Case-Studies of Parameter Estimation in the Stochastic Reaction-Diffusion Master Equation

Stochastic approaches to the reaction-diffusion master equation (RDME) are commonly employed in systems biology to model the intrinsic randomness of diffusing molecular species. For accurate modeling and numerical simulation of the reaction-diffusion process, parameter estimation from experimental or synthetic data is a topic of interest. Parameter estimation is a challenging task in stochastic RDME since the reaction rate parameters are always coupled with the diffusion rate parameters, and the state of the system itself is random. We present a fitting scheme based on a maximum likelihood estimation (MLE) to approximate both the reaction and diffusion rate parameters. The quality of the method is evaluated by applying it to two case-studies from systems biology, such as the birth- death process and the annihilation system. The results obtained from our experiments demonstrate a reasonable approximation of the estimated parameters compared to the true parameter values.