Advertisement

Network Dynamics

  • Herbert M. SauroEmail author
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 541)

Abstract

Probably one of the most characteristic features of a living system is its continual propensity to change as it juggles the demands of survival with the need to replicate. Internally these adjustments are manifest as changes in metabolite, protein, and gene activities. Such changes have become increasingly obvious to experimentalists, with the advent of high-throughput technologies. In this chapter we highlight some of the quantitative approaches used to rationalize the study of cellular dynamics. The chapter focuses attention on the analysis of quantitative models based on differential equations using biochemical control theory. Basic pathway motifs are discussed, including straight chain, branched, and cyclic systems. In addition, some of the properties conferred by positive and negative feedback loops are discussed, particularly in relation to bistability and oscillatory dynamics.

Key words

Motifs control analysis stability dynamic models 

Notes

Acknowledgments

I wish to acknowledge Ravishankar R. Vallabhajosyula for assistance in preparing the simulation data and figures for the gene cascade circuits. This work was support by a generous grant from the NSF (award number CCF- 0432190).

References

  1. 1.
    Altan-Bonnet G, Germain RN (2005). Modeling T cell antigen discrimination based on feedback control of digital ERK responses. PLoS Biol 3(11):1925–1938.CrossRefGoogle Scholar
  2. 2.
    Alves R, Savageau MA (2000). Effect of overall feedback inhibition in unbranched biosynthetic pathways. Biophys J 79:2290–2304.PubMedCrossRefGoogle Scholar
  3. 3.
    Arkin AP (2000). Signal Processing by Biochemical Reaction Networks. In J. Walleczek (Ed.), Self-Organized Biological Dynamics and Nonlinear Control, pp. 112–114. Cambridge University Press.Google Scholar
  4. 4.
    Austin DW, Allen MS, McCollum JM, Dar RD, Wilgus JR, Sayler GS, Samatova NF, et al. (2006). Gene network shaping of inherent noise spectra. Nature 439(7076):608–611.PubMedCrossRefGoogle Scholar
  5. 5.
    Bakker BM, Westerhoff HV, Opperdoes FR, Michels PAM (2000). Metabolic control analysis of glycolysis in trypanosomes as an approach to improve selectivity and effectiveness of drugs. Mol Biochem Parasitology 106:1–10.CrossRefGoogle Scholar
  6. 6.
    Blackman FF (1905). Optima and limiting factors. Ann Botany 19:281–295.Google Scholar
  7. 7.
    Bliss RD, Painter PR, Marr AG (1982). Role of feedback inhibition in stabilizing the classical operon. J Theor Biol 97(2):177–193.PubMedCrossRefGoogle Scholar
  8. 8.
    Blüthgen N, Bruggeman FJ, Legewie S, Herzel H, Westerhoff HV, Kholodenko BN (2006). Effects of sequestration on signal transduction cascades. FEBS J 273(5):895–906.PubMedCrossRefGoogle Scholar
  9. 9.
    Burns JA (1971). Studies on Complex Enzyme Systems. Ph. D. thesis, University of Edinburgh. http://www.cds.caltech.edu/ hsauro/Burns/jimBurns.pdf
  10. 10.
    Burrell MM, Mooney PJ, Blundy M, Carter D, Wilson F, Green J, Blundy KS, et al. (1994). Genetic manipulation of 6-phosphofructokinase in potato tubers. Planta 194:95–101.CrossRefGoogle Scholar
  11. 11.
    Burton AC (1936). The basis of the principle of the master reaction in biology. J Cell Comp Physiol 9(1):1–14.CrossRefGoogle Scholar
  12. 12.
