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Constructing and Analyzing a Large-Scale Gene-to-Gene Regulatory Network-Lasso-Constrained Inference and Biological Validation
July-September 2005 (vol. 2 no. 3)
pp. 254-261
We construct a gene-to-gene regulatory network from time-series data of expression levels for the whole genome of the yeast Saccharomyces cerevisae, in a case where the number of measurements is much smaller than the number of genes in the network. This network is analyzed with respect to present biological knowledge of all genes (according to the Gene Ontology database), and we find some of its large-scale properties to be in accordance with known facts about the organism. The linear modeling employed here has been explored several times, but due to lack of any validation beyond investigating individual genes, it has been seriously questioned with respect to its applicability to biological systems. Our results show the adequacy of the approach and make further investigations of the model meaningful.

[1] H.D. Jong, “Modeling and Simulation of Genetic Regulatory Systems: A Literature Review,” J. Computational Biology, vol. 9, no. 1, pp. 67-103, 2002.
[2] P. Brazhnik, A. de la Fuente, and P. Mendes, “Gene Networks: How to Put the Function in Genomics,” Trends in Biotechnology, vol. 20, pp. 467-472, 2002.
[3] P. D'haeseleer, X. Wen, S. Fuhrman, and R. Somogyi, “Linear Modeling of mRNA Expression Levels During CNS Development and Injury,” Proc. Pacific Symp. Biocomputing, R.B. Altman, A.K. Dunker, L. Hunter, T.E. Klein, and K. Lauderdaule, eds., vol. 4, pp. 41-52, 1999.
[4] M. Hörnquist, J. Hertz, and M. Wahde, “Effective Dimensionality for Principal Component Analysis of Rat CNS Expression Data,” BioSystems, vol. 71, pp. 311-317, 2003.
[5] E.P. van Someren, L.F.A. Wessels, and M.J.T. Reinders, “Linear Modeling of Genetic Networks from Experimental Data,” Proc. Eighth Int'l Conf. Intelligent Systems for Molecular Biology, pp. 355-366, 2000.
[6] N.S. Holter, A. Maritan, M. Cieplak, N.V. Fedoroff, and J.R. Banavar, “Dynamical Modeling of Gene Expression Data,” Proc. Nat'l Academy of the Sciences USA, vol. 98, pp. 1693-1698, 2001.
[7] M.K.S. Yeung, J. Tegnér, and J.J. Collins, “Reverse Engineering Gene Networks Using Singular Value Decomposition and Robust Regression,” Proc. Nat'l Academy of the USA, vol. 99, pp. 6163-6168, 2002.
[8] E.P. van Someren, L.F.A. Wessels, E. Backer, and M.J.T. Reinders, “Multi-Criterion Optimization for Genetic Network Modeling,” Signal Processing, vol. 83, pp. 763-775, 2003.
[9] T.G. Dewey and D.J. Galas, “Dynamic Models of Gene Expression and Classification,” Functional and Integrative Genomics, vol. 1, pp. 269-271, 2001.
[10] E. Segal, M. Shapira, A. Regev, D. Pe'er, D. Botstein, D. Koller, and N. Friedman, “Module Networks: Identifying Regulatory Modules and Their Condition-Specific Regulators from Gene Expression Data,” Nature Genetics, vol. 34, no. 2, pp. 166-176, 2003.
[11] R. Tibshirani, “Regression Shrinkage and Selection via the Lasso,” J. Royal Statistical Soc., Series B, vol. 58, no. 1, pp. 267-288, 1996.
[12] M. Ashburner, C.A. Ball, J.A. Blake, D. Botstein, H. Butler, J.M. Cherry, A.P. Davis, K. Dolinski, S.S. Dwight, J.T. Eppig, M.A. Harris, D.P. Hill, L. Issel-Tarver, A. Kasarskis, S. Lewis, J.C. Matese, J.E. Richardson, M. Ringwald, G.M. Rubin, and G. Sherlock, “Gene Ontology: Tool for the Unification of Biology,” Nature Genetics, vol. 25, pp. 25-29, 2000,
[13] P.T. Spellman, G. Sherlock, M.Q. Zhang, V.R. Iyer, K. Anders, M.B. Eisen, P.O. Brown, D. Botstein, and D. Futcher, “Comprehensive Identification of Cell Cycle-Regulated Genes of the Yeast Saccharomyces Cerevisiae by Microarray Hybridization,” Molecular Biology of the Cell, vol. 9, pp. 3273-3297, 1998.
[14] R.J. Cho, M.J. Campbell, E.A. Winzeler, L. Steinmetz, A. Conway, L. Wodicka, T.G. Wolfsberg, A.E. Gabrielian, D. Landsman, D.J. Lockhart, and R.W. Davis, “A Genome-Wide Transcriptional Analysis of the Mitotic Cell Cycle,” Molecular Cell, vol. 2, pp. 65-73, 1998.
[15] T. Ideker, V. Thorsson, J.A. Ranish, R. Christmas, J. Buhler, J.K. Eng, R. Bumgarner, D.R. Goodlett, R. Aebersold, and L. Hood, “Integrated Genomic and Proteomic Analyses of a Systematically Perturbed Metabolic Networks,” Science, vol. 292, pp. 929-934, 2001.
