622 



HANDBOOK OF PHYSIOLOGY ^^ CIRCULATION I 



not in a steady state, but it is assumed to be introduced 

 in an amount sufficiently small not to disturb the 

 steady state of its unlabeled counterpart either by its 

 quantity, ijy the effects of its radiations, or by its 

 pharmacological effects. 



Exchange processes produce a turnover of the sub- 

 stance in a given compartment. The turnover time is 

 the time interval required for the amount of a sub- 

 stance transferred into or out of a compartment in 

 the steady state to be numerically equal to the 

 amount present in the compartment. Turnover rate 

 has been used in two senses: /) as the reciprocal of 

 the turnover time or fraction per unit time, giving 

 turnover rate the dimensions of time^'; and 2) as 

 the amount of the substance that is turned over per 

 unit time, giving turnover rate the dimensions of 

 mass/time. There being a need for both concepts, 

 several alternative terms have been suggested, such 

 as, for use in the first sense, "relative turnover rate" 

 or, for use in the second sense, "flux rate." In the 

 present discussion, use of the word rate (as in turnover 

 rate, exchange rate, transfer rate, flow rate, etc.) 

 will imply dimensions of mass/time, and the term 

 rate constant will be used when dimensions of time~^ 

 are meant. Rates will be symbolized by p"s and rate 

 constants by ^'s. 



Basic Assumptions 



KINETIC IDENTITY OF LABEL AND CARRIER. Much of 



the misunderstanding of the relationships between a 

 tracer and the material being traced is eliminated if 

 it is made clear that the assumption that the tracer 

 and the substance being traced behave identically 

 applies only at the level of the smallest recognized 

 units, usually atoms or molecules but occasionally 

 larger structures such as erythrocytes. 



Under conditions making the assumption of 

 identical behavior at the unit level valid, there will, 

 of course, remain apparent differences of behavior 

 when large populations of these units are considered. 

 This is not because the tracer is failing to trace 

 properly, but because it is capable of demonstrating 

 processes not otherwise observable. The apparent 

 difference of behavior is, in fact, one of the important 

 features making a tracer experiment of value in 

 kinetic studies. 



For example, the penetration of blood red cells 

 by radioactive potassium, K^-, when there is no ap- 

 parent movement of ordinary potassium across the 

 same mcml)rane, is logically interpreted as indicating 



that ordinary potassium likewise does move into and 

 out of the red cells. The fact that the two rates are 

 equal explains the apparently static situation, and 

 it is not necessary to ascribe any special property 

 other than detectability to the K^- atoms. 



Similarly, if giN'ing a labeled substance by mouth 

 is followed by excretion of an equal amount of the 

 substance, but by very little of the label, this shows 

 that the material excreted was not identically the 

 material ingested, and again is not attributable to 

 selective handling of the labeled form. The role of 

 tracer theory is to pro\'ide a framework whereby the 

 behavior of the tracer, which is observable, can be 

 explained in terms of the otherwise unobservable 

 patterns of behavior of the substance traced. 



Departures from the identity of behax'ior of the 

 labeled and unlabeled forms are, of course, not im- 

 possible. The isotope effect is of importance when 

 hydrogen isotopes are used because deuterium, 

 D or H'-, is about twice as heavy as ordinary hydrogen, 

 H', and tritium, T or H^, is three times as heavy, 

 atom for atom. When these isotopes are part of a 

 large molecule, however, the weights of the labeled 

 and unlabeled forms will not be greatly different, 

 relatively, and the isotope effect is generally neg- 

 ligible. A more serious departure occurs when the 

 label is assumed to be tightly bound to the substance 

 being traced, but in fact is not. Hardly anyone would 

 expect to be able to trace one constituent of an 

 ionizable substance with a label on the other ion, 

 but in organic chemistry, where it may be more diffi- 

 cult to rule out exchange reactions, more subtle 

 problems occur. The assumption of kinetic identity 

 between the label and its carrier implies an assump- 

 tion of stability of composition of the carrier. Even 

 in "simple" systems, for example in water, where the 

 rate of transfer of hydrogen ions across a membrane 

 may be quite different from the rate of transfer of 

 hydroxyl ions or of oxygen as such, such terms as 

 the transfer rate of the carrier may defy unambiguous 

 definition. 



ABSENCE OF DISTURBING EFFECTS A major advantage 

 of the radioisotopic tracers is the fact that even in 

 the case of substances which are normally present 

 only in trace quantities, the amount of tracer which 

 needs to be added to give statistically valid counting 

 rates may be so small that there is no danger that 

 the kinetics of the system will be disturbed, par- 

 ticularly if a carrier-free label is used. 



On the other hand, the use of radioisotopes intro- 

 duces a new complication, the possibility that the 



