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A generic model for open signaling cascades with forward activation

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Abstract

In this work, cellular signal transduction in an open cascade with forward activation was studied. By proposing a generic model which captures the common features of major existing models in the literature, it is showed how signaling profile changes during the propagation along the cascade. In particular, a typical OFF–ON–OFF switch-like transient behavior with prolonged temporary ON state is revealed, where OFF and ON represent the states of low level and high level concentrations, respectively. Analytically this phenomenon is closely related to uniform convergence of the active protein concentration of downstream cycles in the finite time range and its failure in the entire time domain. Consequently a classification of open signaling cascade which can sustain OFF–ON–OFF behavior in the far downstream cycles is accessible. Relevant biological issues, such as delayed activation of downstream reaction cycles, signal amplification and prolonged signal duration, to the generic model is discussed.

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References

  • Alon U (2007) An introduction to systems biology: design principles of biological circuits. Chapman & Hall/CRC, London

    Google Scholar 

  • Arkin A (2000) Signal processing by biochemical reaction network. In: Wallczek J (eds) Self Organized biodynamics and nonlinear control. Cambridge University Press, London, pp 112–144

    Chapter  Google Scholar 

  • Behar M, Hao N, Dohlman H, Elston T (2007) Mathematical and computational analysis of adaptation via feedback inhibition in signal transduction pathways. Biophys J 93(3): 806–821

    Article  Google Scholar 

  • Berg HC, Brown DA (1972) Chemotaxis in escherichia coli analysed by three-dimensional tracking. Nature 239: 500–504

    Article  Google Scholar 

  • Chaves M, Sontag ED, Dinerstein RJ (2004) Optimal length and signal amplification in weakly activated signal transduction cascades. J Phys Chem B 108(39): 15311–15320

    Article  Google Scholar 

  • Chock P, Stadtman E (1977) Superiority of interconvertible enzyme cascades in metabolic regulation: analysis of multicyclic systems. Proc Natl Acad Sci USA 74(7): 2766–2770

    Article  Google Scholar 

  • Feldstein A, Iserles A, Levin D (1995) Embedding of delay equations into an infinite-dimensional ode system. J Differ Equ 117(1): 127–150

    Article  MathSciNet  MATH  Google Scholar 

  • Goldbeter A (1991) A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase. Proc Natl Acad Sci USA 88: 9107–9111

    Article  Google Scholar 

  • Goldbeter A, Koshland DE (1981) An amplified sensitivity arising from covalent modification in biological systems. Proc Natl Acad Sci USA 78(11): 6840–6844

    Article  MathSciNet  Google Scholar 

  • Gonze D, Goldbeter A (2000) A model for a network of phosphorylation-dephosphorylation cycles displaying the dynamics of dominoes and clocks. J Theor Biol 210: 167–186

    Article  Google Scholar 

  • Grubelnik V, Dugonik B, Osebik D, Marhl M (2009) Signal amplification in biological and electrical engineering systems: universal role of cascades. Biophys Chem 143(3): 132–138

    Article  Google Scholar 

  • Hale JK (1980) Ordinary differential equations, 2nd edn. Robert E. Krieger Publishing Co. Inc., Huntington

    MATH  Google Scholar 

  • Hao N, Behar M, Parnell SC, Torres MP, Borchers CH, Elston TC, Dohlman HG (2007) A systems-biology analysis of feedback inhibition in the sho1 osmotic-stress-response pathway. Curr Biol 17(8): 659–667

    Article  Google Scholar 

  • Heinrich R, Neel BG, Rapoport TA (2002) Mathematical models of protein kinase signal transduction. Mol Cell 9(5): 957–970

    Article  Google Scholar 

  • Hohmann S (2002) Osmotic stress signaling and osmoadaptation in yeasts. Microbiol Mol Biol Rev 66(2): 300–372

    Article  Google Scholar 

  • Li Y, Srividhya J (2010) Goldbeter-Koshland model for open signaling cascades: a mathematical study. J Math Biol 61: 781–803

    Article  MathSciNet  MATH  Google Scholar 

  • Ma H, Zhao XM, Yuan YJ, Zeng AP (2004) Decomposition of metabolic network into functional modules based on the global connectivity structure of reaction graph. Bioinformatics 20(12): 1870–1876

    Article  Google Scholar 

  • Ma W, Trusina A, El-Samad H, Lim WA, Tang C (2009) Defining network topologies that can achieve biochemical adaptation. Cell 138(4):760–773. doi:10.1016/j.cell.2009.06.013. http://www.sciencedirect.com/science/article/pii/S0092867409007120

    Google Scholar 

  • MacKeigan JP, Murphy LO, Dimitri CA, Blenis J (2005) Graded mitogen-activated protein kinase activity precedes switch-like c-fos induction in mammalian cells. Mol Cell Biol 25(11): 4676–4682

    Article  Google Scholar 

  • Magan S, Alon U (2003) Structure and function of the feed-forward loop network motif. Proc Natl Acad Sci 100(21): 11980–11985

    Article  Google Scholar 

  • Marhl M, Grubelnik V (2007) Role of cascades in converting oscillatory signals into stationary step-like responses. BioSystems 87: 58–67

    Article  Google Scholar 

  • Matthews HR, Reisert J (2003) Calcium, the two-faced messenger of olfactory transduction and adaptation. Curr Opin Neurobiol 13(4): 469–475

    Article  Google Scholar 

  • Michaelis L, Menten ML (1913) Die kinetik der invertinwirkung. Biochem Z 49(333–369): 352

    Google Scholar 

  • Okamoto M, Takeda Y, Aso Y, Hayashi K (1983) Steady-state approximation of enzyme activation and inhibition. Biotechnol Bioeng 25(6): 1453–1463

    Article  Google Scholar 

  • Ossareh HR, Ventura AC, Merajver SD, Vecchio DD (2011) Long signaling cascades tend to attenuate retroactivity. Biophys J 100(7): 1617–1626

    Article  Google Scholar 

  • Qu Z, Vondriska TM (2009) The effects of cascade length, kinetics and feedback loops on biological signal transduction dynamics in a simplified cascade model. Phys Biol 6(1): 016007

    Article  Google Scholar 

  • Segel IH (1975) Enzyme Kinetics. Behavior and analysis of rapid-equilibrium and steady-state enzyme systems. Wiley-Interscience, New York

    Google Scholar 

  • Smith HL (1995) Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems. Math Surv Monogr 41: 174

    Google Scholar 

  • Srividhya J, Gopinathan M, Schnell S (2007) The effects of time delays in a phosphorylation–dephosphorylation pathway. Biophys Chem 125(2-3): 286–297

    Article  Google Scholar 

  • Srividhya J, Li Y, Pomerening J (2010) Open cascades as simple solutions to providing ultrasensitivity and adaptation in cellular signaling. Phys Biol 61: 781–803

    MATH  Google Scholar 

  • Tyson J (1975) Classification of instabilities in chemical reaction systems. J Chem Phys 62: 1010

    Article  Google Scholar 

  • Ventura AC, Sepulchre JA, Merajver SD (2008) A hidden feedback in signaling cascades is revealed. PLoS Comput Biol 4(3): e1000041

    Article  MathSciNet  Google Scholar 

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Correspondence to Yongfeng Li.

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Li, Y. A generic model for open signaling cascades with forward activation. J. Math. Biol. 65, 709–742 (2012). https://doi.org/10.1007/s00285-011-0480-y

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  • DOI: https://doi.org/10.1007/s00285-011-0480-y

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