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Genomic Signal Processing: From Matrix Algebra to Genetic Networks

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Microarray Data Analysis

Part of the book series: Methods in Molecular Biology™ ((MIMB,volume 377))

Abstract

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.

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Notes

  1. 1.

    *In this chapter, denotes a matrix, |v〉 denotes a column vector, and 〈u| denotes a row vector, such that, , and 〈u|v〉 all denote inner products and |v〉〈u| denotes an outer product.

References

  1. Fodor, S. P., Rava, R. P., Huang, X. C., Pease, A. C., Holmes, C. P., and Adams, C. L. (1993) Multiplexed biochemical assays with biological chips. Nature 364, 555–556.

    Article  PubMed  CAS  Google Scholar 

  2. Schena, M., Shalon, D., Davis, R. W., and Brown, P. O. (1995) Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science 270, 467–470.

    Article  PubMed  CAS  Google Scholar 

  3. Brown, P. O., and Botstein, D. (1999) Exploring the new world of the genome with DNA microarrays. Nat. Genet. 21, 31–37.

    Article  Google Scholar 

  4. Pollack, J. R., and Iyer, V. R. (2002) Characterizing the physical genome. Nat. Genet. 32, 515–521.

    Article  PubMed  CAS  Google Scholar 

  5. Sherlock, G., Hernandez-Boussard, T., Kasarskis, A., et al. (2001) The Stanford microarray database. Nucleic Acids Res. 29, 152–155.

    Article  PubMed  CAS  Google Scholar 

  6. Spellman, P. T., Sherlock, G., Zhang, M. Q., et al. (1998) Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol. Biol. Cell 9, 3273–3297.

    PubMed  CAS  Google Scholar 

  7. Whitfield, M. L., Sherlock, G., Saldanha, A., et al. (2002) Identification of genes periodically expressed in the human cell cycle and their expression in tumors. Mol. Biol. Cell 13, 1977–2000.

    Article  PubMed  CAS  Google Scholar 

  8. Simon, I., Barnett, J., Hannett, N., et al. (2001) Serial regulation of transcriptional regulators in the yeast cell cycle. Cell 106, 697–708.

    Article  PubMed  CAS  Google Scholar 

  9. Wyrick, J. J., Aparicio, J. G., Chen, T., et al. (2001) Genome-wide distribution of ORC and MCM proteins in S. cerevisiae: high-resolution mapping of replication origins. Science 294, 2301–2304.

    Article  Google Scholar 

  10. Newton, I. (1999) The Principia: Mathematical Principles of Natural Philosophy. (Cohen, I. B., and Whitman, A., trans.) University of California Press, Berkeley, CA.

    Google Scholar 

  11. Hubel, D. H., and Wiesel, T. N. (1968) Receptive fields and functional architecture of monkey striate cortex. J. Physiol. 195, 215–243.

    PubMed  CAS  Google Scholar 

  12. Barlow, H. B. (1972) Single units and sensation: a neuron doctrine for perceptual psychology? Perception 1, 371–394.

    Article  PubMed  CAS  Google Scholar 

  13. Olshausen, B. A., and Field, D. J. (1996) Emergence of simple-cell receptive field properties by learning a sparse code for natural images. Nature 381, 607–609.

    Article  PubMed  CAS  Google Scholar 

  14. Bell, A. J., and Sejnowski, T. J. (1997) The “independent components” of natural scenes are edge filters. Vision Res. 37, 3327–3338.

    Article  PubMed  CAS  Google Scholar 

  15. Golub, G. H., and Van Loan, C. F. (1996) Matrix Computation, 3rd ed., Johns Hopkins University, Press, Baltimore, MD.

    Google Scholar 

  16. Alter, O., Brown, P. O., and Botstein, D. (2000) Singular value decomposition for genome-wide expression data processing and modeling. Proc. Natl. Acad. Sci. USA 97, 10,101–10,106.

    Article  PubMed  CAS  Google Scholar 

  17. Alter, O., Brown, P. O., and Botstein, D. (2001) Processing and modeling genome-wide expression data using singular value decomposition. In: Microarrays: Optical Technologies and Informatics, vol. 4266 (Bittner, M. L., Chen, Y., Dorsel, A. N., and Dougherty, E. R., eds.), Int. Soc. Optical Eng., Bellingham, WA, pp. 171–186.

