Skip to main content

Application of Random Matrix Theory to Analyze Biological Data

  • Chapter
  • First Online:
Handbook of Data Intensive Computing

Abstract

The development of high-throughput biological techniques, such as, gene expression microarray [1, 2], mass spectrometry [3], single-nucleotide polymorphism (SNP) arrays [4], next generation sequencing [5], yeast two hybrid screening [6], and synthetic genetic arrays [7] makes it possible to generate genotypic, transcriptional, proteomic, and other measurements about cellular systems on a massive scale. The application of these high-throughput techniques may revolutionize all aspects of biological research.

The research of Luo and Srimani was partially supported by NSF Grant DBI-0960586.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 119.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Lockhart, D.J., et al., Expression monitoring by hybridization to high-density oligonucleotide arrays. Nat Biotechnol, 1996. 14(13): p. 1675–80.

    Article  Google Scholar 

  2. Schena, M., et al., Quantitative monitoring of gene expression patterns with a complementary DNA microarray. Science, 1995. 270(5235): p. 467–70.

    Article  Google Scholar 

  3. Flory, M.R., et al., Advances in quantitative proteomics using stable isotope tags. Trends Biotechnol, 2002. 20(12 Suppl): p. S23–9.

    Article  Google Scholar 

  4. Zhou, X. and D.T.W. Wong, Single Nucleotide Polymorphism Mapping Array Assay. 2007. p. 295–314.

    Google Scholar 

  5. Shendure, J. and H. Ji, Next-generation DNA sequencing. Nat Biotech, 2008. 26(10): p. 1135–1145.

    Article  Google Scholar 

  6. Joung, J.K., E.I. Ramm, and C.O. Pabo, A bacterial two-hybrid selection system for studying protein–DNA and protein–protein interactions. Proc Natl Acad Sci U S A, 2000. 97(13): p. 7382.

    Article  Google Scholar 

  7. Tong, A.H.Y. and C. Boone, Synthetic genetic array analysis in Saccharomyces cerevisiae. METHODS IN MOLECULAR BIOLOGY-CLIFTON THEN TOTOWA-, 2005. 313: p. 171.

    Google Scholar 

  8. Hilario, M. and A. Kalousis, Approaches to dimensionality reduction in proteomic biomarker studies. Brief Bioinform, 2008. 9(2): p. 102–118.

    Article  Google Scholar 

  9. Mehta, M., Random Matrices, 3nd edition. Academic Press, 2004.

    Google Scholar 

  10. Guhr, T., A. Muller-Groeling, and H.A. Weidenmuller, Random-matrix theories in quantum physics: common concepts. Physics Reports, 1998. 299(4–6): p. 189–425.

    Article  MathSciNet  Google Scholar 

  11. Wigner, E., Random Matrices in Physics. SIAM Review, 1967. 9: p. 1–23.

    Article  MATH  Google Scholar 

  12. Hofstetter, E. and M. Schreiber, Statistical properties of the eigenvalue spectrum of the three-dimensional Anderson Hamiltonian. Physical Review B, 1993. 48(23): p. 16979.

    Article  Google Scholar 

  13. Zhong, J.X. and T. Geisel, Level fluctuations in quantum systems with multifractal eigenstates. Physical Review E, 1999. 59: p. 4071–4074.

    Article  Google Scholar 

  14. Zhong, J.X., et al., Level-Spacing Distributions of Planar Quasiperiodic Tight-Binding Models. Physical Review Letters, 1998. 80(18): p. 3996.

    Article  Google Scholar 

  15. Bohigas, O., M.J. Giannoni, and C. Schmit, Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws. Physical Review Letters, 1984. 52(1): p. 1.

    Article  MATH  MathSciNet  Google Scholar 

  16. Seba, P., Random Matrix Analysis of Human EEG Data. Physical Review Letters, 2003. 91(19): p. 198104.

    Article  Google Scholar 

  17. Laloux, L., et al., Noise Dressing of Financial Correlation Matrices. Physical Review Letters, 1999. 83(7): p. 1467.

    Article  Google Scholar 

  18. Plerou, V., et al., Random matrix approach to cross correlations in financial data. Physical Review E, 2002. 65(6): p. 066126.

    Article  Google Scholar 

  19. Plerou, V., et al., Universal and Nonuniversal Properties of Cross Correlations in Financial Time Series. Physical Review Letters, 1999. 83(7): p. 1471.

    Article  Google Scholar 

  20. Kwapien, J., S. Drozdz, and P.O. Oswiecimka, The bulk of the stock market correlation matrix is not pure noise. Physica A: Statistical Mechanics and its Applications, 2006. 359: p. 589–606.

    Article  Google Scholar 

  21. Luo, F., et al., Constructing gene co-expression networks and predicting functions of unknown genes by random matrix theory. BMC Bioinformatics, 2007. 8(1): p. 299.