    Chen KC, Calzone L, Csikasz-Nagy A, Cross FR, Novak B, Tyson JJ (2004). Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell 15(8):3841–3862.PubMedCrossRefGoogle Scholar
  13. 13.
    Conrad ED, Tyson JJ (2006). Modeling Moelcular Interaction Networks with Nonlinear Ordinary Differential Equations. In J. S. Zoltan Szallasi and V. Periwal (Eds.), System Modeling in Cellular Biology From Concepts to Nuts and Bolts, Chapter 6, pp. 97–123. MIT Press.Google Scholar
  14. 14.
    Cornish-Bowden A, Hofmeyr JHS (2002). The Role of Stoichiometric Analysis in Studies of Metabolism: An Example J Theor Biol 216:179–191.PubMedCrossRefGoogle Scholar
  15. 15.
    Cox C, McCollum J, Austin D, Allen M, Dar R, Simpson M (2006). Frequency domain analysis of noise in simple gene circuits. Chaos 16(2):26102–26102.CrossRefGoogle Scholar
  16. 16.
    Deckard A, Sauro HM (2004). Preliminary studies on the in silico evolution of biochemical networks. Chembiochem 5:1423–31.PubMedCrossRefGoogle Scholar
  17. 17.
    Elowitz MB, Leibler S (2000). A synthetic oscillatory network of transcriptional regulators. Nature 403:335–338.PubMedCrossRefGoogle Scholar
  18. 18.
    Fall CP, Marland ES, Wagner JM, Tyson JJ (2002). Computational Cell Biology. Springer-Verlag.Google Scholar
  19. 19.
    Fell DA, Sauro HM (1985a). Metabolic control analysis: additional relationships between elasticities and control coefficients. Eur J Biochem 148:555–561.PubMedCrossRefGoogle Scholar
  20. 20.
    Fell DA, Sauro HM (1985b) Substrate cycles: do they really cause amplification? Biochem Soc Trans 13:762–763.Google Scholar
  21. 21.
    Fell DA, Sauro HM (1990). Metabolic control analysis: the effects of high enzyme concentrations. Eur J Biochem 192:183–187.PubMedCrossRefGoogle Scholar
  22. 22.
    Field RJ, Koros E, Noyes RM (1972). Oscillations in chemical systems, Part 2. Thorough analysis of temporal oscillations in the bromateceriummalonic acid system. J Am Chem Soc 94:8649–8664.CrossRefGoogle Scholar
  23. 23.
    Field RJ, Noyes RM (1974). Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction. J Chem Phys 60(5):1877–1884.CrossRefGoogle Scholar
  24. 24.
    FitzHugh R (1955). Mathematical models of threshold phenomena in the nerve membrane. Bull Math Biophys 17:257–278.CrossRefGoogle Scholar
  25. 25.
    Gardner TS, Cantor CR, Collins JJ (2000). Construction of a genetic toggle switch in Escherichia coli. Nature 403:339–342.PubMedCrossRefGoogle Scholar
  26. 26.
    Geva-Zatorsky N, Rosenfeld N, Itzkovitz S, Milo R, Sigal A, Dekel E, Yarnitzky T, et al. (2006). Oscillations and variability in the p53 system. Mol Syst Biol 2:2006–2006.PubMedCrossRefGoogle Scholar
  27. 27.
    Gillespie DT (1976). A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comp Phys 22:403–434.CrossRefGoogle Scholar
  28. 28.
    Gillespie DT Exact stochastic simulation of coupled chemical reactions. J Phys Chem 81:2340–2361.CrossRefGoogle Scholar
  29. 29.
    Goldbeter A (1997). Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour. Cambridge University Press;.Google Scholar
  30. 30.
    Goldbeter A, Koshland DE (1981). An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci 78:6840–6844.PubMedCrossRefGoogle Scholar
  31. 31.
    Goldbeter A, Koshland DE (1984). Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects. J Biol Chem 259:14441–14447.PubMedGoogle Scholar
  32. 32.
