Advertisement

Inferring Gene Regulatory Networks from Expression Data

  • Lars Kaderali
  • Nicole Radde
Part of the Studies in Computational Intelligence book series (SCI, volume 94)

Summary

Gene regulatory networks describe how cells control the expression of genes, which, together with some additional regulation further downstream, determines the production of proteins essential for cellular function. The level of expression of each gene in the genome is modified by controlling whether and how vigorously it is transcribed to RNA, and subsequently translated to protein. RNA and protein expression will influence expression rates of other genes, thus giving rise to a complicated network structure.

An analysis of regulatory processes within the cell will significantly further our understanding of cellular dynamics. It will shed light on normal and abnormal, diseased cellular events, and may provide information on pathways in dire diseases such as cancer. These pathways can provide information on how the disease develops, and what processes are involved in progression. Ultimately, we can hope that this will provide us with new therapeutic approaches and targets for drug design.

It is thus no surprise that many efforts have been undertaken to reconstruct gene regulatory networks from gene expression measurements. In this chapter, we will provide an introductory overview over the field. In particular, we will present several different approaches to gene regulatory network inference, discuss their strengths and weaknesses, and provide guidelines on which models are appropriate under what circumstances. In addition, we sketch future developments and open problems.

Keywords

Bayesian Network Boolean Function Gene Regulatory Network Boolean Network Dynamic Bayesian Network 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. Akaike, A new look at the statistical model identification, IEEE Trans. Automatic Control 19 (1974), 716–723.CrossRefMathSciNetzbMATHGoogle Scholar
  2. 2.
    T. Akutsu, S. Miyano, and S. Kuhara, Identification of genetic networks from a small number of gene expression patterns under the boolean network model, Pac Symp Biocomput 4 (1999), 17–28.Google Scholar
  3. 3.
    T. Akutsu, S. Miyano, and S. Kuhara, Algorithms for identifying boolean networks and related biological networks based on matrix multiplication and fingerprint function, RECOMB’00: Proceedings of the fourth annual international conference on Computational molecular biology (New York, NY, USA), ACM Press, 2000, pp. 8–14.Google Scholar
  4. 4.
    R. Albert and H.G. Othmer, The topology of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila melanogaster, J Theor Biol 223 (2003), 1–18.CrossRefMathSciNetGoogle Scholar
  5. 5.
    B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, and P. Walter (eds.), Molecular biology of the cell, 4 ed., Garland Publishing, New York, 2002.Google Scholar
  6. 6.
    U. Alon, An introduction to systems biology - design principles of biological circuits, Chapman & Hall/CRC Mathematical and Computational Biology Series, New York, 2007.Google Scholar
  7. 7.
    A. Arkin, J. Ross, and H.H. McAdams, Stochastic kinetic analysis of developmental pathway bifurcation in phage λ - infected Escherichia coli cells, Genetics 149 (1998), no. 4, 1633–1648.Google Scholar
  8. 8.
    J. Bähler, Cell-cycle control of gene expression in budding and fission yeast, Annu. Rev. Genet. 39 (2005), 69–94.CrossRefGoogle Scholar
  9. 9.
    M. Bansal, V. Belcastro, A. Ambesi-Impiombato, and D. di Bernardo, How to infer gene networks from expression profiles, Molecular Systems Biology 3 (2007), 78.Google Scholar
  10. 10.
    M. Bansal, G.D. Gatta, and D. di Bernardo, Inference of gene regulatory networks and compound mode of action from time course gene expression profiles, Bioinformatics 22 (2006), no. 7, 815–822.CrossRefGoogle Scholar
  11. 11.
    K. Basso, A.A. Margolin, G. Stolovitzky, U. Klein, R. Dalla-Favera, and A. Califano, Reverse engineering of regulatory networks in human B-cells, Nature Genetics 37 (2005), 382–390.CrossRefGoogle Scholar
  12. 12.
    J. Beirlant, E. Dudewicz, L. Gyorfi, and E. van der Meulen, Nonparameteric entropy estimation: An overview, Int J Math Stat Sci 6 (1997), no. 1, 17–39.MathSciNetzbMATHGoogle Scholar
  13. 13.
    P. Berg and M. Singer (eds.), Dealing with genes, University Science books, 1992.Google Scholar
  14. 14.
