496 KINETICS OF TRYPSIN DIGESTION 



equivalent to 5 points on the bridge. The table shows that the 

 velocity of hydrolysis increases much more slowly than the substrate 

 concentration and becomes practically independent of it in concen- 

 trations of more than 3 per cent.^ The calculated figures were ob- 

 tained by assuming that the trypsin and gelatin combined according 

 to the reaction 



trypsin + gelatin ^ trypsin — gelatin 



and that the rate of hydrolysis was proportional to the concentration 

 of the trypsin-gelatin compound. 



Applying the law of mass action to this equiUbrium we would have 



or 



ES 



K' + S 



in which E equals total amount of trypsin; C, combined trypsin ( = 

 combined gelatin) ; S, amount of gelatin; a, a proportionality factor 

 to change the units of concentration to those of rate of hydrolysis 

 K, the equihbrium constant; V, the volume of solution; and K', a 

 new constant equal to 



KV 

 a 



It will be seen that if C is considered negligibly small, compared to 

 E, as well as to S, the equation reduces to Rate = kC = KES which 

 is the ordinary form of the law of mass action. 



Evaluation of the Constants. 



Since it is assumed that the rate of hydrolysis is proportional to the amount of 

 the gelatin-trypsin compound (C) present, C is the observed velocity. 



E, the total amount of trypsin, cannot be determined directly but is taken as a 

 value slightly larger than the maximum value obtained for C, when the substrate 

 concentration is such that the hydrolysis proceeds at the maximum rate. Accord- 

 ing to the hypothesis, this maximum value is due to the fact that practically all 

 the enzyme is combined, and since C (the rate of hydrolysis) is a measure of the 

 amount combined, E must be very slightly larger. E is, therefore, an arbitrary 

 constant. After a value for E has been determined for a given amount of trypsin 

 solution, the value to be used with any other amount of trypsin will be propor- 



