EXCHANGE 
 
 ' 
 
 J9 PUlo 
 
Uniformity in Invcrtasc Action 
 
 By 
 DAVID INGERSOLL HITCHCOCK 
 
 DISSERTATION 
 
 SUBMITTED IN PARTIAL FULFILMENT OF Tim REQUIREMENTS FOR Tim 
 
 DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY 
 
 OF PURE SCIENCE, COLUMBIA UNIVERSITY 
 
 Jfotu 1 ark <Efti} 
 
 1922 
 
Uniformity in Invertase Action 
 
 By 
 DAVID INGERSOLL HITCHCOCK 
 
 DISSERTATION 
 
 SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE 
 
 DEGREE OF DOCTOR OF PHILOSOPHY IN THE FACULTY 
 
 OF PURE SCIENCE, COLUMBIA UNIVERSITY 
 
 fork ffitty 
 
 1922 
 
TO MY FATHER AND MOTHER 
 
 478726 
 
ACKNOWLEDGMENT 
 
 The author desires to express his sincere gratitude to Professor John 
 M. Nelson for his kindly direction of this work. He wishes also to thank 
 Dr. Warren C. Vosburgh for much friendly advice. 
 
 To the Harriman Research Laboratory, New York City, thanks are due 
 for financial assistance which made this work possible. 
 
 D. I. H. 
 
 LABORATORY OP ORGANIC CHEMISTRY, 
 
 COLUMBIA UNIVERSITY 
 
 AUGUST, 1921 
 
ABSTRACT OF DISSERTATION. 
 
 1 . What was attempted ? 
 
 2. How far were the attempts successful? 
 
 3. What contribution actually new to the science of Chemistry has 
 been made? 
 
 1. (a) An attempt was made to determine whether or not different 
 preparations of the enzyme invertase would cause the hydrolysis of cane 
 to proceed at correspondingly identical rates in parallel experiments. 
 
 (b) A further attempt was made to find a general expression for 
 the normal course of the hydrolysis of sucrose by invertase under varied 
 conditions of enzyme concentration, temperature, and hydrogen- ion 
 concentration. 
 
 (c) Attempts were also made to determine whether the action of 
 different invertase preparations could be modified so as to make them all 
 act alike. 
 
 2. (a) It was found that not all invertase preparations act quantita- 
 tively alike throughout the hydrolysis, a few preparations allowing the 
 reaction to become abnormally slow after the first twenty per cent of the 
 inversion. . 
 
 (6) For the normal invertase preparations it was found that the 
 hydrolysis-time curves coincided exactly if the proper amounts of inver- 
 tase were used. An empirical equation was obtained and so transformed 
 as to become generally applicable to hydrolyses in which different amounts 
 of invertase were used. It was shown that within certain limits this equa- 
 tion represented the course of the hydrolysis not only for experiments in 
 which the invertase concentration was varied, but also for experiments 
 in which the temperature and hydrogen ion concentration were varied. 
 It was also shown that this equation could be used as a criterion of normal 
 invertase action. 
 
 (c) It was found that the abnormal course of the reaction due to 
 one invertase preparation could be obviated by the addition of boiled 
 normal in\ertase or of sodium chloride, while the action of another ab- 
 normal invertase preparation was not affected by these additions. It 
 was found that a normal invertase preparation could not be rendered 
 abnormal by further dialysis or by partial inactivation by heat or by 
 ultraviolet light. 
 
 3. The new contributions made in the present work are as follows: 
 
 (a) Not all invertase preparations act identically in hydrolyzing 
 sucrose, a few being abnormal in allowing the reaction to slow up after 
 the first twenty per cent more than is the case with the normal majority 
 of invertase preparations. 
 
 (b) For the hydrolysis of sucrose by normal invertase preparations, 
 the time of reaction has for the first time been exactly expressed as a de- 
 finite function of the per cent hydrolyzed. It has been shown that this 
 function is of the same form for changes, within certain limits, in the 
 invertase concentration, temperature, and hydrogen ion concentration. 
 The equation expressing this function yields a constant which is the most 
 satisfactory measure so far proposed of the true activity of the invertase. 
 
 (c) It has been found that the abnormality of one abnormal inver- 
 tase preparation is removed by the presence of boiled normal invertase or 
 sodium chloride, while that of another is not, and also that the normal 
 invertase cannot be made abnormal either by dialysis or by the action of 
 heat or of ultraviolet light. 
 
UNIFORMITY IN INVERTASE ACTION. 
 
 I. Introduction. 
 
 The study of the nature of enzymes has developed chiefly along two 
 distinct lines. So far all attempts to isolate an enzyme as a pure substance 
 of definite chemical composition have been without satisfactory results. 
 Accordingly considerable work has been done to gain an insight into the 
 nature of the enzyme itself by studying the velocity of the reaction which 
 is catalyzed by the enzyme. The object in all these researches on the 
 chemical kinetics of enzyme action has been to find some general law gov- 
 erning the rate of the reaction, and by means of this to make deductions 
 concerning the mechanism of the action and the nature of the enzyme. 
 
 In all such work the tacit assumption has been made that any two 
 preparations of the same enzyme, if the same amount of active enzyme 
 is present, and other conditions are the same, will catalyze the reaction 
 at identical rates at corresponding points throughout. In other words, 
 if the course of the reaction were plotted, the .two curves should be super- 
 imposable. While this assumption has not been definitely stated in the 
 past, it is a necessary implication of the attempt to find a general law for 
 the rate of the catalyzed reaction. Accordingly it seemed desirable, 
 before going further in the attempt to obtain a general law for the hydrol- 
 ysis of cane sugar by the catalytic action of invertase, to find out by direct 
 experiment whether several different enzyme preparations would really 
 give the same quantitative course to the reaction. 
 
 II. Differences in Invertase Action. 
 
 In order to make this comparison, it was necessary to have all the con- 
 ditions alike except for the use of different invertase preparations. The 
 conditions adopted were a temperature of 25, an initial sucrose concen- 
 tration of 10 g. per 100 cc., and a hydrogen-ion concentration of 10~ 44 
 to 10~ 4 - 5 secured by 0.01 M buffer solution of acetic acid and sodium 
 acetate. The amounts of invertase were so adjusted in each experiment 
 that the reaction started off at the same rate. This was accomplished 
 by a few preliminary experiments, making use of the fact noted by Nelson 
 and Vosburgh, 1 that the velocity of inversion is directly proportional to 
 the concentration of the enzyme. The extent of inversion was determined 
 by the polariscopic method. That this method is justifiable has been 
 established by Vosburgh 2 
 
 1 Nelson and Vosburgh, J. Am. Chem. Soc., 39, 790 (1917). 
 
 2 Vosburgh, ibid., 43, 219 (1921). 
 
Table I contains the results of 10 experiments with 4 different invertase 
 preparations. These preparations were all obtained from yeast by modifi- 
 cations of the method of Nelson and Born. No differences in the method 
 of preparation are known which might account for the abnormality of No. 
 3. Further description of the method of preparation will be found under 
 the heading "Experimental Details." 
 
 TABLE I. 
 
 DIFFERENCES IN INVERTASE ACTION. 
 Temp., 25. Cone, of sucrose, 10 g. per 100 cc. Cone. H+, 10~ 4 ' 4 to 10 ~ 4 - 5 moles per 
 
 liter. 
 A. Normal Invertase. 
 
 Expt. 
 Invertase Preparation No. 
 Cc. of Invertase per 100 cc. 
 Initial Rotation, degrees. 
 
 Time 
 
 Bl. B2. B5. B6. 
 8. 8. 2. 2. 
 1.530. 1.530. 7.141. 7.141. 
 13.05. 13.04. 13.17.0 13.18.fl 
 
 Change in rotation, degrees. 
 
 B9. BIO. 
 
 1. 1. 
 
 6.080. 6.080. 
 13.05. 13.04 
 
 Mean 
 
 Inverted 
 
 Min. 
 
 
 
 
 
 . 
 
 
 
 
 
 % 
 
 
 5 
 
 
 
 .54 0. 
 
 54 
 
 0.53 
 
 0.54 
 
 
 
 .52 
 
 ,51 
 
 0.53 
 
 3 
 
 .15 
 
 10 
 
 1 
 
 .07 1. 
 
 07 
 
 1.07 
 
 1.07 
 
 1 
 
 .06 1 
 
 ,06 
 
 1.07 
 
 6 
 
 .35 
 
 15 
 
 1 
 
 .58 1. 
 
 59 
 
 1.58 
 
 1.59 
 
 1 
 
 .58 1 
 
 ,57 
 
 1.58 
 
 9 
 
 .38 
 
 22 
 
 2 
 
 .33 .2. 
 
 34 
 
 2.32 
 
 2.31 
 
 2 
 
 .31 2 
 
 ,31 
 
 2.32 
 
 13 
 
 .77 
 
 30 
 
 3 
 
 .12 3. 
 
 14 
 
 3.12 
 
 3.12 
 
 3 
 
 .12 3 
 
 ,12 
 
 3.12 
 
 18 
 
 .52 
 
 60 
 
 5 
 
 .97 5. 
 
