Although these varying reactions have not yet been exhaustively studied from the kinetic point of view, owing to the experimental difficulties to which allusion has already been made, investigations have nevertheless been carried out on the effect of the variation of concentration of yeast-juice and zymin as a whole, as well as of the carbohydrate. Herzog [[1902], [1904]] has made experiments of this kind with zymin, and Euler [[1905]] with yeast-juice, whilst many of the results [p121] obtained by Buchner and by Harden and Young are also available.
The actual observations made by these authors show that the initial velocity of fermentation is almost independent of the concentration of sugar within certain limits, but decreases slowly as the concentration increases. When the velocity constant is calculated on the assumption that the reaction is monomolecular [see Bayliss, [1914], Chap. VI], approximate constancy is found for the first period of the fermentation. This method of dealing with the results is, however, as pointed out by Slator, misleading, the apparent agreement with the law of monomolecular reactions being probably due to the gradual destruction of the fermenting complex.
Experiments with low concentrations of sugar are difficult to interpret, the influence of the hydrolysis of glycogen and of dextrins on the one hand, and the synthesis of sugar to more complex carbohydrates on the other (p. [31]), having a relatively great effect on the concentration of the sugar. Unpublished experiments (Harden and Young) indicate, however, that the velocity of fermentation remains approximately constant, until a certain very low limit of sugar concentration is reached, and then falls rapidly. The fall in rate, however, only continues over a small interval of concentration, after which the velocity again becomes approximately constant and equal to the rate of autofermentation. During this last phase, as already indicated, the velocity is generally controlled by the rate of production of sugar and no longer by that of phosphate, this substance being now present in excess. In other words, the rate of fermentation of sugar by yeast-juice and zymin is not proportional to the concentration of the sugar present as required by the law of mass, but, after a certain low limit of sugar concentration, is independent of this and is actually slightly decreased by increase in the concentration of the sugar.
The relations here are very similar to those shown to exist by Duclaux [[1899]] and Adrian Brown [[1902]] for the action of invertase on cane sugar and are probably to be explained in the manner suggested by the latter. According to this investigator, the enzyme unites with the fermentable material, or as it is now termed, the substrate or zymolyte, forming a compound which only slowly decomposes so that it remains in existence for a perceptible interval of time. The rate of fermentation depends on the rate of decomposition of this compound and hence varies with its concentration. This conception leads to the result that the rate of fermentation will increase with the concentration of the substrate up to a certain limit and will then remain [p122] constant, unless interfered with by secondary actions. This limit of concentration is that at which there is just sufficient of the material in question present to combine with practically the whole of the enzyme, so that no further increase in its amount can cause a corresponding increase in the quantity of its compound with the enzyme or in the rate of fermentation which depends on the concentration of that compound.
The curve relating the rate of action of such an enzyme with the concentration of the zymolyte therefore consists of two portions, one in which the rate at any moment is proportional to the concentration of the zymolyte, according to the well-known law of the action of mass, and a second in which the rate at any moment is almost independent of that concentration, approximately equal amounts being decomposed in equal times whatever the concentration of the substrate.
The results of the experiments with yeast-juice therefore indicate that what is being measured is a typical enzyme action, but afford no information as to which of the many possible actions is the controlling one, a fact which must be ascertained for each particular case in the manner indicated above.
Clowes [[1909]], using washed zymin free from fermenting power and adding various volumes of boiled yeast extract, found that the velocity of reaction was proportional to the product of the concentrations of zymin and yeast extract up to a certain optimum concentration. He interprets these concentrations as representing the concentrations of zymase and co-enzyme, but they also represent the concentrations of hexosephosphatase (present in the zymin) and phosphate (present in the yeast extract), so that at least four factors were being altered instead of only two.
It has already been mentioned that Euler and Kullberg [[1911, 3]] found the conversion of phosphate into hexosephosphate in presence of excess of glucose to proceed according to a monomolecular reaction (p. [58]).
The rate of fermentation is diminished by dilution of the yeast-juice, but less rapidly than the concentration of the juice. Herzog found that when the relation between concentration of enzyme and the velocity constant of the reaction is expressed by the formula K1/K2 = (C1/C2)n where K1 and K2 are the velocity constants corresponding with the enzyme concentrations C1 and C2, the value for n is 2 for zymin, whilst Euler working with yeast-juice obtained values varying from 1·29 to 1·67 and decreasing as K increased.
The temperature coefficient of fermentation by zymin was found [p123] by Herzog to be K24·5°/K14·5° = 2·88, which agrees well with the value found by Slator for yeast-cells (p. [129]).