Stability analysis of standard genetic regulatory networks with time-varying delays and stochastic perturbations

In this paper, the stability analysis problem is investigated for a standard class of genetic regulatory networks (GRNs) with stochastic disturbances and time-varying delays. The standard GRNs under consideration are based on the model of the recurrent neural networks, the stochastic perturbation is in the form of a scalar Brownian motion, and the time-varying delays exist in the transcription and translation processes. Specifically, we are interested in (1) establishing a standard model for the time-varying delayed GRNs and (2) establishing conditions under which the standard GRNs are exponentially mean-square stable in the presence of time delays and stochastic disturbances. By using the linear matrix inequality (LMI) technique and S-procedure, sufficient conditions are first derived for ensuring globally asymptotic and exponential stability that can be easily solved by using standard software packages. Two numerical examples are exploited to demonstrate the effectiveness of the proposed method.

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

[2]  Zidong Wang,et al.  On multistability of delayed genetic regulatory networks with multivariable regulation functions. , 2010, Mathematical biosciences.

[3]  L. Arnold.  Stochastic Differential Equations: Theory and Applications , 1992 .

[4]  Bore-Kuen Lee,et al.  The applications of stochastic regulation H∞ control to HIV therapy , 2010, 2010 International Conference on Machine Learning and Cybernetics.

[5]  Daniel W. C. Ho,et al.  Robust ${\cal H}_{\infty}$ Finite-Horizon Control for a Class of Stochastic Nonlinear Time-Varying Systems Subject to Sensor and Actuator Saturations , 2010, IEEE Transactions on Automatic Control.

[6]  Zidong Wang,et al.  Monostability and multistability of genetic regulatory networks with different types of regulation functions , 2010 .

[7]  Meiqin Liu,et al.  Delayed Standard Neural Network Models for Control Systems , 2007, IEEE Transactions on Neural Networks.

[8]  Zidong Wang,et al.  Exponential Stabilization of a Class of Stochastic System With Markovian Jump Parameters and Mode-Dependent Mixed Time-Delays , 2010, IEEE Transactions on Automatic Control.

[9]  Xiaofeng Liao,et al.  (Corr. to) Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach , 2002, Neural Networks.

[10]  Zidong Wang,et al.  Robust filtering for stochastic genetic regulatory networks with time-varying delay. , 2009, Mathematical biosciences.

[11]  Wei-Po Lee,et al.  A clustering-based approach for inferring recurrent neural networks as gene regulatory networks , 2008, Neurocomputing.

[12]  Jian-an Fang,et al.  Global stability of stochastic high-order neural networks with discrete and distributed delays , 2008 .

[13]  Peng Shi,et al.  A mode-dependent stability criterion for delayed discrete-time stochastic neural networks with Markovian jumping parameters , 2010, Neurocomputing.

[14]  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.

[15]  J. Hespanha,et al.  Evolution of gene auto-regulation in the presence of noise. , 2009, IET systems biology.

[16]  H. Shimizu,et al.  Relationship between noise characteristics in protein expressions and regulatory structures of amino acid biosynthesis pathways. , 2010, IET systems biology.

[17]  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.

[18]  Xuyang Lou,et al.  Exponential stability of genetic regulatory networks with random delays , 2010, Neurocomputing.

[19]  Xiaodi Li,et al.  LMI Approach for Stationary Oscillation of Interval Neural Networks With Discrete and Distributed Time-Varying Delays Under Impulsive Perturbations , 2010, IEEE Transactions on Neural Networks.

[20]  Jun Hu,et al.  Robust stability of genetic regulatory networks with interval time-varying delays under intrinsic and extrinsic noises , 2010, Proceedings of the 29th Chinese Control Conference.

[21]  Sushmita Mitra,et al.  Genetic Networks and Soft Computing , 2011, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[22]  Zidong Wang,et al.  Exponential stability of delayed recurrent neural networks with Markovian jumping parameters , 2006 .

[23]  Yurong Liu,et al.  Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays , 2006 .

[24]  Li Li,et al.  BMC Bioinformatics Methodology article Discovery of time-delayed gene regulatory networks based on temporal , 2006 .

[25]  Shihuang Shao,et al.  Cellular responding DNA damage: An improved modeling of P53 gene regulatory networks under ion radiation (IR) , 2008, Appl. Math. Comput..

[26]  Jinde Cao,et al.  Asymptotic and robust stability of genetic regulatory networks with time-varying delays , 2008, Neurocomputing.

[27]  Zidong Wang,et al.  An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series , 2009, TCBB.

[28]  J. H. Koo,et al.  Asymptotic stability of neutral functional differential equation model of genetic regulatory networks with time-varying delays , 2010, Proceedings of SICE Annual Conference 2010.

[29]  Jason Li,et al.  Splice site identification using probabilistic parameters and SVM classification , 2006, BMC Bioinformatics.

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