Slow and fast subsystems for complex biochemical reactions

In this study, we define mathematical modelling for some enzyme inhibitors and we minimize the number of variables and parameter based on some techniques of model reductions. We divided this thesis into the six sections. The first section of this thesis gives an introduction regarding to mathematical modeling and modeling process. The second section presents two methods of model reduction for biochemical reactions with an example of simple enzyme reactions. Methods are quasi-steady state approximations and quasi-equilibrium approximations. Then, in section three we define competitive inhibition model and we applied the proposed methods to minimize the number of variables and paraments. After that, we have defined some more complex models such as uncompetitive inhibition and mixed inhibition, we reduce the number of elements based on the suggested techniques and we calculate some analytical solution for such models in sections four and five, respectively. Finally, conclusions and recommendations are given in section six.