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Partial equilibrium approximations in apoptosis. I: The intracellular-signaling subsystem. (English) Zbl 1281.92026

Summary: Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with time scales of widely differing orders of magnitude. By the law of mass action, the process is mathematically described with a large and stiff system of ODEs (ordinary differential equations). The goal of this work is to simplify such systems of ODEs with the PEA (partial equilibrium approximation) method. In doing so, we propose a general framework of the PEA method together with some conditions, under which the PEA method can be justified rigorously.
The main condition is the principle of detailed balance for fast reactions as a whole and the framework provides some meaningful physical insights of the full chemical kinetics. With the justified method as a tool, we simplify the Fas-signaling pathway model due to F. Hua et al. [J. Immunology 175, 985ff (2005)] under the empirical assumption that nine reactions therein can be well regarded as relatively fast. This paper reports our simplification, together with numerical results which confirm the reliability of both our simplified model and the empirical assumption.

MSC:

92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C40 Biochemistry, molecular biology
34C60 Qualitative investigation and simulation of ordinary differential equation models
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