Document Type : Original Research Paper

Author

Faculty of Electrical and Computer Engineering, Arak University of Technology, Arak, Iran

Abstract

Background and Objectives: Regulation of protein expression in cellular level are so challenging. In cellular scale, biochemical processes are intrinsically noisy and many convenient controllers aren’t physically implementable.
Methods: In this paper, we consider standard Lyapunov function and by using Ito formula and stochastic analysis, we derive sufficient conditions for noise to state stability presented in the form of matrix inequalities. In the next step, by defining appropriate change of variables, matrix inequalities are transformed to Linear matrix inequalities which can be used to synthesize controller with the desired structure.
Results: This paper deals with the design of implementable controller for stochastic gene regulatory networks with multiplicative and additive noises. In particular, we consider structural limitations that are present in real cellular systems and design the decentralized feedback that guarantees noise to state stability. Since the proposed conditions for controller design are in the form of linear matrix inequalities, controller gains can be derived efficiently through solving presented LMIs numerically. It is noteworthy that Because of its simple structure, the proposed controller can be implemented universally in many cells. Moreover, we consider a synthetic gene regulatory networks and investigate the effectiveness of the proposed controller by simulations.
Conclusion: Our results provide a new method for designing Decentralized controller in gene regulatory networks with intrinsic and extrinsic noises. the proposed controller can be easily implemented in cellular environment. 


======================================================================================================
Copyrights
©2019 The author(s). This is an open access article distributed under the terms of the Creative Commons Attribution (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, as long as the original authors and source are cited. No permission is required from the authors or the publishers.
======================================================================================================

Keywords

Main Subjects

[1] S. Roostaee , H. R. Ghaffary, "Diagnosis of Heart Disease Based on Meta Heuristic Algorithms and Clustering Methods," Journal of Electrical and Computer Engineering Innovations, 4(2): 105-110, 2016.

[2] A. Khalili, A. Rastegarnia, V. Vahidpour, M. K. Islam, "Adaptive-Filtering-Based Algorithm for Impulsive Noise Cancellation from ECG Signal," Journal of Electrical and Computer Engineering Innovations, 4(2): 169-176, 2016.

[3] R. Kianzad, H. Montazery Kordy, "Automatic sleep stages detection based on EEG signals using combination of classifiers," Journal of Electrical and Computer Engineering Innovations, 1(2): 99-105, 2013.

[4] S. V. Shojaedini, M. Heydari, "A New Method for Sperm Detection in Infertility Cure: Hypothesis Testing Based on Fuzzy Entropy Decision," Journal of Electrical and Computer Engineering Innovations, 2(2): 69-76, 2014.

[5] H. de Jong, "Modeling and Simulation of Genetic Regulatory Systems: A Literature Review," Journal of Computational Biology, 9(1): 67-103, 2002.

[6] C. Li, L. Chen, K. Aihara, "Stability of Genetic Networks with SUM Regulatory Logic: Lur'e System and LMI Approach," IEEE Transactions on Circuits and Systems I: Regular Papers, 53(11): 2451-2458, 2006.

[7] Z. Wang, H. Gao, J. Cao, X. Liu, "On Delayed Genetic Regulatory Networks With Polytopic Uncertainties: Robust Stability Analysis," IEEE Transactions on NanoBioscience, 7(2): 154-163, 2008.

[8] G. Chesi, "Robustness analysis of genetic regulatory networks affected by model uncertainty," Automatica, 47(6): 1131-1138, 2011.

[9] W. Zhang, J.-a. Fang, Y. Tang, "Robust stability for genetic regulatory networks with linear fractional uncertainties," Communications in Nonlinear Science and Numerical Simulation, 17(4): 1753-1765, 2012.

[10] X. Zhang, L. Wu, J. Zou, "Globally Asymptotic Stability Analysis for Genetic Regulatory Networks with Mixed Delays: An M-Matrix-Based Approach," IEEE/ACM Transactions on Computational Biology and Bioinformatics, 13(1): 135-147, 2016.

[11] T. Dong, Q. Zhang, "Stability and oscillation analysis of a gene regulatory network with multiple time delays and diffusion rate," IEEE Transactions on NanoBioscience: 1-1, 2020.

[12] L. Zhang, X. Zhang, Y. Xue, X. Zhang, "New Method to Global Exponential Stability Analysis for Switched Genetic Regulatory Networks with Mixed Delays," IEEE Transactions on NanoBioscience: 1-1, 2020.

[13] Z. Li, D. Chen, Y. Liu, Y. Zhao, "New delay-dependent stability criteria of genetic regulatory networks subject to time-varying delays," Neurocomputing,  207: 763-771, 2016.

