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.
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species. Describing t
he dynamics of such models occasionally requires some techniques of model analysis. Choosing appropriate techniques of model analysis is often a difficult task. We define a prey (mouse) and predator (cat) model. The system is modelled by a pair of non-linear ordinary differential equations using mass action law, under constant rates. A proper scaling is suggested to minimize the number of parameters. More interestingly, we propose a homotopy technique with n expanding parame- ters for finding some analytical approximate solutions. Furthermore, using the local sensitivity method is another important step forward in this study because it helps to identify critical model parameters. Numerical simulations are provided using Matlab for different parameters and initial conditions.
We study kinetic model of Nuclear Receptor Binding to Promoter Regions. This model is written as a system of ordinary differential equations. Model reduction techniques have been used to simplify chemical kinetics.In this case study, the technique of
Pseudo-first order approximation is applied to simplify the reaction rates. CellDesigner has been used to draw the structures of chemical reactions of Nuclear Receptor Binding to Promoter Regions. After model reduction, the general analytical solution for reduced model is given and the number of species and reactions are reduced from 9 species and 6 reactions to 6 species and 5 reactions.
