212 THE HYDROLYZING ENZYMES 



The integration of this equation would lead to the relationship 



loge - - - x = kFt 



which can be shown in many instances to be the relationship which 

 actually does obtain. When x is small, however, that is, in the early 

 stages of the digestion, "a x" is nearly equal to "a;" the velocity 

 equation becomes: 



kFa 

 Velocity of hydrolysis = - 



and the integrated expression becomes: 



x = \/2kFat 



which is the Schiitz-Borissoff rule. 



The following is an instance of the applicability of these relationships: 



DIGESTION OF EGG-ALBUMIN BY PEPSIN FOLLOWED BY THE CHANGES 

 IN THE ELECTRICAL CONDUCTIVITY OF THE MIXTURE (J. SJOQVIST). 



log x 



Protein ka = ks = 



Hours. digested /y/t 



2 . . , ~ . . . 10.5 3.0 7.5 



4 . . . '. . .-:,. 16.4 3.8 8.2 



6 19.9 3.8 8.1 



8 . . . . . . . 22.7 3.8 8.0 



12 27.0 3.7 7.7 



16 ....... 30.4 3.6 7.6 



20 ...'.... 33.7 3.7 7.5 



32 . . . . . . . 40.0 3.4 7.1 



48 ........ 45.1 3.2 6.5 



64 ... . . .-. . 50.8 3.1 6.3 



96 ....... 57.4 2.8 5.9 



Both formulae give tolerably uniform values for the constants, but 

 those obtained by the complete logarithmic formula are more nearly 

 uniform than those obtained by the employment of the partial expres- 

 sion, the Schiitz-Borissoff rule. 



Whatever may be the relationship between the extent of transforma- 

 tion and the time which may chance to obtain in a given instance of an 

 enzymatic hydrolysis, one quantitative relationship remains invariably 

 true, namely, that the time required to attain a given amount of trans- 

 formation of the substrate is inversely proportional to the concentration of 

 the enzyme. There appears to be no deviation from this rule which is 

 not immediately explicable by decomposition of the enzyme or such 

 adventitious factors as fluctuation of temperature, reaction and so 

 forth. The following are instances of the applicability of this, the 

 only universal rule which has been found to govern the action of the 

 hydrolyzing enzymes : j 



