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Inferring Gene Regulatory Networks via Nonlinear State-Space Models and Exploiting Sparsity
July-Aug. 2012 (vol. 9 no. 4)
pp. 1203-1211
E. Serpedin, Dept. of Electr. & Comput. Eng., Texas A& M Univ., College Station, TX, USA
A. Noor, Dept. of Electr. & Comput. Eng., Texas A& M Univ., College Station, TX, USA
M. Nounou, Chem. Eng. Dept., Texas A&M Univ. at Qatar, Doha, Qatar
Hazem N. Nounou, Electr. Eng. Dept., Texas A&M Univ. at Qatar, Doha, Qatar
This paper considers the problem of learning the structure of gene regulatory networks from gene expression time series data. A more realistic scenario when the state space model representing a gene network evolves nonlinearly is considered while a linear model is assumed for the microarray data. To capture the nonlinearity, a particle filter-based state estimation algorithm is considered instead of the contemporary linear approximation-based approaches. The parameters characterizing the regulatory relations among various genes are estimated online using a Kalman filter. Since a particular gene interacts with a few other genes only, the parameter vector is expected to be sparse. The state estimates delivered by the particle filter and the observed microarray data are then subjected to a LASSO-based least squares regression operation which yields a parsimonious and efficient description of the regulatory network by setting the irrelevant coefficients to zero. The performance of the aforementioned algorithm is compared with the extended Kalman filter (EKF) and Unscented Kalman Filter (UKF) employing the Mean Square Error (MSE) as the fidelity criterion in recovering the parameters of gene regulatory networks from synthetic data and real biological data. Extensive computer simulations illustrate that the proposed particle filter-based network inference algorithm outperforms EKF and UKF, and therefore, it can serve as a natural framework for modeling gene regulatory networks with nonlinear and sparse structure.

[1] H. Kitano, "Computational Systems Biology," Nature, vol. 420, pp. 206-210, Nov. 2002.
[2] X. Cai and X. Wang, "Stochastic Modeling and Simulation of Gene Networks," IEEE Signal Processing Magazine, vol. 24, no. 1, pp. 27-36, Jan. 2007.
[3] X. Zhou, X. Wang, and E.R. Dougherty, "Gene Clustering Based on Cluster-Wide Mutual Information," J. Computational Biology, vol. 11, no. 1, pp. 151-165, 2004.
[4] X. Zhou, X. Wang, M. Bittner, and E.R. Dougherty, "A Bayesian Connective-Based Approach to Constructing Probabilistic Gene Regulatory Networks," Bioinformatics, vol. 20, pp. 2918-2927, 2004.
[5] Y. Huang, I.M. Tienda-Luna, and Y. Wang, "Reverse Engineering Gene Regulatory Network," IEEE Signal Processing Magazine, vol. 26, no. 1, pp. 76-97, Jan. 2009.
[6] H. de Jong, "Modeling and Simulation of Genetic Regulatoy Systems: A Literature Review," J. Computational Biology, vol. 9, no. 1, pp. 67-103, 2002.
[7] T. Tian and K. Burrage, "Stochastic Neural Network Models for Gene Regulatory Networks," Proc. IEEE Congress Evolutionary Computation, pp. 162-169, 2003.
[8] N. Friedman, M. Linial, I. Nachman, and D. Pe'er, "Using Bayesian Networks to Analyze Expression Data," J. Computational Biology, vol. 7, pp. 601-620, 2000.
[9] K. Murphy and S. Mia, "Modeling Gene Expression Data Using Dynamic Bayesian Networks," technical report, Berkeley Univ., 1999.
[10] Y. Zhang et al., "Inferring Gene Regulatory Networks from Multiple Data Sources via a Dynamic Bayesian Network with Structural EM," Proc. Int'l Conf. Data Integration in the Life Sciences, pp. 204-214, 2007.
[11] M. Quach, N. Brunel, and F. d'Alche-Buc, "Estimating Parameters and Hidden Variables in Non-Linear State-Space Models Based on ODEs for Biological Networks Inference," Bioinformatics, vol. 23, no. 23, pp. 3209-3216, 2007.
[12] F. Wu, W. Zhang, and A.J. Kusalik, "Modeling Gene Expression from Microarray Expression Data with State-Space Equations," Proc. Pacific Symp. Biocomputing, pp. 581-592, 2004.
[13] N. Friedman, "Inferring Cellular Network Using Probabilistic Graphical Models," Science, vol. 33, pp. 799-805, 2004.
[14] X. Zhou, X. Wang, and E.R. Dougherty, "Construction of Genomic Networks Using Mutual-Information Clustering and Reversible-Jump Markov-Chain-Monte-Carlo Predictor Design," Signal Processing, vol. 83, pp. 261-274, 2002.
[15] H. Toh and K. Horimoto, "Inference of a Genetic Network by a Combined Approach of Cluster Analysis and Graphical Gaussian Modeling," Bioinformatics, vol. 18, pp. 287-297, 2002.
[16] T. Akutsu, S. Miyano, and S. Kuhara, "Identification of Genetic Networks from a Small Number of Gene Expression Patterns under the Boolean Network Model," Proc. Pacific Symp. Biocomputing, vol. 4, pp. 17-28, 1999.
[17] I. Schmulevich et al., "Probabilistic Boolean Networks: A Rule-Based Uncertainty Model for Gene Regulatory Networks," Bioinformatics vol. 18, pp. 261-274, 2002.
