Vietnam Journal of Mathematics

, Volume 45, Issue 1–2, pp 265–293 | Cite as

Derivation of an Effective Model for Metabolic Processes in Living Cells Including Substrate Channeling

  • Markus GahnEmail author
  • Maria Neuss-Radu
  • Peter Knabner


A system of reaction-diffusion equations in a multi-component medium with nonlinear flux-conditions and additional reaction-diffusion equations on the interfaces is considered. The model is motivated by metabolic processes in living cells. Especially, we are interested in modeling the central carbon metabolism in plant cells, with particular emphasis on metabolite channeling. The nonlinear reaction terms arising in the equations and boundary conditions are described by structural conditions, which are fulfilled by the kinetics of multi-species enzymatic reactions encountered in cellular metabolism. Starting from a mathematical model at subcellular level, where cellular structures like organelles are resolved, we derive an effective approximations for the cellular processes, by letting the scale parameter given by the ratio between the size of organelles and that of the cell going to zero. To show convergence of the nonlinear terms, we use homogenization concepts developed in Gahn, Neuss-Radu, and Knabner (SIAM J. Appl. Math. 76, 1819–1843 [21]), based on estimates for the shifting operator for Banach-space-valued functions.


Systems of reaction-diffusion equations Nonlinear flux-conditions Homogenization Carbon metabolism Metabolic channeling Kinetics for multi-species enzymatic reactions 

Mathematics Subject Classfication (2010)

35K57 35Q92 80M35 80M40 



The work of the first author was supported by the Emerging Fields Initiative (EFI) for Synthetic Biology at the Friedrich-Alexander-Universität Erlangen-Nürnberg.


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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Erlangen-NürnbergErlangenGermany

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