On new stochastic approaches for solving forward and backward problems of biochemical networks

There are two distinct problems in the stochastic analysis of biochemical networks, and they are known as the forward and inverse problems. Solutions of the former problem are used for simulating a system of molecular species in time according to the random laws that govern the reactions in which the species participate. Solutions of the latter problem provide estimates of the unknowns in the system that is represented by the biochemical network. The estimates are obtained from measurements that are functions of the number of molecules of some of the species. In the two problems, we have underlying assumptions about the probabilistic models of the studied network. In this paper we present two new methods for addressing these problems. For solving the forward problem we propose a method that does not employ Monte Carlo simulations, whereas for solving the inverse problem we use particle filtering.