    Google Scholar 

  18. Nielsen, T. O., West, R. B., Linn, S. C., et al. (2002) Molecular characterisation of soft tissue tumours: a gene expression study. Lancet 359, 1301–1307.

    Article  PubMed  CAS  Google Scholar 

  19. Alter, O., Brown, P. O., and Botstein, D. (2003) Generalized singular value decomposition for comparative analysis of genome-scale expression data sets of two different organisms. Proc. Natl. Acad. Sci. USA 100, 3351–3356.

    Article  PubMed  CAS  Google Scholar 

  20. Alter, O., Golub, G. H., Brown, P. O., and Botstein, D. (2004) Novel genome-scale correlation between DNA replication and RNA transcription during the cell cycle in yeast is predicted by data-driven models. In: Proc. Miami Nat. Biotechnol. Winter Symp. on the Cell Cycle, Chromosomes and Cancer, vol. 15 (Deutscher, M. P., Black, S., Boehmer, P. E., et al., eds.), Univ. Miami Sch. Med., Miami, FL, http://www.med.miami.edu/mnbws/Alter-.pdf.

    Google Scholar 

  21. Alter, O. and Golub, G. H. (2004) Integrative analysis of genome-scale data by using pseudoinverse projection predicts novel correlation between DNA replication and RNA transcription. Proc. Natl. Acad. Sci. USA 101, 16,577–16,582.

    Article  PubMed  CAS  Google Scholar 

  22. Alter, O., and Golub, G. H. (2005) Reconstructing the pathways of a cellular system from genome-scale signals using matrix and tensor computations. Proc. Natl. Acad. Sci. USA 102, 17,559–17,564.

    Article  PubMed  CAS  Google Scholar 

  23. Alter, O., and Golub, G. H. (2006) Singular value decomposition of genome-scale mRNA lengths distribution reveals asymmetry in RNA gel electrophoresis band broadening. Proc. Natl. Acad. Sci. USA 103, 11,828–11,833.

    Article  PubMed  CAS  Google Scholar 

  24. Alter, O. (2006) Discovery of principles of nature from mathematical modeling of DNA microarray data. Proc. Natl. Acad. Sci. USA 103, 16,063–16,064.

    Article  PubMed  CAS  Google Scholar 

  25. Wigner, E. P. (1960) The unreasonable effectiveness of mathematics in the natural sciences. Commun. Pure Appl. Math. 13, 1–14.

    Article  Google Scholar 

  26. Hopfield, J. J. (1999) Odor space and olfactory processing: collective algorithms and neural implementation. Proc. Natl. Acad. Sci. USA 96, 12,506–12,511.

    Article  PubMed  CAS  Google Scholar 

  27. Sirovich, L., and Kirby, M. (1987) Low-dimensional procedure for the characterization of human faces. J. Opt. Soc. Am. A 4, 519–524.

    Article  PubMed  CAS  Google Scholar 

  28. Turk, M., and Pentland, A. (1991) Eigenfaces for recognition. J. Cogn. Neurosci. 3, 71–86.

    Article  Google Scholar 

  29. Landau, L. D., and Lifshitz, E. M. (1976) Mechanics, 3rd ed. (Sykes, J. B., and Bell, J. S., trans.), Butterworth-Heinemann, Oxford, UK.

    Google Scholar 

  30. Tavazoie, S., Hughes, J. D., Campbell, M. J., Cho, R. J., and Church, G. M. (1999) Systematic determination of genetic network architecture. Nat. Genet. 22, 281–285.

    Article  PubMed  CAS  Google Scholar 

  31. Roberts, C. J., Nelson, B., Marton, M. J., et al. (2000) Signaling and circuitry of multiple MAPK pathways revealed by a matrix of global gene expression profiles. Science 287, 873–880.

    Article  PubMed  CAS  Google Scholar 

  32. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J. D. (1994) Molecular Biology of the Cell, 3rd ed., Garland Pub., New York, NY.

