II THE ORGANISM AS AN OPEN SYSTEM I45 



(c) Kinetics of open systems 



A simple open system is presented in Fig. i . Let there be transport of material 

 A into the system which is proportional to the difference of its concentrations 

 outside and inside the system. This material may form, in a monomolecular and 

 reversible reaction, a component B. On the other hand, A may be catabolized, 



k I ^2 



c 



Fig. I. Simple open system. See text. 



in an irreversible reaction, into C, and C may be removed from the system with a 

 rate proportional to its concentration. As can be seen from the simultaneous 

 differential equations for this system and their solution for the steady state, the 

 ratio of the concentrations of the reactants in the steady state is : 



c*A : ^-^B : c*c = I : ^1/^2 '■ hl^i (2-i) 



This model is not purely imaginary. It applies to isotope experiments where 

 turnover rate of proteins is determined (p. i48f.). Then A stands for amino acids 

 introduced into the organism; B for proteins; and C for products of excretion. 



Some interesting consequences can immediately be seen. i. The composition 

 of the system in the steady state remains constant, although the ratio of the 

 components is not based upon a chemical equilibrium of reversible reactions but 

 the reactions continue and are in part irreversible. 2. The steady-state ratio of the 

 components depends only on the system constants of reaction and transport, not 

 on the external conditions as represented by the outside concentration of A. 

 J. We find c*^ = y-iC^p^j{y.^ + k^) (c^^ = outside concentration of A). Let us 

 suppose that a disturbance from outside raises the rate of catabolism, which 

 amounts to an increase of constant A,. Then c^ must decrease. But since import 

 is proportional to the difference of the concentration of A outside and inside the 

 system, i.e. c^f^ — c^, influx must increase. Hence the system develops forces 

 directed against a disturbance of the steady state. Speaking biologically, the 

 system shows "adaptation" to changes of the environment. Speaking in the lan- 

 guage of physical chemistry, the system shows a behavior corresponding to the 

 principle of Le Chatelier. 



These, however, are the general characteristics of the self -regulation of metabolism 

 of living systems, namely, 



1. Maintenance of a constant ratio between the components which is not due 

 to an equilibrium but maintained in a steady flow of matter; 



2. Independence of the composition of the system from the varying import 

 of material, corresponding to the fact that the composition of the organism 

 remains constant even if imported nutritive materials vary; and 



3. Reestablishment of the steady state after disturbance or, biologically 

 speaking, a 'stimulus'. 



Literature p. 253 



II 



