Theory and Use of Tracers in Determining Transfer Rates in Biological Systems

RACERS, PARTICULARLY radioactive tracers, have made feasible many studies of transfer rates and turnover rates of substances in living systems. For example, the red cell membrane was once thought to be impermeable to sodium and potassium ions (103). The use of radioisotopes has clearly established that actually there is a continuous transfer of both sodium and potassium across the red cell membrane in both directions (63, 81, 84, 85, 92). The basis for the use of tracers in studies of this kind of process transcends such nonessential advantages as the ease or convenience of detection which are often the justification for the use of tracers; non-tracer methods cannot yield the desired information. Feasibility, however, does not imply simplicity, and deduction of transfer or turnover rates from the behavior of tracers generally requires mathematical treatment of the data. The purposes of the present article are to review what has been achieved in the exposition of the practical aspects of the mathematical basis for the interpretation of the behavior of tracers and to examine the applications which have been made in studies of transfer rates. Related studies of uptakes, volumes of distribution and metabolic paths are not considered. The references which are cited were chosen more to document and illustrate the methods of mathematical analysis than to discuss the physiological implications of the results. Some reviews, monographs and symposia on physiological fields in which studies of transfer rates with tracers have