  The multi-grid reaction-diffusion master equation (mgRDME) provides a
generalization of stochastic compartment-based reaction-diffusion modelling
described by the standard reaction-diffusion master equation (RDME). By
enabling different resolutions on lattices for biochemical species with
different diffusion constants, the mgRDME approach improves both accuracy and
efficiency of compartment-based reaction-diffusion simulations. The mgRDME
framework is examined through its application to morphogen gradient formation
in stochastic reaction-diffusion scenarios, using both an analytically
tractable first-order reaction network and a model with a second-order
reaction. The results obtained by the mgRDME modelling are compared with the
standard RDME model and with the (more detailed) particle-based Brownian
dynamics simulations. The dependence of error and numerical cost on the
compartment sizes is defined and investigated through a multi-objective
optimization problem.
