2006 International Conference in Honor of Jacqueline Fleckinger.
Electronic Journal of Differential Equations,
Conference 16 (2007), pp. 155-184. 

Title: Reduction for Michaelis-Menten-Henri kinetics
       in the presence of diffusion

Authors: Leonid V. Kalachev (Univ. of Montana, Missoula, MT, USA)
         Hans G. Kaper  (Argonne National Laboratory, IL, USA)
	 Tasso J. Kaper (Boston Univ., Boston, MA, USA)
         Nikola Popovic (Boston Univ., Boston, MA, USA)
	 Antonios Zagaris (Univ. of Amsterdam, The Netherlands)
 
Abstract: 
 The Michaelis-Menten-Henri (MMH) mechanism is one of the paradigm
 reaction mechanisms in biology and chemistry. In its simplest form,
 it involves a substrate that reacts (reversibly) with an enzyme, forming a
 complex which is transformed (irreversibly) into a product and the enzyme.
 Given these basic kinetics, a dimension reduction has traditionally been
 achieved in two steps, by using conservation relations
 to reduce the number of species and by exploiting the inherent
 fast-slow structure of the resulting equations.
 In the present article, we investigate how the dynamics change
 if the species are additionally allowed to diffuse.
 We study the two extreme regimes of large diffusivities
 and of small diffusivities, as well as an intermediate regime
 in which the time scale of diffusion is comparable
 to that of the fast reaction kinetics.
 We show that reduction is possible in each of these regimes,
 with the nature of the reduction being regime dependent.
 Our analysis relies on the classical method of matched asymptotic
 expansions to derive approximations for the solutions that are
 uniformly valid in space and time.

Published May 15, 2007.
Math Subject Classifications: 35K57, 35B40, 92C45, 41A60.
Key Words: Michaelis-Menten-Henri mechanism; diffusion;
           dimension reduction; matched asymptotics.