Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
Recently, data on multiple gene expression at sequential time points were analyzed, using Singular Value Decomposition (SVD) as a means to capture dominant trends, called characteristic modes, followed by fitting of a linear discrete-time dynamical model in which the expression values at a given time point are linear combinations of the values at a previous time point. We attempt to address several aspects of the method. To obtain the model we formulate a nonlinear optimization problem and present how to solve it numerically using standard MATLAB procedures. We use publicly available data to test the approach. Then, we investigate the sensitivity of the method to missing measurements and its possibilities to reconstruct missing data. Summarizing we point out that approximation of multiple gene expression data preceded by SVD provides some insight into the dynamics but may also lead to unexpected difficulties.
Rocznik
Tom
Strony
MI31--40
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
- Department of Automatic Control, Silesian University of Technology, Gliwice, Poland
autor
- Department of Statistics, Rice University, Houston TX, USA
Bibliografia
- [1] Alter O., P.O. Brown, D. Botstein, Processing and modeling genome-wide expression data using singular value decomposition, Proc. of SPIE 4266 (2001) 171-186.
- [2] Alter O., P.O. Brown, D. Botstein, Singular value decomposition for genome-wide expression data processing and modeling, Proc. Natl. Acad. Sci. USA 97 (2000) 10101-10106.
- [3] Bellman R., Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
- [4] Branch M.A., A.Grace, Matlab Optimization Toolbox. User's Guide, MathWorks, 1996.
- [5] Everitt B.S., G. Dunn, Applied Multivariate Data Analysis, Oxford University Press, New York, 2001.
- [6] Golub G.H.,C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1996.
- [7] Holter N.S., M. Mitra, A. Maritan, M. Cieplak, J.R. Banavar, N.V. Fedoroff, Fundamental patterns underlying gene expression profiles: Simplicity from complexity, Proc. Natl. Acad. Sci. USA 97 (2000) 8409-8414.
- [8] Holter N.S., M. Mitra, A. Maritan, M. Cieplak, N.V. Fedoroff, J.R. Banavar, Dynamic modeling of gene expression data, Proc. Natl. Acad. Sci. USA 98 (2001) 1693-1698.
- [9] Jackson J.E., A User's guide to principal components, Wiley, New York, 1991.
- [10] Radmacher M. D., R. Simon, R.Desper, R. Taetle, A. A. Schaffer, M. A. Nelson, Graph models of oncogenesis with an application to melanoma , J. Theor. Biol. 212 (2001) 535-548.
- [11] Raychaudhuri S., J.M. Stuart, R. Altman, Principal components analysis to summarize microarray experiments:application to sporulation time series, in: R.B.Altman, K.Lauderdale, Dunker A.K., L.Hunter, T.E.Klein, (Eds.), Proc.Pac.Symp.Biocomput.2000, World Scientific, Singapore, 2000, 455-466.
- [12] Simek K., M. Kimmel, A note on estimation of dynamic of multiple gene expression based on singular value decomposition, Mathematical Biosciences [in press].
- [13] Spellman P.T., G. Sherlock, M.Q. Zhang,V.R. Iyer, K.Anders, M.B.Eisen, P.O.Brown, D.Botstein, B.Futcher, Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization, Mol.Biol.Cell 9 (1998) 3273-3297.
- [14] Vogelstein B., E. R. Fearon, S. R. Hamilton, S. E. Kern, A. C. Preisinger, M. Leppert, Y. Nakamura, R. White, A. M. Smits, J. L. Bos, Genetic alterations during colorectal-tumor development, N. Engl. J. Med. 319 (1988) 525-532.
- [15] Wall M.E., P.A. Dyck, T.S. Brettin, Svdman-singular value decomposition analysis of microarray data, Bioinformatics 17 (2001) 566-568.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0023-0009