CATALYSIS AND ENZYMES 



315 



of catalyst at the beginning and deficiency of substrate at the end ; the latter 

 fact causes diminution in rate by mass action. The rate of the reaction, as 

 measured by the amount of ester hydrolysed in unit time, must not be confused 

 with the velocity constant, which increases steadily throughout. 



The difference between true autocatalysis and the effect on enzymes described 

 above is that, in the former process, the actual quantity of the catalyst is 

 altered, positively or negatively, whereas in the latter the enzyme causes the 

 production of substances which act upon itself in a similar positive or negative 

 way, the effect increasing more and more as the reaction progresses, so that 

 the change of concentration of the catalyst is not actual but only effective. 



We may now consider the effect of different concentrations of enzyme as added 

 intentionally at the beginning of the reaction. A practical point of some import- 

 ance may appropriately be mentioned here. As Bredig points out (1902, p. 187), 

 in comparing the results of the action of enzymes under different conditions or 

 concentrations, we ought to compare the reactions at the same stage, since, in this 

 way only, can we be certain of having the same proportion of substrate and 

 products, and, moreover, if the reaction goes in stages, we should otherwise obtain 

 very false information. What we must compare, then, are the times taken to 

 effect equal changes, not the changes produced in the same time. 



In practice this is most conveniently done by taking series of measurements and plotting 

 them as curves. If amounts of change are made ordinates and time abscissae, a horizontal line 

 drawn to cut all the curves at the stage desired will give the time values required. 



What is always found, except when there is very little enzyme in proportion 

 to the substrate, or vice versa, is an obvious disproportion between the amount of 

 enzyme and its effect. This may be seen in the following table taken from an 

 experiment of my own with trypsin and caseinogen (1904). The first column 

 gives the relative amounts of the enzyme added to the same volume of substrate. 

 The second column gives the times taken by each to produce the same amount of 

 change, measured by the electrical conductivity, that is, the increase of the 

 concentration of carboxyl groups (see page 219 above). The third column gives 

 the mean rate in each case, namely, the reciprocal of the time taken (multiplied 

 by 1,000 to avoid long fractions). The fourth column gives a measure of the 

 activity of the enzyme as obtained by division of the actual rate by the amount 

 of enzyme present, or, in other words, it represents the activity of equal amounts 

 of enzyme when present in different concentrations, and may be called " specific 

 activity." 



It is obvious that the smaller quantities of enzyme are considerably more 

 effective in proportion to their concentrations than the larger ones are. Taking 

 the numerical values of enzyme concentrations 2 and 4, for example, we find that 

 the value of 4, instead of being double that of 2, is less than this. Let us suppose 

 that, instead of being multiplied by 2, it is multiplied by some root of 2, 2"*, and 

 let us see what values are to be given to x to satisfy the various data. As a first 

 approximation, try x = 2, then the value of enzyme concentration, 4, should be that 

 of concentration, 2, multiplied by 2~ 2 , that is, 12-4 x 1'4 = 17'4, instead of the 

 experimental value of 18 '2, a fairly satisfactory agreement. This is in fact the 

 rule known as the square root law of Schiitz and Borissov, but we see that it is 

 mereiy an approximation. If we take different stages of the same experiment, we 

 find, in fact, that the value of the exponent increases nearly to 2 towards the middle 

 of the reaction, but may be very nearly unity at the beginning. In this latter case 



