Methods for Dynamical Inference in Intracellular Networks

  • Eleftheria Tzamali
  • Panayiota Poirazi
  • Martin Reczko

Abstract

Equation-based algorithms make hypotheses regarding the biophysical dynamical laws that govern a biological system and in the form of a mathematical expression, aiming to interrelate the system components, in an effort to explain and verify the experimental observations. This approach is what we mainly regard as dynamical inference. Assumptions such as the deterministic or stochastic laws that govern the system dynamics, the degree of modeling spatial phenomena, the exact mathematical representations of these biophysical laws and constraints, comprise some of the main issues of the dynamical inference problem. Another class of algorithms considers the cell as a whole system that orchestrates its components under physio-chemical constraints towards the accomplishment of certain cellular functions. These approaches avoid the search of detailed equation forms as well as the demand of knowledge of the parameters involved in the kinetics, and produce a steady state dynamic picture of the complex, genome-scale metabolic network of chemical reactions at the flux level. The constraint-based methods are essential for the analysis of the metabolic capabilities of organisms as well as the elucidation of systemic properties that cannot be described by descriptions of individual components or sub-systems.

The current biological knowledge, the available data and the computer power, are the issues that actually determine the upper limit for the system size and its complexity that can be simulated, thus defining our level of understanding.

Keywords

Differential equations Stochastic simulation Spatial organization Constraint-based methods Flux balance analysis 