 98 
 
 5.97 
 
 5.96 
 
 5 
 
 .98 5 
 
 97 
 
 5.97 
 
 35 
 
 .43 
 
 90 
 
 8 
 
 .47 8. 
 
 48 
 
 8.46 
 
 8.44 
 
 8.50 8 
 
 49 
 
 8.47 
 
 50 
 
 .27 
 
 120 
 
 10 
 
 .57 10. 
 
 59 
 
 10.55 
 
 10.54 
 
 10 
 
 .58 10, 
 
 59 
 
 10.57 
 
 62 
 
 .73 
 
 180 
 
 13 
 
 .52 13. 
 
 53 
 
 13.53 
 
 13.50 
 
 13 
 
 .55 13. 
 
 .53 
 
 13.53 
 
 80 
 
 .30 
 
 300 
 
 15 
 
 .93 15. 
 
 93 
 
 15.91 
 
 15.93 
 
 15 
 
 .93 15, 
 
 91 
 
 15.92 
 
 94 
 
 .48 
 
 2 to 4 days 
 
 16 
 
 .87 16. 
 
 86 
 
 16.85 
 
 16.87 
 
 16 
 
 .85 16 
 
 85 
 
 16.86 
 
 
 
 ... 
 
 B . Abnormal Invertase . 
 
 Expt. 
 
 Invertase Preparation No. 
 Cc. of Invertase per 100 cc. 
 Initial Rotation, degrees. 
 
 
 B12. 
 3. 
 1 . 905. 
 13.05. 
 
 
 B13. 
 3. 
 1 . 905. 
 13.05. 
 
 B14. 
 3. 
 
 1.905. 
 13.05. 
 
 
 B15. 
 3. 
 1.905. 
 13.05. 
 
 Mean. 
 
 Time. 
 
 Change in 
 
 rotation, 
 
 degrees. 
 
 Inverted 
 
 A 
 
 Min. 
 
 
 
 
 
 
 
 
 
 
 
 
 15 
 
 
 0.55 
 
 
 0.54 
 
 0.54 
 
 
 0.54 
 
 
 
 .54 
 
 3 
 
 ,20 
 
 10 
 
 
 1.07 
 
 
 1.08 
 
 1.07 
 
 
 1.07 
 
 1 
 
 .07 
 
 6 
 
 35 
 
 15 
 
 
 1.59 
 
 
 1.59 
 
 1.59 
 
 
 1.57 
 
 1 
 
 .59 
 
 9 
 
 ,44 
 
 22 
 
 
 2.30 
 
 
 2.31 
 
 2.29 
 
 
 2.30 
 
 2 
 
 .30 
 
 13 
 
 65 
 
 30 
 
 
 3.13 
 
 
 3.11 
 
 3.10 
 
 
 3.08 
 
 3 
 
 .11 
 
 18, 
 
 46 
 
 60 
 
 
 5.92 
 
 
 5.87 
 
 5.88 
 
 
 5.88 
 
 5 
 
 .89 
 
 34 
 
 96 
 
 90 
 
 
 8.33 
 
 
 8.30 
 
 8.32 
 
 
 8.31 
 
 8 
 
 .32 
 
 49, 
 
 38 
 
 120 
 
 
 10.39 
 
 
 10.34 
 
 10.36 
 
 
 10.35 
 
 10 
 
 .36 
 
 61, 
 
 48 
 
 180 
 
 
 13.27 
 
 
 13.26 
 
 13.30 
 
 
 13.28 
 
 13 
 
 .28 
 
 78. 
 
 81 
 
 300 
 
 
 15.77 
 
 
 15.73 
 
 15.78 
 
 
 15.81 
 
 15.77 
 
 93. 
 
 58 
 
 2 to 4 days 
 
 
 16.85 
 
 
 16.85 
 
 16.85 
 
 
 16.85 
 
 16 
 
 .85 
 
 
 
 The high values of these figures are due to the fact that invertase No. 2 itself 
 had an unusually high rotation. 
 
 It will be noticed that the results indicate that in 6 experiments with 
 3 different invertase preparations the invertase is acting alike throughout 
 
9 
 
 the course of the reaction. The results of the last 4 experiments, on the 
 other hand, while agreeing among themselves, do not agree well with the 
 other results beyond about the first 20% of the inversion,. This indicates 
 that invertase preparation No. 3 is in some way different from the other 
 preparations, since the latter part of the reaction is noticeably slower. 
 These results therefore show that not all preparations of invertase have, 
 under a given set of conditions, the same degree of activity. It was thought 
 at first that this retardation might be due to spontaneous destruction of 
 the enzyme. That this was not the case is shown by the results of ex- 
 periment B15, for in this case the invertase was kept in the thermostat 
 for 5 hours before the start of the reaction. It has been shown by O' Sul- 
 livan and Tompson 3 that invertase suffers spontaneous destruction less 
 rapidly in the presence of sucrose than in its absence. Since the results 
 of Expt. B15 indicate no loss in activity of the invertase in 5 hours with- 
 out the presence of sucrose, it is evident that the difference in the action 
 of invertase preparation No. 3 cannot be due to spontaneous destruction 
 of the enzyme. Table I proves, therefore, that while there seems to be 
 a normal course for invertase action, there are also exceptions or abnormal 
 invertase preparations. 
 
 III. Discussion of Equations for Invertase Action. 
 
 If a general equation for normal invertase action were available, it would 
 be comparatively easy to ascertain from experimental data whether any 
 given preparation were normal or abnormal. Nelson and Vosburgh 1 
 and others have shown that the rate of hydrolysis of cane sugar by inver- 
 tase is not proportional to the concentration of the substrate, or, in other 
 words, the reaction does not obey the unimolecular law, 
 
 1 a 
 
 *- 7 log o (1) 
 
 where k is the velocity coefficient, / time in minutes, a the initial cane 
 sugar concentration and x the amount hydrolyzed. 
 
 Henri 4 proposed an empirical equation containing only one constant. 
 
 1 a + x 
 
 k = = lo - 
 
 When this equation was applied to the results with normal invertase given 
 in Table IA, decreasing values for the constant were obtained. 
 Equations of the form 
 
 t = ki log + fax. (3) 
 
 a x 
 
 3 O'Sullivan and Tompson, J. Chem. Soc., 57, 834 (1890). 
 
 4 Henri, "Lois generates de 1'action des diastases," Hermann, Paris, 1903, p. 59. 
 
10 
 
 were deduced by Henri 5 and Bodenstein, 6 by Barendrecht, 7 Michaelis and 
 Menten, 8 and Van Slyke and Cullen. 9 On applying the method of least 
 squares to the present results (Table IA) to determine the constants for 
 an equation of this type, it was found that such an equation would not 
 hold satisfactorily for the whole course of the reaction. However, by 
 using the values obtained for the first half of the hydrolysis only, the fol- 
 lowing equation, obtained by least squares, was found to hold for the 
 first 50% of the hydrolysis. 
 
 t = 135.2 log -^- + 0.9724 p. (4) 
 
 (j(j~ p 
 
 Here t is the number of minutes required for p per cent, of the sucrose to 
 be inverted. When p is expressed in the notation of Equation 1 it is equal 
 to 100 x/a. The accuracy with which the equation fits the results may 
 be seen from the following figures. 
 
 p. t(calc.). t(obs.). p. 
 
 3.15 4.94 5 18.52 30.0 30 
 
 6.35 10.0 10 35.43 60.1 60 
 
 9.37 14.9 15 50.27 89.9 90 
 
 13.77 22.1 22 
 
 By considering the hydrolysis of sucrose as a reversible reaction, uni- 
 molecular in one direction and bimolecular in the other, Visser 10 deduced 
 an equation which, in the symbols previously used, takes the form 
 
 ^= *!(*-*)-***. (5) 
 
 eu 
 
 On applying this to his experiments he obtained increasing values for a 
 quantity which should theoretically have been constant. In order to 
 correct for this increase he introduced a factor I to which for some reason 
 he attributed a chemical significance, and called it "the intensity of the 
 enzyme," giving the equation: 
 
 ^ = [fc(a-*) -***'!/. (6) 
 
 The values of I he obtained from the increasing values of the constant 
 obtained from Equation 5, and he found they could be expressed by the 
 empirical formula 
 
 ~ 
 
 By substituting this expression in Equation 6 and integrating he obtained 
 
 5 Op. cit., p. 79. 
 
 8 Bodenstein, ibid., p. 92. 
 
 7 Barendrecht, Z. physik. Chem., 49, 456 (1904). 
 
 8 Michaelis and Menten, Biochem. Z., 49, 333 (1913). 
 
 9 Van Slyke and Cullen, /. Biol. Chem., 19, 141 (1914). 
 
 10 Visser, Z. physik. Chem., 52, 257 (1905). 
 
11 
 
 a complicated equation which gave constants satisfactory to about =*= 10%. 
 Since Hudson li has shown Visser's theory of reversibility to be unsound, 
 no attempt was made to apply this equation to the present results. 
 
 Visser also proposed a simpler equation for invertase action, obtained 
 by neglecting the reverse reaction, but putting the same factor I into the 
 unimolecular equation. 
 
