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Robust synchronization analysis in nonlinear stochastic cellular networks with time-varying delays, intracellular perturbations and intercellular noise. (English) Zbl 1218.92033

Summary: Naturally, a cellular network consist of a large amount of interacting cells is complex. These cells have to be synchronized in order to emerge their phenomena for some biological purposes. However, the inherently stochastic intra and intercellular interactions are noisy and delayed from biochemical processes. In this study, a robust synchronization scheme is proposed for a nonlinear stochastic time-delay coupled cellular network (TdCCN) in spite of the time-varying process delay and intracellular parameter perturbations. Furthermore, a nonlinear stochastic noise filtering ability is also investigated for this synchronized TdCCN against stochastic intercellular and environmental disturbances. Since it is very difficult to solve a robust synchronization problem with the Hamilton-Jacobi inequality (HJI) matrix, a linear matrix inequality (LMI) is employed to solve this problem via the help of a global linearization method. Through this robust synchronization analysis, we can gain a more systemic insight into not only the robust synchronizability but also the noise filtering ability of TdCCN under time-varying process delays, intracellular perturbations and intercellular disturbances. The measures of robustness and noise filtering ability of a synchronized TdCCN have potential application to the designs of neuron transmitters, on-time mass production of biochemical molecules, and synthetic biology. Finally, a benchmark of robust synchronization design in Escherichia coli repressilators is given to confirm the effectiveness of the proposed methods.

MSC:

92C40 Biochemistry, molecular biology
92C42 Systems biology, networks
37N25 Dynamical systems in biology
15A39 Linear inequalities of matrices
65C20 Probabilistic models, generic numerical methods in probability and statistics
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[1] Fuqua, C., Regulation of gene expression by cell-to-cell communication: acyl-homoserine lactone quorum sensing, Annual Review of Genetics, 35, 439 (2001)
[2] Xavier, K.; Bassler, B., LuxS quorum sensing: more than just a numbers game, Current Opinion in Microbiology, 6, 191 (2003)
[3] Gera, C.; Srivastava, S., Quorum-sensing: the phenomenon of microbial communication, Current Science, 90, 666 (2006)
[4] Hong, D., Extracellular noise-induced stochastic synchronization in heterogeneous quorum sensing network, Journal of Theoretical Biology, 245, 726 (2007) · Zbl 1451.92201
[5] Lazdunski, A., Regulatory circuits and communication in Gram-negative bacteria, Nature Reviews Microbiology, 2, 581 (2004)
[6] Nealson, K., Cellular control of the synthesis and activity of the bacterial luminescent system, Journal of Bacteriology, 104, 313 (1970)
[7] Li, C., Stochastic synchronization of genetic oscillator networks, BMC Systems Biology, 1, 6 (2007)
[8] Hu, A.; Xu, Z., Stochastic linear generalized synchronization of chaotic systems via robust control, Physics Letters A, 372, 3814 (2008) · Zbl 1220.37021
[9] Qiu, J.; Cao, J., Global synchronization of delay-coupled genetic oscillators, Neurocomputing, 72, 845 (2009)
[10] Belykh, V. N., Connection graph stability method for synchronized coupled chaotic systems, Physica D: Nonlinear Phenomena, 195, 159 (2004) · Zbl 1098.82622
[11] Wu, C. W., Synchronization in networks of nonlinear dynamical systems coupled via a directed graph, Nonlinearity, 18, 1057 (2005) · Zbl 1089.37024
[12] Chen, M., Chaos synchronization in complex networks, IEEE Transactions on Circuits and Systems-I - Regular Papers, 55, 1335 (2008)
[13] Yu, W., Global synchronization of linearly hybrid coupled networks with time-varying delay, SIAM Journal on Applied Dynamical Systems, 7, 108 (2008) · Zbl 1161.94011
[14] Zhou, J., Adaptive synchronization of an uncertain complex dynamical network, IEEE Transactions on Automatic Control, 51, 652 (2006) · Zbl 1366.93544
[15] Lu, J.; Cao, J., Adaptive synchronization of uncertain dynamical networks with delayed coupling, Nonlinear Dynamics, 53, 107 (2008) · Zbl 1182.92007
[16] Lu, J.; Chen, G., A time-varying complex dynamical network model and its controlled synchronization criteria, IEEE Transactions on Automatic Control, 50, 841 (2005) · Zbl 1365.93406
[17] Lu, J., Characterizing the synchronizability of small-world dynamical networks, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 51, 787 (2004) · Zbl 1374.34220
[18] Wang, R., Modeling and analyzing biological oscillations in molecular networks, Proceedings of the IEEE, 96, 1361 (2008)
[19] Liu, H., Structure identification of uncertain general complex dynamical networks with time delay, Automatica, 45, 1799 (2009) · Zbl 1185.93031
[20] Yu, W., Estimating uncertain delayed genetic regulatory networks: an adaptive filtering approach, IEEE Transactions on Automatic Control, 54, 892 (2009) · Zbl 1367.93709
[21] Garcia-Ojalvo, J., Modeling a synthetic multicellular clock: Repressilators coupled by quorum sensing, Proceedings of the National Academy of Sciences, 101, 10955 (2004) · Zbl 1064.92019
[22] Gonze, D., Stochastic models for circadian rhythms: effect of molecular noise on periodic and chaotic behaviour, Comptes Rendus-Biologies, 326, 189 (2003)
[23] Johnston, R. J., MicroRNAs acting in a double-negative feedback loop to control a neuronal cell fate decision, Proceedings of the National Academy of Sciences, 102, 12449 (2005)
[24] Ruby, E.; Lee, K., The Vibrio fischeri-Euprymna scolopes light organ association: current ecological paradigms, Applied and Environmental Microbiology, 64, 805 (1998)
[25] Yang, Z., Adaptive synchronization of an uncertain complex delayed dynamical networks, International Journal of Nonlinear Science, 3, 93 (2007)
[26] Vidyasagar, M., Nonlinear Systems Analysis (2002), Society for Industrial Mathematics · Zbl 1006.93001
[27] S.P. Boyd et al., Linear Matrix Inequalities in System and Control Theory: Society for Industrial and Applied, 1994.; S.P. Boyd et al., Linear Matrix Inequalities in System and Control Theory: Society for Industrial and Applied, 1994.
[28] L. Magni et al., Nonlinear model predictive control: towards new challenging applications book, Lecture Notes in Control and Information Sciences, 2009.; L. Magni et al., Nonlinear model predictive control: towards new challenging applications book, Lecture Notes in Control and Information Sciences, 2009.
[29] Ferullo, D. J., Cell cycle synchronization of Escherichia coli using the stringent response, with fluorescence labeling assays for DNA content and replication, Methods, 48, 8 (2009)
[30] Heinemann, M.; Panke, S., Synthetic biology-putting engineering into biology, Bioinformatics, 22, 2790 (2006)
[31] Karn, M., Stochasticity in gene expression: from theories to phenotypes, Nature Reviews Genetics, 6, 451 (2005)
[32] Chen, B.; Chang, Y., A systematic molecular circuit design method for gene networks under biochemical time delays and molecular noises, BMC Systems Biology, 2, 103 (2008)
[33] Wu, C. W.; Chua, L. O., Synchronization in an array of linearly coupled dynamical systems, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42, 430 (1995) · Zbl 0867.93042
[34] Zhang, J., Synchronization and clustering of synthetic genetic networks: A role for cis-regulatory modules, Physical Review E, 79, 41903 (2009)
[35] Rudin, W.; Cofman, J., Principles of Mathematical Analysis (1964), McGraw-Hill: McGraw-Hill New York
[36] B.S. Chen, W.H. Chen, Robust \(HH\); B.S. Chen, W.H. Chen, Robust \(HH\)
[37] Liu, R., On global linearization, SIAM-AMS Proceeding, 93 (1969)
[38] Gordon, W. J.; Wixom, J. A., Shepard’s method of“ metric interpolation” to bivariate and multivariate interpolation, Mathematics of Computation, 32, 253 (1978) · Zbl 0383.41003
[39] P. Gahinet et al., The LMI control toolbox, 1994.; P. Gahinet et al., The LMI control toolbox, 1994. · Zbl 0811.93018
[40] Keener, J., Mathematical Physiology: Cellular Physiology (2008), Springer Verlag · Zbl 1273.92017
[41] Wu, C., Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling, IEEE Transactions on Circuits and Systems II: Express Briefs, 52, 282 (2005)
[42] Hooshangi, S.; Bentley, W., From unicellular properties to multicellular behavior: bacteria quorum sensing circuitry and applications, Current Opinion in Biotechnology, 19, 550 (2008)
[43] Zhang, W.; Chen, B., H-inf control for nonlinear stochastic systems, SIAM Journal of Control Optimization, 44, 1973 (2006)
[44] Taylor, A., Dynamical quorum sensing and synchronization in large populations of chemical oscillators, Science, 323, 614 (2009)
[45] Gahinet, P., LMI Control Toolbox for Use with Matlab (1995), The MATH Works Inc.
