11] STRUCTURE AND ACTIVITY OF PAPAIN 201 



complex. Km and k^ can be determined by the conventional methods 

 of estimating the initial velocity of hydrolysis over a range of substrate 

 concentrations. 



It should be recalled that the complex constant Km = (^o+^~i)/^i- It 

 has been shown for some enzymes that k^k — ^. In these cases, Kwi = 

 kajki. Our studies^ have provided considerable evidence that this is the 

 situation for papain. Therefore, by determining K,n and ätq, we can calcu- 

 late the value of k^, the velocity constant for the formation of the enzyme- 

 substrate complex. The constants have been determined over a broad pH 

 range at three temperatures for the hydrolysis of benzoyl-L-argininamide.^ 

 Let us consider only the calculated values of k^ which are shown in Fig. 8 

 as relative values arbitrarily superimposed at their maxima. It is evident 

 that all of the data have the same general form at the acid pH values but 

 the descending curves on the alkaline side have been displaced at the different 

 temperatures. 



Fig. 8. 

 ki for the 

 (9).) 



EflFect of pH on ky for the hydrolysis of benzoyl-L-argininamide. The average 

 maximum was set equal to 100 for each temperature. (From Stockell and Smith 



These data may be readily explained on the basis of the assumption that 

 the descending portions of the curves represent the titration of groups on 

 the enzyme which are essential for the k^ step. The pH corresponding to 

 kx at half of the maximal value is near pH 3-9, which would represent the 

 pK' of the group being titrated. This pK' value is consistent with that of 

 a carboxyl group. The absence of any appreciable effect of temperature on 

 this pK' value is consistent with the knowledge that the heat of ionization 

 of a carboxyl group is small. ^° 



The alkaline portions of the k-i may be interpreted in a similar manner 

 but it is apparent that the pK' of the group being titrated varies markedly 

 with temperature. The apparent heat of ionization is approximately 9-5 

 kilocal. per mole at 0°. Titratable groups present in proteins which, at first 