    Google Scholar 

  33. Klevecz, R. R., Bolen, J., Forrest, G., and Murray, D. B. (2004) A genomewide oscillation in transcription gates DNA replication and cell cycle. Proc. Natl. Acad. Sci. USA 101, 1200–1205.

    Article  PubMed  CAS  Google Scholar 

  34. Li, C. M., and Klevecz, R. R. (2006) A rapid genome-scale response of the transcriptional oscillator to perturbation reveals a period-doubling path to phenotypic change. Proc. Natl. Acad. Sci. USA 103, 16,254–16,259.

    Article  PubMed  CAS  Google Scholar 

  35. Nicolis, G. and Prigogine, I. (1971) Fluctuations in nonequilibrium systems. Proc. Natl. Acad. Sci. USA 68, 2102–2107.

    Article  PubMed  CAS  Google Scholar 

  36. Rössler O. E. (1976) An equation for continuous chaos. Phys. Lett. A 35, 397–398.

    Article  Google Scholar 

  37. Roux, J.-C., Simoyi, R. H., and Swinney, H. L. (1983) Observation of a strange attractor. Physica D 8, 257–266.

    Article  Google Scholar 

  38. Stuart, J. M., Segal, E., Koller, D., and Kim, S. K. (2003) A gene-coexpression network for global discovery of conserved genetic modules. Science 302, 249–255.

    Article  PubMed  CAS  Google Scholar 

  39. Bergmann, S., Ihmels, J., and Barkai, N. (2004) Similarities and differences in genome-wide expression data of six organisms. PLoS Biol 2, E9.

    Article  PubMed  Google Scholar 

  40. Mushegian, A. R., and Koonin, E. V. (1996) A minimal gene set for cellular life derived by comparison of complete bacterial genomes. Proc. Natl. Acad. Sci. USA 93, 10,268–10,273.

    Article  PubMed  CAS  Google Scholar 

  41. Dwight, S. S., Harris, M. A., Dolinski, K., et al. (2002) Saccharomyces Genome Database (SGD) provides secondary gene annotation using the Gene Ontology (GO). Nucleic Acids Res. 30, 69–72.

    Article  PubMed  CAS  Google Scholar 

  42. Kurihara, L. J., Stewart, B. G., Gammie, A. E., and Rose, M. D. (1996) Kar4p, a karyogamy-specific component of the yeast pheromone response pathway. Mol. Cell. Biol. 16, 3990–4002.

    PubMed  CAS  Google Scholar 

  43. Ewing, B. and Green, P. (2000) Analysis of expressed sequence tags indicates 35,000 human genes. Nat. Genet. 25, 232–234.

    Article  PubMed  CAS  Google Scholar 

  44. Elowitz, M. B., and Leibler, S. (2000) A synthetic oscillatory network of transcriptional regulators. Nature 403, 335–338.

    Article  PubMed  CAS  Google Scholar 

  45. Fung, E., Wong, W. W., Suen, J. K., Butler, T., Lee, S. G., and Liao, J. C. (2005) A synthetic gene-metabolic oscillator. Nature 435, 118–122.

    Article  PubMed  CAS  Google Scholar 

  46. Bussemaker, H. J., Li, H., and Siggia, E. D. (2001) Regulatory element detection using correlation with expression. Nat. Genet. 27, 167–171.

    Article  PubMed  CAS  Google Scholar 

  47. Lu, P., Nakorchevskiy, A., and Marcotte, E. M. (2003) Expression deconvolution: a reinterpretation of DNA microarray data reveals dynamic changes in cell populations. Proc. Natl. Acad. Sci. USA 100, 10,370–10,375.

    Article  PubMed  CAS  Google Scholar 

  48. Chang, V. K., Fitch, M. J., Donate, J. J., hristensen, T. W., Merchant, A. M., and Tye, B. K. (2003) Mcm1 binds replication origins. J. Biol. Client. 278, 6093–6100.

    Article  CAS  Google Scholar 

  49. Donate, J. J., Chung, S. C., and Tye, B. K. (2006) Genome-wide hierarchy of replication origin usage in Saccharomyces cerevisiae. PloS Genet. 2, E9.

