Skip to main content

Modeling and Network Organization

  • Chapter
Systems Biology

Abstract

The use of mathematical modeling and analysis of networks has a long history in biological research. Perhaps the best-known early example of insightful modeling is the work of Hodgkin and Huxley in 1952 describing how sodium and potassium ion channels could function together to produce the membrane action potential in neurons (Hodgkin and Huxley, 1952). For several decades, models and theory were mostly the domain of applied mathematicians, physical scientists and engineers, many of whom worked rather independently of experimental science and the work remained somewhat obscure and theoretical. With the broad availability of computers and IT infrastructure that has emerged in the last several decades, the use of modeling and theory in biological research has expanded greatly, as has the size of the models being developed.

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  • Akutsu, T., S. Miyano and S. Kuhara. 2000. Inferring qualitative relations in genetic networks and metabolic pathways. Bioinformatics 16: 727–734.

    Article  Google Scholar 

  • Albert, R., Y. W. Chiu and H. G. Othmer. 2004. Dynamic receptor team formation can explain the high signal transduction gain in Escherichia coli. Biophys J 86: 2650–2659.

    Google Scholar 

  • Alm, E. and A. P. Arkin. 2003. Biological networks. Curr Opin Struct Biol 13: 193–202.

    Article  Google Scholar 

  • Alon, U., M. G. Surette, N. Barkai and S. Leibler. 1999. Robustness in bacterial chemotaxis. Nature 397: 168–171.

    Article  Google Scholar 

  • Arita, M. 2004. The metabolic world of Escherichia coli is not small. Proc Natl Acad Sci U S A 101: 1543–1547.

    Article  Google Scholar 

  • Barabasi, A. L. and E. Bonabeau. 2003. Scale-free networks. Sci Am 288: 60–69.

    Article  Google Scholar 

  • Barabasi, A. L. and Z. N. Oltvai. 2004. Network biology: understanding the cell's functional organization. Nat Rev Genet 5: 101–113.

    Article  Google Scholar 

  • Bhalla, U. S., P. T. Ram and R. Iyengar. 2002. MAP kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network. Science 297: 1018–1023.

    Article  Google Scholar 

  • Bolouri, H. and E. H. Davidson. 2003. Transcriptional regulatory cascades in development: initial rates, not steady state, determine network kinetics. Proc Natl Acad Sci U S A 100: 9371–9376.

    Article  Google Scholar 

  • Bray, D. and R. B. Bourret. 1995. Computer analysis of the binding reactions leading to a transmembrane receptor-linked multiprotein complex involved in bacterial chemotaxis. Mol Biol Cell 6: 1367–1380.

    Google Scholar 

  • Carlson, J. M. and J. Doyle. 2002. Complexity and robustness. Proc Natl Acad Sci U S A 99 Suppl 1:2538–45.

    Article  Google Scholar 

  • Carlson, J. M. and J. Doyle. 1999. Highly optimized tolerance: a mechanism for power laws in designed systems. Phys Rev E. Stat Phys Plasmas. Fluids Relat Interdiscip Topics 60: 1412–1427.

    Google Scholar 

  • Chassagnole, C., E. Quentin, D. A. Fell, P. de Atauri, and J. P. Mazat. 2003. Dynamic simulation of pollutant effects on the threonine pathway in Escherichia coli. C R. Biol 326: 501–508.

    Article  Google Scholar 

  • Chen, K.C. et al. 2004. Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell 15: 3841–3862.

    Article  Google Scholar 

  • Chow, C. C., B. Gutkin, D. Hansel, C. Meunier and J. Dalibard. 2005. Methods and Models in Neurophysics : Proceedings of the Les Houches Summer School 2003 (École D'été de Physique Théoretique, Les Houches//Proceedings). Elsevier Science.