 This on integration becomes 
 
 + x(fia-x) (9) 
 
 a x 
 
 Visser's application of this equation to his own experiments gave "con- 
 stants" which showed an extreme variation of 30% (0.00108 to 0.00139) 
 and an application of the same equation to the experiments of Table IA 
 likewise gave increasing values for the constant. 
 An equation of similar form, 
 
 / = ki log + hr + fe* f , (10) 
 
 a x 
 
 was obtained from the data of Table IA by the method of least squares, 
 but did not fit the experimental data well enough to be of any use in the 
 present work. 
 
 In order to get satisfactory agreement with the experimental data, it 
 was found necessary to use an equation containing four constants. The 
 following equation was obtained by applying the method of least squares 
 to the mean results of the 6 experiments in Table IA. 
 
 100 
 
 t = 222. 9 log -- |-0.5890/>-0.001975 2 -0.00002034 3 . (n) 
 
 100 p 
 
 The applicability of this equation may be seen from the following figures . 
 
 
 TABLE II. 
 
 
 
 
 APPLICATION OP EMPIRICAL 
 
 EQUATION. 
 
 
 Inversion. 
 
 P 
 
 Time, 
 /(calc.). 
 Min. 
 
 Time, 
 /(obs.). n 
 Min. 
 
 x io. a 
 
 315 
 
 4.96 
 
 5 
 
 443 
 
 6.35 
 
 10.1 
 
 10 
 
 449 
 
 9.38 
 
 14.9 
 
 15 
 
 445 
 
 13.77 
 
 22.1 
 
 22 
 
 449 
 
 18.52 
 
 30.1 
 
 30 
 
 447 
 
 35.43 
 
 60.0 
 
 60 
 
 446 
 
 50.27 
 
 89.8 
 
 90 
 
 445 
 
 62.73 
 
 119.6 
 
 120 
 
 445 
 
 80.30 
 
 180.6 
 
 180 
 
 448 
 
 94.48 
 
 299.9 
 
 300 
 
 447 
 
 
 
 Mean, 
 
 446 
 
 
 
 A. d., 
 
 0.36%. 
 
 a Meaning of n explained below. 
 
 11 Hudson, J. Am. Chem. Soc., 36, 1571 (1914). 
 
12 
 
 IV. An Equation for Experiments with Different Amounts of Invertase. 
 
 Nelson and Vosburgh 1 showed that, in their experiments in which the 
 initial sucrose concentration was constant, the time required for a given 
 percentage of sucrose to be inverted was inversely proportional to the 
 amount of invertase used. In other words, letting t represent the time 
 for 80% inversion, and y the invertase concentration, in experiments 
 in which only the invertase concentration was varied they found the pro- 
 duct ty to be constant. In another series of experiments with a different 
 invertase preparation they called t the time for 40% inversion, and here 
 again ty was constant. They did not, however, compare the times for 
 different degrees of inversion in any one experiment, say t for 40% and t 
 for 80% inversion, because they did not know the law governing the re- 
 lationship between the time and the percentage of inversion, or, mathe- 
 matically, the form of the function, t=i(p). 
 
 It is obvious that one may plot the values for the amounts hydrolyzed 
 in various times against the times, obtaining curves for the hydrolyses 
 which are graphical representations of the function, t = i(p). This was 
 done by Michaelis and Davidsohn 12 in such a way as to compare the form 
 of the function in three experiments with invertase concentrations in the 
 ratio 2:1: 0.4. They plotted the product of the enzyme concentration 
 and the time, ty, against the change in rotation, which is proportional to 
 the percentage inverted, p. They claimed that the points all fell on a 
 smooth curve, and that therefore the form of the hydrolysis curve was 
 independent of the amount of enzyme. However, only 3 experiments 
 were given of which one was represented by only 2 points. Moreover, 
 their whole curve did not appear to extend much beyond the first half of 
 the inversion, and in addition several of their points did not fall on the 
 curve, even on the small scale used in their printed article. Because of 
 these deficiencies, and because the shape of the curve is a fundamental 
 point in the present investigation, it seemed best to amplify their data 
 by the use of the more extensive experiments of Nelson and Vosburgh. 
 
 Accordingly the results of the latter were plotted in a similar way on a 
 large scale. The curves were brought together at one point by using a 
 different time scale for each experiment. When the remainder of each 
 curve was plotted on this new scale, it was found that the curves for experi- 
 ments with the same initial sucrose concentration did superimpose, falling 
 on a single smooth curve. Thus the conclusion drawn by Michaelis and 
 Davidsohn was more firmly established by the results of Expts. 6, 7, 8, 9, 
 10, 22 and 23 of Nelson and Vosburgh, each experiment including at least 
 6 samples and extending over 95% or more of the inversion. This means 
 that the function, t = f (p), representing a single experiment, can be general- 
 ized as nt = J? (p) for experiments with varying amounts of invertase^ 
 12 Michaelis and Davidsohn, Biochem. Z., 35, 386 (1911). 
 
13 
 
 Here n is a constant in any one experiment, but varies in different experi- 
 ments, being proportional to the amount of effective invertase. Moreover 
 the form of the function nt F (p) is, within the limits of these experi- 
 ments, independent of the amount of invertase or of the rate of the hy- 
 drolysis. 
 
 A more exact verification of this relationship was obtained by the use 
 of Equation 11, which gives a definite form to the function, * = f (p), for 
 one particular invertase concentration. In order to make this equation 
 generally applicable to experiments with other invertase concentrations, 
 the coefficient of the logarithmic term was placed equal to l/n and factored 
 out, giving 
 
 + 0.002642^-0. 000008860/> 2 -0.0000001034 3 ] . (12) 
 
 i 
 n 100 p 
 
 If it is generally true that the times for any given percentage of inversion 
 are inversely proportional to the amounts of invertase used, then Equa- 
 tion 12 gives a definite form to the function, t = i (p), for any invertase 
 concentration. Whether or not this is the case can be tested by substi- 
 tuting in Equation 12 the experimental values for p and /, and calculating 
 the values of n. If the latter are constant, the equation applies and the 
 general law holds, and the values of n should be directly proportional to 
 the amounts of active invertase present. 
 
 To recapitulate, we have, if this is true, first an empirical relation be- 
 tween time and percentage inverted which holds for experiments in which 
 different amounts of invertase are used; and, second, we-have in the value 
 of n a relative measure of the amount of the effective invertase. 
 
 In order to decide whether or not Equation 12 applies to a given experi- 
 ment, it is necessary to decide whether or not the values of n are constant. 
 The values of n for the experiments of Table IA, from which the equation 
 was derived, are given in the last column of Table II. The average de- 
 viation from the mean, 0.36%, is an indication of the extent to which the 
 equation fits these original experiments. To determine about what magni- 
 tude of deviation from the mean might be due to experimental error in 
 applying the equation to other experiments, the following calculations 
 were made. 
 
 From the agreement of duplicate experiments in Table I and subsequent 
 experiments, the average error in determining any change in rotation was 
 estimated as 0.02. To determine what error in n could be caused by such 
 an error, the value 0.02 was added to all the changes in rotation of Table 
 IA, and the values of n recalculated, with the results shown in Table III. 
 
 Evidently the form of the relationship is such that errors are magnified 
 in the values of n calculated from the data on the early part of the hy- 
 drolysis. Since in all the experiments of the present work except those 
 of Table I the first sample was taken at about 10% inversion, while the 
 
14 
 
 TABLE III. 
 EFFECT OF ASSUMED ERROR OP 0.02. 
 
 P + error. t. 10* (n + error). 10 8 (n true Error in Dev. from 
 
 values). 10*M. true mean. 
 
 3.26 5 458 443 15 12 
 
 6.47 10 457 449 8 11 
 
 9.50 15 450 445 5 4 
 
 13.89 22 453 449 4 7 
 
 18.64 30 450 447 3 4 
 
 35.55 60 448 446 2 2 
 
 50.39 90 . 446 445 1 
 
 62.85 120 446 445 1 
 
 80.42 180 450 448 2 4 
 
 94.60 300 450 447 3 4 
 
 Mean, 4. 4 = 0.99%. 
 
 Mean,4.8 = 1.08%. 
 
 other 7 samples were distributed about as before, it was decided that 
 a fairer measure of the average error in n would be given by the mean of 
 the last 8 of the above values. This gives an average deviation of 
 0.59% from the individual values of n, or of 0.70% from the mean value 
 of n as the deviation caused by an error of 0.02 in the value of each change 
 in rotation. Hence it may fairly be decided that any experiment giving 
 an average deviation from the mean of 0.7% or less is fitted by the equation, 
 and its curve has the same shape or the function, nt = T? (p), has the same 
 form as in the case of the original experiments of Table IA. 
 
 Since the results of Nelson and Vosburgh were available, including ex- 
 periments in which the concentration of invertase was varied, it was thought 
 that these results might well be used as a test of the general applicability 
 of Equation 12. Accordingly Table IV was prepared by using those of 
 their experiments in which the initial sucrose concentration was 10 g. per 
 100 cc. 
 
