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Domain growth is a key process in many areas of biology, including embryonic development, the growth of tissue, and limb regeneration. As a result, mechanisms for incorporating it into traditional models for cell movement, interaction, and proliferation are of great importance. A previously well-used method to incorporate domain growth into on-lattice reaction-diffusion models causes a buildup of particles on the boundaries of the domain, which is particularly evident when diffusion is low in comparison to the rate of domain growth. Here we present an alternative method which addresses this unphysical buildup of particles at the boundaries and demonstrate that it is accurate for scenarios in which the previous method fails. Further, we discuss for which parameter regimes it is feasible to continue using the original method due to diffusion dominating the domain growth mechanism.
Original languageEnglish
Article number063307
JournalPhysical Review E
Issue number6
Publication statusPublished - 19 Dec 2019


  • Domain growth
  • Mesoscopic modelling
  • Reaction-diffusion master equation
  • Morphogen gradient
  • Uniform growth
  • On-lattice modelling


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