    Goodwin B (1965). Oscillatory behaviour in enzymatic control processes. Adv Enzyme Regul 3:425–438.PubMedCrossRefGoogle Scholar
  33. 33.
    Hearon JZ (1952). Rate behavior of metabolic reactions. Physiol Rev 32:499–523.PubMedGoogle Scholar
  34. 34.
    Heinisch J (1986). Isolation and characterisation of the two structural genes coding for phosphofructokinase in yeast. Mol Gen Genet 202:75–82.PubMedCrossRefGoogle Scholar
  35. 35.
    Heinrich R, Rapoport TA (1974a). A linear steady state treatment of enzymatic chains. Critique of the crossover theorem and a general procedure to identify interaction sites with an effector. Eur J Biochem 42:97–105.PubMedCrossRefGoogle Scholar
  36. 36.
    Heinrich R, Rapoport TA (1974b). A linear steady-state treatment of enzymatic chains; general properties, control and effector strength. Eur J Biochem 42:89–95.PubMedCrossRefGoogle Scholar
  37. 37.
    Heinrich R, Schuster S (1996). The Regulation of Cellular Systems. Chapman and Hall.Google Scholar
  38. 38.
    Higgins J (1965). Dynamics and control in cellular systems. In B. Chance, R. W. Estabrook, and J. R. Williamson (Eds.), Control of Energy Metabolism, pp. 13–46. Academic Press.Google Scholar
  39. 39.
    Higgins J (1967). The Theory of Oscillating Reactions. Ind Eng Chem 59(5):18–62.CrossRefGoogle Scholar
  40. 40.
    Higgins JJ (1959). Ph. D. thesis: A theoretical study of the kinetic properties of sequential enzyme reactions, Univ. Pennsylvania.Google Scholar
  41. 41.
    Hoffmann A, Levchenko A, Scott ML, Baltimore D (2002). The Ikappa B-NF-kappa B signaling module: temporal control and selective gene activation. Science 298:1241–1245.PubMedCrossRefGoogle Scholar
  42. 42.
    Hofmeyr JHS (1986). Steady state modelling of metabolic pathways: a guide for the prespective simulator. Comp Appl Biosci 2:5–11.PubMedGoogle Scholar
  43. 43.
    Hofmeyr JHS (2001). Metabolic Control Analysis in a Nutshell. In Proceedings of the Second International Conference on Systems Biology. Caltech.Google Scholar
  44. 44.
    Hofmeyr JS, Cornish-Bowden A (2000). Regulating the cellular economy of supply and demand. FEBS Lett 476(1–2):47–51.PubMedCrossRefGoogle Scholar
  45. 45.
    Ingalls BP (2004). A frequency domain approach to sensitivity analysis of biochemical systems. J Phys Chem B 108:1143–1152.CrossRefGoogle Scholar
  46. 46.
    Ingolia NT (2004). Topology and robustness in the Drosophila segment polarity network. PLoS Biol 2(6):805–815.CrossRefGoogle Scholar
  47. 47.
    Izhikevich EM (2007). Dynamical systems in neuroscience: the geometry of excitability and bursting. MIT Press.Google Scholar
  48. 48.
    Kacser H (1983). The control of enzyme systems in vivo: elasticity of the steady state. Biochem Soc Trans 11:35–40.PubMedGoogle Scholar
  49. 49.
    Kacser H, Burns JA (1973). The Control of Flux. In D. D. Davies (Ed.), Rate Control of Biological Processes, Volume 27 of Symp Soc Exp Biol, pp. 65–104. Cambridge University Press.Google Scholar
  50. 50.
    Kacser H, Burns JA (1981). The molecular basis of dominance. Genetics 97(3-4):639–666.PubMedGoogle Scholar
  51. 51.
    Kaern M, Weiss R (2006). Synthetic Gene Regulatory Systems. In J. S. Zoltan Szallasi and V. Periwal (Eds.), System Modeling in Cellular Biology From Concepts to Nuts and Bolts, Chapter 13, pp. 269–298. MIT Press.Google Scholar
  52. 52.
    Kholodenko BN (2006). Cell-signalling dynamics in time and space. Nat Rev Mol Cell Biol 7(3):165–176.PubMedCrossRefGoogle Scholar
