The Community for Technology Leaders
RSS Icon
Issue No.05 - Sept.-Oct. (2012 vol.9)
pp: 1459-1471
Francesco Sambo , Dept. of Inf. Eng., Univ. of Padova, Padova, Italy
Marco A. Montes de Oca , Dept. of Math. Sci., Univ. of Delaware, Newark, DE, USA
Barbara Di Camillo , Dept. of Inf. Eng., Univ. of Padova, Padova, Italy
Gianna Toffolo , Dept. of Inf. Eng., Univ. of Padova, Padova, Italy
Thomas Stutzle , IRIDIA-CoDE, Univ. Libre de Bruxelles, Brussels, Belgium
Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.
time series, bioinformatics, nonlinear differential equations, optimisation, reverse engineering, bioinformatics, MORE, reverse engineering mixed optimization algorithm, biological network modeling, sparse systems, nonlinear differential equations, time series data, biological network topology, enforce system sparsity, real-world networks, mixed discrete-continuous optimization approach, Optimization, Algorithm design and analysis, Proteins, Mathematical model, Reverse engineering, Biological information theory, sparse systems of differential equations., Reverse engineering, mixed optimization, biological networks
Francesco Sambo, Marco A. Montes de Oca, Barbara Di Camillo, Gianna Toffolo, Thomas Stutzle, "MORE: Mixed Optimization for Reverse Engineering—An Application to Modeling Biological Networks Response via Sparse Systems of Nonlinear Differential Equations", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.9, no. 5, pp. 1459-1471, Sept.-Oct. 2012, doi:10.1109/TCBB.2012.56
[1] L. Hunter, "Life and Its Molecules: A Brief Introduction," AI Magazine, special issue on AI and bioinformatics, vol. 25, no. 1, pp. 9-22, 2004.
[2] N. Soranzo, G. Bianconi, and C. Altafini, "Comparing Association Network Algorithms for Reverse Engineering of Large-Scale Gene Regulatory Networks: Synthetic versus Real Data," Bioinformatics, vol. 23, no. 13, pp. 1640-1647, July 2007.
[3] L.G. Alexopoulos, J.Saez Rodriguez, B.D. Cosgrove, D.A. Lauffenburger, and P.K. Sorger, "Networks Inferred from Biochemical Data Reveal Profound Differences in TLR and Inflammatory Signaling between Normal and Transformed Hepatocytes," Molecular and Cellular Proteomics, vol. 9, no. 9, pp. 1849-65, 2010.
[4] J. Saez-Rodriguez, L.G. Alexopoulos, J. Epperlein, R. Samaga, D.A. Lauffenburger, S. Klamt, and P.K. Sorger, "Discrete Logic Modelling as a Means to Link Protein Signalling Networks with Functional Analysis of Mammalian Signal Transduction," Molecular Systems Biology, vol. 5, article 331, Dec. 2009.
[5] R.J. Prill, D. Marbach, J. Saez-Rodriguez, P.K. Sorger, L.G. Alexopoulos, X. Xue, N.D. Clarke, G. Altan-Bonnet, and G. Stolovitzky, "Towards a Rigorous Assessment of Systems Biology Models: The DREAM3 Challenges," PLoS ONE, vol. 5, no. 2,e9202 (epub), 2010.
[6] I.-C. Chou and E.O. Voit, "Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems," Math. Biosciences, vol. 219, no. 2, pp. 57-83, 2009.
[7] H.V. Westerhoff, A. Kolodkin, R. Conradie, S.J. Wilkinson, F.J. Bruggeman, K. Krab, J.H. van Schuppen, H. Hardin, B.M. Bakker, M.J. Moné, K.N. Rybakova, M. Eijken, H.J. van Leeuwen, and J.L. Snoep, "Systems Biology toward Life in Silico: Mathematics of the Control of Living Cells," J. Math. Biology, vol. 58, nos. 1/2, pp. 7-34, Jan. 2009.
[8] S. Kimura, S. Nakayama, and M. Hatakeyama, "Genetic Network Inference as a Series of Discrimination Tasks," Bioinformatics, vol. 25, no. 7, pp. 918-925, 2009.
[9] R. Xu, D. WunschII, and R. Frank, "Inference of Genetic Regulatory Networks with Recurrent Neural Network Models Using Particle Swarm Optimization," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 4, no. 4, pp. 681-692, Oct.-Dec. 2007.
[10] M. Arnone and E. Davidson, "The Hardwiring of Development: Organization and Function of Genomic Regulatory Systems," Development, vol. 124, pp. 1851-1864, 1997.
