We study the evolution of several chemical species in a given space domain. Every molecule undergo random movement, and molecules interact with each other when they are close enough, through a given set of chemical reactions. Several modelling techniques can be used to understand the dynamic of the system. We briefly discuss the deterministic PDE models, which are a macroscopic view of the system. Some interesting and beautiful patterns can emerge from them.
But the atomic nature of molecules suggests a microspic view of the state of the system. We devise a stochastic process describing the position of a set of individual molecules evolving through time, and we link this microscopic model to the macroscopic one when the number of molecules goes to infinity. The main mathematical tool used to show this link is the martingale problem.
We will finish by an application of this framework to the dynamic of actin polymerisation in the cell cortex during division.