Portisch, S. (2017). A novel approach to dimension reduction in enzyme kinetics [Diploma Thesis, Technische Universität Wien]. reposiTUm. http://hdl.handle.net/20.500.12708/78990
tropical geometry; enzyme kinetics; geometric singular perturbation theory
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Abstract:
This thesis presents a novel approach to analysing multiple time scale systems inspired by concepts and methods of tropical geometry. The analysis is carried out in the context of the specific problem of justifying dimension reduction for the Michaelis Menten model of enzyme reactions. An ε-dependent exponential variable transformation allows to handle very different orders of magnitudes of variables and parameters at once. Applying these ideas to the Michaelis Menten model, we prove the existence of an invariant, attracting and one-dimensional slow manifolds for small values of the parameter ε . This thesis is a first step to fully understand the Michaelis Menten model in all parameter regimes and to further develop the tropical approach as a tool in geometric singular perturbation theory (GSPT).