Gene Regulatory Network Identification from Gene Expression Time Series Data Using Swarm Intelligence

A Gene Regulatory Network (GRN) usually is modelled as a directed graph, where the nodes represent genes and the directed arc from a given node i to node j represents the causal influence of gene i over gene j. The causal influence represented by an arc is enumerated by a signed weight associated with that arc. In this article, we model GRN by a recurrent fuzzy neural network, and attempt to identify the signed weights from the time response data of the gene micro-array. A cost function has been constructed to describe the weight identification as an optimization problem, and Particle Swarm Optimization algorithm has been used to optimize the cost function. The fuzzy membership distribution used to model network weights enhances search efficiency and hence computational overhead in the identification problem. Because of the nonlinearity in causal relationship between genes, there exist multiple solutions to the weight identification problem of GRN. In order to cater for the theoretical best solution, the identification problem has been decoupled into two sub-problems: i) determination of the existence/non-existence about the causal influence, and ii) determination of the sign and magnitude of the influence between any two genes of the network. The solutions obtained from these two sub-problems are then combined to accurately identify the both non-existing connections, and the sign and magnitude of weights to existing connections. Computer simulation reveals that the proposed realization outperforms the most recently reported work in this field in detecting the sign and magnitude and also the structure of the overall network.

[1]  Michael Ruogu Zhang,et al.  Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. , 1998, Molecular biology of the cell.

[2]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[3]  M.H. Hassoun,et al.  Fundamentals of Artificial Neural Networks , 1996, Proceedings of the IEEE.

[4]  Mike Lin,et al.  Effects of the neural network s-Sigmoid function on KDD in the presence of imprecise data , 2006, Comput. Oper. Res..

[5]  R. Storn,et al.  Differential evolution a simple and efficient adaptive scheme for global optimization over continu , 1997 .

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

[7]  Satoru Miyano,et al.  Inferring Gene Regulatory Networks from Time-Ordered Gene Expression Data of Bacillus Subtilis Using Differential Equations , 2002, Pacific Symposium on Biocomputing.

[8]  Russell C. Eberhart,et al.  A new optimizer using particle swarm theory , 1995, MHS'95. Proceedings of the Sixth International Symposium on Micro Machine and Human Science.

[9]  Michal Linial,et al.  Using Bayesian Networks to Analyze Expression Data , 2000, J. Comput. Biol..

[10]  Yu Zhang,et al.  A new dynamic Bayesian network for integrating multiple data in estimating gene networks , 2007, Third International Conference on Natural Computation (ICNC 2007).

[11]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[12]  Yashwant Prasad Singh,et al.  Dynamic tunneling technique for efficient training of multilayer perceptrons , 1999, IEEE Trans. Neural Networks.

[13]  Amit Konar,et al.  Computational Intelligence: Principles, Techniques and Applications , 2005 .

[14]  Amit Konar,et al.  Metaheuristic Clustering , 2009, Studies in Computational Intelligence.

[15]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[16]  Philippe De Wilde,et al.  Practical Applications of Computational Intelligence Techniques , 2001 .

[17]  Donald C. Wunsch,et al.  Modeling of gene regulatory networks with hybrid differential evolution and particle swarm optimization , 2007, Neural Networks.

[18]  S. Masri,et al.  Training neural networks by adaptive random search techniques , 1999 .

[19]  Russell C. Eberhart,et al.  A discrete binary version of the particle swarm algorithm , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[20]  M Wahde,et al.  Coarse-grained reverse engineering of genetic regulatory networks. , 2000, Bio Systems.

[21]  Qiang Ji,et al.  Active affective State detection and user assistance with dynamic bayesian networks , 2005, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[22]  R. Blumenthal,et al.  Mapping regulatory networks in microbial cells. , 1999, Trends in microbiology.

[23]  Ziv Bar-Joseph,et al.  Analyzing time series gene expression data , 2004, Bioinform..

[24]  Ting Chen,et al.  Modeling Gene Expression with Differential Equations , 1998, Pacific Symposium on Biocomputing.