Suggested Reading

  1. 1.
    Chen, B.S., et al., A new measure of the robustness of biochemical networks. Bioinformatics, 2005. 21(11): p. 2698–2705.PubMedGoogle Scholar
  2. 2.
    Mahadevan, R. and C.H. Schilling, The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng, 2003. 4(5): p. 264–276.Google Scholar
  3. 3.
    Orphanides, G. and D. Reinberg, A unified theory of gene expression. Cell, 2002. 4(108): p. 439–451.Google Scholar
  4. 4.
    Ribeiro, A., R. Zhu, and S.A. Kauffman, A general modeling strategy for gene regulatory networks with stochastic dynamics. J Comput Biol, 2006. 9(13): p. 1630–1639.Google Scholar
  5. 5.
    Chen, K.C., et al., A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae. Bioinformatics, 2005. 12(21): p. 2883–2890.Google Scholar
  6. 6.
    McAdams, H.H. and A. Arkin, Stochastic mechanisms in gene expression. Proc Natl Acad Sci U S A, 1997. 3(94): p. 814–819.Google Scholar
  7. 7.
    Joshi, A. and B.O. Palsson, Metabolic dynamics in the human red cell. Part I—A comprehensive kinetic model. J Theor Biol, 1989. 4(141): p. 515–528.Google Scholar
  8. 8.
    Nakayama, Y., A. Kinoshita, and M. Tomita, Dynamic simulation of red blood cell metabolism and its application to the analysis of a pathological condition. Theor Biol Med Model, 2005. 1(2): p. 18.Google Scholar
  9. 9.
    Chen, K.C., et al., Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell, 2004. 8(15): p. 3841–3862.Google Scholar
  10. 10.
    Ingram, P.J., M.P. Stumpf, and J. Stark, Network motifs: structure does not determine function. BMC Genomics, 2006. 7: p. 108.PubMedGoogle Scholar
  11. 11.
    Yang, C.R., et al., A mathematical model for the branched chain amino acid biosynthetic pathways of Escherichia coli K12. J Biol Chem, 2005. 12(280): p. 11224–11232.Google Scholar
  12. 12.
    Goryanin, I., T.C. Hodgman, and E. Selkov, Mathematical simulation and analysis of cellular metabolism and regulation. Bioinformatics, 1999. 9(15): p. 749–758.Google Scholar
  13. 13.
    Widder, S., J. Schicho, and P. Schuster, Dynamic patterns of gene regulation I: Simple two-gene systems. J Theor Biol, 2007.Google Scholar
  14. 14.
    Mocek, W.T., R. Rudnicki, and E.O. Voit, Approximation of delays in biochemical systems. Math Biosci, 2005. 2(198): p. 190–216.Google Scholar
  15. 15.
    Carey, M., The enhanceosome and transcriptional synergy. Cell, 1998. 1(92): p. 5–8.Google Scholar
  16. 16.
    Spudich, J.L. and D.E. Koshland, Jr., Non-genetic individuality: chance in the single cell. Nature, 1976. 5568(262): p. 467–471.Google Scholar
  17. 17.
    Hasty, J., et al., Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci U S A, 2000. 5(97): p. 2075–2080.Google Scholar
  18. 18.
    Elowitz, M.B., et al., Stochastic gene expression in a single cell. Science, 2002. 5584(297): p. 1183–1186.Google Scholar
  19. 19.
    Gillespie, D.T., Stochastic Simulation of Chemical Kinetics. Annu Rev Phys Chem, 2006.Google Scholar
  20. 20.
    Lacalli, T.C., Modeling the Drosophila pair-rule pattern by reaction-diffusion: gap input and pattern control in a 4-morphogen system. J Theor Biol, 1990. 2(144): p. 171–194.Google Scholar
  21. 21.
    Aranda, J.S., E. Salgado, and A. Munoz-Diosdado, Multifractality in intracellular enzymatic reactions. J Theor Biol, 2006. 2(240): p. 209–217.Google Scholar
  22. 22.
    Schnell, S. and T.E. Turner, Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol, 2004. 85(2–3): p. 235–260.PubMedGoogle Scholar
  23. 23.
    Weiss, M., et al., Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys J, 2004. 5(87): p. 3518–3524.Google Scholar
  24. 24.
    de Hoon, M.J., et al., Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations. Pac Symp Biocomput. 2003: p. 17–28.Google Scholar
  25. 25.
    D'Haeseleer, P., et al., Linear modeling of mRNA expression levels during CNS development and injury. Pac Symp Biocomput, 1999: p. 41–52.Google Scholar
  26. 26.
    van Someren, E.P., L.F. Wessels, and M.J. Reinders, Linear modeling of genetic networks from experimental data. Proc Int Conf Intell Syst Mol Biol, 2000. 8: p. 355–366.PubMedGoogle Scholar
