Parameter estimation of biological phenomena modeled by S-systems: An Extended Kalman filter approach

Recent advances in high-throughput technologies for biological data acquisition have spurred a broad interest in the development of mathematical models for biological phenomena. S-systems, which offer a good compromise between accuracy and mathematical flexibility, are a promising framework for modeling the dynamical behavior of genetic regulatory networks (GRNs), as well as that of biochemical pathways. In the S-system modeling framework, the number of unknown parameters is much more than the number of metabolites and this makes the parameter estimation task a challenging one. In this paper, a new parameter estimation algorithm is developed based on the Extended Kalman filter (EKF) approach. It is first shown that the conventional EKF approach is not capable of estimating the unknown parameters of S-systems. To remedy this problem, a new iterative extended Kalman Filtering algorithm is developed in which the EKF algorithm is applied iteratively to the available noisy time profiles of the metabolites. The proposed estimation algorithm is applied to a generic branched pathway and the Cad system of E.coli. The simulation results demonstrate the effectiveness of the proposed scheme.