KINETICS OF GROWTH 95 



in connection with growth factor requirements of microorganisms. The 

 mere fact that microbiological assay methods have been developed for 

 many of the known vitamins and amino acids provides convincing 

 evidence for the thesis that a single nutrient factor may determine the 

 extent of growth. However, with a very few exceptions, these contribu- 

 tions too are based upon measuring final yields rather than rates. And 

 where the latter are employed, as for example in the thiamin assay by 

 means of yeast fermentation (9), it is the metabolic, not the growth 

 rates, that are the basis for the determination. 



Before 1942 only a few investigations on the kinetics of microbial 

 growth in relation to nutrient concentration were reported. The results 

 have been well summarized by Rahn ( 10, p. 251 ) in the following state- 

 ment : 



"With increasing amounts of food, the crop, i.e. the final number of 

 cells in a culture, usually increases. 



"With a liberal supply of building material, increase of energy food 

 will cause no acceleration in growth, but a longer growth period, and, 

 therefore, a larger crop. This is limited by accumulation of fermenta- 

 tion products or of inhibiting cell secretions. 



"With all food components increasing, the crop will still be limited by 

 fermentation products or cell excretions. The law of diminishing returns 

 becomes quite evident." 



While these conclusions were based upon experiments with bacteria 

 and yeasts, they apply equally to the growth of protozoa in pure culture, 

 as was first established by Phelps (11). His studies also revealed a 

 direct proportionality between cell yield and food concentration within 

 very wide limits, a situation which, wrote Phelps, "has not yet been 

 demonstrated in the bacteria nor in most of the work on yeasts." ( 11, p. 



494). 



Two years later, however, Dagley and Hinshelwood (12) supplied 



the experimental evidence that in bacterial cultures also the rate of 

 growth is independent of the concentration of nutrient materials over 

 a wide range, while the final crop of organisms is directly proportional 

 to this concentration. The latter part of these conclusions was corrobo- 

 rated by studies on the growth of Escherichia coli in beef broth (13). 

 All of the earlier studies on the kinetics of growth in relation to 

 nutrient concentration were carried out with complex media in which 

 not one but all constituents were present in varying amounts. It was 

 only recently that Monod (7) started his investigations in a manner 

 more likely to furnish basic information. By using bacteria which can 



