Biological reaction networks consist of many substances and reactions between them. Like many other biological systems, they have a modular structure. Therefore, a division of a biological reaction network into smaller units highly facilitates its investigation. The authors propose an algorithm to divide an ordinary differential equation (ODE) model of a biological reaction network hierarchically into functional units. For every compound, an activity function dependent on concentration or concentration change rate is defined. After performing suitable simulations, distances between the compounds are computed by comparing the activities along the trajectories of the simulation. The distance information is used to generate a dendrogram revealing the internal structure of the reaction network. The algorithm identifies functional units in two models of different networks: catabolite repression in Escherichia coli and epidermal growth factor (EGF) signal transduction in mammalian cells.
Get full access to this article
View all access options for this article.
References
1.
[1] Lengeler, J. W., G. Drews, and H. G. Schlegel, eds. 1999. Biology of the prokaryotes. Stuttgart, Germany: Georg Thieme Verlag .
2.
[2] Bailey, J. E. 1998. Mathematical modeling and analysis in biochemical engineering: Past accomplishments and future opportunities . Biotechnology Progress14: 8-20 .
3.
[3] Chassagnole, C., N. Noisommit-Rizzi, J. W. Schmid, K. Mauch, and M. Reuss. 2002. Dynamic modeling of the central carbon metabolism of Escherichia coli . Biotechnology Bioengineering79(1): 53-73 .
4.
[4] Kitano, H. 2000. Perspectives on systems biology . New Generation Computing18 (3): 199-216 .
5.
[5] Kremling, A., T. Sauter, E. Bullinger, M. Ederer, F. Allgöwer, and E. D. Gilles. 2001. Biosystems engineering: Applying methods from systems theory to biological systems . In Proceedings of the 2nd International Conference on Systems Biology, Pasadena, CA.
6.
[6] Shu, J., and M. L. Shuler. 1989. A mathematical model for the growth of a single cell of E. coli on a glucose/glutamine/ammonium medium . Biotechnology Bioengineering33: 1117-1126 .
7.
[7] Kremling, A., T. Sauter, E. Bullinger, S. Fischer, J. Doyle, F. Allgöwer, and E. D. Gilles. 2002. A benchmark problem for methods in reverse engineering and model discrimination . In Proceedings of the 3rd International Conference on Systems Biology, December, Stockholm, Sweden.
8.
[8] Sauter, T., A. Kremling, K. Bettenbrock, S. Fischer, and E. D. Gilles. 2002. Analysis of the dynamics of the Escherichia coli glucose PTS in different time windows . In Proceedings of the Fifth German Workshop on Artificial Life, March, Lübeck, Germany, pp. 33-42 .
9.
[9] Keener, J., and J. Sneyd. 2001. Mathematical physiology. 2d ed. New York: Springer-Verlag .
10.
[10] Segel, I. H. 1975. Enzyme kinetics: Behavior and analysis of rapid equilibrium and steady-state enzyme system. New York: John Wiley .
11.
[11] Hartwell, L. H., J. L. Hopfield, S. Leibler, and A. W. Murray. 1999. From molecular to modular cell biology . Nature402: C47-C52 .
12.
[12] Kitano, H., ed. 2001. Foundations of systems biology. Cambridge, MA: MIT Press .
13.
[13] Krakauer, D. C. 2003. Robustness in biological systems: A provisional taxonomy. In Complex systems science in biomedicine, edited by T. S. Deisboeck, J. Y. Kresh, and T. B. Kepler. New York: Kluwer .
14.
[14] Lengeler, J. 2000. Metabolic networks: A signal-oriented approach to cellular models . Biological Chemistry381: 911-920 .
15.
[15] Lipson, H., J. B. Pollack, and N. P. Suh. 2002. On the origin of modular variation . International Journal of Organic Evolution56 (8): 1549-1556 .
16.
[16] Ravasz, E., A. L. Somera, D. A. Mongru, Z. N. Oltvai, and A.-L. Barabasi. 2002. Hierarchical organization of modularity in metabolic networks . Science297: 1551-1555 .
17.
[17] Rives, A. W., and T. Galitski. 2003. Modular organization of cellular networks . PNAS100 (3): 1128-1133 .
18.
