A B S T R A C T Three separate approaches were applied to examine the general relationship between R, the rate of induction of specific enzymes (mitochondrial a-glycerophosphate dehydrogenase and cytosolic malic enzyme) and q, the fractional nuclear occupancy by triiodothyronine in male Sprague-Dawley rats. Daily 200-,ug injections of triiodothyronine per 100 g body wt for 7 days resulted in saturation of the hepatic nuclear sites and the achievement of an apparent new steady state of enzyme levels. The increase achieved over base-line hypothyroid levels was then compared with the increment over hypothyroid base line characteristic of intact euthyroid animals with 47% of nuclear sites occupied. The maximal theoretical rate of steadystate enzyme induction could be projected on the basis of the observed maximal increase in enzyme activity observed 1 day after the injection of graded doses of hormone and X, the known fractional rate of enzyme dissipation. The 24-h dose-response studies were used to generate R as a continuous function of q, both in hypothyroid as well as in euthyroid animals. This approach involved the numerical solution of an ordinary differential equation describing the rate of change of enzyme as a function of R, which was assumed to be uniquely related to q. Results of these analyses indicated that the ratio of the maximal rate of induction
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