  53. 53.
    Klipp E, Herwig R, Kowald A, Wierling C, Lehrach H (2005). Systems Biology in Practice. Wiley-VCH Verlag.CrossRefGoogle Scholar
  54. 54.
    Lahav G, Rosenfeld N, Sigal A, Geva-Zatorsky N, Levine AJ, Elowitz MB, Alon U (2004). Dynamics of the p53-Mdm2 feedback loop in individual cells. Nat Gen 36(2):147–150.CrossRefGoogle Scholar
  55. 55.
    LaPorte DC, Walsh K, Koshland DE (1984). The branch point effect. Ultrasensitivity and subsensitivity to metabolic control. J Biol Chem 259(22):14068–14075.PubMedGoogle Scholar
  56. 56.
    Laurent M, Kellershohn N (1999). Multistability: a major means of differentiation and evolution in biological systems. TIBS 24:418–422.PubMedGoogle Scholar
  57. 57.
    Levandoski MM, Tsodikov OV, Frank DE, Melcher SE, Saecker RM, Record MT, Jr (1996). Cooperative and anticooperative effects in binding of the first and second plasmid Osym operators to a LacI tetramer: evidence for contributions of non-operator DNA binding by wrapping and looping. J Mol Biol 260(5):698–717.CrossRefGoogle Scholar
  58. 58.
    Lotka AJ (1920). Undamped oscillations derived from the law of mass action. J Am Chem Soc 42:1595–1599.CrossRefGoogle Scholar
  59. 59.
    Mangan S, Alon U Structure and function of the feed-forward loop network motif. Proc Natl Acad Sci USA 100(21):11980–11985.PubMedCrossRefGoogle Scholar
  60. 60.
    Markevich NI, Hoek JB, Kholodenko BN (2004). Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. J Cell Biol 164:353–359.PubMedCrossRefGoogle Scholar
  61. 61.
    Mettetal JT, Muzzey D, Pedraza JM, Ozbudak EM, van Oudenaarden A (2006). Predicting stochastic gene expression dynamics in single cells. Proc Natl Acad Sci USA 103(19):7304–7309.PubMedCrossRefGoogle Scholar
  62. 62.
    Morales MF (1921). A note on limiting reactions and tempertature coefficients. J Cell Comp Physiol 30:303–313.CrossRefGoogle Scholar
  63. 63.
    Nicolis G (1971). Stability and dissipative structures in open systems far from equilibrium. Adv Chem Phys 19:209–324.CrossRefGoogle Scholar
  64. 64.
    Ortega F, Garcés JL, Mas F, Kholodenko BN, Cascante M (2006). Bistability from double phosphorylation in signal transduction. FEBS J 273(17):3915–3926.PubMedCrossRefGoogle Scholar
  65. 65.
    Paladugu S, Chickarmane V, Deckard A, Frumkin J, McCormack M, Sauro H (2006). In silico evolution of functional modules in biochemical networks. IEE Proc–Systems Biol 153:223–235.PubMedCrossRefGoogle Scholar
  66. 66.
    Paulsson J, Elf J (2006). Stochastic Modeling of Intracellular Kinetics. In J. S. Zoltan Szallasi and V. Periwal (Eds.), System Modeling in Cellular Biology From Concepts to Nuts and Bolts, Chapter 8, pp. 149–175. MIT Press.Google Scholar
  67. 67.
    Pomerening JR, Sontag ED, Ferrell JE (2003). Building a cell cycle oscillator: hysteresis and bistability in the activation of Cdc2. Nat Cell Biol 5(4):346–351.PubMedCrossRefGoogle Scholar
  68. 68.
    Rao CV, Sauro HM, Arkin AP (2004). Putting the ‘Control’ in Metabolic Control Analysis. 7th International Symposium on Dynamics and Control of Process Systems, DYCOPS, 7.Google Scholar
  69. 69.
    Reder C (1988). Metabolic control theory: a structural approach. J Theor Biol 135:175–201.PubMedCrossRefGoogle Scholar
  70. 70.
    Reder C, Mazat JP (1988). Aspects geometriques de la théorie du contrôle du métabolisme in: Le contrôle du métabolisme. Master's thesis, Bordeaux.Google Scholar
