In the case of a transport system obeying Michaelis-Menten kinetics, completely general relationships are shown to exist between the final ratio of internal and external substrate concentrations, alpha, and the V/Km ratios found in zero-trans-entry, zero-trans-exit and equilibrium-exchange experiments (where V is a maximum substrate flux and Km a substrate half-saturation constant). The proof depends on a new method of derivation proceeding from the form of the experimental data rather than, as has been the practice in kinetic analysis, from a hypothetical reaction scheme. These general relationships, which will be true of all mechanisms giving rise to a particular type of behaviour (here Michaelis-Menten kinetics), provide a test for internal consistency in a set of experimental data. Other relationships, which are specific, can be derived from individual reaction schemes, with the use of traditional procedures in kinetic analysis. The specific relationships include constants for infinite trans entry and exit in addition to constants involved in the general relationships. In conjunction, the general and specific relationships provide a stringent test of mechanism. A set of results that fails to satisfy the general relationships must be rejected; here systematic error or unexpected changes in the transport system in different experiments may have distorted the calculated constants, or the system may not actually obey Michaelis-Menten kinetics. Results in accord with the general relationships, on the other hand, can be applied in specific tests of mechanism. The usefulness of the theorem is illustrated in the cases of the glucose-transport and choline-transport systems of erythrocytes. Experimental results taken from several studies in the literature, which were in accord with hyperbolic substrate kinetics, had previously been shown to disagree with relationships derived for the carrier model, and the model was rejected. The new analysis shows that the data violated the general relationships and therefore cannot decide the issue. More recent results on the glucose-transport system satisfy the general relations and agree with the carrier model.

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