202 Essays in Biochemistry 



was abundantly present in the diet, the deuterium concentration in 

 glycogen approached asymptotically a maximal value of about 30% 

 of that in the body water. However, when lactate served as the source 

 of glycogen carbon, glycogen containing about 60% as high a concen- 

 tration of deuterium as body water was recovered, 2 and this value 

 approximated the fraction of all hydrogen in glycogen which is carbon- 

 bound. 



From these results it could be concluded that glycogen was under- 

 going turnover at the expense of available glucose. This glucose was 

 isotopically labeled insofar as it was synthesized in the D 2 0-enriched 

 medium, but was subject to dilution prior to glycogenosis by such 

 glucose as might be derived from the diet. 



In order to translate the results of these experiments into meaningful 

 quantities, certain assumptions were made and equations were derived 

 designed to relate the change in isotope abundance as a function of 

 time to the turnover rate of glycogen. It could be shown that, if: 



i = isotope concentration in glycogen at time / 

 imax — maximal isotope concentration, achieved at t = <» 



then : 



-I tmax 



K = - In 



'■ hnux ~ 



where k is the turnover rate constant, the fraction of the total pool 

 replaced per unit time. The turnover rate, as weight of glycogen 

 replaced per unit time, could then be evaluated as the product of k 

 and the total weight of glycogen in the tissue. By this method, esti- 

 mates of a half-life of about 1 day for liver glycogen and 4 days for 

 muscle glycogen of rats were made. 



The several assumptions upon which this treatment rests include 

 the following: 



1. That the pool size remains constant over the period of observa- 

 tion; that the rates of entry into and departure from the pool be equal. 



2. That these rates in turn be constant. 



3. That each new molecule of glycogen entering the pool be enriched 

 with deuterium at the same concentration, namely, i max - 



4. That perfect mixing take place; that the deuterium concentration 

 of each molecule of glycogen leaving the pool be the same as the 

 average deuterium concentration of the pool at that time, namely, i. 



The first three of these assumptions appear to us to be entirely 

 plausible. The last assumption, however, is much more troublesome. 



