andrew Wilkinson.  Compendium of Chemical Terminology , 1997 .

[42]  Mustafa Bayram,et al.  Derivation of conservation relationships for metabolic networks using MAPLE , 2000, Appl. Math. Comput..

[43]  Péter Érdi,et al.  Mathematical Models of Chemical Reactions: Theory and Applications of Deterministic and Stochastic Models , 1989 .

[44]  Tamás Turányi,et al.  Uncertainty of Arrhenius parameters , 2011 .

[45]  Maximum likelihood estimation of reaction-rate constants , 1988 .

[46]  L. Dickson.  Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors , 1913 .

[47]  János Tóth,et al.  Stochastic simulation of chemical reaction by digital computer, I. The model , 1974 .

[48]  Thanh N. Truong,et al.  Application of Chemical Graph Theory for Automated Mechanism Generation , 2003, J. Chem. Inf. Comput. Sci..

[49]  R. Femat,et al.  Dynamic equivalence in tangent spaces from vector fields of chemical reaction networks , 2012 .

[50]  A. I Vol’pert.  DIFFERENTIAL EQUATIONS ON GRAPHS , 1972 .

[51]  Single-molecule, real-time measurement of enzyme kinetics by alternating-laser excitation fluorescence resonance energy transfer. , 2010, Chemical communications.

[52]  Tamás Turányi,et al.  Mathematical Tools for the Construction, Investigation and Reduction of Combustion Mechanisms , 1998 .