856 General Discussion 



Eout so that the inequality would be abolished. Under these condi- 

 tions there is a precise relationship between the output and input 

 potentials, as given in the figure. The potentials are equal when Ap 

 is large. 



The chemical analogue of the electrical feedback amplifier is 

 difficult to draw, as illustrated by two examples. If the voltages 

 represent the analogues of chemical concentration, the system 

 requires a chemosynthetic system as an amplifier (A) and a device 

 for expending the input chemical as a feedback network (p). Another 

 approach is to apply the formal relationship for the feedback 

 amplifier to the Michaelis-Menten equation by comparing 



E 



out 



Ein 1 + AP 



with 



P_ 1 



e 1 + K^/x 



The negative feedback system represents the Michaelis-Menten 

 system if Ap = K^^/x where, for example, A = 1/x and p = K^. 

 This appears to be an unrealistic model, for amplifier gain is equated 

 to reciprocal concentration. 



The fruitful analogue of feedback in a metabolic control system 

 is afforded by the analogue of the mass-law equations for the system 

 (Fig. IB). The inputs to this analogue are chemical concentrations, 

 E, X which are multiplied to give products of concentration (E-P)X 

 where bimolecular reactions are involved. Rates of reaction are 

 obtained from the products of the concentrations and reaction 

 velocity constants, and thereby rates of formation and rates of 

 utilization of intermediates can be specified (kiX(E-P), kgP). 

 Integration of the differences between rates of formation and rate of 

 utilization will give the chemical concentrations of the intermediate 

 (P) which may be increasing, decreasing, or steady (as in the steady 

 state); this can be subtracted by a feedback connexion to regulate 

 the amount of free enzyme available. Thus, chemical feedback in a 

 mass-law system is obtained from the integration of differences 

 between rates of formation and rates of utilization. 



Such a system bears little formal relationship to the block 

 diagram of the negative amplifier (Fig. lA). In fact, only a remote 

 resemblance is indicated by the integrator circuit itself which is a 

 type of feedback amplifier in which the feedback current is supplied 

 through a condenser. 



In summary, feedback in a chemical system is not directly com- 

 parable to the negative feedback of electronic circuitry; none of the 



