Journal of Mathematical Chemistry

, Volume 56, Issue 6, pp 1759–1781 | Cite as

Quasi-steady state reduction for the Michaelis–Menten reaction–diffusion system

  • Martin Frank
  • Christian Lax
  • Sebastian Walcher
  • Olaf Wittich
Original Paper


The Michaelis–Menten mechanism is probably the best known model for an enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS reductions are well known, but this is not the case when chemical species are allowed to diffuse. We will discuss QSS reductions for both the irreversible and reversible Michaelis–Menten reaction in the latter case, given small initial enzyme concentration and slow diffusion. Our work is based on a heuristic method to obtain an ordinary differential equation which admits reduction by Tikhonov–Fenichel theory. We will not give convergence proofs but we provide numerical results that support the accuracy of the reductions.


Reaction–diffusion equations Enzyme Singular perturbations 

Mathematics Subject Classification

92C45 34E15 80A32 35B4 



Christian Lax was supported by the DFG Research Training Group “Experimental and Constructive Algebra” (GRK 1632).


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Karlsruhe Institute of TechnologySteinbuch Center for ComputingEggenstein-LeopoldshafenGermany
  2. 2.Lehrstuhl A f. MathematikRWTH AachenAachenGermany

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