    Google Scholar 

  • Christopher, R. et al. 2004. Data-driven computer simulation of human cancer cell. Ann NY Acad Sci 1020:132–53

    Article  Google Scholar 

  • Crampin, E. J. et al. 2004. Computational physiology and the Physiome Project. Exp Physiol 89: 1–26.

    Article  Google Scholar 

  • Cruywagen, G. C., Maini, P. K. & Murray, J. D. 1994. Travelling waves in a tissue interaction model for skin pattern formation. J Math Biol 33: 193–210.

    Article  MATH  MathSciNet  Google Scholar 

  • Csete, M. E. and Doyle, J. C. 2002. Reverse engineering of biological complexity. Science 295: 1664–1669.

    Article  Google Scholar 

  • Davidson, L. A., M. A. Koehl, R. Keller and G. F. Oster. 1995. How do sea urchins invaginate? Using biomechanics to distinguish between mechanisms of primary invagination. Development 121: 2005–2018.

    Google Scholar 

  • Dayan, P. and L. F. Abbott. 2001. Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems. The MIT Press.

    Google Scholar 

  • Dixit, N. M., J. E. Layden-Almer, T. J. Layden, and A. S. Perelson. 2004. Modeling how ribavirin improves interferon response rates in hepatitis C virus infection. Nature 432: 922–924.

    Article  Google Scholar 

  • Doi, A., S. Fujita, H. Matsuno, M. Nagasaki and S. Miyano. 2004. Constructing biological pathway models with hybrid functional Petri nets. In Silico Biol 4: 271–291.

    Google Scholar 

  • Ebenhoh, O., T. Handorf and R. Heinrich. 2004. Structural analysis of expanding metabolic networks. Genome Inform Ser Workshop Genome Inform 15: 35–45.

    Google Scholar 

  • Erban, R. and H. G. Othmer. 2004. From individual to collective behavior in bacterial chemotaxis. SIAM J Appl Math 65(2): 361–391.

    Article  MATH  MathSciNet  Google Scholar 

  • Garny, A., P. Kohl, P. J. Hunter, M. R. Boyett and D. Noble. 2003. One-dimensional rabbit sinoatrial node models: benefits and limitations. J Cardiovasc Electrophysiol 14: S121–S132.

    Article  Google Scholar 

  • Gilchrist, M. A., D. Coombs, and A. S. Perelson. Optimizing within-host viral fitness: infected cell lifespan and virion production rate. J Theor Biol 229: 281–288.

    Google Scholar 

  • Goldbeter, A. 2002. Computational approaches to cellular rhythms. Nature 420: 238–245.

    Article  Google Scholar 

  • Goldbeter, A. et al. 2001. From simple to complex oscillatory behavior in metabolic and genetic control networks. Chaos 11: 247–260.

    Article  MATH  Google Scholar 

  • Hodgkin, A. L. and A. F. Huxley. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117: 500–544.

    Google Scholar 

  • Hucka, M. et al. 2003. The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19: 524–531.

    Article  Google Scholar 

  • Igoshin, O. A., R. Welch, D. Kaiser and G. Oster. 2004. Waves and aggregation patterns in myxobacteria. Proc Natl Acad Sci U S A 101: 4256–4261.

    Article  Google Scholar 

  • Jeong, H., B. Tombor, R. Albert, Z. N. Oltvai and A. L. Barabasi. 2000. The large-scale organization of metabolic networks. Nature 407: 651–654.

    Article  Google Scholar 

  • Kaazempur-Mofrad, M. R. et al. 2004. Characterization of the atherosclerotic carotid bifurcation using MRI, finite element modeling, and histology. Ann Biomed Eng 32: 932–946.

    Article  Google Scholar 

  • Kitano, H. 2004. Biological robustness. Nat Rev Genet 5: 826–837.

    Article  Google Scholar 

  • Kitano, H. et al. 2004. Metabolic syndrome and robustness tradeoffs. Diabetes 53: Suppl 3:S6–S15.

