A multi-scaled approach for simulating chemical reaction systems

Kevin Burrage, Tianhai Tian, Pamela Burrage

Research output: Contribution to journalArticleResearchpeer-review

99 Citations (Scopus)


In this paper we give an overview of some very recent work, as well as presenting a new approach, on the stochastic simulation of multi-scaled systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and present a new approach which couples the three regimes mentioned above. We then apply this approach to a biologically inspired problem involving the expression and activity of LacZ and LacY proteins in E. coli, and conclude with a discussion on the significance of this work.

Original languageEnglish
Pages (from-to)217-234
Number of pages18
JournalProgress in Biophysics and Molecular Biology
Issue number2-3
Publication statusPublished - 1 Jun 2004


  • 60C35
  • 65C30
  • 80A30
  • Biological applications
  • Chemical reaction systems
  • Multi-scaled approaches
  • Poisson Runge-Kutta methods
  • Stochastic simulation methods

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