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Inferring causal relationships among numerous cellular components is one of the fundamental problems in understanding biological behaviors. The model of gene regulatory networks (GRNs) is widely considered as a nonlinear dynamic stochastic model consisting of a gene measurement equation and a gene regulation equation, in which the extended Kalman filter (EKF) is sometimes used for estimating both the model parameters and the actual value of gene expression levels. First-order approximations, however, unavoidably result in modelling errors, but the EKF based method does not take either unmodelled dynamics or parametric uncertainties into account, which makes its estimation performances not very satisfactory. As a result, estimation performances of the EKF based method may not be satisfied with slow convergence speed and low estimation accuracy. To overcome these problems, a sensitivity penalization based robust state estimator is suggested for reconstructing the structure of a GRN. The suggested method has been used to identify an artificially constructed non-linear GRN. Compared with the widely adopted EKF based method, simulation results show that the convergence speed is distinctly improved, and parametric estimation accuracy is significantly increased, which make both the false positive error and the false negative error significantly reduced. Moreover, computation results with a real GRN of extit{yeast} show that the proposed method can identify causal relationships effectively, which may help us to better understand the structure and dynamics of GRNs in practice. |
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Keywords:Causal relationships, Extended Kalman filter, Gene regulatory networks, Robust state estimator, Modelling error |
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