  71. 71.
    Reich JG, Selkov EE (1981). Energy metabolism of the cell. Academic Press.Google Scholar
  72. 72.
    Sauro HM (1994). Moiety-conserved cycles and metabolic control analysis: problems in sequestration and metabolic channelling. BioSystems 33:15–28.CrossRefGoogle Scholar
  73. 73.
    Sauro HM, Ingalls B (2004). Conservation analysis in biochemical networks: computational issues for software writers. Biophys Chem 109(1):1–15.PubMedCrossRefGoogle Scholar
  74. 74.
    Sauro HM, Kholodenko BN (2004). Quantitative analysis of signaling networks. Prog Biophys Mol Biol 86:5–43.PubMedCrossRefGoogle Scholar
  75. 75.
    Savageau MA (1972). The behaviour of intact biochemical control systems. Curr Topics Cell Reg 6:63–130.Google Scholar
  76. 76.
    Savageau MA (1974). Optimal design of feedback control by inhibition: steady-state considerations. J Mol Evol 4:139–156.PubMedCrossRefGoogle Scholar
  77. 77.
    Savageau MA (1976). Biochemical systems analysis: a study of function and design in molecular biology. Addison-Wesley.Google Scholar
  78. 78.
    Scott M, Ingalls B, Kærn M (2006). Estimations of intrinsic and extrinsic noise in models of nonlinear genetic networks. Chaos 16(2):26107–26107.CrossRefGoogle Scholar
  79. 79.
    Small JR, Fell DA (1990). Covalent modification and metabolic control analysis: modification to the theorems and their application to metabolic systems containing covalently-modified enzymes. Eur J Biochem 191:405–411.PubMedCrossRefGoogle Scholar
  80. 80.
    Stucki JW (1978). Stability analysis of biochemical systems – a practical guide. Prog Biophys Mol Biol 33:99–187.PubMedCrossRefGoogle Scholar
  81. 81.
    Thomas S, Fell DA (1994). MetaCon – a program for the algebraic evaluation of control coefficients of arbitary metabolic networks. In H. V. Westerhoff (Ed.), Biothermokinetics, pp. 225–229. Intercept Ltd.Google Scholar
  82. 82.
    Tyson J, Othmer HG (1978). The dynamics of feedback control circuits in biochemical pathways. In R. Rosen and F. M. Snell (Eds.), Progress in Theoretical Biology, 5:1–62.Google Scholar
  83. 83.
    Tyson JJ (1975). Classification of instabilities in chemical reaction systems. J Chem Phys 62:1010–1015.CrossRefGoogle Scholar
  84. 84.
    Tyson JJ, Chen KC, Novak B (2003). Sniffers, buzzers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr Opin Cell Biol 15:221–231.PubMedCrossRefGoogle Scholar
  85. 85.
    Vallabhajosyula RR, Chickarmane V, Sauro HM (2006). Conservation analysis of large biochemical networks. Bioinformatics 22(3):346–353.PubMedCrossRefGoogle Scholar
  86. 86.
    van der Pol B, van der Mark J (1928). The heartbeat considered as a relaxation oscillation, and an electrical model of the heart. Philos Mag Suppl 6:763–775.Google Scholar
  87. 87.
    Voit E, Neves AR, Santos H (2006). The intricate side of systems biology. Proc Natl Acad Sci USA 103(25):9452–9457.PubMedCrossRefGoogle Scholar
  88. 88.
    Westerhoff HV, Chen YD (1984). How do enzyme activities control metabolite concentrations? Eur J Biochem 142:425–430.PubMedCrossRefGoogle Scholar
  89. 89.
    Wilkinson DJ (2006). Stochastic Modelling for Systems Biology. Chapman and Hall.Google Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of BioengineeringUniversity of WashingtonSeattleUSA

Personalised recommendations