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Hyperbolic Saturation

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Abstract

Several hyperbolically saturating empirical models, such as the Michaelis–Menten rate equation, Monod’s relative population growth rate, competitive inhibition, and Langmuir’s adsorption, are rederived from a simple queuing relation. The resulting derivations reveal and potentially explain the underlying structure and meaning of such empirical models. This view is proposed as a unifying heuristic.

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References

  • Cleland, W.W., 1963. The kinetics of enzyme-catalyzed reactions with two or more substrates or products: I. Nomenclature and rate equations. Biochim. Biophys. Acta 67, 104–137.

    Article  Google Scholar 

  • Ingraham, J.L., Maaloe, O., Neidhardt, F.C., 1983. Growth of the Bacterial Cell. Sinauer Associates, Inc., Sunderland.

    Google Scholar 

  • Jackson, J.H., Schmidt, T.M., Herring, P.A., 2008. A systems approach to model natural variation in reactive properties of bacterial ribosomes. BMC Syst. Biol. 2, 62.

    Article  Google Scholar 

  • Kastner, J., 2003. Modeling a Hox Gene Network: Stochastic Simulation with Experimental Perturbation. Dissertation, California Institute of Technology.

  • Kenakin, T., 2004. A Pharmacology Primer. Elsevier, Amsterdam.

    Google Scholar 

  • Langmuir, I., 1918. The adsorption of gases on plane surfaces of glass, mica, and platinum. J. Am. Chem. Soc. 40(9), 1361–1403.

    Article  Google Scholar 

  • MacCluer, C.R., 2004. Boundary Value Problems and Fourier Expansions. Dover, New York.

    MATH  Google Scholar 

  • Michaelis, L., Menten, M., 1913. Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333–369.

    Google Scholar 

  • Monod, J., 1949. The growth of bacterial cultures. Annu. Rev. Microbiol. 3, 371–394.

    Article  Google Scholar 

  • Smith, W., 1971. Stochastic models for an enzyme reaction in an open linear system. Bull. Math. Biol. 33(1), 97–115.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Microbiology and Molecular Genetics, Michigan State University, East Lansing, MI, 48824, USA

    J. H. Jackson

  2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA

    C. R. MacCluer

Authors
  1. J. H. Jackson
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  2. C. R. MacCluer
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Correspondence to J. H. Jackson.

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Jackson, J.H., MacCluer, C.R. Hyperbolic Saturation. Bull. Math. Biol. 72, 1315–1322 (2010). https://doi.org/10.1007/s11538-009-9475-x

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  • DOI: https://doi.org/10.1007/s11538-009-9475-x

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