    Article  Google Scholar 

  • Koch, C. 2004. Biophysics of Computation: Information Processing In Single Neurons. Oxford University Press.

    Google Scholar 

  • Koch, C. and I. Segev. 1998. Methods in Neuronal Modeling: From Ions to Networks. The MIT Press.

    Google Scholar 

  • Kremling, A. et al. 2004. A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. Genome Res 14: 1773–1785.

    Article  Google Scholar 

  • Itzkovitz, S. and U. Alon. 2005. Subgraphs and network motifs in geometric networks. Phys Rev E Stat Nonlin Soft Matter Phys 71: 026117.

    Google Scholar 

  • Lee, E., A. Salic, R. Kruger, R. Heinrich and M. W. Kirschner. 2003. The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway. PLoS Biol 1: E10.

    Article  Google Scholar 

  • Leloup, J. C. & A. Goldbeter. 2003. Toward a detailed computational model for the mammalian circadian clock. Proc Natl Acad Sci U S A 100: 7051–7056.

    Article  Google Scholar 

  • Lipkow, K., S. S. Andrews and D. Bray. 2005. Simulated diffusion of phosphorylated CheY through the cytoplasm of Escherichia coli. J Bacteriol 187: 45–53.

    Article  Google Scholar 

  • Luo, C. H. and Y. Rudy. 1994. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ Res 74: 1071–1096.

    Google Scholar 

  • Luo, C. H. and Y. Rudy. 1994. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ Res 74: 1097–1113.

    Google Scholar 

  • Marino, S. and D. E. Kirschner. 2004. The human immune response to Mycobacterium tuberculosis in lung and lymph node. J Theor Biol 227: 463–486.

    Article  Google Scholar 

  • Markhasin, V. S. et al. 2003. Mechano-electric interactions in heterogeneous myocardium: development of fundamental experimental and theoretical models. Prog Biophys Mol Biol 82: 207–220.

    Article  Google Scholar 

  • Matsuoka, S., N. Sarai, H. Jo and A. Noma. 2004. Simulation of ATP metabolism in cardiac excitation-contraction coupling. Prog Biophys Mol Biol 85: 279–299.

    Article  Google Scholar 

  • McCulloch, A. D., P. J. Hunter, and B. H. Smaill. 1992. Mechanical effects of coronary perfusion in the passive canine left ventricle. Am J Physiol 262: H523–H530.

    Google Scholar 

  • McGee, P. 2005. Modeling Success with In Silico Tools. Drug Discovery and Development 8(4): 24–28.

    Google Scholar 

  • Morohashi, M. et al. 2002. Robustness as a measure of plausibility in models of biochemical networks. J Theor Biol 216: 19–30.

    Article  MathSciNet  Google Scholar 

  • Noble, D. 2002. Modeling the heart: insights, failures and progress. Bioessays 24: 1155–1163.

    Article  Google Scholar 

  • Novak, B. and J. J. Tyson. 2003. Modeling the controls of the eukaryotic cell cycle. Biochem Soc Trans 31: 1526–1529.

    Article  Google Scholar 

  • Park, C. S., I. C. Schneider and J. M. Haugh. 2003. Kinetic analysis of platelet-derived growth factor receptor/phosphoinositide 3-kinase/Akt signaling in fibroblasts. J Biol Chem 278: 37064–37072.

    Article  Google Scholar 

  • Patnaik, R. and J. C. Liao. 1994. Engineering of Escherichia coli central metabolism for aromatic metabolite production with near theoretical yield. Appl Environ Microbiol 60: 3903–3908.

    Google Scholar 

  • Patnaik, R. and R. G. L. J. C. Spitzer. 1995. Pathway Engineering for Production of Aromatics in Escherichia coli: Confirmation of Stoichiometric Analysis by Independent Modulation of AroG, TktA, and Pps activities. Biotech Bioeng 46: 361–370.

