Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial diffe...

Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments, and diffusive motion is approximated by jumps between these compartments. Trea...

In order to model fundamental cell biological processes including the transcription, translation, and nuclear membrane transport of biological molecules within a eukaryotic cell it is necessary to be able to approximate the stochastic reaction and diffusion of a small number of molecules in the complex three dimensional geometry of a cell. For this reason a method is developed that incorporates...

UNLABELLED MesoRD is a tool for stochastic simulation of chemical reactions and diffusion. In particular, it is an implementation of the next subvolume method, which is an exact method to simulate the Markov process corresponding to the reaction-diffusion master equation. AVAILABILITY MesoRD is free software, written in C++ and licensed under the GNU general public license (GPL). MesoRD runs ...

The macroscopic behavior of dissipative stochastic partial differential equations usually can be described by a finite dimensional system. This article proves that a macroscopic reduced model may be constructed for stochastic reaction-diffusion equations with cubic nonlinearity by artificial separating the system into two distinct slow-fast time parts. An averaging method and a deviation estima...

Reaction and diffusion processes are used to model chemical and biological processes over a wide range of spatial and temporal scales. Several routes to the diffusion process at various levels of description in time and space are discussed and the master equation for spatially discretized systems involving reaction and diffusion is developed. We discuss an estimator for the appropriate compartm...

In biological systems, biochemical networks play a crucial role, implementing a broad range of vital functions from regulation and communication to resource transport and shape alteration. While biochemical networks naturally occur at low copy numbers and in a spatial setting, this fact often is ignored and well-stirred conditions are assumed for simplicity. Yet, it is now increasingly becoming...

Hellander, S. 2013. Stochastic Simulation of Reaction-Diffusion Processes. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1042. 46 pp. Uppsala. ISBN 978-91-554-8667-9. Numerical simulation methods have become an important tool in the study of chemical reaction networks in living cells. Many systems can, with hi...