  27. 27.
    Wu, F.X., W.J. Zhang, and A.J. Kusalik, Modeling gene expression from microarray expression data with state-space equations. Pac Symp Biocomput, 2004: p. 581–592.Google Scholar
  28. 28.
    Gustafsson, M., M. Hornquist, and A. Lombardi, Constructing and analyzing a large-scale gene-to-gene regulatory network–lasso-constrained inference and biological validation. IEEE/ACM Trans Comput Biol Bioinform, 2005. 3(2): p. 254–261.Google Scholar
  29. 29.
    Chen, T., H.L. He, and G.M. Church, Modeling gene expression with differential equations. Pac Symp Biocomput, 1999: p. 29–40.Google Scholar
  30. 30.
    Glass, L. and S.A. Kauffman, The logical analysis of continuous, non-linear biochemical control networks. J Theor Biol, 1973. 1(39): p. 103–129.Google Scholar
  31. 31.
    Drulhe, S., Ferrari-Trecate, G., H. de Jong, and A. Viari, Reconstruction of Switching Thresholds in Piece-wise-Affine Models of Genetic Regulatory Networks. LECTURE NOTES IN COMPUTER SCIENCE, 2006(3927): p. 184–199.Google Scholar
  32. 32.
    Vercruysse, S. and M. Kuiper, Simulating genetic networks made easy: network construction with simple building blocks. Bioinformatics, 2005. 2(21): p. 269–271.Google Scholar
  33. 33.
    Radde, N., J. Gebert, and C.V. Forst, Systematic component selection for gene-network refinement. Bioinformatics, 2006. 21(22): p. 2674–2680.Google Scholar
  34. 34.
    Mason, J., et al., Evolving complex dynamics in electronic models of genetic networks. Chaos, 2004. 3(14): p. 707–715.Google Scholar
  35. 35.
    Edwards, R., P. van den Driessche, and L. Wang, Periodicity in piece-wise-linear switching networks with delay. J Math Biol, 2007.Google Scholar
  36. 36.
    Casey, R., H. de Jong, and J.L. Gouze, Piece-wise-linear models of genetic regulatory networks: equilibria and their stability. J Math Biol, 2006. 1(52): p. 27–56.Google Scholar
  37. 37.
    Ben-Hur, A. and H.T. Siegelmann, Computation in gene networks. Chaos, 2004. 1(14): p. 145–151.Google Scholar
  38. 38.
    Mestl, T., E. Plahte, and S.W. Omholt, A mathematical framework for describing and analysing gene regulatory networks. J Theor Biol, 1995. 2(176): p. 291–300.Google Scholar
  39. 39.
    Hu, X., A. Maglia, and D. Wunsch, A general recurrent neural network approach to model genetic regulatory networks. Conf Proc IEEE Eng Med Biol Soc, 2005. 5: p. 4735–4738.PubMedGoogle Scholar
  40. 40.
    Vohradsky, J., Neural network model of gene expression. Faseb J, 2001. 3(15): p. 846–854.Google Scholar
  41. 41.
    Wahde, M. and J. Hertz, Modeling genetic regulatory dynamics in neural development. J Comput Biol, 2001. 4(8): p. 429–442.Google Scholar
  42. 42.
    Xu, R., X. Hu, and D. Wunsch Ii, Inference of genetic regulatory networks with recurrent neural network models. Conf Proc IEEE Eng Med Biol Soc, 2004. 4: p. 2905–2908.PubMedGoogle Scholar
  43. 43.
    Weaver, D.C., C.T. Workman, and G.D. Stormo, Modeling regulatory networks with weight matrices. Pac Symp Biocomput, 1999: p. 112–123.Google Scholar
  44. 44.
    Vohradsky, J., Neural model of the genetic network. J Biol Chem, 2001. 39(276): p. 36168–36173.Google Scholar
  45. 45.
    Sorribas, A., R. Curto, and M. Cascante, Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior. Math Biosci, 1995. 1(130): p. 71–84.Google Scholar
  46. 46.
    Voit, E.O. and T. Radivoyevitch, Biochemical systems analysis of genome-wide expression data. Bioinformatics, 2000. 11(16): p. 1023–1037.Google Scholar
  47. 47.
    Alvarez-Vasquez, F., C. Gonzalez-Alcon, and N.V. Torres, Metabolism of citric acid production by Aspergillus niger: model definition, steady-state analysis and constrained optimization of citric acid production rate. Biotechnol Bioeng, 2000. 1(70): p. 82–108.Google Scholar
  48. 48.
    Kitayama, T., et al., A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles. Theor Biol Med Model, 2006. 3: p. 24.PubMedGoogle Scholar
  49. 49.
