128 PHYSIOLOGY OF BACTERIA 



Integrated, this equation changes to 



KcQt = In ^ 



h - y 

 h 



b - y 

 h - y 



= ^KaQt 



KoQt 



b 



b -y = b-e-^"^^ 



The expression b — y is the amount of enzyme still active after the 

 time t, and is the same as the letter E in the first equation. 



Table 21 gives the calculated amounts of enzyme which remain 

 active after exposure to different temperatures for different times. 

 The data K^^o = 1.84 and B = 20,000 are taken from the experi- 

 mental data of Tammann. 



Substituting this value for E in the equation representing the rate 

 of enzyme action, we obtain 



— -^ = koqE{a — x) = k^qbe- ^°^'^{a — x) 



Upon integration, the amount of salicin decomposed at any time and 

 temperature is found to be 



= aLl 



e 



This expression has been used by Rahn (1915) for the computation 

 of the data in Table 22 which also gives the experimental data 

 obtained by Tammann. 



Tammann explains the disagreement between calculated and 

 measured amounts at 65°C. by the protective action of the substrate 

 upon the enzyme. The ^-values of the formula have been calculated 

 from data obtained by heating emulsin in water. In the presence 

 of salicin, the emulsin is more resistant. That is the reason why 

 the calculated amounts are a little too low, even at 45°C. The 

 principle remains unaltered by the protective action of the substrate. 



Computation of the temperature coefficients reveals Qio = 1.26 

 for enzyme action, and Q\q = 6.36 for enzyme deterioration. Raising 