    Article  Google Scholar 

  • Peirce, S. M., E. J. Van Gieson and T. C. Skalak. 2004. Multicellular simulation predicts microvascular patterning and in silico tissue assembly. FASEB J 18: 731–733.

    Google Scholar 

  • Poolman, M. G., H. E. Assmus and D. A. Fell. 2004. Applications of metabolic modeling to plant metabolism. J Exp Bot 55: 1177–1186.

    Article  Google Scholar 

  • Pribyl, M., C. B. Muratov and S. Y. Shvartsman. 2003. Discrete models of autocrine cell communication in epithelial layers. Biophys J 84, 3624–3635.

    Google Scholar 

  • Pribyl, M., C. B. Muratov and S. Y. Shvartsman. 2003. Transitions in the model of epithelial patterning. Dev Dyn 226: 155–159.

    Article  Google Scholar 

  • Ramanujan, S., G. C. Koenig, T. P. Padera, B. R. Stoll, and R. K. Jain. 2000. Local imbalance of proangiogenic and antiangiogenic factors: a potential mechanism of focal necrosis and dormancy in tumors. Cancer Res 60: 1442–1448.

    Google Scholar 

  • Ramsey, S., D. Orrell, and H. Bolouri. 2005. Dizzy: stochastic simulation of large-scale genetic regulatory networks. J Bioinform Comput Biol 3: 415–436.

    Article  Google Scholar 

  • Sarkar, C. A. et al. 2002. Rational cytokine design for increased lifetime and enhanced potency using pH-activated “histidine switching.” Nat Biotechnol 20: 908–913.

    Article  Google Scholar 

  • Sarkar, C. A. and D. A. Lauffenburger. 2003. Cell-level pharmacokinetic model of granulocyte colony-stimulating factor: implications for ligand lifetime and potency in vivo. Mol Pharmacol 63: 147–158.

    Article  Google Scholar 

  • Savoie, C. J. et al. 2003. Use of gene networks from full genome microarray libraries to identify functionally relevant drug-affected genes and gene regulation cascades. DNA Res 10: 19–25.

    Article  Google Scholar 

  • Schafer, J. R., D. A. Fell, D. Rothman and R. G. Shulman. 2004. Protein phosphorylation can regulate metabolite concentrations rather than control flux: the example of glycogen synthase. Proc Natl Acad Sci U S A 101: 1485–1490.

    Article  Google Scholar 

  • Schmid, J. W., K. Mauch, M. Reuss, E. D. Gilles, and A. Kremling. 2004. Metabolic design based on a coupled gene expression-metabolic network model of tryptophan production in Escherichia coli. Metab Eng 6: 364–377.

    Article  Google Scholar 

  • Schoeberl, B., U. B. Nielsen, D. A. Lauffenburger, and P. K. Sorger. 2003. Network topology and distinct protein expression levels: enough to predict signal transduction in silico? Proceedings of the International Congress of Systems Biology, 64–65.

    Google Scholar 

  • Segal, E. et al. 2003. Module networks: identifying regulatory modules and their conditionspecific regulators from gene expression data. Nat Genet. 34: 166–176.

    Article  Google Scholar 

  • Shimizu, T. S., S. V. Aksenov, and D. Bray 2003. A spatially extended stochastic model of the bacterial chemotaxis signalling pathway. J Mol Biol 329: 291–309.

    Article  Google Scholar 

  • Stelling, J. and E. D. Gilles. 2004. Mathematical modeling of complex regulatory networks. IEEE Trans Nanobioscience 3: 172–179.

    Article  Google Scholar 

  • Stelling, J., E. D. Gilles, and F. J. Doyle III. 2004. Robustness properties of circadian clock architectures. Proc Natl Acad Sci U S A 101: 13210–13215.

    Article  Google Scholar 

  • Stelling, J., S. Klamt, K. Bettenbrock, S. Schuster, and E. D. Gilles. 2002. Metabolic network structure determines key aspects of functionality and regulation. Nature 420: 190–193.

