Parameter estimation for the reaction–diffusion master equation

In this paper, we present a novel method to estimate chemical reaction and diffusion rates for biochemical reaction–diffusion dynamics from a time series of observations. Our approach leverages iterated particle filtering as a means to fit a high-dimensional stochastic and discrete spatiotemporal model to sparse time series data, often with some chemical species present in low copy numbers. We demonstrate the feasibility of this approach on three realistic reaction–diffusion systems. In each case, the method recovered known true values for all rate parameters with a great degree of accuracy.