  There are many mathematical models of biochemical cell signaling pathways
that contain a large number of elements (species and reactions). This is
sometimes a big issue for identifying critical model elements and describing
the model dynamics. Thus, techniques of model reduction can be used as a
mathematical tool in order to minimize the number of variables and parameters.
In this thesis, we review some well-known methods of model reduction for cell
signaling pathways. We have also developed some approaches that provide us a
great step forward in model reduction. The techniques are quasi steady state
approximation (QSSA), quasi equilibrium approximation (QEA), lumping of species
and entropy production analysis. They are applied on protein translation
pathways with microRNA mechanisms, chemical reaction networks, extracellular
signal regulated kinase (ERK) pathways, NFkB signal transduction pathways,
elongation factors EFTu and EFTs signaling pathways and Dihydrofolate reductase
(DHFR) pathways. The main aim of this thesis is to reduce the complex cell
signaling pathway models. This provides one a better understanding of the
dynamics of such models and gives an accurate approximate solution. Results
show that there is a good agreement between the original models and the
simplified models.
