SELF-REGULATORY OR FEEDBACK SYSTEMS 369 



the inhibition by histidine of the formation of compound III, an inter- 

 mediate in histidine biosynthesis (Moyed and Friedman, 1959); the inhi- 

 bition by uridine diphosi^hate of the reaction orotidylic acid -^ uridine 

 monophosphate in pyrimidine biosynthesis of rat liver (Potter and Blair, 

 1959); the inhibition of deoxycytidylate deaminase by two products sub- 

 sequent to deoxycytidylate, namely deoxyuridylate and deoxythymidy- 

 late, in rat liver (Maley and Maley, 1959); and the inhibition by trypto- 

 phan of the synthesis of its precursor, anthranilate, in Aerobacter aerogenes 

 (Doy and Pittard, 1960). An interesting situation occurs in certain mu- 

 tants of E. coli where 5-amino-4-imidazolecarboxamide riboside accumu- 

 lates because no transformylase is present (Gots and Gollub, 1959). The 

 accumulation of this compound ceases when any purine that can support 

 growth is added. The accumulation is also depressed when purine analogs 

 are added to the medium. These analogs sufficiently resemble the natural 

 purines to act as feedback inhibitors. Since these analogs may also inter- 

 fere with the metabolism in the later stages of purine nucleotide biosyn- 

 thesis, they may inhibit at two sites. An example of negative feedback on 

 enzyme synthesis is the suppression of ornithine transcarbamylase by the 

 final product arginine (Ennis and Gorini, 1959). The kinetic behavior of 

 such systems and their response to inhibition are interesting and justify 

 more than the superficial treatment presented below. 



Dependence of Rate on the Concentration of Substrate 

 A simple negative feedback system may be be represented as: 



A^B^C^D (7-53) 



where the intermediate C inhibits E^ competitively. Competitive inhibition 

 is assumed because it is likely that most feedback inhibition will be of this 

 nature, due to the structural similarity of A and C. Reaction 3 is included 

 so that (C) may be kept constant in a steady state. The individual rate 

 expressions are: 



^^(^) (7-54) 



(A) + K, 



F.(B) 



(B) + K, 



(C) + K, 



1 + ''' 



K. 



(7-55) 



(7-56) 



