Partial equilibrium approximations in apoptosis. I. The intracellular-signaling subsystem

• We develop a mathematically valid method for simplifying biochemical kinetics.
• We apply our method to simplify the Fas-induced apoptotic pathway model.
• We found that nine of reactions in the model can be well regarded as relatively fast.
• This paper reports our simplification of the model together with numerical results.
• The numerical results contain the analyses of accuracy, sensitivity, and M-D transition behaviors of the simplified model.

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 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 Hua et al. [6] 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.