[16] O. Troyanskaya, M. Cantor, G. Sherlock, P. Brown, T. Hastie, R. Tibshirani, D. Botstein, and R.B. Altman, “Missing Value Estimation Methods for DNA Microarrays,” Bioinformatics, vol. 17, no. 6, pp. 520-525, 2001.
[17] C. deBoor, A Practical Guide to Splines. New-York: Springer, 1978.
[18] E.I. George, “The Variable Selection Problem,” J. Am. Statistical Assoc., vol. 95, no. 452, pp. 1304-1308, 2000.
[19] Å. Björck, Numerical Methods for Least Squares Problems. Philadelphia: SIAM, 1996.
[20] N.R. Draper and H. Smith, Applied Regression Analysis, third ed. New York: Wiley, 1998.
[21] M.R. Osborne, B. Presnell, and B.A. Turlach, “On the Lasso and Its Dual,” J. Computational and Graphical Statistics, vol. 9, no. 2, pp. 319-337, 2000.
[22] W.H. Press, S.A. Teukolsky, W.T. Vetteling, and B.P. Flannery, Numerical Recipes. Cambridge Univ. Press, 1996.
[23] M.R. Segal, “Regression Approaches for Microarray Data Analysis,” J. Computational Biology, vol. 10, no. 6, pp. 961-980, 2003, .
[24] R. Milo, S. Shen-Orr, S. Itzkovitz, N. Kashtan, D. Chklovskii, and U. Alon, “Network Motifs: Simple Building Blocks of Complex Networks,” Science, vol. 298, no. 5594, pp. 824-827, 2002, .
[25] Handbook of Graphs and Networks, From the Genome to the Internet, S. Bornholdt and H.G. Schuster, eds., Weinheim: Wiley, 2003.
[26] L. Li, D. Alderson, R. Tanaka, J.C. Doyle, and W. Willinger, “Towards a Theory of Scale-Free Graphs: Definition, Properties, and Implications (Extended Version),” Technical Report CIT-CDS-04-006, California Institute of Technology, Pasadena, 2005.
[27] K. Dolinski, R. Balakrishnan, K.R. Christie, M.C. Costanzo, S.S. Dwight, S.R. Engel, D.G. Fisk, J.E. Hirschman, E.L. Hong, L. Issel-Tarver, A. Sethuraman, C.L. Theesfeld, G. Binkley, C. Lane, M. Schroeder, S. Dong, S. Weng, R. Andrada, D. Botstein, and J.M. Cherry, “Saccharomyces Genome Database,” 106652703322756177 cgi/content/abstract/298/5594 824www.yeastgenome. org, Sept. 2003.
[28] D.E. Featherstone and K. Broadie, “Wrestling with Pleiotropy: Genomic and Topological Analysis of the Yeast Gene Expression Network,” BioEssays, vol. 24, pp. 267-274, 2002.
[29] K.A. Eriksen, M. Hörnquist, and K. Sneppen, “Visualization of Large-Scale Correlations in Gene Expressions,” Functional and Integative Genomics, vol. 4, pp. 241-245, 2004.
[30] L. Ljung, System Identification: Theory for the User, second ed. Englewood Cliffs, N.J.: Prentice-Hall, 1999.
[31] H.-C. Chen, H.-C. Lee, T.-Y. Lin, W.-H. Li, and B.-S. Chen, “Quantitative Characterization of the Transcriptional Regulatory Network in the Yeast Cell Cycle,” Bioinformatics, vol. 20, no. 12, pp. 1914-1927, 2004, .
[32] M. Zou and S.D. Conzen, “A New Dynamic Bayesian Network (DBN) Approach for Identifying Gene Regulatory Networks from Time Course Microarray Data,” Bioinformatics, vol. 21, no. 1, pp. 71-79, 2005, .
[33] D. Husmeier, “Sensitivity and Specificity of Inferring Genetic Regulatory Interactions from Microarray Experiments with Dynamic Bayesian Networks,” Bioinformatics, vol. 19, no. 17, pp. 2,271–2,282, 2003, .
[34] M.B. Eisen, P.T. Spellman, P.O. Brown, and D. Botstein, “Cluster Analysis and Display of Genome-Wide Expression Patterns,” Proc. Nat'l Academy of the Sciences USA, vol. 95, pp. 14,863-14,868, Dec. 1998.
[35] S. Datta and S. Datta, “Comparisons and Validation of Statistical Clustering Techniques for Microarray Gene Expression Data,” Bioinformatics, vol. 19, no. 4, pp. 459-466, 2003.

Index Terms:
Index Terms- Biology and genetics, time series analysis, network problems, gene network, network inference, Lasso, yeast, validation, outdegree.
Mika Gustafsson, Michael H?rnquist, Anna Lombardi, "Constructing and Analyzing a Large-Scale Gene-to-Gene Regulatory Network-Lasso-Constrained Inference and Biological Validation," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 2, no. 3, pp. 254-261, July-Sept. 2005, doi:10.1109/TCBB.2005.35
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