38 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



rapidly mixed with the nonradioactive phosphates of extracellular and 

 intracellular fluids, bone phosphates, etc., so that its specific activity 

 decreases with time. If plasma phosphate is the immediate precursor of 

 phospholipid, the phospholipid that is formed at the earliest intervals will 

 have a high specific activity because the specific activity of the plasma 

 phosphate is high at this time. The specific activity of the total phospho- 

 lipid phosphorus will increase, but there will be a competing process since 

 the loss of label by breakdown will also increase. At a time when the 

 specific activity of the newly formed phospholipid equals that of the phos- 

 pholipid breaking down, the tissue phospholipid will have reached its max- 

 imum specific activity. It is concluded that, at a time when the specific 

 activity of the tissue phospholipid has reached its maximum, its specific 

 activity will equsd that of the precursor. These relationships have been 

 treated mathematically and are presented in Fig. 1-8. The derivations 

 are based on the following assumptions : (a) The rate of appearance equals 

 the rate of disappearance. (6) The rates are constant during the exper- 

 iment, (c) There is only a single precursor, (d) The appearance and 

 disappearance of all molecules proceed at random; that is, the organism 

 does not distinguish between old and newly formed molecules. 



These theoretical curves provide the following criteria for decision as to 

 whether the precursor measured is the immediate precursor: The precursor 

 specific activity must exceed the substance specific activity until the latter 

 reaches its maximum, at which time the two specific activities become 

 equal. Thereafter the specific activity of the substance is greater than 

 that of the precursor. 



The turnover time can be estimated graphically (see Fig. 1-8) by 

 determining the shaded area as indicated and dividing by m, the increase 

 in specific activity of the substance between the times ^i and ^2 (68) : 



_ shaded area n Qn 



tt — (i-o4j 



ni 



It is noted that the estimation of ft from the disappearance of the label, as 

 described on page 27, is generally much simpler. 



General Considerations. The rate processes discussed up to this point 

 are essentially first-order reactions and as such are probably most widely 

 applicable. For a general mathematical treatment the reader is referred 

 to the more sophisticated papers of Branson (85, 86), Sheppard and 

 Householder (74), Hearon (87), and Reiner (88, 89). The paper of 

 Ussing (29) should be consulted for a detailed review of the use of tracers 

 in exploring the mechanism of permeability. 



The classic study of Shemin and Rittenberg (90) on the incorporation 

 of glycine into hemoglobin and the determination of the life span of the 

 red cell represents a nonexponential process that may be described nar- 



