Abstract The studies of biomedicine show that the expression level of p53 (tumor suppressor gene) is related with the tumor forming. Researches of the p53 related signal transduction networks would provide new ideas for revealing the pathogenesis of cancer or tumor and looking for the treatment method. As the p53-Mdm2 negative feedback network plays core roles, the study of the p53-Mdm2 regulation net work is of great significance. In this paper, based on the gene expression time series data of human leukemia cells after ionizing radiation, the nonlinear dynamic continuous random biological networks with time delay were established, then continuous-discrete extended Kalman filter (EKF) algorithm was used to simulate the dynamic regulation of p53 and Mdm2. Meanwhile, the accuracy of the model established in this paper was validated and we found that the error rate of the model was only 0.85%. Results showed that the algorithm thatis convergent could predict gene expression level at any time and simulate accurately the damped oscillation process of p53-Mdm2 regulatory networks after ionizing radiation. The response process was consistent with biological experiment results. The algorithm proposed in this paper provided an effective method for biological experiment modeling, and supplied the foundation for the research of system dynamics.
Jiang Li,Li Yurong. Research of p53-Mdm2 Regulatory Networks Based on Modeling by Continuous-Discrete Extended Kalman Filter[J]. Chinese Journal of Biomedical Engineering, 2017, 36(2): 180-186.
[1] Taberlay PC, Jones PA. DNA methylation and cancer [J]. Oncogene, 2012, 21(35): 89-95. [2] Yang Y, Lee KS, Xiang C, et al. Biological mechanisms revealed by a mathematical model for p53-Mdm2 core regulation [J]. Iet Systems Biology, 2009, 3(4): 229-238. [3] Voropaeva OF, Shokin YI, Nepomnyaschchikh LM, et al. Mathematical modeling of the tumor markers network [C] // International Conference on Biomedical Engineering and Computational Technologies. Novosibirsk: IEEE, 2015: 225-229. [4] Wang Shaomeng, Sun Wei, Zhao Yujun, et al. SAR405838: an optimized inhibitor of MDM2-p53 interaction that induces complete and durable tumor regression [J]. Cancer Research, 2014, 74(20): 5855-5865. [5] 孙延哲. P53信号转导网络动力学模型研究 [D]. 南京: 南京大学, 2014. [6] 毕远宏, 杨卓琴, 何小燕. Mdm2生成速率调控的p53-Mdm2振子的全局动力学和稳定性 [J]. 物理学报, 2016, 65(2): 360-367. [7] Mihalas GI, Simon Z, Balea G, et al. Possible oscillatory behavior in p53-Mdm2 interaction computer simulation [J]. Journal of Biological Systems, 2011, 08(1): 21-29. [8] Lavoie H, Hogues H, Mallick J, et al. Evolutionary tinkering with conserved components of a transcriptional regulatory network [J]. PLoS Biology, 2010, 8(3): e1000329. [9] Wang Zidong, Liu Xiaohui, Liu Yurong, et al. An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series [J]. IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2009, 6(3): 410-419. [10] Xiong Jie, Zhou Tong. Structure identification for gene regulatory networks via linearization and robust state estimation [J]. Automatica, 2013, 50(11): 2765-2776. [11] Zhang Yongqing, Pu Yifei, Zhang Haisen, et al. An extended fractional Kalman filter for inferring gene regulatory networks using time-series data [J]. Chemometrics & Intelligent Laboratory Systems, 2014, 138: 57-63. [12] Kulikova MV, Kulikov GY. Adaptive ODE solvers in extended Kalman filtering algorithms [J]. Journal of Computational & Applied Mathematics, 2014, 262(10): 205-216. [13] Barenco M, Tomescu D, Brewer D, et al. Ranked prediction of p53 targets using hidden variable dynamic modeling [J]. Genome Biology, 2006, 7(3): R25. [14] Vilborg A, Glahder JA, Wilhelm MT, et al. The p53 target Wig-1 regulates p53 mRNA stability through an AU-rich element [J]. Proceedings of the National Academy of Sciences of the United States of America, 2009, 106(37): 15756-15761. [15] Hatami E, Salarieh H, Vosoughi N. Design of a fault tolerated intelligent control system for a nuclear reactor power control: using extended Kalman filter [J]. Journal of Process Control, 2014, 24(7): 1076-1084. [16] Huang S, Dissanayake G. Convergence and consistency analysis for extended Kalman filter based SLAM [J]. IEEE Transactions on Robotics, 2007, 23(5): 1036-1049. [17] Krener AJ. The convergence of the extended Kalman filter [J]. Mathematics, 2003, 286: 173-182. [18] Zeng Nianyin, Wang Zidong, Li Yurong, et al. Inference of nonlinear state-space models for Sandwich-Type lateral flow immunoassay using extended Kalman filtering [J]. IEEE Transactions on Biomedical Engineering, 2011, 58(7): 1959-1966. [19] Tu CT, Chen BS. On the increase in network robustness and decrease in network response ability during the aging process: a systems biology approach via microarray data [J]. IEEE/ACM Transactions on Computational Biology & Bioinformatics, 2013, 10(2): 468-480. [20] Lahav G, Rosenfeld N, Sigal A, et al. Dynamics of the p53-Mdm2 feedback loop in individual cells [J]. Nature Genetics, 2004, 36(2):147-150. [21] Bar-Or RL, Maya R, Segel LA, et al. Generation of oscillations by the p53-Mdm2 feedback loop: a theoretical and experimental study [J]. Proceedings of the National Academy of Sciences of the United States of America, 2000, 97(21): 11250-11255. [22] 张小鹏, 刘锋, 王炜. p53信号网络的非线性动力学研究 [J]. 中国科学:物理学力学天文学, 2014(12): 1311-1318. [23] Lahav G. The strength of indecisiveness: oscillatory behavior for better cell fate determination [J]. Journal of Health Services Research & Policy, 2014, 19(1): 1-2.
