Partial equilibrium approximations in Apoptosis

Apoptosis is one of the most basic biological processes. In apoptosis, tens of species are involved in many biochemical reactions with times 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. With the justified method as a tool, we made many attempts via numerical tests to simplify the Fas-signaling pathway model due to Hua et al. (2005) and found that nine of reactions therein can be well regarded as relatively fast. This paper reports our simplification of Hua at el.’s model with the PEA method based on the fastness of the nine reactions, together with numerical results which confirm the reliability of our simplified model.