An extended fractional Kalman filter for inferring gene regulatory networks using time-series data

•A fractional gene regulatory algorithm is firstly proposed.•Show how the EFKF was used to estimate parameters of gene regulatory network.•The performance of our method was validated by microarray time-series data.

In recent years, inference of gene regulatory networks has received ever increasing attention in the systems biology field. In this paper, for the first time, a fractional gene regulatory algorithm by extended fractional Kalman filter (EFKF) is proposed to estimate the hidden states as well as the unknown static parameters of the model, which can provide insight into the underlying regulatory relations among genes in the biological system. In the proposed method, gene regulatory networks are inferred via evolutionary modeling based on time-series microarray measurements. The gene regulatory network is considered as a fractional order discrete stochastic dynamic model that consists of the gene measurement equation and the gene regulation equation. After specifying the model structure, we apply the EFKF algorithm for identifying both the model parameters and the actual value of gene expression levels. In this paper, the main advantages of using fractional order systems, increasing the flexibility and improving the accuracy of the system state equation in EFKF are highlighted. The performance of the EFKF algorithm is compared with EKF and other nonlinear algorithms in predicting the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed algorithm outperforms EKF and other methods, and therefore, it can serve as a natural framework for inference gene regulatory networks with a nonlinear structure.