138 PHYSIOLOGY OF BACTERIA 



vary for each enzyme and each chemical compound, but is constant 

 under a given set of conditions. Thus we get 



-^ = k-E(a-xKl-\-c^) 



At the same time, the deterioration of the enzyme is increased by 

 the catalyst at the rate of c"». The deterioration is given by the 

 equation 



-I = ^'(^ - ^) 



and, in the presence of the poison, or catalyst, 

 -f = k'ib -y){l + c") 



b — y is the amount of enzyme present at any given time, it is the 

 same as the expression E in the first equation. By substituting the 

 value for E from the last equation in the second, we have a mathe- 

 matical formulation which will essentially work out like the Tammann 

 principle. There appears a false optimum, shifting with time from 

 higher to lower concentrations, and an increased rate of reaction 

 immediately after the poison begins to act, followed by a more rapid 

 destruction of the enzyme, which, ultimately, leads to complete 

 inactivation. 



No data sufficiently complete to try the mathematical 

 treatment are known, but the stimulation of enzyme 

 action by poisons is known and the shifting of the 

 optimum with time from the higher to the lower concen- 

 trations of the poison has also been established in some 

 cases. A very striking one is the addition of arsenate 

 to zymase (Buchner, Buchner and Hahn). 



The respiration of mold mycelium seems to be readily 

 stimulated by chemicals. Watterson (1904) observed 

 the C02-production by Aspergillus niger to rise from 439 

 to 868.5 mg. and from 885.4 to 1,138.2 mg. by addition 

 of 0.004% of zinc sulfate to the medium. Gustafson 