[14] S. Chen, P. Harrigan, B. Heineike, J. Stewart-Ornstein, H. El-Samad, "Building robust functionality in synthetic circuits using engineered feedback regulation," Current Opinion in Biotechnology, 24(4): 790-796, 2013.

[15] M. Chevalier, M. Gómez-Schiavon, A. H. Ng, H. El-Samad, "Design and Analysis of a Proportional-Integral-Derivative Controller with Biological Molecules," Cell Systems, 9(4): 338-353.e10, 2019.

[16] B. Yordanov, J. Kim, R. L. Petersen, A. Shudy, V. V. Kulkarni, A. Phillips, "Computational Design of Nucleic Acid Feedback Control Circuits," ACS Synthetic Biology, 3(8): 600-616, 2014.

[17] A. Milias-Argeitis et al., "In silico feedback for in vivo regulation of a gene expression circuit," Nature Biotechnology, 29(12): 1114-1116, 2011.

[18] J.-B. Lugagne, M. J. Dunlop, "Cell-machine interfaces for characterizing gene regulatory network dynamics," Current Opinion in Systems Biology, 14: 1-8, 2019.

[19] B. Yordanov, J. Kim, R. L. Petersen, A. Shudy, V. V. Kulkarni, A. Phillips, "Computational Design of Nucleic Acid Feedback Control Circuits," ACS Synthetic Biology,  3(8): 600-616, 2014.

[20] S. K. Aoki, G. Lillacci, A. Gupta, A. Baumschlager, D. Schweingruber, M. Khammash, "A universal biomolecular integral feedback controller for robust perfect adaptation," Nature,  570(7762): 533-537, 2019.

[21] D. Del Vecchio, H. Abdallah, Y. Qian, J. J. Collins, "A Blueprint for a Synthetic Genetic Feedback Controller to Reprogram Cell Fate," Cell Systems,  4(1): 109-120.e11, 2017.

[22] S. Bruno, M. A. Al-Radhawi, E. D. Sontag, D. D. Vecchio, "Stochastic analysis of genetic feedback controllers to reprogram a pluripotency gene regulatory network," in 2019 American Control Conference (ACC), : 5089-5096, 2019.

[23] L. Bakule, "DECENTRALIZED CONTROL: AN OVERVIEW," IFAC Proceedings Volumes, 40(9): 39-48, 2007.

[24] J. M. Raser, E. K. Shea, "Noise in Gene Expression: Origins, Consequences, and Control," Science, 309(5743): 2010, 2005.

[25] H. Shokouhi-Nejad, A. Rikhtehgar-Ghiasi, "Robust H∞ observer-based controller for stochastic genetic regulatory networks," Mathematical Biosciences, 250: 41-53, 2014.

[26] H. Moradi, V. J. Majd, "Robust control of uncertain nonlinear switched genetic regulatory networks with time delays: A redesign approach," Mathematical Biosciences, 275: 10-17, 2016.

[27] M. S. Ali, N. Gunasekaran, C. K. Ahn, P. Shi, "Sampled-Data Stabilization for Fuzzy Genetic Regulatory Networks with Leakage Delays," IEEE/ACM Transactions on Computational Biology and Bioinformatics, 15(1): 271-285, 2018.

[28] D. Hua, M. Krstic, R. J. Williams, "Stabilization of stochastic nonlinear systems driven by noise of unknown covariance," IEEE Transactions on Automatic Control, 46(8): 1237-1253, 2001.

[29] M. B. Elowitz, S. Leibler, "A synthetic oscillatory network of transcriptional regulators," Nature, 403(6767): 335-338, 2000.

[30] T. S. Gardner, C. R. Cantor, J. J. Collins, "Construction of a genetic toggle switch in Escherichia coli," Nature, 403(6767): 339-342, 2000.


LETTERS TO EDITOR

Journal of Electrical and Computer Engineering Innovations (JECEI) welcomes letters to the editor for the post-publication discussions and corrections which allows debate post publication on its site, through the Letters to Editor. Letters pertaining to manuscript published in JECEI should be sent to the editorial office of JECEI within three months of either online publication or before printed publication, except for critiques of original research. Following points are to be considering before sending the letters (comments) to the editor.


[1] Letters that include statements of statistics, facts, research, or theories should include appropriate references, although more than three are discouraged.

[2] Letters that are personal attacks on an author rather than thoughtful criticism of the author’s ideas will not be considered for publication.

[3] Letters can be no more than 300 words in length.

[4] Letter writers should include a statement at the beginning of the letter stating that it is being submitted either for publication or not.

[5] Anonymous letters will not be considered.

[6] Letter writers must include their city and state of residence or work.

[7] Letters will be edited for clarity and length.

CAPTCHA Image