    Article  Google Scholar 

  22. Luo, F., et al., Application of random matrix theory to microarray data for discovering functional gene modules. Phys Rev E Stat Nonlin Soft Matter Phys, 2006. 73(3 Pt 1): p. 031924.

    Article  Google Scholar 

  23. Yang, Y., et al., Characterization of the Shewanella oneidensis Fur gene: roles in iron and acid tolerance response. BMC Genomics, 2008. 9 Suppl 1: p. S11.

    Google Scholar 

  24. Ficklin, S.P., F. Luo, and F.A. Feltus, The Association of Multiple Interacting Genes with Specific Phenotypes in Rice Using Gene Coexpression Networks. Plant Physiol., 2010. 154(1): p. 13–24.

    Article  Google Scholar 

  25. Zhou, J., et al., Functional Molecular Ecological Networks. mBio, 2010. 1(4): p. e00169-10–e00169-19.

    Google Scholar 

  26. Luo, F., et al., Application of random matrix theory to biological networks. Physics Letters A, 2006. 357(6): p. 420–423.

    Article  MATH  Google Scholar 

  27. Barabasi, A.L. and Z.N. Oltvai, Network biology: understanding the cell’s functional organization. Nat Rev Genet, 2004. 5(2): p. 101–13.

    Article  Google Scholar 

  28. Sengupta, A.M. and P.P. Mitra, Distributions of singular values for some random matrices. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics, 1999. 60(3): p. 3389–92.

    Article  Google Scholar 

  29. Drozdz, S., et al., Collectivity embedded in complex spectra of finite interacting Fermi systems: Nuclear example. Physical Review E, 1998. 57(4): p. 4016.

    Article  Google Scholar 

  30. Malevergne, Y. and D. Sornette, Collective origin of the coexistence of apparent random matrix theory noise and of factors in large sample correlation matrices. Physica A: Statistical Mechanics and its Applications, 2003. 331(3–4): p. 660–668.

    MathSciNet  Google Scholar 

  31. Bruus, H. and J.-C. Angl‘es d’Auriac, Energy level statistics of the two-dimensional Hubbard model at low filling. Physical Review B, 1997. 55(14): p. 9142.

    Google Scholar 

  32. Cowan, G. A survey of unfolding methods for particle physics. 2002.

    Google Scholar 

  33. Hartwell, L.H., et al., From molecular to modular cell biology. Nature, 1999. 402(6761 Suppl): p. C47–52.

    Article  Google Scholar 

  34. Spellman, P.T., et al., Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization. Mol Biol Cell, 1998. 9(12): p. 3273–97.

    Google Scholar 

  35. Troyanskaya, O., et al., Missing value estimation methods for DNA microarrays. Bioinformatics, 2001. 17(6): p. 520–5.

    Article  Google Scholar 

  36. Cherry, J.M., et al., SGD: Saccharomyces Genome Database. Nucleic Acids Res, 1998. 26(1): p. 73–9.

    Article  Google Scholar 

  37. Mewes, H.W., et al., MIPS: a database for protein sequences, homology data and yeast genome information. Nucleic Acids Res, 1997. 25(1): p. 28–30.

    Article  Google Scholar 

  38. Quackenbush, J., Genomics. Microarrays–guilt by association. Science, 2003. 302(5643): p. 240–1.

    Google Scholar 

  39. Bhan, A., D.J. Galas, and T.G. Dewey, A duplication growth model of gene expression networks. Bioinformatics, 2002. 18(11): p. 1486–93.

    Article  Google Scholar 

  40. Shen-Orr, S.S., et al., Network motifs in the transcriptional regulation network of Escherichia coli. Nat Genet, 2002. 31(1): p. 64–8.

    Article  Google Scholar 

  41. Butte, A.J. and I.S. Kohane, Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements. Pac Symp Biocomput, 2000: p. 418–29.

    Google Scholar 

  42. Gasch, A.P., et al., Genomic expression programs in the response of yeast cells to environmental changes. Mol Biol Cell, 2000. 11(12): p. 4241–57.

    Google Scholar 

  43. Hong EL, B.R. Christie, KR, Costanzo MC, Dwight SS, Engel SR, Fisk DG, Hirschman JE, Livstone MS, Nash R, Park J, Oughtred R, Skrzypek M, Starr B, Theesfeld CL, Andrada R, Binkley G, Dong Q, Lane C, Hitz B, Miyasato S, Schroeder M, Sethuraman A, Weng S, Dolinski K, Botstein D, and Cherry JM., Saccharomyces Genome Database.

    Google Scholar 

  44. Barabasi, A.-L. and Z.N. Oltvai, Network biology: understanding the cell’s functional organization. Nature Reviews Genetics, 2004. 5(2): p. 101–113.

    Article  Google Scholar 

  45. Ito, T., et al., A comprehensive two-hybrid analysis to explore the yeast protein interactome. Proc Natl Acad Sci U S A, 2001. 98(8): p. 4569–74.

