Estimation of stochastic rate constants and tracking of species in biochemical networks with second-order reactions

In a recent work we applied particle filtering to simple biochemical networks composed of first-order reactions with the objective of estimating unknowns in the studied system that include stochastic rate constants and species with time-evolving numbers of molecules. In this paper we extend that effort to biochemical networks which have second-order reactions. We model the unknown stochastic rate constants by Gamma distributions and the number of reactions in a given time interval as Poisson random variables. The observations are nonlinear functions of some of the species in the system, and they are distorted by noises with known distributions. With these assumptions, we develop a particle filter that tracks the number of molecules of all the species in the network with time and estimates the unknown stochastic rate constants. We demonstrate the method on a reaction of importance in studying Ras regulation.