title: Analysis of metabolic systems with complex slow and fast dynamics.
abstract: We briefly review the results of other authors concerning the analysis of systems with time hierarchy, especially the Tikhonov theorem. A theorem, recently proved by the authors, making possible rigorous analysis of systems with complex fast dynamics is stated and discussed. A model example of a simple enzymatic reaction with product activation and slow (genetically driven) enzyme turnover is rigorously studied. It is shown that even in such a simple model there exist certain regions of parameters for which fast variables oscillate. Thus the classical Tikhonov theorem is not applicable here and we are forced to use another method--for example the author's presented theorem--or a purely numerical solution. These two methods are compared.
authors.forename: I
authors.initials: I
authors.lastname: Dvorák
authors.forename: J
authors.initials: J
authors.lastname: Siska
mesh_terms: D004798:Enzymes / Q000378:metabolism; D007700:Kinetics; D008660:Metabolism; D008954:Models, Biological; D008962:Models, Theoretical
chemical_list: D004798:Enzymes