Abstract
It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.
Highlights
Cells are complex interconnected web of dynamic systems
Janus kinase (JAK)/STAT which is initiated by cytokines is an important signal transduction pathway in regulating immune response [4,33]
To evaluate its performance for estimation of parameters in nonlinear state-space model of biochemical networks, the extended Kalman Filter (EKF) was applied to simulation data, the real experimental data of the JAK-STAT pathway and Ras/Raf/MEK/ERK pathway
Summary
Cells are complex interconnected web of dynamic systems. To gain a deep understanding about the biological systems requires modeling of biochemical reaction networks. Mathematical and computational modeling of biochemical reaction networks can comprehensively integrate experimental knowledge into forming and testing hypotheses and help to gain into system level understanding of biochemical networks, which will not been seen if the components of biochemical networks are separately studied. Developing mathematical models of biological systems holds a key to understanding and predicting the dynamic behaviors of the biological systems under perturbation of external stimuli and a major task of systems biology and is the keystones of systems biology [5]
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