    Article  Google Scholar 

  50. Diffley, J. F. X., Cocker, J. H., Dowell, S. J., and Rowley, A. (1994) Two steps in the assembly of complexes at yeast replication origins in vivo. Cell 78, 303–316.

    Article  PubMed  CAS  Google Scholar 

  51. Kelly, T. J. and Brown, G. W. (2000) Regulation of chromosome replication. Annu. Rev. Biochem. 69, 829–880.

    Article  PubMed  CAS  Google Scholar 

  52. Micklem, G., Rowley, A., Harwood, J., Nasmyth, K., and Diffley, J. F. X. (1993) Yeast origin recognition complex is involved in DNA replication and transcriptional silencing. Nature 366, 87–89.

    Article  PubMed  CAS  Google Scholar 

  53. Fox, C. A. and Rine, J. (1996) Influences of the cell cycle on silencing. Curr. Opin. Cell Biol. 8, 354–357.

    Article  PubMed  CAS  Google Scholar 

  54. Ihmels, J., Levy, R., and Barkai, N. (2004) Principles of transcriptional control in the metabolic network of Saccharomyces cerevisiae. Nat. Biotechnol. 60, 86–92.

    Article  Google Scholar 

  55. Carlson, J. M. and Doyle, J. (1999) Highly optimized tolerance: a mechanism for power laws in designed systems. Phys. Rev. E 60, 1412–1427.

    Article  CAS  Google Scholar 

  56. Arkin, A. P. and Ross, J. (1994) Computational functions in biochemical reaction networks. Biophys. J. 67, 560–578.

    Article  PubMed  CAS  Google Scholar 

  57. Ptashne, M. (1992) Genetic Switch: Phage Lambda and Higher Organisms, 2nd ed., Blackwell Publishers, Oxford, UK.

    Google Scholar 

  58. McAdams, H. H. and Shapiro, L. (1995) Circuit simulation of genetic networks. Science 269, 650–656.

    Article  PubMed  CAS  Google Scholar 

  59. Schilling, C. H. and Palsson, B. O. (1998) The underlying pathway structure of biochemical reaction networks. Proc. Natl. Acad. Sci. USA 95, 4193–4198.

    Article  PubMed  CAS  Google Scholar 

  60. Yeung, M. K., Tegner, J., and Collins, J. J. (2002) Reverse engineering gene networks using singular value decomposition and robust regression. Proc. Natl. Acad. Sci. USA 99, 6163–6168.

    Article  PubMed  CAS  Google Scholar 

  61. Price, N. D., Reed, J. L., Papin, J. A., Famili, L, and Palsson, B. O. (2003) Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices. Biophys. J. 84, 794–804.

    Article  PubMed  CAS  Google Scholar 

  62. Vlad, M. O., Arkin, A. P., and Ross, J. (2004) Response experiments for nonlinear systems with application to reaction kinetics and genetics. Proc. Natl. Acad. Sci. USA 101, 7223–7228.

    Article  PubMed  CAS  Google Scholar 

  63. Doyle, J. and Stein, G. (1981) Multivariable feedback design: Concepts for a classical/modern synthesis. IEEE Trans. Automat. Contr. 26, 4–16.

    Article  Google Scholar 

  64. Broomhead, D. S. and King, G. P. (1986) Extracting qualitative dynamics from experimental-data. Physica D 20, 217–236.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biomedical Engineering, Institute for Cellular and Molecular Biology and Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX

    Orly Alter

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  1. Orly Alter
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Editors and Affiliations

  1. Department of Electrical and Computer Engineering, Queen’s University, Kingston, Ontario, Canada

    Michael J. Korenberg

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© 2007 Humana Press Inc., Totowa, NJ

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Alter, O. (2007). Genomic Signal Processing: From Matrix Algebra to Genetic Networks. In: Korenberg, M.J. (eds) Microarray Data Analysis. Methods in Molecular Biology™, vol 377. Humana Press. https://doi.org/10.1007/978-1-59745-390-5_2

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  • DOI: https://doi.org/10.1007/978-1-59745-390-5_2

  • Publisher Name: Humana Press

  • Print ISBN: 978-1-58829-540-8

  • Online ISBN: 978-1-59745-390-5

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