By discretising space into compartments and letting system dynamics be governed by the reaction–diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However, there are many implementation choices involved in this process, such as the choice of discretisation and method of derivation of the diffusive jump rates, and it is not clear a priori how these affect model predictions. To shed light on this issue, in this work we explore how a variety of discretisations and methods for derivation of the diffusive jump rates affect the outputs of stochastic simulations of reaction–diffusion models, in particular using Turing’s model of pattern formation as a key example. We consider both static and uniformly growing domains and demonstrate that, while only minor differences are observed for simple reaction–diffusion systems, there can be vast differences in model predictions for systems that include complicated reaction kinetics, such as Turing’s diffusion-driven instability model of pattern formation. Our work highlights that care must be taken in using the reaction–diffusion master equation framework to make predictions as to the dynamics of stochastic reaction–diffusion systems.

通过将空间离散成各个部分，并让系统动力学受反应扩散主方程控制，可以在任意域上推导和模拟反应和扩散的随机模型。不过，也有参与这个过程中的许多实现选择，如离散和扩散跳率的推导方法的选择，这是不明确的先验这些因素如何影响模型预测。为了阐明这一问题，在这项工作中，我们探索了各种离散化和推导扩散跳跃率的方法如何影响反应扩散模型的随机模拟输出，特别是使用图灵的模式形成模型作为关键示例。我们同时考虑了静态域和均匀增长域，并证明，虽然简单的反应扩散系统仅观察到很小的差异，但对于包含复杂反应动力学的系统的模型预测，例如图灵的扩散驱动的不稳定性模型，其模型预测中可能会有很大的差异。模式形成。我们的工作强调，在使用反应扩散主方程框架进行随机反应扩散系统动力学的预测时必须格外小心。