[11] A.-L. Barabasi and R. Albert, "Emergence of Scaling in Random Networks," Science, vol. 286, no. 5439, pp. 509-512, Oct. 1999.
[12] E. Ravasz, A.L. Somera, D.A. Mongru, Z.N. Oltvai, and A.L. Barabasi, "Hierarchical Organization of Modularity in Metabolic Networks," Science, vol. 297, no. 5586, pp. 1551-1555, Aug. 2002.
[13] P. Le Phillip, A. Bahl, and L.H. Ungar, "Using Prior Knowledge to Improve Genetic Network Reconstruction from Microarray Data," Silico Biology, vol. 4, no. 3, pp. 335-353, 2004.
[14] 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, pp. 41-52, 1999.
[15] T.S. Gardner, D.di Bernardo, D. Lorenz, and J.J. Collins, "Inferring Genetic Networks and Identifying Compound Mode of Action via Expression Profiling," Science, vol. 301, no. 5629, pp. 102-105, July 2003.
[16] M. Bansal, G.D. Gatta, and D. di Bernardo, "Inference of Gene Regulatory Networks and Compound Mode of Action from Time Course Gene Expression Profiles," Bioinformatics, vol. 22, no. 7, pp. 815-822, 2006.
[17] D. Nam, S.H. Yoon, and J.F. Kim, "Ensemble Learning of Genetic Networks from Time-Series Expression Data," Bioinformatics, vol. 23, no. 23, pp. 3225-3231, 2007.
[18] S. Kimura, K. Ide, A. Kashihara, M. Kano, M. Hatakeyama, R. Masui, N. Nakagawa, S. Yokoyama, S. Kuramitsu, and A. Konagaya, "Inference of S-System Models of Genetic Networks Using a Cooperative Coevolutionary Algorithm," Bioinformatics, vol. 21, no. 7, pp. 1154-1163, 2005.
[19] R. Xu, G.K. Venayagamoorthy, and D.C. WunschII, "Modeling of Gene Regulatory Networks with Hybrid Differential Evolution and Particle Swarm Optimization," Neural Networks, vol. 20, no. 8, pp. 917-927, 2007.
[20] P.-K. Liu and F.-S. Wang, "Inference of Biochemical Network Models in S-System Using Multiobjective Optimization Approach," Bioinformatics, vol. 24, no. 8, pp. 1085-1092, 2008.
[21] C.M. Chen, C. Lee, C.L. Chuang, C.C. Wang, and G. Shieh, "Inferring Genetic Interactions via a Nonlinear Model and an Optimization Algorithm," BMC Systems Biology, vol. 4, no. 1,article no. 16, 2010.
[22] R. Tibshirani, "Regression Shrinkage and Selection via the Lasso," J. Royal Statistical Soc. (Series B), vol. 58, pp. 267-288, 1996.
[23] H. Zou and T. Hastie, "Regularization and Variable Selection via the Elastic Net," J. Royal Statistical Soc. Series B, vol. 67, no. 2, pp. 301-320, 2005.
[24] F. Ferrazzi, P. Sebastiani, M.F. Ramoni, and R. Bellazzi, "Bayesian Approaches to Reverse Engineer Cellular Systems: A Simulation Study on Nonlinear Gaussian Networks," BMC Bioinformatics, vol. 8, Suppl. 5, S2 (epub) 2007.
[25] G.-W. Weber, O. Defterli, S.Z. Alparslan Gök, and E. Kropat, "Modeling, Inference and Optimization of Regulatory Networks Based on Time Series Data," European J. Operational Research, vol. 211, pp. 1-14, 2011.
[26] R. Albert, "Scale-Free Networks in Cell Biology," J. Cell Science, vol. 118, pp. 4947-4957, 2005.
[27] D. Marbach, C. Mattiussi, and D. Floreano, "Replaying the Evolutionary Tape: Biomimetic Reverse Engineering of Gene Networks," Annals of the New York Academy of Sciences, vol. 1158, pp. 234-245, 2009.
[28] D. Marbach, C. Mattiussi, and D. Floreano, "Combining Multiple Results of a Reverse Engineering Algorithm: Application to the DREAM Five Gene Network Challenge," Ann. New York Academy of Sciences, vol. 1158, pp. 102-113, 2009.
[29] T. Jones and S. Forrest, "Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms," Proc. Sixth Int'l Conf. Genetic Algorithms, pp. 184-192, 1995.