[18] H. Hache, H. Lehrach, and R. Herwig, "Reverse Engineering of Gene Regulatory Networks: A Comparative Study," EURASIP J. Bioinformatics and Systems Biology, vol. 2009, Article ID 617281, p. 12, 2009.
[19] B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications: Artech House. Artech House, 2004.
[20] P.M. Djuric, J.H. Kotecha, J. Zhang, Y. Huang, T. Ghirmai, M.F. Bugallo, and J. Miguez, "Particle Filtering," IEEE Signal Processing Magazine, vol. 20, no. 5, pp. 19-38, Sept. 2003.
[21] O. Cappe, S.J. Godsill, and E. Moulines, "An Overview of Existing Methods and Recent Advances in Sequential Monte Carlo," Proc. IEEE, vol. 95, no. 5, pp. 899-924, May 2007.
[22] L. Qian, H. Wang, and E.R. Dougherty, "Inference of Noisy Nonlinear Differential Equation Models for Gene Regulatory Networks Using Genetic Programming and Kalman Filtering," IEEE Trans. Signal Processing, vol. 56, no. 7, pp. 3327-3339, July 2008.
[23] Z. Wang, X. Liu, Y. Liu, J. Liang, and V. Vinciotti, "An Extended Kalman Filtering Approach to Modeling Nonlinear Dynamic Gene Regulatory Networks via Short Gene Expression Time Series," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 3, pp. 410-419, July-Sept. 2009.
[24] Z. Wang, H. Gao, J. Cao, and X. Liu, "On Delayed Genetic Regulatory Networks with Polytopic Uncertainties: Robust Stability Analysis," IEEE Trans. NanoBioscience, vol. 7, no. 2, pp. 44-55, June 2008.
[25] Z. Wang, F. Yang, D.W.C. Ho, S. Swift, A. Tucker, and X. Liu, "Stochastic Dynamic Modeling of Short Gene Expression Time Series Data," IEEE Trans. NanoBioscience, vol. 7, no. 1, pp. 44-55, Mar. 2008.
[26] W. Zhao, E. Serpedin, and E.R. Dougherty, "Inferring Connectivity of Genetic Regulatory Networks Using Information-Theoretic Criteria," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 3, pp. 410-419, Apr.-June 2008.
[27] W. Zhao, E. Serpedin, and E.R. Dougherty, "Inferring Gene Regulatory Networks from Time Series Data Using the Minimum Description Length Principle," Bioinformatics, vol. 22, pp. 2129-2135, 2006.
[28] J. Dougherty, I. Tabus, and J. Astola, "Inference of Gene Regulatory Networks Based on a Universal Minimum Description Length," EURASIP J. Bioinformatics and Systems Biology, vol. 2008, article 5, Jan. 2008.
[29] F. Markowetz and R. Spang, "Inferring Cellular Networks - A Review," BMC Bioinformatics, vol. 8, p. S5, Sept. 2007.
[30] T. Schlitt and A. Brazma, "Current Approaches to Gene Regulatory Network Modeling," BMC Bioinformatics, vol. 8, p. S9, Sept. 2007.
[31] X. Zhou, X. Wang, and E.R. Dougherty, "Genomic Networks: Statistical Inference from Microarray Data," Wiley Encyclopedia of Biomedical Engineering, John Wiley & Sons, Inc., 2006.
[32] R. Yamaguchi, R. Yoshida, S. Imoto, T. Higuche, and S. Miyano, "Finding Module-Based Gene Networks with State-Space Models," IEEE Signal Processing Magazine, vol. 24, no. 1, pp. 37-46, Jan. 2007.
[33] R. Tibshirani, "Regression Shrinkage and Selection via the LASSO," J. Royal Statistical Soc. B, vol. 58, no. 1, pp. 267-288, 1996.
[34] S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge Univ. Press, 2004.
[35] J.C. Costello et al., "Gene Networks in Droshophila Melanogaster: Integrating Experimental Data to Predict Gene Function," Genome Biology, vol. 10, no. 9, pp. R97.1-R97.29, 2009.
[36] www.droid.org, 2012.
[37] P. Li, C. Zhang, E.J. Perkins, P. Gong, and Y. Deng, "Comparison of Probabilistic Boolean Network and Dynamic Bayesian Network Approaches for Inferring Gene Regularoty Networks," BMC Bioinformatics, vol. 8, p. S13, Nov. 2007.
[38] M. Gustafsson, M. Hornquist, and A. Lombardi, "Constructing and Analyzing a Large-Scale Gene-to-Gene Regulatory Network - Lasso-Constrained Inference and Biological Validation," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 2, no. 3, pp. 254-261, July-Sept. 2005.

Index Terms:
time series,bioinformatics,cellular biophysics,genetics,Kalman filters,least squares approximations,sparse structure,gene regulatory network,nonlinear state space models,sparsity exploitation,gene expression time series data,particle filter-based state estimation algorithm,parameter vector,microarray data,LASSO-based least squares regression,extended Kalman filter,unscented Kalman filter,mean square error,fidelity criterion,particle filter-based network inference algorithm,Kalman filters,Mathematical model,Data models,Estimation,Approximation algorithms,Gene expression,Noise,LASSO.,Gene regulatory network,particle filter,Kalman filter,parameter estimation
Citation:
E. Serpedin, A. Noor, M. Nounou, Hazem N. Nounou, "Inferring Gene Regulatory Networks via Nonlinear State-Space Models and Exploiting Sparsity," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 4, pp. 1203-1211, July-Aug. 2012, doi:10.1109/TCBB.2012.32
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