Applications in Chemistry

  • Peter Schuster
Part of the Springer Series in Synergetics book series (SSSYN)


In chemistry the master equation is the best suited and most commonly used tool to model stochasticity in reaction kinetics. We review the common elementary reactions in mass action kinetics and discuss Michaelis–Menten kinetics as an example of combining several elementary steps into an overall reaction. Multistep reactions or reaction networks are considered and a formal mathematical theory that provides tools for the derivation of general properties of networks is presented. Then we digress into theory and empirical determination of rate parameters. The chemical master equation is introduced as the most popular tool for modeling stochasticity in chemical reactions, and the single reaction step approach is extended to reaction networks. The chemical Langevin equation is discussed as an alternative to the master equation: it has a number of convenient features but is not always applicable. Then, a selection of one-step reactions is presented for which the master equation can be solved exactly. The exact solutions are also used to illustrate the relation between the mathematical approach and the recorded data. A separate chapter deals with correlation functions, fluctuation spectroscopy, single molecule data, and stochastic modeling. Deterministic and stochastic parts of solutions can be separated by means of size expansions. Most reaction mechanisms are not accessible to the analytical approach and therefore we present a simulation method that is exact within the concept of the chemical master equation, and apply it to some selected examples of chemical reactions.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Peter Schuster
    • 1
  1. 1.Institut für Theoretische ChemieUniversität WienWienAustria

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