[30] T. Jones, "Evolutionary Algorithms, Fitness Landscapes and Search," Working Papers 95-05-048, Santa Fe Inst., May 1995.
[31] F. Sambo, M. Montes de Oca, B. Di Camillo, and T. Stützle, "On the Difficulty of Inferring Gene Regulatory Networks: A Study of the Fitness Landscape Generated by Relative Squared Error," Proc. Ninth Int'l Conf. Artificial Evolution, P. Collet, N. Monmarché, P. Legrand, M. Schoenauer, and E. Lutton, eds., pp. 74-85, 2010.
[32] M.J.D. Powell, "The NEWUOA Software for Unconstrained Optimization," Large-Scale Nonlinear Optimization, ser. Nonconvex Optimization and Its Applications, vol. 83, pp. 255-297, Springer-Verlag, 2006.
[33] N. Hansen, "The CMA Evolution Strategy: A Comparing Review," Towards a New Evolutionary Computation, Advances on Estimation of Distribution Algorithms, pp. 75-102, Springer, 2006.
[34] B. Di Camillo, G. Toffolo, and C. Cobelli, "A Gene Network Simulator to Assess Reverse Engineering Algorithms," Ann. New York Academy of Sciences, vol. 1158, no. 1, pp. 125-142, 2009.
[35] B. Di Camillo, M. Falda, G. Toffolo, and C. Cobelli, "SimBioNeT: A Simulator of Biological Network Topology," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 9, no. 2, pp. 592-600, Mar./Apr. 2012.
[36] J.F. Kolen and S.C. Kremer, A Field Guide to Dynamical Recurrent Networks. IEEE Press, 2001.
[37] B.A. Pearlmutter, "Dynamic Recurrent Neural Networks," Technical Report CMU-CS-90-196, Carnegie Mellon Univ., Pittsburgh, PA, 1990.
[38] T.T. Vu and J. Vohradsky, "Nonlinear Differential Equation Model for Quantification of Transcriptional Regulation Applied to Microarray Data of Saccharomyces Cerevisiae," Nucleic Acids Research, vol. 35, no. 1, pp. 279-287, Jan. 2007.
[39] J. Kennedy, R. Eberhart, and Y. Shi, Swarm Intelligence. Morgan Kaufmann, 2001.
[40] E. Fehlberg, "Low-Order Classical Runge-Kutta Formulas with Step Size Control and Their Application to Some Heat Transfer Problems," Technical Report 315, NASA, 1969.
[41] F. He, R. Balling, and A.-P. Zeng, "Reverse Engineering and Verification of Gene Networks: Principles, Assumptions, and Limitations of Present Methods and Future Perspectives," J. Biotechnology, vol. 144, no. 3, pp. 190-203, 2009.
[42] Y. Wang, Y. Ma, and R.J. Carroll, "Variance Estimation in the Analysis of Microarray Data," J. Royal Statistical Soc.: Series B (Statistical Methodology), vol. 71, no. 2, pp. 425-445, 2009.
[43] M. Anderle, S. Roy, H. Lin, C. Becker, and K. Joho, "Quantifying Reproducibility for Differential Proteomics: Noise Analysis for Protein Liquid Chromatography-Mass Spectrometry of Human Serum," Bioinformatics, vol. 20, no. 18, pp. 3575-3582, 2004.
[44] N. Noman and I. Iba, "Reverse Engineering Genetic Networks Using Evolutionary Computation," Genome Informatics, vol. 16, no. 2, pp. 205-214, 2005.
[45] C. Spieth, R. Worzischek, F. Streichert, J. Supper, N. Speer, and A. Zell, "Comparing Evolutionary Algorithms on the Problem of Network Inference," Proc. Genetic and Evolutionary Computation Conf. (GECCO '06), M. Cattolico, ed., pp. 305-306, 2006.
[46] A. Auger, N. Hansen, J.M. Perez Zerpa, R. Ros, and M. Schoenauer, "Empirical Comparisons of Several Derivative Free Optimization Algorithms," Acte du 9ime colloque nat'l en calcul des structures, May 2009.
[47] A.R. Conn, N.I.M. Gould, and P.L. Toint, Trust-Region Methods. ser. MPS-SIAM Series in Optimization. SIAM, 2000.
[48] H.H. Hoos and T. Stützle, Stochastic Local Search : Foundations & Applications, The Morgan Kaufmann Series in Artificial Intelligence. Morgan Kaufmann, Sept. 2004.
258 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool