402 1SOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 15 



general integral equation given above, with n equations for the n related 

 phases. To these are added the equations for the labeled substances. The 

 form of these equations can be simplified to some extent by proper choice of 

 the experimental conditions. Thus, if the substance Mi is labeled with an 

 isotope, designated by the subscript j, and introduced into phase i, relations 

 of the form 



M%{t) = MfjFi 



are obtained, where F{ is the metabolizing function of the phase and is not 

 influenced by the particular isotopic label. In addition, if the precursor 

 of Mi is labeled with the isotopic tracer k, a set of relations are obtained in 

 the form 



MUt) = j* RiFi dd 



In each such phase (M )* k is zero since initially no labeled metabolite is 

 present and none appears until it is provided by the precursor through 

 normal processes. 



For most of the elements of biological interest, there are now available 

 several species of isotopes, e.g., H 2 and H 3 , C 13 and C 14 , and the several 

 useful isotopes of iron. While the technical difficulties often increase 

 rapidly with the multiplicity of tracers used in a single experiment, the 

 more extended field of applications open to multiple-tracer techniques in 

 complex systems should not be overlooked. The technique is still relatively 

 undeveloped, but already many instances are found where systems are 

 accessible to detailed investigation only through such techniques and, per- 

 haps as well, through more advanced mathematical treatment such as that 

 outlined above. 



REFERENCES FOR CHAP. 15 



1. Gest, H., M. D. Kamen, and J. R. Reiner: Arch. Biochem., 12, 273 (1947). 



2. Kamen, M. D.: "Radioactive Tracers in Biology," Academic Press, New York, 1947. 



3. Branson, K.:Bull. Math. Biophys., 8, 159 (1946); 9, 93 (1947). 



4. Margenau, H., and G. M. Murphy: "The Mathematics of Physics and Chemistry," 

 p. 506, D. Van Nostrand Company, Inc., New York, 1943. 



5. Webster, A. G.: "Partial Differential Equations of Mathematical Physics," p. 379, 

 G. E. Stechert & Company, New York, 1933. 



6. Zilversmit, D. B., C. Enteman, and M. C. Fishler: /. Gen. Physiol, 26, 325 (1943). 



7. Zilversmit, D. B., C. Enteman, M. C. Fishler, and I. L. Chaikoff: /. Gen. Physiol., 

 26, 333 (1943). 



