An Example The Glycolytic Pathway

An application of the pulse method outlined above is instructive. We choose as a model a part of the glycolytic pathway shown in fig. 5.11. This model includes many of the known activations and inhibitions of enzymes by metabolites. The hexokinase reaction is assumed to be at a constant rate, which neglects the infiuence of ATP and glucose 

6-phosphate. The concentrations of glucose, lactic acid, and the adenine nucleotide pool (the sum of the concentrations of AMP, ADP, and ATP) are taken to be constant. We represent the kinetics of this system by deterministic rate equations (see [1] for details), apply a pulse of concentration of one species to the system in a nonequilibrium stationary state, and calculate the response of the following independent species fructose 

11 Chemical reaction mechanism for an abbreviated model of the glycolytic pathway. The mechanism includes many of the known activations and inhibitions of enzymes by metabolites. Broken lines indicate activation (0) or inhibition (0) of enzymes by metabolites. The abbreviations for the enzymes are hexokinase (HK), phosphofrnctokinase (PFK), and pyruvate kinase (PK) the abbreviations for the five independent variables are fructose 6-phosphate (F6P), fructose 1,6-bisphosphate (FDP), phosphoenolpyruvate (PEP), pyruvate (PYR), and ATP (in fig. 5.12, these are labeled 1-5, respectively). (From [1].) 

The responses of all species to a pulse perturbation of species 2 are shown in fig. 5.12(b). The initial slopes of 3 and 4 are nonzero, which indicates that species 2 has a direct effect (activation) on the conversion of 3 to 4, and 2 slowly converts to 3. The minimum in 3 precedes the maximum in 4 2 directly produces 3. If that were not the case, then the minimum in 3 would follow the maximum in 4, which is not the case. Species 1 does not respond to this perturbation, which shows that the reaction of 1 to 2 is highly irreversible. The initial slope of 5 equals that of 4, and hence 5 is produced at the same rate as 4 in the conversion of 3 to 4, which is new information. 

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