[18] Kremling, A., K. Bettenbrock, B. Laube, J. W. Lengeler, and E. D. Gilles. 2001. The organization of metabolic reaction networks: III. Application for diauxic growth on glucose and lactose . Metabolic Engineering3 (4): 362-379 .
19.
[19] Kremling, A., and E. D. Gilles. 2001. The organization of metabolic reaction networks: II. Signal processing in hierarchical structured functional units . Metabolic Engineering3 (2): 138-150 .
20.
[20] Kremling, A., K. Jahreis, J. W. Lengeler, and E. D. Gilles. 2000. The organization of metabolic reaction networks: A signal-oriented approach to cellular models . Metabolic Engineering2 (3): 190-200 .
21.
[21] Wang, J., E. D. Gilles, J. W. Lengeler, and K. Jahreis. 2001. Modeling of inducer exclusion and catabolite repression based on a PTS-dependent sucrose and non-PTS-dependent glycerol transport systems in Escherichia coli K-12 and its experimental verification . Journal of Biotechnology92: 133-158 .
22.
[22] Ginkel, M., A. Kremling, T. Nutsch, R. Rehner, and E. D. Gilles. 2003. Modular modeling of cellular systems with ProMoT/Diva . Bioinformatics19 (9): 1169-1176 .
23.
[23] Schilling, C. H., D. Letscher, and B. O. Palsson. 2000. Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective . Journal of Theoretical Biology203: 229-248 .
24.
[24] Rohwer, J. M., S. Schuster, and H. V. Westerhoff. 1996. How to recognize monofunctional units in a metabolic system . Journal of Theoretical Biology179 (3): 213-228 .
25.
[25] Kholodenko, B. N., S. Schuster, J. M. Rohwer, M. Cascante, and H. V. Westerhoff. 1995. Composite control of cell function: Metabolic pathways behaving as single control units . FEBS368: 1-4 .
26.
[26] Bullinger, E., T. Sauter, F. Allgöwer, and E. D. Gilles. 2002. On deriving a hybrid model for carbohydrate uptake in Escherichia coli .In Proceedings of the 15th IFAC World Congress, Barcelona.
27.
[27] Schulze, A., and J. Downward. 2001. Navigating gene expression using microarrays—a technology review . Nature Cell Biology3 (8): E190-E195 .
28.
[28] Ederer, M., E. Bullinger, and T. Sauter. 2002. Structuring of the cellular metabolism into functional units with mathematical methods . In Proceedings of the 3rd European Interdisciplinary School on Nonlinear Dynamics for System and Signal Analysis, EUROAT-TRACTOR 2002, June, Warsaw.
29.
[29] Ljung, L. 1999. System identification: Theory for the user. Englewood Cliffs, NJ: Prentice Hall .
30.
[30] Tjärnström, F., and L. Ljung. 2002. L2 model reduction and variance reduction . Automatica38 (9): 1517-1530 .
31.
[31] Moniruzzaman, M., X. Lai, S. W. York, and L. O. Ingram. 1997. Extracellular melibiose and fructose are intermediates in raffinose catabolism during fermentation to ethanol by engineered enteric bacteria . Journal of Bacteriology179 (6): 1880-1886 .
32.
[32] Jain, A. K., M. N. Murty, and P. J. Flynn. 1999. Data clustering: A review . ACM Computing Surveys31 (3): 264-323 .
33.
[33] Zwick, M. 2004. An overview of reconstructability analysis . Kybernetes, in press.
34.
[34] Klir, G. J. 1969. An approach to general systems theory. New York: Van Nostrand Reinhold .
35.
[35] Sauter, T., and E. D. Gilles. 2000. Simulation studies on the bacterial phospho-transferase system and experimental validation . In Proceedings of the 4th International Congress on Biochemical Engineering, Stuttgart, Germany.
36.
[36] Wang, J. 2001. A systematic approach for cellular systems and its application on transport and catabolism of four carbohydrates in Escherichia coli. Ph.D. diss., Universität Stuttgart.
37.
[37] Schoeberl, B., C. Eichler-Jonsson, E. D. Gilles, and G. Müller. 2002. Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors . Nature Biotechnology20: 370-375 .
38.
[38] Cobb, M. H. 1999. MAP kinase pathways . Progress in Biophysics and Molecular Biology71: 479-500 .