[25]  S Fuhrman,et al.  Reveal, a general reverse engineering algorithm for inference of genetic network architectures. , 1998, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing.

[26]  Geoffrey E. Hinton,et al.  Learning representations by back-propagating errors , 1986, Nature.

[27]  Marcel J. T. Reinders,et al.  A Comparison of Genetic Network Models , 2000, Pacific Symposium on Biocomputing.

[28]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[29]  Marcel J. T. Reinders,et al.  Linear Modeling of Genetic Networks from Experimental Data , 2000, ISMB.

[30]  J. Vohradský.  Neural network model of gene expression , 2001, FASEB journal : official publication of the Federation of American Societies for Experimental Biology.

[31]  Dirk Husmeier,et al.  Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks , 2003, Bioinform..

[32]  Li Shaoqian,et al.  Chaotic spreading sequences with multiple access performance better than random sequences , 2000 .

[33]  Xinye Cai,et al.  Simultaneous structure discovery and parameter estimation in gene networks using a multi-objective GP-PSO hybrid approach , 2009, Int. J. Bioinform. Res. Appl..

[34]  Patrik D'haeseleer,et al.  Linear Modeling of mRNA Expression Levels During CNS Development and Injury , 1998, Pacific Symposium on Biocomputing.

[35]  Janet Wiles,et al.  Asynchronous dynamics of an artificial genetic regulatory network , 2004 .

[36]  Aurélien Mazurie,et al.  Gene networks inference using dynamic Bayesian networks , 2003, ECCB.

[37]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[38]  Janet Wiles,et al.  Evolving Genetic Regulatory Networks Using an Artificial Genome , 2004, APBC.

[39]  C. Espinosa-Soto,et al.  A Gene Regulatory Network Model for Cell-Fate Determination during Arabidopsis thaliana Flower Development That Is Robust and Recovers Experimental Gene Expression Profilesw⃞ , 2004, The Plant Cell Online.

[40]  Goldberg,et al.  Genetic algorithms , 1993, Robust Control Systems with Genetic Algorithms.

[41]  Chris Joslin,et al.  Networked virtual park , 2001 .

[42]  Alvis Brazma,et al.  Current approaches to gene regulatory network modelling , 2007, BMC Bioinformatics.

[43]  Jong-Hwan Kim,et al.  Multi-objective evolutionary generation process for specific personalities of artificial creature , 2008, IEEE Computational Intelligence Magazine.

[44]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[45]  Satoru Miyano,et al.  Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model , 1998, Pacific Symposium on Biocomputing.

[46]  Satoru Miyano,et al.  Estimation of Genetic Networks and Functional Structures Between Genes by Using Bayesian Networks and Nonparametric Regression , 2001, Pacific Symposium on Biocomputing.

[47]  Geoffrey E. Hinton,et al.  Learning representations by back-propagation errors, nature , 1986 .

[48]  Sanjoy Das,et al.  A Multiobjective Evolutionary-Simplex Hybrid Approach for the Optimization of Differential Equation Models of Gene Networks , 2008, IEEE Transactions on Evolutionary Computation.

[49]  N. K. Bose,et al.  Neural Network Fundamentals with Graphs, Algorithms and Applications , 1995 .

[50]  Marcel J. T. Reinders,et al.  Genetic network models: a comparative study , 2001, SPIE BiOS.

[51]  H. Iba,et al.  Inferring Gene Regulatory Networks using Differential Evolution with Local Search Heuristics , 2007, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[52]  Roland Somogyi,et al.  Modeling the complexity of genetic networks: Understanding multigenic and pleiotropic regulation , 1996, Complex..

[53]  Amit Konar,et al.  A recurrent fuzzy neural model of a gene regulatory network for knowledge extraction using differential evolution , 2009, 2009 IEEE Congress on Evolutionary Computation.

[54]  John A. Hertz,et al.  Modeling Genetic Regulatory Dynamics in Neural Development , 2002, J. Comput. Biol..

[55]  Shuhui Li,et al.  Extended Kalman Filter Training of Neural Networks on a SIMD Parallel Machine , 2002, J. Parallel Distributed Comput..