Waves in a Stochastic Cell Motility Model

Christian Hamster*, Peter van Heijster

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


In Bhattacharya et al. (Sci Adv 6(32):7682, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied at two levels. The microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction–diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction–diffusion system, or chemical Langevin equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction–diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

Original languageEnglish
Article number70
JournalBulletin of Mathematical Biology
Issue number8
Publication statusPublished - Aug 2023


  • Cell motility
  • Chemical Langevin equation
  • Gillespie algorithms
  • Mesoscopic patterns
  • SPDEs


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