The significance of abrupt transitions in Lineweaver–Burk plots with particular reference to glutamate dehydrogenase. Negative and positive co-operativity in catalytic rate constants

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Abstract
1. Lineweaver–Burk plots for glutamate dehydrogenase, glucose 6-phosphate dehydrogenase and several other enzymes show one or more abrupt transitions between apparently linear sections. These transitions correspond to abrupt increases in the apparent Km and Vmax. with increasing concentration of the varied substrate. 2. The generalized reciprocal initial-rate equation for a multi-site enzyme requires several restrictions to be put on it in order to generate such plots. These mathematical conditions are explored. 3. It is shown that the effective omission of a term in the denominator of the reciprocal initial-rate equation represents a minimal requirement for generation of abrupt transitions. This corresponds in physical terms to negative co-operativity followed by positive co-operativity affecting the catalytic rate constant for the reaction. 4. Previous models for glutamate dehydrogenase cannot adequately account for the results. On the other hand, the model based on both negative and positive co-operativity gives a good fit to the experimental points. 5. The conclusions are discussed in relation to current knowledge of the structure and mechanism of glutamate dehydrogenase.