JOHN H. NORTHROP 479 



digestion.) The value of Q then (the active pepsin concentration) 

 at any moment of the reaction would be that defined by equation 

 (2) or 



vc 



The differential equation for the whole process^^ would then be 



dx 



— = kQU-x) (4) 

 at 



in which Q has the value expressed in equation (3) , and A is the active 

 concentration of substrate present at the beginning of the reaction. 

 (It seems quite probable that the active substrate concentration is 

 related to the total substrate concentration in the same way as the 

 active and total enzyme concentrations are related. This question 

 will be discussed later. For the present it is assumed that the rate 

 is proportional to the substrate concentration. At low dilutions of 

 substrate this is an experimental fact.) If this value for Q is substi- 

 tuted in equation (4) it becomes too unwieldy in the integral form to 

 use conveniently. The equation may be tested in the differential 

 form, however, by choosing a small constant value for Ax (taken as 

 10 per cent of the total change in these experiments) and determining 

 At experimentally. The reciprocal of the time necessary to cause the 

 change will then be proportional to the mean rate of reaction during 

 the first 10 per cent of the hydrolysis. This rate is of course decreas- 

 ing constantly due (1) to the decrease in substrate concentration, 

 and (2) to the decrease in the concentration of active pepsin since some 

 pepsin is removed by combination with the products of reaction. 

 The relative decrease in Q due to (1) is the same in every case and can- 

 cels out in comparative experiments, such as are considered here, 

 since the total substrate concentration is kept the same in every ex- 

 periment. The relative decrease in rate (Q) due to (2), however (as 

 may be seen from equation (2)), will not always be the same but will 

 depend to some extent on the relative values of E, d, and x. It will 

 be shown later that a 5 per cent egg albumin solution when com- 

 pletely digested contains about 10 units of peptone (Table III). The 



^^ Neglecting any effect of the reverse reaction. 



