600 SUBSTRATE CONCENTRATION AND HYDROLYSIS 



traLion 10 S than at (substrate) concentration S. According to the 

 saturation theory, the rate of digestion in concentration 10 6" is Hmited 

 only by the concentration of enzyme while the rate at concentration 

 5 is limited both by the concentration of enzyme and by the concen- 

 tration of substrate;, hence changing the enzyme concentration should 

 have a greater effect at substrate concentration 10 5 than at substrate 

 concentration S. The experiments show that this prediction is not 

 fulfilled. The relative increase in the rate of digestion of substrate 

 at concentration S, caused by increasing the concentration of enzyme 

 from E to 10 E, is identical with the relative increase in rate of diges- 

 tion of the substrate at concentration 10 5, caused by the same increase 

 in enz3'me concentration. 



If, on the other hand, the relative decrease in rate with increase 

 in concentration of substrate is due to an equilibrium in the substrate 

 solution which causes the concentration of active molecules to differ 

 from the total concentration, the rate of hydrolysis of the substrate 

 at concentration 10 5 should be always five times the rate of digestion 

 at concentration S (in the example just discussed), irrespective of 

 the enzyme concentration. Experiments show that this is actually 

 the case. It is necessary, of course, in making such experiments to 

 be sure that the range covered is such that the enzyme cannot be 

 considered saturated in both substrate concentrations. That is, the 

 range of substrate concentrations must be such as to show nearly 

 direct proportionahty between the rate of digestion and the substrate 

 concentration in the lower, but not in the higher concentrations of 

 substrate. It is also necessary to measure the time required to cause 

 a constant change in the substrate and not a constant percentage 

 change or the change made in a given time. The failure to recognize 

 this has led to much confusion in discussion of the kinetics of enzyme 

 reactions (cf. Bredig).'' 



This is due to the fact that in most enzyme reactions the products retard the 

 action of the enzyme. It will be clear therefore (irrespective of the mechanism 

 by which this retardation takes place), that comparative results can be obtained 

 only when a constant amount of products is formed. The actual amount of 

 products formed for example by 10 per cent hydrolysis of varying substrate con- 

 centrations will be very different. The larger the concentration of substrate the 

 greater the amount of products formed by 10 per cent hydrolysis and the greater 



