Model reduction of the intracellular-signaling subsystem of apoptosis

- A mathematical method for reducing biochemical kinetics is presented.
- The method is applied to reduce the FAS-induced apoptotic intracellular-signaling subsystem (of 28 dimensions).
- Nine linear integrals (conserved relations) of the original model are reported and used to reduce the system dimension without any loss of the accuracy.
- Four additional relations allow us to further reduce the system dimension. Three of them represent a combination of fast synchronizing reactions regarded as relatively fast and relaxed and one presents an additional non-linear system integral.
- The reduced model together with numerical simulations results of the comparison between detailed and reduced models are reported.
- The numerical results show the high accuracy of the reduced model.

In recent few decades numerical treatment has become a standard tool in the system analysis and investigation of complex chemical reactions networks of reacting flows. The information about certain networks of biochemical reactions constantly increases. This leads to detailed descriptions of biochemical processes as a system of differential equations of high complexity and dimension. Nowadays methods, which are able automatically reduce the system dimension and complexity, are highly desirable. Recently several methods were developed for model reduction in combustion and chemical kinetics aiming at automatic numerical treatment and constructing the reduced system. The reduced system represents reliable description reproducing the detailed system behavior accurately enough. In this work the method of qualitative ODEs system analysis and the global quasi-linearization method (GQL) for kinetic mechanism reduction of combustion models are applied to the biochemical reaction network of the apoptosis. It is shown that the original model of the apoptosis can be essentially simplified firstly by using linear system integrals (9 dimensions) of the ODEs system, secondly the results of GQL analysis reveals the possibility of a further reduction (4 dimensions). It means that the final system dimension reaches 15 compare to the original 28 without any noticeable accuracy losses.