A stable simplification of a fas-signaling pathway model for apoptosis

Apoptosis is important for maintaining normal embryonic development, tissue homeostasis and normal immune-system operation in multicellular organisms. Its malfunction may result in serious diseases such as cancer, autoimmunity, and neurodegeneration. In apoptosis, tens of species are present in many biochemical reactions with times scales of widely differing orders of magnitude. According to the law of mass action, apoptosis is usually described with a large and stiff system of ODEs (ordinary differential equations). The goal of this work is to derive a simple system of ODEs by using the classical PEA (partial equilibrium approximation) method. For this purpose, we firstly justify the mathematical correctness of the PEA in a quite general framework. On the basis of this result, we simplify the Fas-signaling pathway model proposed by Hua et al. (2005) by assuming the fastness of several reversible reactions. Numerical simulations and sensitivity analysis show that our simplification model is reliable.