The mathematical expression for the velocity of the reaction is
dx/dt = k(a − x)
where
a = original concentration of solution
x = the quantity transformed in time t
k = coefficient of velocity of the reaction
By integrating the above equation, it may be shown that
1/t log a/a – x = k
For the experiment of J. O’Sullivan with invertase, k has a mean value of 0·0013; for Wilhelmy’s experiment with acid, k has a mean value of 0·001377.
Enzymes are produced by the living cell, with other secretions, and as a consequence are found in all plants and animals. Certain organs, however, produce enzymes in large quantities, or appear to be specially set apart for their production. In plants, the seeds are the chief seat of enzyme activity; in animals, certain glands, such as the salivary glands and the pancreas. The mucous membrane of the stomach and intestines also secrete enormous quantities.
The production of enzymes by bacteria was observed by Wortmann in 1882. It has been found that the secretion of the enzymes depends upon the composition of the nutrient medium in which the bacteria are grown. For instance, Pfeffer found that the secretion of diastase by Bacillus megatherium depended upon the amount of cane sugar in the nutrient medium. The cane sugar checked the secretion of the diastase, and the same effect was observed in the case of the common mould Penicillium glaucum. In Bacillus mesentericus vulgatus, diastase has been found to exist side by side with four other enzymes. Passini,[97] in studying the putrefactive anaerobic bacteria of the normal human intestines, succeeded in separating from B. putrificus a proteolytic enzyme filtered free from bacteria, and which caused proteolysis in media which were too acid to permit of the bacteria growing. The enzyme easily dissolved, without previous neutralization, the coagulated casein caused in milk by old coli cultures. Acid gelatin media were also liquefied by the enzyme.
From the evidence we have at present it seems probable that every variety of enzyme, hydrolysing, oxidizing, ammoniacal, etc., can be produced by bacteria.