Particle filtering and the inverse problem of biochemical networks

In this paper we address the inverse problem of biochemical networks composed of first-order reactions. Based on noisy measurements of the number of molecules of some of the species that participate in the reactions of a given network, we propose a method for estimating recursively the numbers of molecules and the stochastic rate constants in the network. The evolution of the number of molecules of the species is modeled by Poisson random processes, and the observations are assumed to be (non)linear functions of the number of molecules. Our method employs particle filtering where we propose particles of the stochastic rate constants from their posteriors. We demonstrate the performance of the proposed method with several examples.