ENEEGY SUPPLY OF THE CELL 109 



The concentration of the substrate must become very low 

 before it exerts a retarding influence because the rate 

 of fermentation is almost independent of the concentra- 

 tion of the substrate, as will be shown in the next sub- 

 chapter, p. 114. 



Some very good material on the gradual decrease of the 

 rate of fermentation we owe to Rubner (1913) . Rubner's 

 original data are expressed in calories, as he studied the 

 heat produced by yeast in sugar solutions free from 

 nitrogenous materials. Rahn (1929b) computed from 

 these data the amount of sugar fermented, and Table 

 15 shows one of these sets, where 5 gm. of yeast fermented 

 250 c.c. of sugar solution. This table shows the same 

 yeast in sucrose solutions of 20%, 10%, 5%, 2.5% and 

 1.25%. 



The retarding effect of alcohol upon the fermentation 

 can be formulated definitely. 



The simplest form would be the assumption that decrease in the 

 rate is proportional to the amount of alcohol, or that the rate is 

 proportional to the original rate decreased by a certain amount which 

 is proportional to the alcohol already present. This might be 

 written in the following way: 



Rate at any time = Initial Rate (1 — k X alcohol concentration) 



Since a fermentation comes to a stop at a fairly definite concentration, 

 which is characteristic for the organism used, the alcohol concentra- 

 tion can be best expressed in terms of this limiting concentration 

 which we will designate as L. 



Rate at any time = Initial Rate (1 j — ] 



If the alcohol concentration has reached the limiting concentration, 



the fraction — j — equals 1, and the rate of fermentation equals 



Initial Rate X (1 — 1) which is zero; the fermentation comes to a 

 stop. 