    Kimura, S., et al., Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics, 2005. 7(21): p. 1154–1163.Google Scholar
  50. 50.
    Noman, N. and H. Iba, Reverse engineering genetic networks using evolutionary computation. Genome Inform, 2005. 2(16): p. 205–214.Google Scholar
  51. 51.
    Gonzalez, O.R., et al., Parameter estimation using Simulated Annealing for S-system models of biochemical networks. Bioinformatics, 2007. 4(23): p. 480–486.Google Scholar
  52. 52.
    Voit, E.O., Smooth bistable S-systems. Syst Biol (Stevenage), 2005. 4(152): p. 207–213.Google Scholar
  53. 53.
    Marino, S. and E.O. Voit, An automated procedure for the extraction of metabolic network information from time series data. J Bioinform Comput Biol, 2006. 3(4): p. 665–691.Google Scholar
  54. 54.
    Chou, I.C., H. Martens, and E.O. Voit, Parameter estimation in biochemical systems models with alternating regression. Theor Biol Med Model, 2006. 3: p. 25.PubMedGoogle Scholar
  55. 55.
    Hernandez-Bermejo, B., V. Fairen, and A. Sorribas, Power-law modeling based on least-squares minimization criteria. Math Biosci, 1999. 161(1–2): p. 83–94.PubMedGoogle Scholar
  56. 56.
    Savageau, M.A., A theory of alternative designs for biochemical control systems. Biomed Biochim Acta, 1985. 6(44): p. 875–80.Google Scholar
  57. 57.
    Cai, X. and Z. Xu, K-leap method for accelerating stochastic simulation of coupled chemical reactions. J Chem Phys, 2007. 7(126): p. 074102.Google Scholar
  58. 58.
    Cao, Y., D.T. Gillespie, and L.R. Petzold, Efficient step size selection for the tau-leaping simulation method. J Chem Phys, 2006. 4(124): p. 044109.Google Scholar
  59. 59.
    Chatterjee, A., et al., Time accelerated Monte Carlo simulations of biological networks using the binomial tau-leap method. Bioinformatics, 2005. 9(21): p. 2136–2137.Google Scholar
  60. 60.
    Tian, T. and K. Burrage, Binomial leap methods for simulating stochastic chemical kinetics. J Chem Phys, 2004. 21(121): p. 10356–10364.Google Scholar
  61. 61.
    Puchalka, J. and A.M. Kierzek, Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J, 2004. 3(86): p. 1357–1372.Google Scholar
  62. 62.
    Simpson, M.L., C.D. Cox, and G.S. Sayler, Frequency domain chemical Langevin analysis of stochasticity in gene transcriptional regulation. J Theor Biol, 2004. 3(229): p. 383–394.Google Scholar
  63. 63.
    Haseltine, E.L. and J.B. Rawlings, On the origins of approximations for stochastic chemical kinetics. J Chem Phys, 2005. 16(123): p. 164115.Google Scholar
  64. 64.
    Salis, H. and Y. Kaznessis, Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J Chem Phys, 2005. 5(122): p. 54103.Google Scholar
  65. 65.
    Achimescu, S. and O. Lipan, Signal propagation in non-linear stochastic gene regulatory networks. Syst Biol (Stevenage), 2006. 3(153): p. 120–134.Google Scholar
  66. 66.
    Reinker, S., R.M. Altman, and J. Timmer, Parameter estimation in stochastic biochemical reactions. Syst Biol (Stevenage), 2006. 4(153): p. 168–178.Google Scholar
  67. 67.
    Wang, S.C., Reconstructing genetic networks from time ordered gene expression data using Bayesian method with global search algorithm. J Bioinform Comput Biol, 2004. 3(2): p. 441–458.Google Scholar
  68. 68.
    Goutsias, J., A hidden Markov model for transcriptional regulation in single cells. IEEE/ACM Trans Comput Biol Bioinform, 2006. 1(3): p. 57–71.Google Scholar
  69. 69.
    Inoue, L.Y., et al., Cluster-based network model for time-course gene expression data. Biostatistics, 2006.Google Scholar
  70. 70.
    Grima, R. and S. Schnell, A systematic investigation of the rate laws valid in intracellular environments. Biophys Chem, 2006. 1(124): p. 1–10.Google Scholar
  71. 71.
    Mayawala, K., D.G. Vlachos, and J.S. Edwards, Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations. Biophys Chem, 2006. 3(121): p. 194–208.Google Scholar
  72. 72.
    Loew, L.M. and J.C. Schaff, The virtual cell: a software environment for computational cell biology. Trends Biotechnol, 2001. 10(19): p. 401–406.Google Scholar
