  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.