    Article  Google Scholar 

  46. Uetz, P., et al., A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae. Nature, 2000. 403(6770): p. 623–7.

    Article  Google Scholar 

  47. Vo, T.D., H.J. Greenberg, and B.O. Palsson, Reconstruction and functional characterization of the human mitochondrial metabolic network based on proteomic and biochemical data. J Biol Chem, 2004. 279(38): p. 39532–40.

    Article  Google Scholar 

  48. Ma, H. and A.P. Zeng, Reconstruction of metabolic networks from genome data and analysis of their global structure for various organisms. Bioinformatics, 2003. 19(2): p. 270–7.

    Article  Google Scholar 

  49. Horvath, S. and J. Dong, Geometric Interpretation of Gene Coexpression Network Analysis. PLoS Comput Biol, 2008. 4(8): p. e1000117.

    Article  MathSciNet  Google Scholar 

  50. Stuart, J.M., et al., A Gene-Coexpression Network for Global Discovery of Conserved Genetic Modules. Science, 2003. 302(5643): p. 249–255.

    Article  Google Scholar 

  51. Patrick, N.M. and M. Michael, Laplacian spectra as a diagnostic tool for network structure and dynamics. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 2008. 77(3): p. 031102.

    Google Scholar 

  52. Mohar, B., The Laplacian spectrum of graphs, in Graph Theory, Combinatorics, and Applications, G.C. Y. Alavi, O. R. Oellermann, A. J. Schwenk, Editor. 1991, Wiley. p. 871–898.

    Google Scholar 

  53. Song, C., S. Havlin, and H.A. Makse, Self-similarity of complex networks. Nature, 2005. 433(7024): p. 392–5.

    Article  Google Scholar 

  54. Xenarios, I., et al., DIP, the Database of Interacting Proteins: a research tool for studying cellular networks of protein interactions. 2002. p. 303–305.

    Google Scholar 

  55. Deane, C.M., et al., Protein interactions: two methods for assessment of the reliability of high throughput observations. Mol Cell Proteomics, 2002. 1: p. 349–356.

    Article  Google Scholar 

  56. Jeong, H., et al., The large-scale organization of metabolic networks. Nature, 2000. 407(6804): p. 651–654.

    Article  Google Scholar 

  57. Overbeek, R., et al., WIT: integrated system for high-throughput genome sequence analysis and metabolic reconstruction. Nucleic Acids Res, 2000. 28(1): p. 123.

    Article  Google Scholar 

  58. Farkas, I., et al., The topology of the transcription regulatory network in the yeast, Saccharomyces cerevisiae. Physica A: Statistical Mechanics and its Applications, 2003. 318(3–4): p. 601–612.

    Article  MathSciNet  Google Scholar 

  59. Winzeler, E.A., et al., Functional characterization of the S. cerevisiae genome by gene deletion and parallel analysis. Science, 1999. 285(5429): p. 901.

    Google Scholar 

  60. Erd s, P. and A. Rényi, On the evolution of random graphs. 1960: Citeseer.

    Google Scholar 

  61. Watts, D.J. and S.H. Strogatz, Collective dynamics of ‘small-world’ networks. Nature, 1998. 393(6684): p. 440–2.

    Article  Google Scholar 

  62. Barabasi, A.L. and R. Albert, Emergence of scaling in random networks. Science, 1999. 286(5439): p. 509–12.

    Article  MathSciNet  Google Scholar 

  63. Enright, A.J. and C.A. Ouzounis, BioLayout – an automatic graph layout algorithm for similarity visualization. Bioinformatics, 2001. 17(9): p. 853–4.

    Article  Google Scholar 

  64. Cohen, J.D. and F. Tong, NEUROSCIENCE: The Face of Controversy. Science, 2001. 293(5539): p. 2405–2407.

    Article  Google Scholar 

  65. Jalan, S. and J.N. Bandyopadhyay, Random matrix analysis of complex networks. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 2007. 76(4): p. 046107.

    Google Scholar 

  66. Bandyopadhyay, J.N. and S. Jalan, Universality in complex networks: Random matrix analysis. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 2007. 76(2): p. 026109.

    Google Scholar 

  67. Maslov, S. and K. Sneppen, Specificity and stability in topology of protein networks. Science, 2002. 296(5569): p. 910–3.

    Article  Google Scholar 

  68. Alon, U., et al., Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proc Natl Acad Sci U S A, 1999. 96(12): p. 6745–50.

    Article  Google Scholar 

  69. Singh, D., et al., Gene expression correlates of clinical prostate cancer behavior. Cancer Cell, 2002. 1(2): p. 203–9.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pradip K. Srimani .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Luo, F., Srimani, P.K., Zhou, J. (2011). Application of Random Matrix Theory to Analyze Biological Data. In: Furht, B., Escalante, A. (eds) Handbook of Data Intensive Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1415-5_28

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-1415-5_28

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-1414-8

  • Online ISBN: 978-1-4614-1415-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics