classic Michaelis-Menten relationship. It shows that the velocity is not a linear function of the substrate concentration, as in Eq. 1. However, when using tracer concentrations of a radioactive species and if the concentrations of the native substrates are in steady state (see Compartmental Modeling Assumptions), the linear form of Eq. 1 still holds. In the presence of a native substrate with concentration C, and the radioactive analog with concentration C, the reaction rate for the generation of radioactive product v* is as follows:
V* and Km are the maximal velocity and half-maximal substrate concentration for the radioactive analog. If the radioactive species has high specific activity (the concentration ratio of labeled to unlabelled compound in the injectate) so that its total concentration (labeled and unlabelled) is small compared to the native substrate, i.e., CVK* « C/Km, then Eq. (6.10) reduces to
The term in large brackets in Eq. 11 is composed of terms that are assumed to be constant throughout a tracer experiment. Therefore, when using radiopharmaceuticals at tracer concentrations, enzyme-catalyzed reactions can be described with a linear relationship as the product of a rate constant k and the radioactive substrate concentration C* The rate constant k includes information about the transport enzyme and the concentration of unlabelled substrate.
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