 In the last three of these experiments the average deviation from the 
 mean of the values of n is below the value 0.7%. As has been already 
 pointed out, this deviation might be caused by experimental error, and 
 accordingly the equation fits these three experiments satisfactorily. In 
 Expts. 6, 8, and 9 the first sample was taken before the inversion was 10% 
 complete. Now it has been already pointed out that in this part of the 
 inversion a small experimental error may cau^se a large error in the value 
 of n. Accordingly for these experiments the mean of the remaining values 
 of n was calculated, omitting the first, and the average deviations were 
 found to be 0.64%, 0.40%, and 0.10% for Expts. 6, 8 and 9, respectively. 
 Therefore the equation really does fit 6 of the 7 experiments in Table IV, 
 and it may be concluded with more certainty than before that the shape 
 of the hydrolysis curve or the form of the function, n = F (p), isindepend- 
 
15 
 
 TABLE IV. 
 
 EFFECT OF VARYING AMOUNTS OF INVERTASE. (EXPERIMENTS OF NELSON AND Vos- 
 
 BURGH.) 
 
 Initial sucrose concentration, 10 g. per 100 cc. Hydrogen-ion concentration, 3.2 X 
 10 ~ 5 to 2.1 X 10 ~ 6 moles per liter. Temperature, 37. Invertase preparation A 
 used in Expts. 6 to 10, Preparation B in Expts. 22 and 23. 
 
 Inv. per Time. 
 Expt. 100. /. 
 Cc. Min. 
 
 Amt. in- 
 verted, 
 P,%. 
 
 xio. 
 
 66 14 
 
 8.32 
 
 422 
 
 30 
 
 17.92 
 
 433 
 
 70 
 
 39.85 
 
 437 
 
 120 
 
 61.90 
 
 437 
 
 185 
 
 80.59 
 
 439 
 
 320 
 
 94.97 
 
 431 
 
 
 Mean, 
 
 433 
 
 Av 
 
 . dev., 1 . 
 
 04%. 
 
 8 4 20 
 
 8.31 
 
 295 
 
 45 
 
 18.69 
 
 301 
 
 105 
 
 41.17 
 
 302 
 
 175 
 
 62.11 
 
 301 
 
 265 
 
 80.09 
 
 303 
 
 450 
 
 94.85 
 
 305 
 
 
 Mean, 
 
 301 
 
 Av. 
 
 dev., 0. 
 
 73%. 
 
 10 2 50 
 
 10.01 
 
 143 
 
 100 
 
 20.14 
 
 146 
 
 221 
 
 42.09 
 
 147 
 
 315 
 
 56.10 
 
 146 
 
 345 
 
 60.04 
 
 146 
 
 570 
 
 81.60 
 
 147 
 
 1365 
 
 98.06 
 
 (131) 
 
 
 Mean, 
 
 146 
 
 Av. dev., 
 
 .57%. 
 
 23 2 14 
 
 10.34 
 
 526 
 
 28 
 
 20.49 
 
 533 
 
 60 
 
 41.81 
 
 538 
 
 100 
 
 62.62 
 
 533 
 
 156 
 
 81.70 
 
 537 
 
 280 
 
 95.70 
 
 (517) 
 
 
 Mean, 
 
 533 
 
 Inv. per 
 Expt. 100. 
 Cc. 
 
 Time Amt. in- 
 t. verted. 
 Min. p, %. 
 
 nX10. 
 
 7 5 
 
 22 
 
 11.08 
 
 360 
 
 
 40 
 
 20.15 
 
 366 
 
 
 90 
 
 43.21 
 
 372 
 
 
 138 
 
 60.98 
 
 372 
 
 
 215 
 
 80.30 
 
 375 
 
 
 373 
 
 95 '.04 
 
 370 
 
 
 
 Mean 
 
 , 369 
 
 
 Av 
 
 .dev., 1, 
 
 14%. 
 
 9 3 
 
 33 
 
 9.57 
 
 206 
 
 
 70 
 
 20.49 
 
 213 
 
 
 150 
 
 41.50 
 
 213 
 
 
 250 
 
 62.44 
 
 212 
 
 
 376 
 
 80.09 
 
 213 
 
 
 660 
 
 95.28 
 
 213 
 
 
 
 Mean 
 
 , 212 
 
 
 Av. 
 
 dev., 0. 
 
 80%. 
 
 22 1 
 
 30 
 
 10.91 
 
 259 
 
 
 60 
 
 21.50 
 
 261 
 
 
 122 
 
 41.21 
 
 260 
 
 
 200 
 
 61.49 
 
 260 
 
 
 305 
 
 79.65 
 
 260 
 
 
 600 
 
 96.08 
 
 (248) a 
 
 
 
 Mean, 
 
 260 
 
 Av. dev., 0.17%. 
 
 Av. dev., 0.60%. 
 
 a These values are for points beyond the limit of p, 95%, for which the equation 
 was derived, and hence were not used in taking the mean. 
 
 ent of the invertase concentration, and that Equation 12 gives a definite 
 form to this function, F(^). 
 
 In view of the fact that the extreme variation in the invertase concen- 
 tration in these experiments was from 6 cc. to 2 cc. or in the ratio 3:1, while 
 the range covered by the rather unsatisfactory experiments of Michaelis 
 and Davidsohn was 5 :1, it seemed best to try the effect of a wider variation 
 
16 
 
 in invertase concentration on the shape of the curve. The highest con- 
 centration used was selected so as to make the hydrolysis as rapid as possi- 
 ble without causing error in the timing of samples, and the lowest concen- 
 tration was such that the first and last samples could just conveniently 
 be taken on the same day. In view of the difficulty encountered in a pre- 
 vious investigation 13 in obtaining reproducible results with very dilute 
 invertase solutions, it seemed unwise to attempt to study slower reactions 
 than this. The results of the experiments with the extreme invertase 
 concentrations used, in the ratio 12:1, are given in Table V. 
 
 TABLE V. 
 
 EXTREME CHANGES IN INVERTASE CONCENTRATION. 
 
 Expts. B60 and B61. 
 6 cc. of Invertase 8 per 100 cc. 
 
 Expt. B62. 
 . 5 cc. of Invertase 8 per 100 cc. 
 
 Time, 
 t. 
 Min. 
 
 
 5 
 
 Rotation, 
 B60. B61. 
 Degrees. 
 
 13.09 13.09 
 11.11 11.11 
 
 Amt. 
 inverted, nXlO*. 
 P, % 
 
 11.75 168 
 
 Time. 
 t. 
 
 Min. 
 
 
 
 60 
 
 Rotation, 
 degrees. 
 
 13.04 
 11.11 
 
 Amt. 
 inverted, nX10 B . 
 P, % 
 
 11.45 
 
 136 
 
 10 
 
 9.24 
 
 9.25 
 
 22.85 
 
 167 
 
 120 
 
 9.28 
 
 22.31 
 
 136 
 
 15 
 
 7.50 
 
 7.51 
 
 33,18 
 
 166 
 
 180 
 
 7.58 
 
 32.40 
 
 135 
 
 21 
 
 5.57 
 
 5.58 
 
 44.63 
 
 166 
 
 252 
 
 5.68 
 
 43.68 
 
 135 
 
 28 
 
 3.59 
 
 3.59 
 
 56.38 
 
 165 
 
 336 
 
 3.76 
 
 55.07 
 
 134 
 
 37 
 
 1.49 
 
 1.49 
 
 68.84 
 
 166 
 
 444 
 
 1.70 
 
 67.30 
 
 133 
 
 52 
 
 -0.93 
 
 -0.94 
 
 83.26 
 
 168 
 
 624 
 
 -0.70 
 
 81.54 
 
 134 
 
 70 
 
 -2.43 
 
 -2.43 
 
 92.11 
 
 170 
 
 840 
 
 -2.26 
 
 90.80 
 
 134 
 
 1-7 days 
 
 -3.76 
 
 -3.76 
 
 Mean, 
 
 167 
 
 11 days 
 
 -3.81 
 
 Mean, 
 
 135 
 
 Av.dev., 0.75% Av. dev.,0.65% 
 
 The values of n are sufficiently constant so that the equation may be 
 said to hold for these concentrations. 
 
 If the time for any given percentage of in version is inversely proportional 
 to the concentration of invertase, the value of n divided by the number 
 of cubic centimeters of invertase used per 100 cc. of solution should be a 
 constant for any given invertase preparation. For Expts. Bl and B2 
 (Table IA) this value is 0.00292; for Vosburgh and Nelson's Expt. IB 
 (Table VI), it is 0.00290; for B60 and B61, 0.00278; and for B62, 0.00270. 
 These experiments were all made with Invertase 8. The difference be- 
 tween the former two and the latter two values is due to slow deterioration 
 of the invertase, even when kept in the ice-box, for a period of 8 months 
 had elapsed between the two sets of experiments. The smaller difference 
 between the latter two values can hardly be so explained, as the experi- 
 ments were run on successive days, but must be taken to mean that for 
 this range of concentrations the effective activity of the invertase is not 
 strictly proportional to the actual concentration used. However, since 
 the equation applies equally well in both cases, it may be stated as a fact 
 13 Nelson and Hitchcock, "The Activity of Adsorbed Invertase," J. Am. Chem. 
 Soc., 43, 1956 (1921). 
 
