Reversible DOI and Smoluchowski kinetics for high-order reactions

James Cavallo, Mark B. Flegg

Research output: Contribution to journalArticleResearchpeer-review


In recent years, modeling of biochemical systems has attracted much attention. Traditionally, these systems have been modeled with differential equations. However, specific biological processes tend to produce a lot of intrinsic noise, which has led to the development of a number of stochastic models for such processes. One such framework is that of Smoluchowski, which is used to model bimolecular reactions. In this model, particles diffuse with Brownian motion until they come within a critical separation distance and undergo a chemical reaction. This theory has undergone a number of developments, notably the extension of the theory to deal with reversible reactions, which has made available various software packages for stochastic reaction-diffusion simulations. Recent work has extended Smoluchowski theory to irreversible reactions of order greater than two. In this paper, we build on that theory and develop a model that includes reversible reactions of any order. This type of chemical kinetics is critical to many catalytic systems in biology. We use our new modeling framework to simulate the response of the core destruction regulation cycle to sharp changes in Wnt signaling, generating behavior not seen in classical ODE models.

Original languageEnglish
Pages (from-to)594-618
Number of pages25
JournalSIAM Journal on Applied Mathematics
Issue number2
Publication statusPublished - 9 Apr 2019


  • Biochemical systems
  • Cell signaling
  • Diffusion-limited reactions
  • High-order reactions
  • Reversible reactions
  • Smoluchowski kinetics

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