Time-scale separation – Michaelis and Menten's old idea, still bearing fruit


  • Jeremy Gunawardena

    Corresponding author
    1. Department of Systems Biology, Harvard Medical School, Boston, MA, USA
    • Correspondence

      J. Gunawardena, Department of Systems Biology, Harvard Medical School, 200 Longwood Avenue, Boston, MA 02115, USA

      Fax: +1 617 432 5012

      Tel: +1 617 432 4839

      E-mail: jeremy@hms.harvard.edu

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Michaelis and Menten introduced to biochemistry the idea of time-scale separation, in which part of a system is assumed to be operating sufficiently fast compared to the rest so that it may be taken to have reached a steady state. This allows, in principle, the fast components to be eliminated, resulting in a simplified description of the system's behaviour. Similar ideas have been widely used in different areas of biology, including enzyme kinetics, protein allostery, receptor pharmacology, gene regulation and post-translational modification. However, the methods used have been independent and ad hoc. In the present study, we review the use of time-scale separation as a means to simplify the description of molecular complexity and discuss recent work setting out a single framework that unifies these separate calculations. The framework offers new capabilities for mathematical analysis and helps to do justice to Michaelis and Menten's insights about individual enzymes in the context of multi-enzyme biological systems.