17 
 
 that over this range Q invertase concentrations (12: 1) the form of the 
 function, wZ = F(), is the same and is expressed by Equation 12, while 
 the value of n represents accurately the true activity of the invertase 
 even better than its relative concentration. 
 
 V. Effect of Temperature. 
 
 Since the experiments of Nelson and Vosburgh were carried out at 37 
 while the present experiments were run at 25, it seemed that the effect 
 of temperature differences in any two experiments might be constant for 
 all stages of the reaction. Inasmuch as some experiments on the course 
 of the hydrolysis at various temperatures had recently been made in this 
 
 TABLE VI. 
 
 EFFECT OF TEMPERATURE. (EXPERIMENTS OF VOSBURGH AND NELSON.) 
 Initial sucrose concentration, 10 g. per 100 cc. Hydrogen-ion concentration, 4 . 4 X 10 ~ 5 
 to 4.0 X 10 ~ 5 moles per liter. Invertase preparation No. 8, 1 cc. per 100 cc. 
 
 Expt. Temp. 
 C 
 
 Time, 
 /. 
 Min. 
 
 Amt. 
 inverted, 
 P, % 
 
 X10 5 . Expt. Temp. 
 C. 
 
 Time, 
 t. 
 Min. 
 
 Amt. 
 inverted, 
 
 nXlO 
 
 11B 15 
 
 21 
 
 5.22 
 
 175 15B 20 
 
 16 
 
 5.04 
 
 222 
 
 
 63 
 
 14.54 
 
 166 
 
 38 
 
 11.87 
 
 223 
 
 
 110 
 
 24.39 
 
 163 
 
 65 
 
 19.82 
 
 222 
 
 
 162 
 
 34.72 
 
 162 
 
 120 
 
 34.90 
 
 220 
 
 
 250 
 
 50.45 
 
 161 
 
 155 
 
 43.68 
 
 219 
 
 
 350 
 
 65.04 
 
 161 
 
 190 
 
 51.40 
 
 217 
 
 
 441 
 
 75.07 
 
 161 
 
 254 
 
 63.92 
 
 216 
 
 
 586 
 
 85.88 
 
 162 
 
 320 
 
 74.18 
 
 217 
 
 
 
 Mean, 
 
 164 
 
 420 
 
 84.87 
 
 218 
 
 
 Av, 
 
 , dev., 2.07%. 
 
 Mean, 
 
 219 
 
 
 
 
 
 Av. 
 
 dev., 0.96%. 
 
 IB 25 
 
 15 
 
 6.17 
 
 290 5B 30 
 
 9 
 
 4.93 
 
 381 
 
 
 36 
 
 14.60 
 
 292 
 
 29 
 
 15.07 
 
 374 
 
 
 63 
 
 24.80 
 
 289 
 
 50 
 
 25.22 
 
 371 
 
 
 105 
 
 39.70 
 
 290 
 
 71 
 
 35.05 
 
 373 
 
 
 165 
 
 57.39 
 
 287 
 
 107 
 
 49.79 
 
 370 
 
 
 235 
 
 73.24 
 
 289 
 
 153 
 
 65.34 
 
 370 
 
 
 360 
 
 88.84 
 
 290 
 
 190 
 
 75.07 
 
 373 
 
 
 
 Mean 
 
 , 290 
 
 246 
 
 84.93 
 
 374 
 
 
 Av 
 
 . dev., 0. 
 
 34%. 
 
 
 Mean, 
 
 373. 
 
 Av. dev., 0.60%. 
 
 7B 35 
 
 8 
 
 24 
 
 42 
 
 60 
 
 90 
 
 120 
 
 155 
 
 195 
 
 5.46 
 15.76 
 26.59 
 36.91 
 52.11 
 64.63 
 76.02 
 84.93 
 
 482 
 473 
 467 
 467 
 465 
 464 
 467 
 471 
 
 Mean, 469 
 Av. dev., 0.91%. 
 
18 
 
 laboratory by Vosburgh and Nelson, 14 it seemed inadvisable to repeat 
 this work. Accordingly the effect of temperature on the shape of the 
 hydrolysis curve was tested by applying Equation 12 to these experiments, 
 with the results shown in Table VI. 
 
 In all of these experiments the first sample was taken at a point con- 
 siderably below 10% inversion. Therefore, in order to compare the average 
 deviation with that which might be due to experimental error, the values 
 obtained from the first sample should be omitted in taking the mean. 
 If this is done the values for the average deviation are as follows: Kxpt. 
 11B, 0.68%; 15B, 0.91%; IB, 0.34%; 5B, 0.43%; and 7B, 0.56%. All 
 of these except that for Expt. 15B are less than 0.7%, and accordingly 
 Equation 12 fits these experiments fairly well. This establishes for the 
 first time the fact that temperature differences, at least between 15 and 
 35, have no effect on the shape of the hydrolysis curve or the form of 
 the function, nt = 'P (p). In other words, an increase in the temperature 
 has the same quantitative effect as an increase in the amount of the inver- 
 tase used. 
 
 VI. Effect of Hydrogen-ion Concentration. 
 
 In his classical study of the effect of hydrogen -ion concentration on in- 
 vertase action, Sorensen 15 found that the velocity coefficient k calculated 
 according to the unimolecular law in the form 
 
 1 axi 
 
 k = In 
 
 h h axz 
 
 increased considerably as the reaction progressed in nearly neutral solu- 
 tions (C H + = 10~ 6 to 10~ 7 ), increased less around the optimum (C H + = 
 10 ~ 4 to 10 ~ 5 ), remained constant in slightly more acid solutions (C H + = 
 1.2X10" 4 ), and decreased in still more acid solutions (C H + = 2.1X10~ 4 ). 
 This means that the shape of the hydrolysis curve or the form of the func- 
 tion nt = 3? (p) was not the same, in his experiments, for different hydrogen- 
 ion concentrations. Michaelis and Davidsohn 12 have pointed out that 
 this variation may be explained in part by destruction of the invertase 
 in the more acid solutions at the rather high temperature, 52, at which 
 Sorensen carried on his experiments. By using a lower temperature, 
 22.3, they obtained values of k calculated from the equation 
 
 k - i log JL 
 
 t a-x 
 
 which increased in experiments at hydrogen-ion concentrations less than 
 3.0X10" 3 , where they remained constant. Nelson and Vosburgh, 1 on 
 the other hand, found that at 37 the values of k increased in experiments 
 
 14 Vosburgh and Nelson, "The Temperature Coefficient of Invertase Action," (to 
 be published later). 
 
 15 Sorensen, ^Biochem. Z., 21, 131-304 (1909); also Compt. rend. Lab. Carlsberg, 
 8, 1 (1909). 
 
19 
 
 at the optimum hydrogen-ion concentration, 3.2X10" 6 , but increased 
 more slowly or remained constant at 3. 2X10 ~ 6 . They noticed, however, 
 that there were some changes in the hydrogen-ion concentration during 
 the latter half of the inversion at about 3.2X10" 6 . 
 
 The equation of the present work will not fit experiments in which the 
 values of the unimolecular "" are constant or decrease, because it was 
 derived for experiments for which the unimolecular '"k" increased. In 
 order to test the effect of hydrogen-ion concentration on the shape of the 
 curve the equation was applied to some recent experiments of Vosburgh 
 and Nelson (to be published later) in which the hydrogen-ion concentra- 
 tion was held constant at 10 ~ 6 moles per liter by means of citrate buffers 
 and the improved procedure recommended by Vosburgh 16 was used. 
 These results are given in Table VII. 
 
 (EXPERIMENTS OF Vos- 
 
 VII. 
 
 EFFECT OF A DIFFERENT HYDROGEN-ION CONCENTRATION. 
 
 BURGH AND NELSON.) 
 
 Initial sucrose concentration, 10 g. per 100 cc. Hydrogen-ion concentration, 1 . 10 X 10 ~ 6 
 to 1 . 13 X 10 ~ 6 moles per liter. Invertase preparation No. 8, 1 cc. per 100 cc. 
 
 Expt. Temp. 
 C. 
 
 Time, 
 t. 
 Min. 
 
 Amt. 
 inverted, 
 
 P,%. 
 
 nXlO'. 
 
 Time 
 Expt. Temp. t. 
 C. Min. 
 
 , Amt. 
 inverted, 
 P, %- 
 
 nX10. 
 
 13B 15 
 
 23 
 
 4.99 
 
 153 
 
 2B 25 30 
 
 11,10 
 
 264 
 
 
 75 
 
 15.43 
 
 148 
 
 55 
 
 19.76 
 
 261 
 
 
 126 
 
 25.34 
 
 148 
 
 80 
 
 28.13 
 
 261 
 
 
 183 
 
 35.67 
 
 148 
 
 101 
 
 34.84 
 
 260 
 
 
 282 
 
 51.57 
 
 147 
 
 138 
 
 45.58 
 
 258 
 
 
 390 
 
 65. .46 
 
 146 
 
 217 
 
 64.87 
 
 258 
 
 
 490 
 
 75.43 
 
 146 
 
 350 
 
 84.69 
 
 261 
 
 
 642 
 
 85.52 
 
 146 
 
 
 Mean, 
 
 260 
 
 
 
 Mean, 
 Av. dev., 1. 
 
