Abstract
Spurred by advances in cDNA microarray technology, gene expression data are increasingly becoming available. In time-ordered data, the expression levels are measured at several points in time following some experimental manipulation. A gene regulatory network can be inferred by fitting a linear system of differential equations to the gene expression data. As biologically the gene regulatory network is known to be sparse, we expect most coefficients in such a linear system of diffierential equations to be zero. In previously proposed methods to infer such a linear system, ad hoc assumptions were made to limit the number of nonzero coefficients in the system. Instead, we propose to infer the degree of sparseness of the gene regulatory network from the data, where we determine which coefficients are nonzero by using Akaike's Information Criterion.
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References
Spellman, P., Sherlock, G., Zhang, M., Iyer, V., Anders, K., Eisen, M., Brown, P., Botstein, D., Futcher, B.: Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell 9 (1998) 3273–3297.
DeRisi, J., Iyer, V., Brown, P.: Exploring the metabolic and genetic control of gene expression on a genomic scale. Science 278 (1997) 680–686.
Hihara, Y., Kamei, A., Kanehisa, M., Kaplan, A., Ikeuchi, M.: DNA microarray analysis of cyanobacterial gene expression during acclimation to high light. The Plant Cell 13 (2001) 793–806.
De Hoon, M., Imoto, S., Miyano, S.: Statistical analysis of a small set of timeordered gene expression data using linear splines. Bioinformatics, in press.
Eisen, M., Spellman, P., Brown, P., Botstein, D.: Cluster analysis and display of genome-wide expression patterns. Proc. Natl. Acad. Sci.USA 95 (1998) 14863–14868.
Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Kitareewan, S., Dmitrovsky, E., Lander, E., Golub, T.: Interpreting patterns of gene expression with self-organizing maps: Methods and application to hematopoietic differentiation. Proc. Natl. Acad. Sci. USA 96 (1999) 2907–2912.
Liang, S., Fuhrman, S., Somogyi, R.: REVEAL, a general reverse engineering algorithm for inference of genetic network architectures. Proc. Pac. Symp. on Biocomputing 3 (1998) 18–29.
Akutsu, T., Miyano, S., Kuhara, S.: Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics 16 (2000) 727–734.
Friedman, N., Linial, M., Nachman, I., Pe'er, D.: Using Bayesian networks to analyze expression data. J. Comp. Biol. 7 (2000) 601–620.
Imoto, S., Goto, T., Miyano, S.: Estimation of genetic networks and functional structures between genes by using Bayesian networks and nonparametric regression. Proc. Pac. Symp. on Biocomputing 7 (2002) 175–186.
Imoto, S., Sunyong, K., Goto, T., Aburatani, S., Tashiro, K., Kuhara, S., Miyano, S.: Bayesian network and nonparametric heteroscedastic regression for nonlinear modeling of genetic network. Proceedings of the IEEE Computer Society Bioinformatics Conference, Stanford, California (2002) 219–227.
Sakamoto, E., Iba, H.: Evolutionary inference of a biological network as differential equations by genetic programming. Genome Informatics 12 (2001) 276–277.
Chen, T., He, H., Church, G.: Modeling gene expression with differential equations. Proc. Pac. Symp. on Biocomputing 4 (1999) 29–40.
Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press, Cambridge, UK (1999).
Akaike, H.: Information theory and an extension of the maximum likelihood principle. Research Memorandum No. 46, Institute of Statistical Mathematics, Tokyo (1971). In Petrov, B. and Csaki, F. (editors): 2nd Int. Symp. on Inf. Theory. Akadémiai Kiadó, Budapest (1973) 267–281.
Akaike, H.: A new look at the statistical model identification. IEEE Trans. Automat. Contr. AC-19 (1974) 716–723.
Priestley, M.: Spectral Analysis and Time Series. Academic Press, London (1994).
Matsuno, H., Doi, A., Hirata, Y., Miyano, S.: XML documentation of biopathways and their simulation in Genomic Object Net. Genome Informatics 12 (2001) 54–62.
Smith, V., Jarvis, E., Hartemink, A.: Evaluating functional network inference using simulations of complex biological systems. Bioinformatics 18 (2002) S216–S224.
Ong, I., Glasner, J., Page, D.: Modelling regulatory pathways in E. coli from time series expression profiles. Bioinformatics 18 (2002) S241–S248.
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de Hoon, M., Imoto, S., Miyano, S. (2002). Inferring Gene Regulatory Networks from Time-Ordered Gene Expression Data Using Differential Equations. In: Lange, S., Satoh, K., Smith, C.H. (eds) Discovery Science. DS 2002. Lecture Notes in Computer Science, vol 2534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36182-0_24
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DOI: https://doi.org/10.1007/3-540-36182-0_24
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