VARIATION OF ENZYME INHIBITION WITH pH 705 



If the initial inhibition rate, uncomplicated by the reverse reaction, 

 can be measured, Eq. 12-16 may be rewritten as: 



i = 1 - e-^iwtu (14-127) 



and for the rate of inhibition at any time: 



^ =K -^ e-^i^h)t:u (14-128) 



at fi 



where /^ is the appropriate pH function for the inhibitor. The value of ki 

 can be determined by plotting log (1 — i) against t, since the resulting slope 

 will be — ^i(I;)/2.3/,. Therefore, k^ = k-^^lfi- It is easy to determine if 

 such a pH function is involved or whether k^ itself is changed. Let us as- 

 sume that I is the active form of a monobasic inhibitor, so that: 



^■' - TTTSW7 '"-^^«' 



which may be rewritten in logarithmic form as: 



Vk,' = p/ti + vKa - pH (14-130) 



where pA-j = — log A\, when the pH is below the pii^^, so that a plot of i[)k^' 

 against pH will, in this region, be linear with a slope of — 1 if the varia- 

 tion is due only to changes in (I). If it does not so conform, it may be sus- 

 pected that A-j varies with pH. If the rate of reversal of the inhibition can 

 be measured at different pH's, any changes in k'_i must be due to changes 

 in A;_i since the dissociation rate of the EI complex depends only on this 

 rate constant, and if k_i changes it is likely that k^ is also altered. 



When the reverse reaction (the dissociation of EI) cannot be neglected, 

 Eqs. 12-11 and 12-13 must be used with the substitution of (I,)//; for (I). 

 The value of k/ obtained from the slope of a plot of log {if — i) against t 

 will be given by: 



''' = - a^: 



but the true rate constant is: 



k,= ^^ (14-132) 



(I.) + m, 



so that now k^ does not equal fjc-i^. 



In the ionic interactions we have been considering, variations in k^ or 

 A.'_x would be due to the altered electric fields at the active center brought 

 about by changes in the pH. The activation energy for the formation of the 