 148 
 
 01%. 
 
 
 Av. dev., 
 
 .62%. 
 
 9B 35 
 
 10 
 
 5.88 
 
 415 
 
 
 
 
 
 26 
 
 15.01 
 
 415 
 
 
 
 
 
 44 
 
 24.75 
 
 413 
 
 
 
 
 
 64 
 
 35.10 
 
 414 
 
 
 
 
 
 98 
 
 50.56 
 
 412 
 
 
 
 
 
 135 
 
 64.45 
 
 411 
 
 
 
 
 
 171 
 
 74.96 
 
 413 
 
 
 
 
 
 225 
 
 85.52 
 
 416 
 
 
 
 
 
 
 Mean, 
 
 414 
 
 
 
 
 Av. dev., 0.34%. 
 
 Except for the first value in Expt. 13B, the deviation of which may be 
 due to a slight experimental error, as has been already pointed out, the 
 constancy of n is very satisfactory. This means that at a hydrogen-ion 
 concentration of 10 ~ 6 moles per liter the curve has the same shape or the 
 16 Vosburgh, "Some Errors in the Study of Invertase Action," /. Am. Chem. Soc., 
 43, 1693 (1921). 
 
20 
 
 function nt = F(p) has the same form as at the optimum hydrogen-ion 
 concentration. The differences found by Nelson and Vosburgh 1 at C H + 
 3!2X10~ 6 must be ascribed to changes in the hydrogen-ion concentration 
 or in the amount of active invertase due to the use of hydrochloric acid 
 without buffer. The nature of the buffer, however, does not seem to 
 affect the shape of the curve, for the experiments of the present work were 
 made with a 0.01 M buffer mixture of acetic acid and sodium acetate, 
 while the experiments of Vosburgh and Nelson quoted in Tables VI and 
 VII were made with a similar concentration of citric acid and sodium 
 citrate. Very recently the range for which the equation holds has been 
 extended to C H + 3.2X10" 7 by some experiments of Nelson and Bloom- 
 field (not yet published). These results mean that within the limits given 
 changes in hydrogen-ion concentration affect the activity of the invertase 
 in just the same way as changes in temperature or in the amount of in- 
 vertase used; either there is actually a change in the amount of the active 
 substance present throughout the experiment or else the activity of the 
 amount present is uniformly reduced or increased by the change and re- 
 mains constant throughout the experiment. 
 
 VII. A Criterion of Normal Invertase Action. 
 
 Above, in Part II of this paper, experiments were given which showed 
 that not all invertase preparations impart the same shape to the hydrolysis 
 curve. Equation 12 was made to fit the experiments in Table IA, made 
 with invertase preparations which were classified as normal. Accordingly 
 it seemed probable that it would not fit the experiments in Table IB, and 
 hence might be used as a means of distinguishing between normal and 
 
 TABLE VIII. 
 APPLICATION OP THE EQUATION AS A CRITERION OF NORMAL INVERTASE ACTION. 
 
 Expts. B 12-15. Expts. B17 and B18. 
 
 1 .905 cc. of Invertase 3 per 100 cc. 10.45cc. of Invertase 6 per 100 cc. 
 
 Time 
 Min. 
 
 Amt. 
 inverted, 
 
 P, % 
 
 nX10. 
 
 Time, 
 t. 
 Min. 
 
 Rotation, 
 B17. B18. 
 Degrees. 
 
 Amt. 
 inverted, 
 P.%. 
 
 nXlO*. 
 
 
 
 
 
 
 
 
 13.15 13.15 
 
 
 
 
 5 
 
 3.20 
 
 450 
 
 15 
 
 11.47 11.46 
 
 10.03 
 
 476 
 
 10 
 
 6.35 
 
 449 
 
 30 
 
 9.88 9.88 
 
 19.41 
 
 470 
 
 15 
 
 9.44 
 
 448 
 
 50 
 
 7.90 7.90 
 
 31.16 
 
 466 
 
 22 
 
 13.65 
 
 445 
 
 70 
 
 6.10 6.10 
 
 41.84 
 
 461 
 
 30 
 
 18.46 
 
 446 
 
 90 
 
 4.52 4.49 
 
 51.34 
 
 457 
 
 60 
 
 34.96 
 
 440 
 
 115 
 
 2.75 
 
 61.72 
 
 454 
 
 90 
 
 49.38 
 
 436 
 
 140 
 
 1.35 1.32 
 
 70.15 
 
 451 
 
 120 
 
 61.48 
 
 433 
 
 180 
 
 -0.36 -0.40 
 
 80.30 
 
 448 
 
 180 
 
 78.81 
 
 431 
 
 240 
 
 -1.95 -1.96 
 
 89.67 
 
 449 
 
 300 
 
 93.59 
 
 426 
 
 300 
 
 -2.74 -2.74 
 
 94.30 
 
 443 
 
 
 Mean, 
 
 440 
 
 2 to 7 days 
 
 -3.71 -3.71 
 
 Mean, 
 
 457 
 
 
 Av. dev., 1 
 
 .4%. 
 
 
 
 Av. dev., 
 
 1.9%. 
 
, 21 
 
 abnormal invertase preparations. Equation 12, therefore, was applied 
 to the results of Table IB, and also to experiments with two other invertase 
 preparations, Nos. 6 and 7, with the results shown in Table VIII. 
 
 Expts. B20 and B21. 
 3.60 cc. of Invertase 7 per 100 cc. 
 
 Time, Rotation, Amt.- 
 
 /. B20. B21. inverted, n X 10. 
 
 Min. Degrees. p, %. 
 
 13.07 13.08 
 
 15 11.47 11.47 9.55 453 
 
 30 9.89 9.91 18.87 456 
 
 50 7.94 . 7.96 30.45 454 
 
 70 6.17 6.16 41.00 451 
 
 90 4.53 4.54 50.68 450 
 
 117 2.64 2.66 61.90 448 
 
 140 1.29 1.33 69.85 448 
 
 180 -0.49 -0.43 80.36 449 
 
 240 -2.06 -2.06 89.85 452 
 
 300 -2.85 -2.81 94.42 446 
 
 2 to 7 days -3.78 -3.78 Mean, 450 
 
 Av. dev., 0.56%. - 
 
 It will be noticed in Expts. B 12-15, Table VIII, that for those points 
 where the data of Table IB coincided with those of Table I A, or up to 
 20% of the inversion, the values of n are fairly constant, even for abnormal 
 invertase. The abnormality, however, shows up later in the decreasing 
 values of n, and is indicated by the larger values of the average deviation 
 of a single value of n from the mean, which is well above 0.7% for the ex- 
 periments with Invertase 3. Expts. B17 and B18 indicate that Invertase 
 6 is also an abnormal invertase preparation, since the values of n decrease 
 and the average deviation is well above 0.7%. Invertase 7, on the other 
 hand, is a normal invertase preparation, as is shown by Expts. B20 and 
 B21, since the values of n exhibit satisfactory constancy. These experi- 
 ments indicate that Equation 12 may be used as a criterion of normal 
 invertase action. In order to decide whether invertase preparations are 
 normal or abnormal, then, it is no longer necessary to use them at initially 
 equivalent effective concentrations, but the experiments may be made with 
 any concentration, at least within the limits of the experiments in Table 
 V. If the average deviation of the values of n is under 0.7%, the invertase 
 preparation may be classified as normal; if the values of n decrease and 
 the average deviation is much over 0.7%, then the invertase preparation 
 is abnormal. 
 
 VIII. Attempts to Make the Abnormal Invertase Act Normally. 
 
 There were no known differences in the method used in obtaining the 
 normal and abnormal invertase preparations. However, it was deemed 
 advisable to find out whether the abnormality could be due to some im- 
 
22 
 
 purity which might be removed by further dialysis. Accordingly a sample 
 of Invertase 6 was dialyzed for 3 days more in a collodion bag against 
 running tap water. During the dialysis its volume was about doubled 
 and its activity decreased by about x /2 on that account ; this was designated 
 as Invertase 6B. To avoid this loss in activity, a sample of Invertase 3 
 was concentrated by evaporation in a collodion bag by fanning at room 
 temperature 17 until it had lost about half its volume, and then dialyzed 
 for 4 days, when it had regained about its original volume ; this was desig- 
 nated as Invertase 3B. The results of experiments with these dialyzed 
 preparations are given in Table IX. 
 
 TABLE IX. 
 EFFECT OF DIALYSIS ON ABNORMAL INVERTASE. 
 
 Expt. B22. 
 16 cc. of Invertase 6B per 100 cc. 
 
 Time, Amt. 
 
 inverted, 
 
 Expt. B24. 
 
 Min. 
 
 Rotation, 
 degrees. 
 
 
 
 13.10 
 
 15 
 
 11.41 
 
 30 
 
 9.78 
 
 50 
 
 7.74 
 
 70 
 
 5.89 
 
 90 
 
 4.24 
 
 115 
 
 2.53 
 
 140 
 
 1.10 
 
 180 
 
 -0.58 
 
 240 
 
 -2.08 
 
 300 
 
 -2.83 
 
 nXlO*. 
 
