Conclusions
The ability to efficiently infer the structure of Boolean networks has immense potential for understanding the regulatory interactions in real genetic networks. We have considered a learning strategy that is well suited for situations in which inconsistencies in observations are likely to occur. This strategy produces a Boolean network that makes as few misclassifications as possible and is a generalization of the well-known Consistency Problem. We have focused on the computational complexity of this problem. It turns out that for many function classes, the Best-Fit Extension Problem for Boolean networks is polynomial-time solvable, including those networks having bounded indegree and those in which no assumptions whatsoever about the functions are made. This promising result provides motivation for developing efficient algorithms for inferring network structures from gene expression data.
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References
Akutsu, T., Kuhara, S., Maruyama, O. and Miyano, S. (1998) Identification of gene regulatory networks by strategic gene disruptions and gene overexpressions. Proc. the 9th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA’ 98), 695–702.
Akutsu, T., Miyano, S. and Kuhara, S. (1999) Identification of Genetic Networks from a Small Number of Gene Expression Patterns Under the Boolean Network Model. Pacific Symposium on Biocomputing 4, 17–28.
Akutsu, T., Miyano, S., and Kuhara, S. (2000) Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics 16, 727–734.
Alter, O., Brown, P. O. and Botstein, (2000) D. Singularvalue decomposition for genome-wide expression data processing and modeling. Proc. Natl. Acad. Sci. USA 97:18, 10101–10106.
Angluin, D. (1987) Learning regular sets from queries and counterexamples. Information and Computation, 75:2, 87–106.
Ben-Dor, A. and Yakhini, Z. (1999) Clustering Gene Expression Patterns Proc. of the 3rd International Conference on Computational Molecular Biology, 3342. Lyon, France: ACM Press.
Boros, E., Ibaraki, T., and Makino, K. (1998) Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions. Information and Computation, 140, 254–283.
Brazma, A. and Vilo, J. (2000) Gene expression data analysis. FEBS Letters 480, 17–24.
Celis, J. E., Kruhøffer, M., Gromova, I., Frederiksen, C., Østergaard, M., Thykjaer, T., Gromov, P., Yu, J., Pálsdóttir, H., Magnusson, N., & Ørntoft, T. F. (2000) Gene expression profiling: monitoring transcription and translation products using DNA microarrays and proteomics. FEBS Letteers 480, 2–16.
D’Haeseleer, P., Wen, X., Fuhrman, S. and Somogyi, R. (1999) Linear modeling of mRNA expression levels during CNS development and injury Pacific Symposium on Biocomputing, 4, 41–52.
DeRisi, J.L., Iyer, V.R., and Brown, P.O. (1997) Exploring the metabolic and genetic contol of gene expression on a genomic scale. Science, 278, 680–686.
Eisen, M. B., Spellman, P. T., Brown, P. O., & Botstein, D. (1998) Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci. USA, 95, 14863–14868.
Friedman, N., Linial, M., Nachman, I. and Pe’er, D. (2000) Using Bayesian Network to Analyze Expression Data. Journal of Computational Biology, 7, 601–620.
Gabbouj, M., Yu, P-T., and Coyle, E. J. (1992) Convergence behavior and root signal sets of stack filters. Circuits Systems & Signal Processing, 11:1, 171–193.
Holter, N. S., Mitra, M., Maritan, A., Cieplak, M., Banavar, J. R., & Fedoroff, N. V. (2000) Fundamental patterns underlying gene expression profiles: Simplicity from complexity. Proc. Natl. Acad. Sci. USA, 97, 8409–8414.
Huang, S. (1999) Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. Journal of Molecular Medicine 77, 469–480.
Iyer, V. R., Eisen, M. B., Ross, D. T., Schuler, G., Moore, T., Lee, J. C. F., Trent, J. M., Staudt, L. M., Hudson Jr., J., Boguski, M. S., Lashkari, D., Shalon, D., Botstein, D., and Brown, P. O. (1999) The transcriptional program in the response of human fibroblasts to serum. Science, 283, 83–87.
Kaski, S., Nikkilä, J., Törrönen, P., Castrén, E., and Wong, G. (2001) Analysis and visualization of gene expression data using self-organizing maps. IEEE — EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP-01), Baltimore, Maryland, June 3–6.
Kauffman, S. A. (1993) The origins of order: Self-organization and selection in evolution, Oxford University Press, New York.
Kearns, M. J. and Vazirani, U. V. (1994) An Introduction to Computational Learning Theory, MIT Press.
Liang, S., Fuhrman, S. and Somogyi, R. (1998) REVEAL, A General Reverse Engineering Algorithm for Inference of Genetic Network Architectures. Pacific Symposium on Biocomputing 3, 18–29.
Moran, G. (1995) On the period-two-property of the majority operator in infinite graphs. Trans. Amer. Math. Soc. 347, No. 5, 1649–1667.
Murphy, K. and Mian, S. (1999) Modelling Gene Expression Data using Dynamic Bayesian Networks. Technical Report, University of California, Berkeley.
Schena, M., Shalon, D., Davis, R. W., and Brown, P.O. (1995) Quantitative monitoring of gene expression pattern with a complementing DNA microarray. Science, 270, 467–470.
Shmulevich, I. and Zhang, W. (in press) Binary Analysis and Optimization-Based Normalization of Gene Expression Data, Bioinformatics.
Shmulevich, I., Dougherty, E. R., Kim, S., and Zhang, W. (in press) Probabilistic Boolean Networks: A Rule-based Uncertainty Model for Gene Regulatory Networks. Bioinformatics.
Szallasi, Z. and Liang, S. (1998) Modeling the Normal and Neoplastic Cell Cycle With Realistic Boolean Genetic Networks: Their Application for Understanding Carcinogenesis and Assessing Therapeutic Strategies. Pacific Symposium on Biocomputing 3, 66–76.
Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, S., Dmitrovsky, E., Lander, E. S., & Golub, T. R. (1999) Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. USA 96, 2907–2912.
Thieffry, D., Huerta, A. M., Pérez-Rueda, E., and Collado-Vides, J. (1998) From specific gene regulation to genomic networks: a global analysis of transcriptional regulation in Escherichia coli. BioEssays, 20:5, 433–440.
van Someren, E. P., Wessels, L.F.A., and Reinders, M.J.T. (2000) Linear modeling of genetic networks from experimental data. Intelligent Systems for Molecular Biology (ISMB 2000), San Diego, August 19–23.
Valiant, L. G. (1984) A theory of the learnable. Comm. Assoc. Comput. Mach, 27, 1134–1142.
Weaver, D.C., Workman, C.T. and Stormo, G.D. (1999) Modeling Regulatory Networks with Weight Matrices. Pacific Symposium on Biocomputing, 4, 112–123.
Wen, X., Fuhrman, S., Michaels, G. S., Carr, D. B., Smith, S., Barker, J. L., and Somogyi, R. (1998) Large-Scale Temporal Gene Expression Mapping of Central Nervous System Development. Proc Natl Acad Sci USA, 95, 334–339.
Wuensche, A. (1998) Genomic Regulation Modeled as a Network with Basins of Attraction. Pacific Symp. on Biocomp. 3, 89–102.
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Shmulevich, I., Saarinen, A., Yli-Harja, O., Astola, J. (2003). Inference of Genetic Regulatory Networks Via Best-Fit Extensions. In: Zhang, W., Shmulevich, I. (eds) Computational and Statistical Approaches to Genomics. Springer, Boston, MA. https://doi.org/10.1007/0-306-47825-0_11
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DOI: https://doi.org/10.1007/0-306-47825-0_11
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