690 



14. EFFECTS OF pH ON ENZYME INHIBITION 



inflect at a pH equivalent to pA',, at high pH the slope being zero (num- 

 ber 1 in Fig. 14-10). 



When both forms of the inliibitor can combine with the enzyme (Case 

 I b), the experimentally determined K/ is given by: 



K/ = 



/ifi'fhi' 



tK, 



(14-114) 



/*// + fhi 

 Taking the logarithm of both sides and writing out the pH functions 



^K,' = \:>Ki - log [.i - log 



log 



/t + 1 + 



(14-115) 



Expressions for pA/ at low and high pH values may be derived to give: 



Low pH: pK/ = p/i, - log // + pH - pA'^ -f- log /< - pH + pA^ 



pA/ = pA, (14-116) 



High pH: pA/ = pA, - log // + pA„ - pH - pA„ + pH 

 pA,' = pA, - log fi 



(14-117) 



In the low pH range the slope will be but as the pH is increased there 

 will be either a decrease or increase to a new level of slope 0; if // is greater 

 than unity, the level will drop, and if // is less than unity, it will rise. If 

 the system is known to follow this mechanism, the value of // may be 

 calculated from the difference in pA/ at low and high pH's. The curves are 

 shown in number 10 of Fig. 14-10. 



Finally, the case in which the enzyme ionizes and the inhibition is com- 

 petitive on the active enzyme form HE (Case IV a) may be examined. By 

 the same procedures as above: 



A/ = 



(I) 



A, 



(I) + (A/ - 1)A, 

 pA,' = pA, - log (I) + log 



Low pH: pA/ = pA, 



High pH: pA/ = - log (I) - pA„ + pH 



'^'^ + w ^^ 



(14-118) 



(14-119) 



(14-120) 

 (14-121) 



Thus at low ranges of pH the slope will be but an inflection will occur 

 at pH = pA^ so that the curve in the high pH range will have a slope of 1 



