Share This Article:

Robust estimation of stochastic gene-network systems

Abstract Full-Text HTML Download Download as PDF (Size:185KB) PP. 213-222
DOI: 10.4236/jbise.2013.62A026    3,138 Downloads   4,778 Views  

ABSTRACT

Gene networks in biological systems are highly complicated because of their nonlinear and stochastic features. Network dynamics typically involve crosstalk mechanism and they may suffer from corruption due to intrinsic and extrinsic stochastic molecular noises. Filtering noises in gene networks using biological techniques accompanied with a systematic strategy is thus an attractive topic. However, most states of biological systems are not directly accessible. In practice, these immeasurable states can only be predicted based on the measurement output. In the lab experiment, green fluorescent protein (GFP) is commonly adopted as the reporter protein since it is able to reflect intensity of the gene expression. On this basis, this study considers a nonlinear stochastic model to describe the stochastic gene networks and shows that robust state estimation using Kalman filtering techniques is possible. Stability of the robust estimation scheme is analyzed based on the Ito’s theorem and Lyapunov stability theory. Numerical examples in silico are illustrated to confirm performance of the proposed design.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Chuang, C. and Lin, C. (2013) Robust estimation of stochastic gene-network systems. Journal of Biomedical Science and Engineering, 6, 213-222. doi: 10.4236/jbise.2013.62A026.

References

[1] Kitano, H. (2002) Systems biology: A brief overview. Science, 295, 1662-1664. doi:10.1126/science.1069492
[2] Palsson, B.Q. (2006) Systems biology: properties of re constructed networks. Cambridge University Press, New York. doi:10.1017/CBO9780511790515
[3] Alon, U. (2007) An introduction to systems biology: De sign principles of biological circuits. Chapman & Hall/ CRC, Boca Raton.
[4] Voit, E.O. (2000) Computational analysis of biochemical systems: A practical guide for biochemists and molecular biologists. Cambridge University Press, New York.
[5] Karlebach, G. and Shamir, R. (2008) Modelling and analysis of gene regulatory networks. Nature Reviews Molecular Cell Biology, 9, 770-780. doi:10.1038/nrm2503
[6] El-Samad, H. and Khammash, M. (2010) Modelling and analysis of gene regulatory network using feedback control theory. International Journal of Systems Science, 41, 17-33. doi:10.1080/00207720903144545
[7] McAdams, H.H. and Arkin, A. (1997) Stochastic mechanisms in gene expression. Proceedings of the National Academy of Sciences of the United States of America, 94, 814-819. doi:10.1073/pnas.94.3.814
[8] Elowitz, M.B., Levine, A.J., Siggia, E.D. and Swain, P.S. (2002) Stochasticity gene expression in a single cell. Science, 297, 1183-1186. doi:10.1126/science.1070919
[9] Paulsson, J. (2004) Summing up the noise in gene net works. Nature, 427, 415-418. doi:10.1038/nature02257
[10] Wang, Z., Liu, X., Liu, Y., Liang, J. and Vinciotti, V. (2009) An extended Kalman filtering approach to modeling nonlinear dynamic gene regulatory networks via short gene expression time series. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 6, 410-419. doi:10.1109/TCBB.2009.5
[11] Chen, B.S., Wang, Y.C., Wu, W.S. and Li, W.H. (2005) A new measure of the robustness of biochemical net works. Bioinformatics, 21, 2698-2705. doi:10.1093/bioinformatics/bti348
[12] Lin, C.L., Lui, Y.W. and Chuang, C.H. (2009) Control design for signal transduction networks. Bioinformatics and Biology Insights, 3, 1-14.
[13] Chen, B.S. and Wu, W.S. (2008) Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises. Mathematical Biosciences, 211, 342-355. doi:10.1016/j.mbs.2007.11.002
[14] Gelb, A. (1974) Applied optimal estimation. The MIT Press, Cambridge.
[15] Reif, K., Gunther, S., Yaz, E. and Unbehauen, R. (2000) Stochastic stability of the continuous-time extended Kalman filter. IEE Proceedings Control Theory and Applications, 147, 45-52. doi:10.1049/ip-cta:20000125
[16] Liang, J. and Lam, J. (2010) Robust state estimation for stochastic genetic regulatory networks. International Journal of Systems Science, 41, 47-63. doi:10.1080/00207720903141434
[17] Lillacci, G. and Valigi, P. (18-21 May 2008) State estimation for a model of gene expression. Proceedings of IEEE International Symposium on Circuits and Systems, Seattle, 2046-2049.
[18] Cacace, F., Germani, A. and Palumbo, P. (2012) The state observer as a tool for the estimation of gene expression. Journal of Mathematical Analysis and Applications, 391, 382-396. doi:10.1016/j.jmaa.2012.02.026
[19] Su, W.W., Liu, B., Lu, W.B., Xu, N.S., Du, G.C. and Tan, J.L. (2005) Observer-based online compensation of inner filter effect in monitoring fluorescence of GFP-expressing plant cell cultures. Biotechnology and Bioengineering, 91, 213-226. doi:10.1002/bit.20510
[20] Chuang, C.H. and Lin, C.L. (2010) On robust state estimation of gene networks. Biomedical Engineering and Computational Biology, 2, 23-36.
[21] Choukroun, D. (16-18 December 2009) Ito stochastic modeling for attitude quaternion filtering. Proceedings of IEEE Conference on Decision and Control, Shanghai, 733-738.
[22] Gardiner, C.W. (1980) Handbook of stochastic methods of differential equations. Sijthoff and Noordhoff, Alphen aan den Rijn.
[23] Chen, B.S. and Wu, C.H. (2009) A systematic design method for robust synthetic biology to satisfy design specifications. BMC Systems Biology, 3, 1-18. doi:10.1186/1752-0509-3-66
[24] Poor, V. and Looze, D.P. (1981) Minimax state estimation for linear stochastic systems with noise uncertainty. IEEE Transactions on Automatic Control, 26, 902-906. doi:10.1109/TAC.1981.1102756
[25] Bartle, S. (2000) Introduction to real analysis. 3rd ed. John Wiley & Sons, New York.

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.