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Continuum Mechanics and Thermodynamics

, Volume 27, Issue 4–5, pp 659–684 | Cite as

New trends and perspectives in nonlinear intracellular dynamics: one century from Michaelis–Menten paper

  • Alberto M. Bersani
  • Enrico Bersani
  • Guido Dell’Acqua
  • Morten G. Pedersen
Original Article

Abstract

One century after the seminal work by Leonor Michaelis and Maud Menten devoted to the theoretical study of the enzymatic reactions, in this paper, we give an overview of the most recent trends concerning the mathematical modeling of several enzymatic mechanisms, focusing on its asymptotic analysis, which needs the use of advanced mathematical tools, such as center manifold theory, normal forms, and bifurcation theory. Moreover, we present some perspectives, linking the models here presented with similar models, arising from different research fields.

Mathematics Subject Classification (2010)

92C40 92C45 41A99 

Keywords

Michaelis–Menten kinetics Quasi-steady-state approximations Asymptotic expansions Singular perturbations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alberto M. Bersani
    • 1
  • Enrico Bersani
    • 2
  • Guido Dell’Acqua
    • 3
  • Morten G. Pedersen
    • 4
  1. 1.Dipartimento SBAISapienza UniversityRomeItaly
  2. 2.Laboratorio di Strutture e Materiali IntelligentiSapienza UniversityCisterna di LatinaItaly
  3. 3.Ministero dell’Istruzione dell’Università e della RicercaRomeItaly
  4. 4.Department of Information EngineeringUniversity of PadovaPaduaItaly

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