II THE ORGANISM AS AN OPEN SYSTEM I49 



which, compared with (2.2) shows that 



A= ^ ,B = g Jl^ (2.8) 



E + S P ^ ^ 



From this S and P can be calculated. Under consideration of the N content per kg tissue, r 

 (turnover rate of protein per unit body weight and day) can be calculated, giving the 

 figures of Table i . 



This is a somewhat simplified version of the model Fig. i. The equation for c^ in this 

 model is, import being assumed constant: 



da/dt = a^ — k^a + Ajj^ — ^'3^ (2-9) 



if concentrations for simplicity are written by simple letters {c^ = a etc.). 



Suppose the administered amino acid was labeled; that tracer is incorporated in the 

 body proteins and the metabolic pool in ratios a/a' and b/b' and that the supply of tracer 

 was stopped at t =0. Then the rate of disappearance of tracer will follow an equation: 



— da/dt = k^aja — k2blb' + k-^aja (2.10) 



which is identical with Sprinson and Rittenberg's expression (2.4) 



— d'KJdt = S-kjP + £X/P (2. II ) 



under the assumption that ^2 i^ small, i.e. breakdown of proteins into amino acids is 

 negligible in comparison to the other terms. 



Reiner (1953) has solved the more complete systein of simultaneous equations, the first 

 of which is (2.9) and found that, under the given conditions, the approximation is within 

 the experimental error. 



[e) Energy requirements of protein synthesis 



The synthesis of high-molecular compounds and the maintenance of the 

 organism in a steady state require energy. For this reason, even abstracting from 

 the complication of the processes in detail and taking it as an overall balance of 

 processes, an open system like Fig. i is only a partial model. It does not take into 

 account the energetics of anabolic processes which deserve consideration. 



Protein synthesis cannot be conceived of as an equilibrium reaction based upon 

 the reversal of hydrolysis of proteins into amino acids and water. For in the 

 reaction amino acids ~^ proteins + H-,0 the equilibrium is almost completely on 

 the left hand side, that is, the breakdown of proteins into amino acids. Therefore 

 it is easy to break down proteins into component amino acids by hydrolytic agents, 

 but difficult or rather at present impossible to unite amino acids into proteins 

 in vitro. 



According to G. V. Schulz (1950), the number w*^ of moles of a polymer of a 

 degree of polymerization P in equilibrium (per mole of monomer) is expressed 

 by the equation: 



© 



2.12 



with K = equilibrium constant, «„, = number of moles of water per mole of 

 monomer and polymer. K can be calculated from the enthalpy and entropy of 

 the reactions concerned. Using appropriate empirical values in equation (2.12), 

 the equilibrium concentration of proteins vs. amino acids can be calculated 

 (Table 2). Under conditions resembling those in the organism, the concentration 

 even of the dimer is very small and the appearance of higher polymers corre- 



Literature p. 253 