    Article  Google Scholar 

  • Stoll, B. R., C. Migliorini, A. Kadambi, L. L. Munn, and R. K. Jain. 2003. A mathematical model of the contribution of endothelial progenitor cells to angiogenesis in tumors: implications for antiangiogenic therapy. Blood 102: 2555–2561.

    Article  Google Scholar 

  • Sveiczer, A., J. J. Tyson, and B. Novak. 2004. Modeling the fission yeast cell cycle. Brief Funct Genomic Proteomic 2: 298–307.

    Article  Google Scholar 

  • Swameye, I., T. G. Muller, J. Timmer, O. Sandra, and U. Klingmüller. 2003. Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. Proc Natl Acad Sci U S A 100: 1028–1033.

    Article  Google Scholar 

  • ten Tusscher, K. H., D. Noble, P. J. Noble, and A. V. Panfilov. 2004. A model for human ventricular tissue. Am J Physiol Heart Circ Physiol 286: H1573–H1589.

    Article  Google Scholar 

  • Thomas, S., P. J. Mooney, M. M. Burrell, and D. A. Fell. 1997. Metabolic control analysis of glycolysis in tuber tissue of potato (Solanum tuberosum): explanation for the low control coefficient of phosphofructokinase over respiratory flux. Biochem J 322: 119–127.

    Google Scholar 

  • Tranquillo, R. T. and J. D. Murray. 1993. Mechanistic model of wound contraction. J Surg Res 55: 233–247.

    Article  Google Scholar 

  • Trimmer, J., C. McKenna, B. Sudbeck, and R. Ho. 2005. Use of Systems Biology in Clinical Development: Design and Prediction of a Type 2 Diabetes Clinical Trial. PAREXEL Pharmaceutical R&D Sourcebook 2004/2005, 131–132.

    Google Scholar 

  • von Dassow, G., E. Meir, E. M. Munro and G. M. Odell. 2000. The segment polarity network is a robust developmental module. Nature 406: 188–192.

    Article  Google Scholar 

  • von Dassow, G. and G. M. Odell. 2002. Design and constraints of the Drosophila segment polarity module: robust spatial patterning emerges from intertwined cell state switches. J Exp Zool 294: 179–215.

    Article  Google Scholar 

  • Winslow, R.L. et al. 2000. Electrophysiological modeling of cardiac ventricular function: from cell to organ. Annu Rev Biomed Eng 2:119–55.

    Article  Google Scholar 

  • Woolf, P.J. and J. J. Linderman. 2003. Untangling ligand induced activation and desensitization of G-protein-coupled receptors. Biophys J 84: 3–13.

    Google Scholar 

  • Wuchty, S., Z. N. Oltvai and A. L. Barabasi. 2003. Evolutionary conservation of motif constituents in the yeast protein interaction network. Nat Genet 35: 176–179.

    Article  Google Scholar 

  • Yi, T. M., H. Kitano and M. I. Simon. 2003. A quantitative characterization of the yeast heterotrimeric G protein cycle. Proc Natl Acad Sci U S A 100: 10764–10769.

    Article  Google Scholar 

  • Yook, S. H., H. Jeong and A. L. Barabasi. 2002. Modeling the Internet's large-scale topology. Proc Natl Acad Sci U S A 99: 13382–13386.

    Article  Google Scholar 

  • Zwolak, J. W., J. J. Tyson, and L. T. Watson. 2005. Parameter estimation for a mathematical model of the cell cycle in frog eggs. J Comput Biol 12: 48–63.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer

About this chapter

Cite this chapter

Stokes, C., Arkin, A. (2007). Modeling and Network Organization. In: CASSMAN, M., ARKIN, A., DOYLE, F., KATAGIRI, F., LAUFFENBURGER, D., STOKES, C. (eds) Systems Biology. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-5468-6_4

Download citation

Publish with us

Policies and ethics