  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 method 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 model of pattern formation. Our
work highlights that care must be taken in using the reaction-diffusion master
equation to make predictions as to the dynamics of stochastic
reaction-diffusion systems.
