148 GROWTH — • PRINCIPLES AND THEORY 2 



TABLE 1 



PROTEIN TURNOVER DETERMINED BY INTRODUCTION OF GLYCINE 

 LABELLED WITH ^^N 



After Sprinson and Rittenberg, 1949b 



Turnover Half-life time 

 rate (r) (i^/2) ^''' '^^J^ 



Rat: Total protein 



Proteins of liver, plasma and internal organs 

 Rest of body 



Man: Total protein 



Proteins of liver and serum 



Protein of musculature and other organs 



into organic compounds; these eventually are catabolized and the end-products 

 excreted. The isotope method has shown that the stream of matter which passes 

 and at the same time maintains the living organism takes place at an unexpectedly 

 high rate. Proteins, carbohydrates, lipids, and even seemingly inert material such 

 as the mineral substances of dentine and the bone, are in a continuous process 

 of degeneration and regeneration. Some estimates of turnover rates are presented 

 in Table i . Calculation of turnover rate is a special case of the kinetics of open 

 systems. 



For example, the calculation of protein turnover according to Sprinson and Rittenberg 

 (1949a, b; Table i) : Empirically it is found that the excretion of labelled N decreases ex- 

 ponentially with time: 



A£ = \A (i -e-B') (2.2) 



where A£ is the amount of ^^N (in mequiv.) excreted up to time t after an amount Xq of 

 ^^N was fed as amino acid at t =0, and A and B are constants. Theoretically, if X is the 

 amount of ^^N left in the metabolic pool at time t, it can be assumed that 



— dk = -Edt + - Sdt — Qdt (2.3) 



where P is the metabolic pool, and E, S, and Q, are coefficients for excretion, synthesis, 

 and deliverance into the metabolic pool, respectively. A^ is small compared to P and hence 

 also the change of P, Qdt, is negligible. This gives 



— dX E + S ^ , , 



= — ^— dt (2.4) 



and X = Xq e -l(E+S)IP]t (2.5) 



According to (2.3J the amount of ^^N excreted is 



X 

 P 



dlE = - Edt (2.6) 



Insertion of (2.5) and integration gives: 



X£ = Xo -^ (I - e lc£+5)//']r) (2.7) 



