Model Reductions in Biochemical Reaction Networks

Many complex kinetic models in the field of biochemical reactions contain a large number of species and reactions. These models often require a huge array of computational tools to analyse. Techniques of model reduction, which arise in various theoretical and practical applications in systems biology, represent key critical elements (variables and parameters) and substructures of the original system. This thesis aims to study methods of model reduction for biochemical reaction networks. It has three goals related to techniques of model reduction. The primary goal provides analytical approximate solutions of such models. In order to have this set of solutions, we propose an algorithm based on the Duhamel iterates. This algorithm is an explicit formula that can be studied in detail for wide regions of concentrations for optimization and parameter identification purposes. Another goal is to simplify high dimensional models to smaller sizes in which the dynamics of original models and reduced models should be similar. Therefore, we have developed some techniques of model reduction such as geometric singular perturbation method for slow and fast subsystems, and entropy production analysis for identifying non–important reactions. The suggested techniques can be applied to some models in systems biology including enzymatic reactions, elongation factors EF–Tu and EF–Ts signalling pathways, and nuclear receptor signalling. Calculating the value of deviation at each reduction stage helps to check that the approximation of concentrations is still within the allowable limits. The final goal is to identify critical model parameters and variables for reduced models. We study the methods of local sensitivity in order to find the critical model elements. The results are obtained in numerical simulations based on Systems Biology Toolbox (SBToolbox) and SimBiology Toolbox for Matlab. The simplified models would be accurate, robust, and easily applied by biologists for various purposes such as reproducing biological data and functions for the full models.