 Time, 
 
 t. 
 Min. 
 
 Rotation, 
 degrees. 
 
 : SB per 
 
 100 cc. 
 
 Amt. 
 
 
 averted. 
 
 nX10. 
 
 
 
 
 9.55 
 
 453 
 
 18.75 
 
 453 
 
 35.43 
 
 446 
 
 49.97 
 
 442 
 
 61.72 
 
 435 
 
 78.58 
 
 429 
 
 87.95 
 
 422 
 
 92.94 
 
 412 
 
 Mean, 
 
 437 
 
 ... 13.05 
 
 10.03 476 15 11.44 
 
 19.70 477 30 9.89 
 
 31.81 476 60 7.08 
 
 42.79 473 90 4.63 
 
 52.58 470 120 2.65 
 
 62.73 464 180 -0.19 
 
 71.22 462 240 -1.77 
 
 81.19 459 300 -2.61 
 
 90.09 456 4 days -3.80 
 
 94.54 449 Av. dev., 2.75%. 
 
 Mean, 466 
 
 Av. dev., 1.76%. 
 
 The decrease in the values of n and the large average deviations show that 
 the invertase was still abnormal.. 
 
 Since the abnormality could not be removed by purification by dialysis, 
 it was thought that it might be due to the absence of some substance con- 
 tained in the normal invertase. A sample of Invertase 8 was inactivated 
 by boiling, and was proved to be totally inactive by the absence of any 
 action on sugar solutions. Experiments were then conducted in which 
 the solutions contained 10 cc. of this inactive invertase per 100 cc. in addi- 
 tion to the abnormal invertase under investigation. The results are given 
 in Table X. 
 
 The figures in Table X indicate that the presence of boiled normal in- 
 vertase caused preparation No. 3 to act normally, giving constant values 
 of n, while it was practically without effect on preparation No. 6. This 
 apparently means that there are different kinds of abnormality in different 
 invertase preparations. 
 
 17 Kober, J. Am. Chem. Soc., 39, 944 (1917). 
 
23 
 
 TABLE X. 
 EFFECT OF BOILED NORMAL INVERTASE ON THE ACTION OF ABNORMAL INVERTASE. 
 
 
 Expt. 
 
 B25. 
 
 
 10 cc. 
 
 of boiled Invertase 8 and 
 
 1.905cc. 
 
 
 of Invertase 3 
 
 per 100 cc. 
 
 
 Time, 
 
 
 Amt. 
 
 
 
 Rotation, 
 
 inverted, 
 
 X10. 
 
 Min. 
 
 degrees. 
 
 P, % 
 
 
 
 
 13.17 
 
 
 
 . . 
 
 15 
 
 11.61 
 
 9.26 
 
 439 
 
 30 
 
 10.10 
 
 18.22 
 
 440 
 
 60 
 
 7.31 
 
 34.78 
 
 437 
 
 90 
 
 4.85 
 
 49.38 
 
 436 
 
 120 
 
 2.78 
 
 61.66 
 
 434 
 
 180 
 
 -0.19 
 
 79.29 
 
 437 
 
 240 
 
 -1.85 
 
 89.14 
 
 440 
 
 300 
 
 -2.68 
 
 94.07 
 
 437 
 
 3 days 
 
 -3.68 
 
 Mean, 437 
 
 
 
 Av. dev., 
 
 0.34%. 
 
 Expt. B26. 
 10 cc. of boiled Invertase 8 and 1 .943 cc. 
 
 
 of Invertase 3 
 
 perlOO cc. 
 
 
 Time, 
 Min. 
 
 Rotation, 
 degrees. 
 
 Amt. 
 inverted, 
 
 xio. 
 
 
 
 13.17 
 
 
 
 
 15 
 
 11. '59 
 
 9.38 
 
 445 
 
 30 
 
 10.06 
 
 18.46 
 
 446 
 
 60 
 
 7.24 
 
 35.19 
 
 443 
 
 90 
 
 4.76 
 
 49.91 
 
 441 
 
 120 
 
 2.67 
 
 62.31 
 
 441 
 
 180 
 
 -0.26 
 
 79.70 
 
 441 
 
 240 
 
 -1.91 
 
 89.50 
 
 446 
 
 300 
 
 -2.72 
 
 94.30 
 
 443 
 
 3days 
 
 -3.71 
 
 Mean 
 
 , 443 
 
 10.45 
 
 Expts. B36 and B38. 
 cc. of Invertase 6 per 100 cc. 
 
 Av. dev., 0.40%. 
 
 Expts. B35 and B37. 
 
 10 cc. of boiled Invertase 8 and 10.45 cc. 
 of Invertase 6 per 100 cc. 
 
 Time, 
 Min. 
 
 Rotation, 
 B36. B38. 
 Degrees. 
 
 Amt. 
 inverted, 
 P, % 
 
 wX10. 
 
 Time, 
 Min. 
 
 Rotation, Amt. 
 B35. B37. inverted, nX10. 
 Degrees. p, %. 
 
 
 
 13.14 
 
 13 
 
 ,13 
 
 
 
 . . . 
 
 
 
 13.25 
 
 13 
 
 .24 
 
 
 
 
 15 
 
 11.55 
 
 11 
 
 .57 
 
 9.38 
 
 445 
 
 15 
 
 11.67 
 
 11 
 
 .67 
 
 9.38 
 
 445 
 
 30 
 
 10.04 
 
 10 
 
 ,06 
 
 18.34 
 
 443 
 
 30 
 
 10.15 
 
 10 
 
 .16 
 
 18.34 
 
 443 
 
 60 
 
 7.27 
 
 7, 
 
 ,29 
 
 34.78 
 
 437 
 
 60 
 
 7.36 
 
 7 
 
 .39 
 
 34.84 
 
 438 
 
 90 
 
 4.87 
 
 4.88 
 
 49.02 
 
 432 
 
 90 
 
 4.94 
 
 4 
 
 .98 
 
 49.20 
 
 434 
 
 120 
 
 2.84 
 
 2, 
 
 .84 
 
 61.13 
 
 429 
 
 120 
 
 2.92 
 
 2 
 
 .94 
 
 61.25 
 
 430 
 
 180 
 
 -0.04 
 
 -0 
 
 06 
 
 78.28 
 
 426 
 
 180 
 
 -0.01 
 
 
 
 .04 
 
 78.52 
 
 428 
 
 240 
 
 -1.72 
 
 -1 
 
 .71 
 
 88.13 
 
 424 
 
 240 
 
 -1.67 
 
 -1 
 
 .64 
 
 88.43 
 
 429 
 
 300 
 
 -2.61 
 
 -2 
 
 59 
 
 93.41 
 
 422 
 
 300 
 
 -2.53 
 
 -2 
 
 .50 
 
 93.53 
 
 425 
 
 3-6 days, 
 
 ,-3.72 
 
 -3 
 
 .72 
 Av. 
 
 Mean 
 , dev., 1 
 
 , 433 
 
 .67%. 
 
 2-5 das. 
 
 -3.60 
 
 o 
 
 .61 
 Av. 
 
 Mean 
 dev. 1. 
 
 , 434 
 38%. 
 
 In order to show that preparation No. 3 had not become normal simply 
 on standing, but that the normal course of the reaction was really pro- 
 duced by the presence of the boiled invertase, other experiments were 
 run with Invertase 3 alone, and were found to give decreasing values of 
 n, as before. These values, however, were somewhat smaller than those 
 obtained in Expts. B12 to B15, indicating that this preparation had 
 appreciably lost activity on being kept in the ice-box for less than 5 months. 
 
 Further experiments were made with the abnormal invertase prepa- 
 rations Nos. 3 and 6 in the presence of different concentrations of sodium 
 chloride. The results are given in Table XI. 
 
 The figures in Table XI indicate that increasing concentrations of 
 sodium chloride exert an increasing retarding effect on the action of the 
 
24 
 
 TABLE XI. 
 EFFECT OF SODIUM CHLORIDE ON ABNORMAL INVERTASE. 
 
 Expt. B44. Expt. B43. 
 1 .905 cc. of Invertase 3 per 100 cc. in .02 M NaCl. 1 .905 cc. of Invertase 3 per 100 cc. 
 
 in 0.05 M NaCl. 
 
 Time, 
 /. 
 Min. 
 
 
 17 
 
 Rotation, 
 degrees. 
 
 13.05 
 11.34 
 
 Amt. 
 inverted, wXlO 8 . 
 P, % 
 
 Time, 
 
 /. 
 Min. 
 
 
 15 
 
 Rotation, 
 degrees. 
 
 13.05 
 11.54 
 
 Amt. 
 inverted, X10*. 
 