    A. Bernard and J. Hartemink, Informative structure priors: Joint learning of dynamic regulatory networks from multiple types of data, Pac Symp Biocomput (2005), 459–70.Google Scholar
  15. 15.
    H. Bolouri and E.H. Davidson, Modeling transcriptional regulatory networks, BioEssays 24 (2002), 1118–1129.CrossRefGoogle Scholar
  16. 16.
    S. Bornholdt, Less is more in modeling large genetic networks, Science 310 (2005), no. 5747, 449–450.CrossRefGoogle Scholar
  17. 17.
    E. Boros, T. Ibaraki, and K. Makino, Error-free and best-fit extension of partially defined boolean functions, Information and Computation 140 (1998), 254–283.CrossRefMathSciNetzbMATHGoogle Scholar
  18. 18.
    S. Bulashevska and R. Eils, Inferring genetic regulatory logic from expression data, Bioinformatics 21 (2005), no. 11, 2706–2713.CrossRefGoogle Scholar
  19. 19.
    W. Buntine, Theory refinement on bayesian networks, Proceedings of the 7th Conference on Uncertainty in Artificial Intelligence (Los Angeles, CA, USA) (B. D’Ambrosio, P. Smets, and P. Bonissone, eds.), Morgan Kaufmann Publishers, 1991, pp. 52–60.Google Scholar
  20. 20.
    A. Butte and I. Kohane, Mutual information relevance networks: functional genomic clustering using pairwise entropy measurements, Pac Symp Biocomput, 2000, pp. 418–429.Google Scholar
  21. 21.
    A.J. Butte, P. Tamayo, D. Slonim, T.R. Golub, and I.S. Kohane, Discovering functional relationships between rna expression and chemotherapeutic susceptibility using relevance networks, Proc Natl Acad Sci U S A 97 (2000), no. 22, 12182–12186.CrossRefGoogle Scholar
  22. 22.
    K.-C. Chen, T.-Y. Wang, H.-H. Tseng, C.-Y.F. Huang, and C.-Y. Kao, A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae, Bioinformatics 21 (2005), no. 12, 2883–2890.CrossRefGoogle Scholar
  23. 23.
    L. Chen and K. Aihara, A model for periodic oscillation for genetic regulatory systems, IEEE Trans. Circuits and Systems I 49 (2002), no. 10, 1429–1436.CrossRefMathSciNetGoogle Scholar
  24. 24.
    T. Chen, H.L. He, and G.M. Church, Modeling gene expression with differential equations, Pac Symp Biocomput, 1999, pp. 29–40.Google Scholar
  25. 25.
    D.M. Chickering, D. Geiger, and D. Heckerman, Learning bayesian networks: Search methods and experimental results, Proceedings of the Fifth Conference on Artificial Intelligence and Statistics (Ft. Lauderdale), Society for Artificial Intelligence and Statistics, 1995, pp. 112–128.Google Scholar
  26. 26.
    D.-Y. Cho, K.-H. Cho, and B.-T. Zhang, Identification of biochemical networks by S-tree based genetic programming, Bioinformatics 22 (2006), no. 13, 1631–1640.CrossRefGoogle Scholar
  27. 27.
    J. Collado-Vides and R. Hofestädt (eds.), Gene regulations and metabolism - postgenomic computational approaches, MIT Press, 2002.Google Scholar
  28. 28.
    G.M. Cooper and R.E. Hausman (eds.), The cell: A molecular approach, 4 ed., ASM Press and Sinauer Associates, 2007.Google Scholar
  29. 29.
    H. de Jong, Modeling and simulation of genetic regulatory systems: A literature review, J Comput Biol 9 (2002), no. 1, 67–103.CrossRefGoogle Scholar
  30. 30.
    H. de Jong, J.-L. Gouzé, C. Hernandez, M. Page, T. Sari, and J. Geiselmann, Qualitative simulation of genetic regulatory networks using piecewise-linear models, Bull Math Biol 66 (2004), no. 2, 301–340.CrossRefMathSciNetGoogle Scholar
  31. 31.
    H. de Jong and M. Page, Qualitative simulation of large and complex genetic regulatory systems, Proceedings of the 14th European Conference on Artificial Intelligence (W. Horn, ed.), 2000, pp. 141–145.Google Scholar
  32. 32.
    P. D’Haeseler, Reconstructing gene networks from large scale gene expression data, Ph.D. thesis, University of New Mexico, 2000.Google Scholar
  33. 33.
    M. Drton and M.D. Perlman, Model selection for gaussian concentration graphs, Biometrika 91 (2004), no. 3, 591–602.CrossRefMathSciNetzbMATHGoogle Scholar
  34. 34.
    R. Edwards and L. Glass, Combinatorial explosion in model gene networks, Chaos 10 (2000), no. 3, 691–704.CrossRefMathSciNetzbMATHGoogle Scholar
  35. 35.
    B. Ermentrout, Simulating, analyzing and animating dynamical systems: A guide to xppaut for researchers and students, 1 ed., Soc. for Industrial & Applied Math., 2002.Google Scholar
  36. 36.
    N. Friedman, M. Linial, I. Nachman, and D. Pe’er, Using bayesian networks to analyze expression data, J Comput Biol 7 (2000), no. 3-4, 601–620.CrossRefGoogle Scholar
  37. 37.
    N. Friedman, K. Murphy, and S. Russell, Learning the structure of dynamical probabilistic networks, Proceedings of the 14th Annual Conference on Uncertainty in Artificial Intelligence (San Francisco, CA, USA), Morgan Kaufmann Publishers, 1998, pp. 139–147.Google Scholar
  38. 38.
    J. Gebert and N. Radde, Modelling procaryotic biochemical networks with differential equations, AIP Conference Proceedings, vol. 839, 2006, pp. 526–533.CrossRefGoogle Scholar
  39. 39.
    D.T. Gillespie, Exact stochastic simulation of coupled chemical reactions, J Phys Chem 81 (1977), no. 25, 2340–2361.CrossRefGoogle Scholar
  40. 40.
    L. Glass and S.A. Kauffman, The logical analysis of continuous, non-linear biochemical control networks, J Theor Biol 39 (1973), 103–129.CrossRefGoogle Scholar
  41. 41.
    J.L. Gouze, Positive and negative circuits in dynamical systems, J Biological Systems 6 (1998), no. 21, 11–15.CrossRefzbMATHGoogle Scholar
  42. 42.
    J. Guckenheimer and P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer Series, New York, 1983.zbMATHGoogle Scholar
  43. 43.
    M. Gustafsson, M. Hörnquist, and A. Lombardi, Constructing and analyzing a large-scale gene-to-gene regulatory network - lasso-constrained inference and biological validation, IEEE Transaction on Computational Biology and Bioinformatics 2 (2005), no. 3, 254–261.CrossRefGoogle Scholar
  44. 44.
    J. Hasty, D. McMillen, F. Isaacs, and J.J. Collins, Computational studies of gene regulatory networks: in numero molecular biology, Nature Review Genetics 2 (2001), no. 4, 268–279.CrossRefGoogle Scholar
  45. 45.
    D. Heckerman, A tutorial on learning with bayesian networks, Technical Report MSR-TR-95-06, Microsoft Research, Redmond, WA, USA, 1995.Google Scholar
  46. 46.
    D. Heckerman, D. Geiger, and D.M. Chickering, Learning bayesian networks: The combination of knowledge and statistical data, Machine Learning 20 (1995), 197–243.zbMATHGoogle Scholar
  47. 47.
    D. Heckerman, A. Mamdani, and M. Wellman, Real-world applications of bayesian networks, Communications of the ACM 38 (1995), no. 3, 24–30.CrossRefGoogle Scholar
  48. 48.
    S. Huang, Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery, Journal of Molecular Medicine 77 (1999), 469–480.CrossRefGoogle Scholar
  49. 49.
    F. Jacob and J. Monod, Genetic regulatory mechanisms in the synthesis of proteins, J Mol Biol 3 (1961), 318–356.CrossRefGoogle Scholar
  50. 50.
    L. Kaderali, A hierarchical bayesian approach to regression and its application to predicting survival times in cancer, Shaker Verlag, Aachen, 2006.zbMATHGoogle Scholar
  51. 51.
    L. Kaderali, T. Zander, U. Faigle, J. Wolf, J.L. Schultze, and R. Schrader, Caspar: A hierarchical bayesian approach to predict survival times in cancer from gene expression data, Bioinformatics 22 (2006), no. 12, 1495–1502.CrossRefGoogle Scholar
  52. 52.
    S. Kauffman, Metabolic stability and epigenesis in randomly constructed genetic nets, J Theor Biol 22 (1969), 437–467.CrossRefMathSciNetGoogle Scholar
  53. 53.
    S. Kikuchi, D. Tominaga, M. Arita, K. Takahashi, and M. Tomita, Dynamic modeling of genetic networks using genetic algorithm and S-systems, Bioinformatics 19 (2003), no. 5, 643–650.CrossRefGoogle Scholar
  54. 54.
    H. Lähdesmäki, I. Shmulevich, and O. Yli-Harja, On learning gene regulatory networks under the boolean network model, Machine Learning 52 (2003), 147–167.CrossRefzbMATHGoogle Scholar
  55. 55.
    W. Lam and F. Bacchus, Using causal information and local measures to learn bayesian networks, Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (Washington, DC, USA), Morgan Kaufmann Publishers, 1993, pp. 243–250.Google Scholar
  56. 56.
    R. Laubenbacher and B. Stigler, A computational algebra approach to the reverse engineering of gene regulatory networks, J Theor Biol 229 (2004), no. 4, 523–537.CrossRefMathSciNetGoogle Scholar
  57. 57.
    F. Li, T. Long, Y. Lu, Q. Ouyangm, and C. Tang, The yeast cell-cycle network is robustly designed, Proc. Natl. Acad. Sci. U. S. A 101 (2004), 4781–4786.CrossRefGoogle Scholar
  58. 58.
    S. Liang, S. Fuhrman, and R. Somogyi, Reveal, a general reverse engineering algorithm for inference of genetic network architectures, Pac Symp Biocomput 3 (1998), 18–29.Google Scholar
  59. 59.
    D. Madigan, J. Garvin, and A. Raftery, Eliciting prior information to enhance the predictive performance of bayesian graphical models, Communications in Statistics: Theory and Methods 24 (1995), 2271–2292.CrossRefMathSciNetzbMATHGoogle Scholar
  60. 60.
    J.M. Mahaffy, D.A. Jorgensen, and R.L. van der Heyden, Oscillations in a model of repression with external control, J Math Biol 30 (1992), 669–691.CrossRefMathSciNetzbMATHGoogle Scholar
  61. 61.
    J.M. Mahaffy and C.V. Pao, Models of genetic control by repression with time delays and spatial effects, J Math Biol 20 (1984), 39–57.CrossRefMathSciNetzbMATHGoogle Scholar
  62. 62.
    L. Mao and H. Resat, Probabilistic representation of gene regulatory networks, Bioinformatics 20 (2004), no. 14, 2258–2269.CrossRefGoogle Scholar
  63. 63.
    A.A. Margolin, I. Nemenman, K. Basso, C. Wiggins, G. Stolovitzky, R. Dalla-Favera, and A. Califano, Aracne: An algorithm for the reconstruction of gene regulatory networks in a mammalian cellular context, BMC Bioinformatics 7 (Suppl 1) (2006), S7.CrossRefGoogle Scholar
  64. 64.
    A.A. Margolin, K. Wang, W.K. Lim, M. Kustagi, I. Nemenman, and A. Califano, Reverse engineering cellular networks, Nature Protocols 1 (2006), 663–672.CrossRefGoogle Scholar
  65. 65.
    H.H. McAdams and A. Arkin, Stochastic mechanisms in gene expression, Proc. Natl. Acad. Sci. U. S. A. 94 (1997), 814–819.CrossRefGoogle Scholar
  66. 66.
    T. Mestl, E. Plahte, and S.W. Omholt, A mathematical framework for describing and analyzing gene regulatory networks, J Theor Biol 176 (1995), no. 2, 291–300.CrossRefMathSciNetGoogle Scholar
  67. 67.
    K. Murphy and S. Mian, Modelling gene expression data using dynamic bayesian networks, Tech. report, Computer Science Division, University of California, Berkeley, CA, USA, 1999.Google Scholar
  68. 68.
    I. Nachman, A. Regev, and N. Friedman, Inferring quantitative models of regulatory networks from expression data, Bioinformatics 20 (2004), no. 1, i248–i256.CrossRefGoogle Scholar
  69. 69.
    S. Ott, S. Imoto, and S. Miyano, Finding optimal models for small gene networks, Pac Symp Biocomput 9 (2004), 557–567.Google Scholar
  70. 70.
    J. Pearl, Causality: Models, reasoning and inference, Cambridge University Press, Cambridge, 2000.zbMATHGoogle Scholar
  71. 71.
    J. Pearl and T. Verma, A theory of inferred causation, Knowledge Representation and Reasoning: Proceedings of the Second International Conference (New York) (J. Allen, R. Fikes, and E. Sandewal, eds.), Morgan Kaufmann Publishers, 1991, pp. 441–452.Google Scholar
  72. 72.
    D. Pe’er, Bayesian network analysis of signaling networks: A primer, Science STKE 281 (2005), p 14.Google Scholar
  73. 73.
    B.-E. Perrin, L. Ralaivola, A. Mazurie, et al., Gene networks inference using dynamic bayesian networks, Bioinformatics 19 Suppl. II (2003), i138–i148.Google Scholar
  74. 74.
    N. Radde, J. Gebert, and C.V. Forst, Systematic component selection for gene network refinement, Bioinformatics 22 (2006), 2674–2680.CrossRefGoogle Scholar
  75. 75.
    N. Radde and L. Kaderali, Bayesian inference of gene regulatory networks using gene expression time series data, BIRD 2007, LNBI 4414 (2007), 1–15.Google Scholar
  76. 76.
    R.W. Robinson, Counting labeled acyclic graphs, New Directions in the Theory of Graphs (F. Harary, ed.), Academic Press, New York, 1973, pp. 239–273.Google Scholar
  77. 77.
    C. Sabatti and G.M. James, Bayesian sparse hidden components analysis for transcription regulation networks, Bioinformatics 22 (2006), no. 6, 739–746.CrossRefGoogle Scholar
  78. 78.
    M. Santillán and M.C. Mackey, Dynamic regulation of the tryptophan operon: A modeling study and comparison with experimental data, Proc. Natl. Acad. Sci. U. S. A. 98 (2001), no. 4, 1364–1369.CrossRefGoogle Scholar
  79. 79.
    M.J. Schilstra and H. Bolouri, Modelling the regulation of gene expression in genetic regulatory networks, Document for NetBuilder, a graphical tool for building logical representations of genetic regulatory networks.Google Scholar
  80. 80.
    C.E. Shannon and W. Weaver, The mathematical theory of communication, University of Illinios Press, 1963.Google Scholar
  81. 81.
    I. Shmulevich, E.R. Dougherty, and W. Zhang, From boolean to probabilistic boolean networks as models of genetic regulatory networks, Proceedings of the IEEE 90 (2002), no. 11, 1778–1792.CrossRefGoogle Scholar
  82. 82.
    I. Shmulevich, A. Saarinen, O. Yli-Harja, and J. Astola, Inference of genetic regulatory networks under the best-fit extension paradigm, Proceedings of the IEEE EURASIP Workshop on Nonlinear Signal and Image Proc. (W. Zhang and I. Shmulevich, eds.), 2001.Google Scholar
  83. 83.
    A. Silvescu and V. Honavar, Temporal boolean network models of genetic networks and their inference from gene expression time series, Complex Systems 13 (1997), no. 1, 54–75.MathSciNetGoogle Scholar
  84. 84.
    P.W.F. Smith and J. Whittaker, Edge exclusion tests for graphical gaussian models, Learning in Graphical Models (M. Jordan, ed.), MIT Press, 1999, pp. 555–574.Google Scholar
  85. 85.
    P. Smolen, D.A. Baxter and J.H. Byrne, Modeling transcriptional control in gene networks, Bull Math Biol 62 (2000), 247–292.CrossRefGoogle Scholar
  86. 86.
    R.V. Solé, B. Luque, and S.A. Kauffman, Phase transitions in random networks with multiple states, Technical Report 00-02-011, Santa Fe Institute, 2000.Google Scholar
  87. 87.
    P.T. Spellman, G. Sherlock, M.Q. Zhang, et al., Comprehensive identification of cell cycle-regulated genes of the yeast Saccharomyces cerevisiae by microarray hybridization, Mol Biol Cell 9 (1998), 3273–3297.Google Scholar
  88. 88.
    D. Spiegelhalter, A. Dawid, S. Lauritzen, and R. Cowell, Bayesian analysis in expert systems, Statistical Science 8 (1993), 219–282.CrossRefMathSciNetzbMATHGoogle Scholar
  89. 89.
    P. Sprites, C. Glymour, and R. Scheines, Causation, prediction, and search, Springer Verlag, New York, 1993.Google Scholar
  90. 90.
    H. Steck and T. Jaakkola, On the dirichlet prior and bayesian regularization, Advances in Neural Information Processing Systems 15 (Cambridge, MA, USA), MIT Press, 2002.Google Scholar
  91. 91.
    J. Suzuki, A construction of bayesian networks from databases based on an mdl scheme, Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence (Washington, DC, USA), Morgan Kaufmann Publishers, 1993, pp. 266–273.Google Scholar
  92. 92.
    D. Thieffry and R. Thomas, Qualitative analysis of gene networks, Pac Symp Biocomput 3 (1998), 77–88.Google Scholar
  93. 93.
    R. Thomas, On the relation between the logical structure of systems and their ability to generate multiple steady states or sustained oscillations, Springer Series in Synergetics 9 (1981), 180–193.Google Scholar
  94. 94.
    R. Thomas and R. d’Ari, Biological feedback, CRC Press, Boca Raton, FL, USA, 1990.zbMATHGoogle Scholar
  95. 95.
    R. Thomas, S. Mehrotra, E.T. Papoutsakis, and V. Hatzimanikatis, A model-based optimization framework for the inference on gene regulatory networks from dna array data, Bioinformatics 20 (2004), no. 17, 3221–3235.CrossRefGoogle Scholar
  96. 96.
    R. Thomas, D. Thieffry, and M. Kauffman, Dynamical behaviour of biological regulatory networks – I. biological role of feedback loops and practical use of the concept of the loop-characteristic state, Bull Math Biol 57 (1995), 247–276.zbMATHGoogle Scholar
  97. 97.
    M. Tomita, Whole-cell simulation: A grand challenge for the 21st century, Trends Biotechnol. 19 (2001), no. 6, 205–210.CrossRefGoogle Scholar
  98. 98.
    E.P. van Someren, B.L.T. Vaes, W.T. Steegenga, A.M. Sijbers, K.J. Dechering, and J.T. Reinders, Least absolute regression network analysis of the murine osteoblast differentiation network, Bioinformatics 22 (2006), no. 4, 477–484.CrossRefGoogle Scholar
  99. 99.
    E.P. van Someren, L.F.A. Wessels, and M.J.T. Reinders, Linear modeling of genetic networks from experimental data, ISMB 2000: Proceedings of the 8th International Conference on Intelligent Systems for Molecular Biology, 2000, pp. 355–366.Google Scholar
  100. 100.
    E.O. Voit, Computational analysis of biochemical systems, Cambridge University Press, 2000.Google Scholar
  101. 101.
    E.O. Voit and J. Almeida, Decoupling dynamical systems for pathway identification from metabolic profiles, Bioinformatics 20 (2004), no. 11, 1670–1681.CrossRefGoogle Scholar
  102. 102.
    J. von Neumann, The theory of self-reproducing automata, University of Illinois Press, 1966.Google Scholar
  103. 103.
    A. Wagner, Circuit topology and the evolution of robustness in two-gene circadian oscillators, Proc. Natl. Acad. Sci. U. S. A. 102 (2005), 11775–11780.CrossRefGoogle Scholar
  104. 104.
    D.C. Weaver, Modeling regulatory networks with weight matrices, Pac Symp Biocomput, 1999, pp. 112–123.Google Scholar
  105. 105.
    G. Yagil and E. Yagil, On the relation between effector concentration and the rate of induced enzyme synthesis, Biophysical Journal 11 (1971), no. 1, 11–27.CrossRefGoogle Scholar
  106. 106.
    M. Zou and S.D. Conzen, A new dynamic bayesian network (dbn) approach for identifying gene regulatory networks from time course microarray data, Bioinformatics 21 (2005), no. 1, 71–79.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lars Kaderali
    • 1
  • Nicole Radde
    • 2
  1. 1.Viroquant Research Group Modeling, Bioquant BQ26University of HeidelbergHeidelbergGermany
  2. 2.Institute for Medical Informatics, Statistics and EpidemiologyUniversity of LeipzigLeipzigGermany

Personalised recommendations