[46] Henrion, D.; Lasserre, J. B., GloptiPoly: Global optimization over polynomials with Matlab and SeDuMi, ACM Transactions on Mathematical Software, 29, 165 (2003) · Zbl 1070.65549
[47] R. Nikoukhah et al., LMITOOL: a Package for LMI Optimization in Scilab, Rapport technique, vol. 170.; R. Nikoukhah et al., LMITOOL: a Package for LMI Optimization in Scilab, Rapport technique, vol. 170.
[48] Nesterov, Y.; Nemirovsky, A., Interior-point polynomial methods in convex programming, Studies in Applied Mathematics, vol. 13 (1994), SIAM: SIAM Philadelphia, PA · Zbl 0824.90112
[49] Yamashita, M., Implementation and evaluation of SDPA 6.0 (semidefinite programming algorithm 6.0), Optimization Methods and Software, 18, 491 (2003) · Zbl 1106.90366
[50] Ko vara, M.; Stingl, M., PENNON: A code for convex nonlinear and semidefinite programming, Optimization Methods and Software, 18, 317 (2003) · Zbl 1037.90003
[51] Swain, P., Intrinsic and extrinsic contributions to stochasticity in gene expression, Proceedings of the National Academy of Sciences, 99, 12795 (2002)
[52] Chen, B.; Liu, X., Delay-dependent robust H_inf control for T-S fuzzy systems with time delay, IEEE Transactions on Fuzzy Systems, 13, 544 (2005)
[53] Chen, B. S., Mixed \(H2/H\)∞ fuzzy output feedbackcontrol design for nonlinear dynamic systems: an LMI approach, IEEE Transactions on Fuzzy Systems, 8, 249 (2000)
[54] Danino, T., A synchronized quorum of genetic clocks, Nature, 463, 326 (2010)
[55] You, L., Programmed population control by cell-cell communication and regulated killing, Nature, 428, 868 (2004)
[56] Pai, A., Engineering multicellular systems by cell-cell communication, Current Opinion in Biotechnology (2009)
[57] Kaplan, H.; Greenberg, E., Diffusion of autoinducer is involved in regulation of the Vibrio fischeri luminescence system, Journal of Bacteriology, 163, 1210 (1985)
[58] Sturm, J. F., Implementation of interior point methods for mixed semidefinite and second order cone optimization problems, Optimization Methods and Software, 17, 1105 (2002) · Zbl 1032.90021
[59] Brenner, K., Engineered bidirectional communication mediates a consensus in a microbial biofilm consortium, Proceedings of the National Academy of Sciences, 104, 17300 (2007)
[60] Chen, G., Linear Stochastic Control Systems (1995), CRC Press
[61] Chang, Y.-T.; Chen, B.-S., A fuzzy approach for robust reference tracking control design of nonlinear distributed parameter time-delayed systems and its application, IEEE Transactions on Fuzzy Systems, 18, 1144 (2010)
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