  73. 73.
    Slepchenko, B.M., et al., Quantitative cell biology with the virtual cell. Trends Cell Biol, 2003. 11(13): p. 570–576.Google Scholar
  74. 74.
    Hirschberg, K., et al., Kinetic analysis of secretory protein traffic and characterization of golgi to plasma membrane transport intermediates in living cells. J Cell Biol, 1998. 6(143): p. 1485–1503.Google Scholar
  75. 75.
    Von Dassow, G. and G.M. Odell, Design and constraints of the Drosophila segment polarity module: robust spatial patterning emerges from intertwined cell state switches. J Exp Zool, 2002. 3(294): p. 179–215.Google Scholar
  76. 76.
    Schaff, J., et al., A general computational framework for modeling cellular structure and function. Biophys J, 1997. 3(73): p. 1135–1346.Google Scholar
  77. 77.
    Wylie, D.C., et al., A hybrid deterministic-stochastic algorithm for modeling cell signaling dynamics in spatially inhomogeneous environments and under the influence of external fields. J Phys Chem B Condens Matter Mater Surf Interfaces Biophys, 2006. 25(110): p. 12749–12765.Google Scholar
  78. 78.
    Vitaly V. Gursky, J.J., Konstantin N. Kozlov, John Reinitz, Alexander M. Samsonova, Pattern formation and nuclear divisions are uncoupled in Drosophila segmentation: comparison of spatially discrete and continuous models. Physica D, 2004. 197: p. 286–302.Google Scholar
  79. 79.
    Smith, A.E., et al., Systems analysis of Ran transport. Science, 2002. 5554(295): p. 488–491.Google Scholar
  80. 80.
    Broderick, G., et al., A life-like virtual cell membrane using discrete automata. In Silico Biol, 2005. 2(5): p. 163–178.Google Scholar
  81. 81.
    Weimar, J.R. and J.P. Boon, Class of cellular automata for reaction-diffusion systems. Physical Review. E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1994. 2(49): p. 1749–1752.Google Scholar
  82. 82.
    Shimizu, T.S., S.V. Aksenov, and D. Bray, A spatially extended stochastic model of the bacterial chemotaxis signalling pathway. J Mol Biol, 2003. 2(329): p. 291–309.Google Scholar
  83. 83.
    Dab, D., et al., Cellular-automaton model for reactive systems. Physical Review Letters, 1990. 20(64): p. 2462–2465.Google Scholar
  84. 84.
    Wishart, D.S., et al., Dynamic cellular automata: an alternative approach to cellular simulation. In Silico Biol, 2005. 2(5): p. 139–161.Google Scholar
  85. 85.
    Kier, L.B., et al., A cellular automata model of enzyme kinetics. J Mol Graph, 1996. 4(14): p. 227–231, 226.Google Scholar
  86. 86.
    Andrews, S.S. and D. Bray, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol, 2004. 1(3–4): p. 137–151.PubMedGoogle Scholar
  87. 87.
    Erban, R. and S.J. Chapman, Reactive boundary conditions for stochastic simulations of reaction-diffusion processes. Phys Biol, 2007. 1(4): p. 16–28.Google Scholar
  88. 88.
    Elf, J. and M. Ehrenberg, Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. Syst Biol (Stevenage), 2004. 2(1): p. 230–236.Google Scholar
  89. 89.
    Chiam, K.H., et al., Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways. Phys Rev E Stat Nonlin Soft Matter Phys, 2006. 74(5 Pt 1): p. 051910.PubMedGoogle Scholar
  90. 90.
    Sanbonmatsu, K.Y. and C.S. Tung, High performance computing in biology: multimillion atom simulations of nanoscale systems. J Struct Biol, 2007. 3(157): p. 470–480.Google Scholar
  91. 91.
    Phillips, J.C., et al., Scalable molecular dynamics with NAMD. J Comput Chem, 2005. 16(26): p. 1781–1802.Google Scholar
  92. 92.
    Covert Markus, Schilling Christophe, and P. Bernhard, Regulation of Gene Expression in Flux Balance Models of Metabolism. 2001: p. 73–78.Google Scholar
  93. 93.
    Varma, A. and B.O. Palsson, Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl Environ Microbiol, 1994. 10(60): p. 3724–3731.Google Scholar
  94. 94.
    Cakir, T., B. Kirdar, and K.O. Ulgen, Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks. Biotechnol Bioeng, 2004. 3(86): p. 251–260.Google Scholar
  95. 95.
