Chapter 6.  Rates and state changes in MesoRD

Table of Contents

State changes
Rates and probabilities
Scale dependent association rate constants
Mean-field time evolution


Chemical reactions are stochastic event, meaning that is not possible to know when and where the next reaction will occur. The probabilities for the reaction events can however be modelled and the time evolution of the system can therefore be described probabilistically. Stochastic reaction-diffusion kinetics is commonly modelled by the reaction-diffusion master equation (RDME) [Kuramoto 1974] [Gardiner et al. 1976] [Baras and Mansour 1997] Stochastic reactions-diffusion kinetics can be modelled in many other ways and at different levels of detail, but the stochastic simulations performed by MesoRD do only represent the RDME level.

In the RDME framework the total system volume is divided into a large number of subvolumes and the state is described by how many molecules there are of the different species in the different subvolumes. The subvolumes must be small enough to be homogenised by diffusion on the timescale of the chemical reactions. Commonly the association and dissociation rate constants used for the reactive part of the RDME include not only reactivity but also a term related to the time to reach the reaction target by diffusion. Using this type of macroscopic reaction rate constants, the size of the subvolumes must be significantly larger than the molecules themselves [Elf and Ehrenberg 2004] so that different molecules can be fully dissociated within a subvolume. This restriction can be alleviated using the theory presented in [Fange et al. 2010], which is also implemented in the latest MesoRD release. To get a proper spatial resolution for the system of interests, we may need hundreds of thousands of subvolumes to correctly discretise a 3D reaction volume.