Derivation of an effective model for metabolic processes in living cells including substrate channeling. (English) Zbl 1371.35154
Summary: 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 [M. Gahn et al., SIAM J. Appl. Math. 76, No. 5, 1819–1843 (2016; Zbl 1355.35105)], based on estimates for the shifting operator for Banach-space-valued functions.
MSC:
| 35K57 | Reaction-diffusion equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 80M35 | Asymptotic analysis for problems in thermodynamics and heat transfer |
| 80M40 | Homogenization for problems in thermodynamics and heat transfer |
| 35K61 | Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations |
Keywords:
systems of reaction-diffusion equations; nonlinear flux-conditions; homogenization; carbon metabolism; metabolic channeling; kinetics for multi-species enzymatic reactionsCitations:
Zbl 1355.35105References:
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