    Klamt, S. and J. Stelling, Combinatorial complexity of pathway analysis in metabolic networks. Mol Biol Rep, 2002. 29(1–2): p. 233–236.PubMedGoogle Scholar
  96. 96.
    Carlson, R., D. Fell, and F. Srienc, Metabolic pathway analysis of a recombinant yeast for rational strain development. Biotechnol Bioeng, 2002. 2(79): p. 121–134.Google Scholar
  97. 97.
    Wiback, S.J. and B.O. Palsson, Extreme pathway analysis of human red blood cell metabolism. Biophys J, 2002. 2(83): p. 808–818.Google Scholar
  98. 98.
    Papin, J.A., et al., The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J Theor Biol, 2002. 1(215): p. 67–82.Google Scholar
  99. 99.
    Schilling, C.H., et al., Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. Biotechnol Bioeng, 2000. 4(71): p. 286–306.Google Scholar
  100. 100.
    Henry, C.S., L.J. Broadbelt, and V. Hatzimanikatis, Thermodynamics-based metabolic flux analysis. Biophys J, 2007. 5(92): p. 1792–1805.Google Scholar
  101. 101.
    Shlomi, T., O. Berkman, and E. Ruppin, Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proc Natl Acad Sci U S A, 2005. 21(102): p. 7695–7700.Google Scholar
  102. 102.
    Herrgard, M.J., S.S. Fong, and B.O. Palsson, Identification of genome-scale metabolic network models using experimentally measured flux profiles. PLoS Comput Biol, 2006. 7(2): p. e72.Google Scholar
  103. 103.
    Mahadevan, R., J.S. Edwards, and F.J. Doyle, 3rd, Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J, 2002. 3(83): p. 1331–1340.Google Scholar
  104. 104.
    Herrgard, M.J., et al., Integrated analysis of regulatory and metabolic networks reveals novel regulatory mechanisms in Saccharomyces cerevisiae. Genome Res, 2006. 5(16): p. 627–635.Google Scholar
  105. 105.
    Patil, K.R., et al., Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics, 2005. 6: p. 308.PubMedGoogle Scholar
  106. 106.
    Knorr, A.L., R. Jain, and R. Srivastava, Bayesian-based selection of metabolic objective functions. Bioinformatics, 2007. 3(23): p. 351–357.Google Scholar
  107. 107.
    Forster, J., et al., Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res, 2003. 2(13): p. 244–253.Google Scholar
  108. 108.
    Borodina, I., P. Krabben, and J. Nielsen, Genome-scale analysis of Streptomyces coelicolor A3(2) metabolism. Genome Res, 2005. 6(15): p. 820–829.Google Scholar
  109. 109.
    Edwards, J.S., R.U. Ibarra, and B.O. Palsson, In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol, 2001. 2(19): p. 125–130.Google Scholar
  110. 110.
    Feist, A.M., et al., Modeling methanogenesis with a genome-scale metabolic reconstruction of Methanosarcina barkeri. Mol Syst Biol, 2006. 2: p. 2006 0004.PubMedGoogle Scholar
  111. 111.
    Becker, S.A. and B.O. Palsson, Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation. BMC Microbiol, 2005. 1(5): p. 8.Google Scholar
  112. 112.
    Duarte, N.C., M.J. Herrgard, and B.O. Palsson, Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res, 2004. 7(14): p. 1298–1309.Google Scholar
  113. 113.
    Almaas, E., Z. Oltvai, and A. Barabasi, The Activity Reaction Core and Plasticity of Metabolic Networks. PloS Computational Biology, 2005. 1(7).Google Scholar
  114. 114.
    Hoops, S., et al., COPASI–a COmplex PAthway SImulator. Bioinformatics, 2006. 24(22): p. 3067–3674.Google Scholar
  115. 115.
    Snoep, J.L., et al., Towards building the silicon cell: a modular approach. Biosystems, 2006. 83(2–3): p. 207–216.PubMedGoogle Scholar
  116. 116.
    Klipp, E., et al., Integrative model of the response of yeast to osmotic shock. Nat Biotechnol, 2005. 8(23): p. 975–982.Google Scholar

Copyright information

© Humana Press, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Eleftheria Tzamali
    • 1
  • Panayiota Poirazi
    • 2
  • Martin Reczko
    • 3
  1. 1.University of CreteHeraklionGreece
  2. 2.Foundation for Research and Technology-HellasHeraklionGreece
  3. 3.Institute of Computer Science (ICS), Foundation of Research and Technology-Hellas (FORTH), Vassilika VoutonHeraklionGreece

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