26 RADIOISOTOPES IN BIOLOGY AND AGRICULTURE 



in the adult organism, in which many constituents are characterized by 

 a constancy of composition, these relative reaction rates must be equal 

 for such substances. Likewise in younger animals this situation may be 

 approximated, where the net change in concentration of a substance may 

 be small over some given time period. Theoretically, isotope techniques 

 can be used to estimate the rates of such opposing reactions, and in actual- 

 ity the validity of kinetic experiments will primarily depend upon the 

 choice of a sufficiently simple system. 



The following considerations apply only to steady-state conditions in a 

 uniformly mixed system, in other words, to situations where there is zero 

 net concentration change as a result of equal rates of formation and 

 degradation. It must be remembered that these are constant rates, in 

 contradistinction to the exponential rates discussed previously. The 

 term turnover refers to the renewal of a substance, and the term turnover 

 rate or renewal rate is used to indicate the amount of a substance renewed 

 in a given time. A useful term, turnover time, is defined as the time 

 required to renew completely the amount of substance present in the 

 tissue. The turnover rate or turnover time may perhaps be most readily 

 estimated by measurement of the rate of disappearance of the label from 

 the substance of interest. The primary advantage of this procedure is 

 that no information is rec^uired in regard to the precursor. 



This situation differs in one important respect from those cases already 

 discussed in that the label introduced disappears at an exponential rate, 

 whereas the substance is renewed at a constant rate because its concentra- 

 tion remains constant. Essentially the problem is to determine this constant 

 rate of renewal from measurements of the label concentration, which is being 

 decreased exponentially . In this treatment it is assumed that there will 

 be no significant reentry of the label into phase 1. At the risk of repeti- 

 tion, it is emphasized that in cases up to now the radiotracer and the 

 substance it labels have moved at the same rate at all times. We are now 

 considering a very important typical biological system in which the label 

 is removed but the substance it labels remains constant because of 

 replenishment. 



This system may be illustrated by the studies of Zilversmit, Chaikoff, 

 and associates (68, 69), who injected labeled plasma phosphatides into 

 the dog and calculated the amount of phosphatides removed from the 

 plasma and replaced by tissue phosphatides per unit time from the rate 

 of disappearance of the label. A schematic representation is given in 

 Fig. 1-5. 



If p = rate of disappearance of phospholipids .4 from plasma 

 A* = amount of labeled phospholipids present at time t 

 A* = amount of labeled phosphofipids present at zero time 



