Synchronization in networks of genetic oscillators with delayed coupling

This paper studies the global synchronization problem for gene networks of coupled oscillators with a coupling delay. Several synchronization conditions are obtained for coupled genetic oscillators by means of Lyapunov functional theory and matrix inequality approach. More specifically, two conditions are first presented in terms of matrix inequalities, under which the synchronization can be achieved irrespective of how large the coupling delay is. Then, a sufficient condition is further proposed to ensure the synchronization of coupled genetic oscillators for a certain range of coupling delays. A numerical example of coupled Goodwin oscillators is given to illustrate the effectiveness of these conditions. Both theoretical and numerical results show that the coupling delay can affect the dynamic behaviors of coupled genetic oscillators, and the synchronized state can be significantly different from that of a single oscillator when a coupling delay is present. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

[1]  James Lam,et al.  Filtering for Nonlinear Genetic Regulatory Networks With Stochastic Disturbances , 2008, IEEE Transactions on Automatic Control.

[2]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[3]  Shengyuan Xu,et al.  A survey of linear matrix inequality techniques in stability analysis of delay systems , 2008, Int. J. Syst. Sci..

[4]  J. Hasty,et al.  Synchronizing genetic relaxation oscillators by intercell signaling , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[5]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[6]  Huijun Gao,et al.  STABILITY ANALYSIS OF UNCERTAIN DISCRETE‐TIME SYSTEMS WITH TIME‐VARYING STATE DELAY: A PARAMETER‐DEPENDENT LYAPUNOV FUNCTION APPROACH , 2006 .

[7]  N. Monk.  Oscillatory Expression of Hes1, p53, and NF-κB Driven by Transcriptional Time Delays , 2003, Current Biology.

[8]  Fuwen Yang,et al.  Stochastic Dynamic Modeling of Short Gene Expression Time-Series Data , 2008, IEEE Transactions on NanoBioscience.

[9]  K. Aihara,et al.  Synchronization of coupled nonidentical genetic oscillators , 2006, Physical biology.

[10]  James Lam,et al.  Disturbance Analysis of Nonlinear Differential Equation Models of Genetic SUM Regulatory Networks , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[11]  Luonan Chen,et al.  Synchronization of genetic oscillators. , 2008, Chaos.

[12]  D. A. Baxter,et al.  Mathematical Modeling of Gene Networks , 2000, Neuron.

[13]  Kazuyuki Aihara,et al.  Stability of Genetic Networks With SUM Regulatory Logic: Lur'e System and LMI Approach , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Maurício C. de Oliveira,et al.  Investigating duality on stability conditions , 2004, Syst. Control. Lett..

[15]  Yeung Sam Hung,et al.  Stability analysis of uncertain genetic sum regulatory networks , 2008, Autom..

[16]  A. Goldbeter,et al.  Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms. , 2004, Journal of Theoretical Biology.

[17]  James Lam,et al.  Exponential estimates and stabilization of uncertain singular systems with discrete and distributed delays , 2008, Int. J. Control.

[18]  Wenwu Yu,et al.  Estimating Uncertain Delayed Genetic Regulatory Networks: An Adaptive Filtering Approach , 2009, IEEE Transactions on Automatic Control.

[19]  James Lam,et al.  On the Transient and Steady-State Estimates of Interval Genetic Regulatory Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[20]  Jinde Cao,et al.  Genetic oscillation deduced from Hopf bifurcation in a genetic regulatory network with delays. , 2008, Mathematical biosciences.

[21]  Eduardo D. Sontag,et al.  Synchronization of Interconnected Systems With Applications to Biochemical Networks: An Input-Output Approach , 2009, IEEE Transactions on Automatic Control.

[22]  Jinde Cao,et al.  On Delayed Genetic Regulatory Networks With Polytopic Uncertainties: Robust Stability Analysis , 2008, IEEE Transactions on NanoBioscience.

[23]  M. Rosenblum,et al.  Delayed feedback control of collective synchrony: an approach to suppression of pathological brain rhythms. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[25]  Shengyuan Xu,et al.  Stability analysis of delayed genetic regulatory networks with stochastic disturbances , 2009 .

[26]  S. Yamaguchi,et al.  Synchronization of Cellular Clocks in the Suprachiasmatic Nucleus , 2003, Science.

[27]  L. Glass,et al.  Chaos in high-dimensional neural and gene networks , 1996 .

[28]  J. Collins,et al.  Construction of a genetic toggle switch in Escherichia coli , 2000, Nature.

[29]  B. Goodwin.  Oscillatory behavior in enzymatic control processes. , 1965, Advances in enzyme regulation.

[30]  Tianping Chen,et al.  Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay , 2006 .

[31]  C. Tomlin,et al.  Biology by numbers: mathematical modelling in developmental biology , 2007, Nature Reviews Genetics.

[32]  M. Elowitz,et al.  A synthetic oscillatory network of transcriptional regulators , 2000, Nature.

[33]  Jinde Cao,et al.  Exponential Stability of Discrete-Time Genetic Regulatory Networks With Delays , 2008, IEEE Transactions on Neural Networks.