StoSpa2: A C++ software package for stochastic simulations of spatially extended systems - Bartmanski, BJ; Baker, RE (Open Journals, 2020)
Mathematical modelling of complex biological phenomena allows us to understand the contributions of different processes to observed behaviours. Many of these phenomena involve the reaction and diffusion of molecules and so we use so-called reaction-diffusion models to describe them mathematically. Reaction-diffusion models are often subdivided into three types (Hellander & Petzold, 2017): macroscopic, mesoscopic and microscopic. Models that describe a system in terms of concentrations are termed macroscopic models. At the other end of the spectrum we have microscopic models that describe a system by specifying the positions (and often velocities) of each molecule. The middle ground between these two scales is covered by mesoscopic models, in which stochasticity and some individual-level details are included without directly tracking the position of every single molecule. Macroscale models ignore crucial details such as stochastic effects, while microscale models tend to be computationally intensive (Osborne, Fletcher, Pitt-Francis, Maini, & Gavaghan, 2017; Van Liedekerke, Palm, Jagiella, & Drasdo, 2015). Mesoscale models offer a good balance in that they include stochastic effects without incurring enormous computational overheads. The frameworks of the chemical master equation (CME) and its spatial extension, the reaction-diffusion master equation (RDME) (Isaacson, 2009, 2013; Van Kampen, 1992), provide mesoscopic models of reaction and diffusion. However, in the majority of these cases, models built in the CME/RDME framework are analytically intractable and so model behaviours must be explored using stochastic simulation algorithms.