 P, % 
 
 
 8.96 424 
 
 10.15 
 
 425 
 
 30 
 
 10.08 
 
 17.63 
 
 425 
 
 30 
 
 10.12 
 
 17.39 
 
 419 
 
 60 
 
 7.38 
 
 33.65 
 
 422 
 
 60 
 
 7.44 
 
 33.29 
 
 417 
 
 90 
 
 4.99 
 
 47.83 
 
 420 
 
 90 
 
 5.08 
 
 47.30 
 
 414 
 
 120 
 
 2.99 
 
 59.70 
 
 416 
 
 120 
 
 3.03 
 
 59.47 
 
 414 
 
 180 
 
 0.00 
 
 77.45 
 
 417 
 
 180 
 
 0.05 
 
 77.15 
 
 414 
 
 240 
 
 -1.73 
 
 87.72 
 
 419 
 
 240 
 
 -1.69 
 
 1 87.48 
 
 415 
 
 300 
 
 -2.64 
 
 93.14 
 
 416 
 
 300 
 
 -2.61 
 
 92.94 
 
 412 
 
 2-3 days 
 
 -3.80 
 
 Mean, 
 
 420 
 
 2-4 days 
 
 -3.82 
 
 Mean 
 
 , 416 
 
 
 
 Av. dev., . 
 
 71%. 
 
 
 
 Av. dev., 0. 
 
 70%. 
 
 Expt. B42. 
 1 .905 cc. of Invertase 3 per 100 cc. in . 1 M NaCl. 
 
 Expt. B48. 
 
 10 .45 cc. of Invertase 6 per 100 cc. 
 in 0.1 MNaCl. 
 
 Time, 
 t. 
 Min. 
 
 Rotation, 
 degrees. 
 
 Amt. 
 inverted, 
 P,%. 
 
 HXIO'. 
 
 Time, 
 t. 
 Min. 
 
 Rotation, . 
 degrees. 
 
 Amt. 
 inverted 
 P, %. 
 
 WX10S. 
 
 
 
 13.05 
 
 'o 
 
 . . . 
 
 
 
 13.13 
 
 
 
 
 15 
 
 11.58 
 
 8.72 
 
 413 
 
 15 
 
 11.61 
 
 9.02 
 
 427 
 
 30 
 
 10.16 
 
 17.15 
 
 413 
 
 30 
 
 10.17 
 
 17.57 
 
 423 
 
 60 
 
 7.50 
 
 32.94 
 
 410 
 
 60 
 
 7.52 
 
 33.29 
 
 417 
 
 90 
 
 5.14 
 
 46.94 
 
 410 
 
 90 
 
 5.19 
 
 47.12 
 
 412 
 
 120 
 
 3.13 
 
 58.87 
 
 408 - 
 
 123 
 
 3.02 
 
 60.00 
 
 408 
 
 180 
 
 0.14 
 
 76.62 
 
 408 
 
 165 
 
 0.86 
 
 72.82 
 
 407 
 
 240 
 
 -1.66 
 
 87.30 
 
 413 
 
 225 
 
 -1.17 
 
 84.87 
 
 408 
 
 300 
 
 -2.59 
 
 92.82 
 
 410 
 
 300 
 
 -2.47 
 
 92.58 
 
 405 
 
 3 days 
 
 -3.84 
 
 Mean, 
 
 411 
 
 3-6 days 
 
 -3.75 
 
 Mean 
 
 , 414 
 
 Av. dev., 0.46%. 
 
 Av. dev., 1.67%. 
 
 invertase. This was not observed in the work of Fales and Nelson 18 at 
 the optimum hydrogen-ion concentration, but this may be due to the fact 
 that they worked with a very much smaller sugar concentration, 0.5 g. 
 per 100 cc. This retardation, however, seems to have more effect at the 
 beginning of the hydrolysis than at the end in the case of Invertase 3, for 
 in Expt. B42, with 0.1 M sodium chloride, the values of n were constant 
 and the action must be classed as that of normal invertase. Invertase 6, 
 however, was not made normal by 0.1 M sodium chloride, for in Expt. 
 B48 the values of n decreased as much as ever. An experiment with 
 0.5 M sodium chloride and Invertase 6 gave values which decreased some- 
 what less, but still were not constant enough for the action to be regarded 
 
 18 Fales and Nelson, J. Am. Chem. Soc., 37, 2769 (1915). 
 
25 
 
 as normal. Unfortunately the supply of Invertase 6 became too low for 
 further experiments to be carried out with it. 
 
 Further experiments were made with Invertase 3 to determine the effect 
 of invertase concentration on the abnormal action. The results are given 
 in Table XII. 
 
 TABLE XII. 
 ABNORMAL INVERTASE AT DIFFERENT CONCENTRATIONS. 
 
 Expts. B58 and B59. 
 .5 cc. of Invertase 3 per 100 cc. 
 
 Expts. B54 and B55. 
 3 cc. of Invertase 3 per 100 cc. 
 
 Time, 
 /. 
 Min. 
 
 Rotation, Amt. 
 B58. B59. inverted, nXlQ 6 . 
 Degrees. p, %. 
 
 Time, 
 Min. 
 
 Rotation, 
 B54. B55. 
 Degrees. 
 
 Amt. 
 inverted, 
 P, %. 
 
 xio. 
 
 
 
 13 
 
 .05 
 
 13.05 
 
 
 
 
 . . . 
 
 ' 
 
 13.06 
 
 13.06 
 
 
 
 
 60 
 
 11 
 
 .53 
 
 11.51 
 
 9 
 
 .08 
 
 108 
 
 10 
 
 11.46 
 
 11.48 
 
 9.44 
 
 671 
 
 120 
 
 10 
 
 .06 
 
 10.05 
 
 17 
 
 .80 
 
 107 
 
 20 
 
 9.96 
 
 9.98 
 
 18.34 
 
 664 
 
 195 
 
 8 
 
 .35 
 
 8.33 
 
 27 
 
 .95 
 
 106 
 
 30 
 
 8.52 
 
 8.55 
 
 26.88 
 
 662 
 
 270 
 
 6 
 
 .72 
 
 6.77 
 
 37 
 
 .45 
 
 106 
 
 45 
 
 6.50 
 
 6.53 
 
 38.87 
 
 660 
 
 360 
 
 5 
 
 .06 
 
 5.06 
 
 47 
 
 .42 
 
 104 
 
 70 
 
 3.62 
 
 3.67 
 
 55.91 
 
 654 
 
 450 
 
 3 
 
 .50 
 
 3.54 
 
 56 
 
 .56 
 
 103 
 
 100 
 
 0.98 
 
 
 71.69 
 
 654 
 
 540 
 
 2 
 
 .22 
 
 2.20 
 
 64 
 
 .33 
 
 102 
 
 120 
 
 -0.29 
 
 -0.28 
 
 79.23 
 
 654 
 
 1101 
 
 -1. 
 
 96 
 
 .... 
 
 89 
 
 .08 
 
 96 
 
 150 
 
 -1.62 
 
 -1.62 
 
 87.12 
 
 656 
 
 7 to 12 
 
 Mean, 
 
 104 
 
 3 to 8 
 
 
 
 Mean, 
 
 659 
 
 days 
 
 -3 
 
 .79 
 
 -3.79 
 
 Av. 
 
 dev., 
 
 2.7% 
 
 days 
 
 -3.79 
 
 -3.79 
 
 Av. dev., 
 
 .74%. 
 
 Time, 
 
 
 f t 
 
 B56. 
 
 Min. 
 
 
 
 
 13.12 
 
 6 
 
 11.21 
 
 12 
 
 9.40 
 
 18 
 
 7.72 
 
 26 
 
 5.66 
 
 35 
 
 3.62 
 
 48 
 
 1.25 
 
 65 
 
 -0.88 
 
 85 
 
 -2.26 
 
 4 to 5 days 
 
 -3.75 
 
 Expts. B56 and B57. 
 6 cc. of Invertase 3 per 100 cc. 
 
 Rotation, 
 
 Degrees. 
 
 B57. 
 
 Amt. 
 inverted, 
 
 MX10. 
 
 13.12 
 
 11.23 11.28 134 
 
 9.43 22.02 134 
 
 7.72 32.05 133 
 
 5.66 44.27 133 
 
 3.62 56.38 132 
 
 1.30 70.33 132 
 
 -0.84 82.97 134 
 
 91 .28 135 
 
 -3.74 Mean, 133 
 
 Av. dev., 0.67%. 
 
 These results show that in the case of Invertase 3 the abnormality decreases 
 with increasing amount of invertase or increases with decreasing amount 
 of invertase or increasing time of reaction. 
 
 It is not possible to explain these changes in the abnormality of Inver- 
 tase 3 at the present time. 
 
 IX. Attempts to Make Normal Invertase Become Abnormal. 
 
 Since the presence of sodium chloride had seemed to some extent to 
 favor the normal course of invertase action, it seemed worth while to find 
 out whether further dialysis, by removing any last traces of salt, could 
 
26 
 
 make a specimen of normal invertase act abnormally. Accordingly a 
 sample of Invertase 8 was dialyzed for a week in a collodion bag against 
 8 changes of distilled water. This was designated as Invertase 8A, and 
 when tested was found to be still normal, as is shown by the results in 
 Table XIII, Expt. B46. 
 
 Another sample of Invertase 8 was partially inactivated by heating for 
 1 hour on a water-bath at 50, and then for l /z hour more at about 57. 
 This reduced its activity by about one-half. This invertase, No. 8E, 
 was also found to be still normal, as is shown by Expts. B50 and B51, 
 Table XII. 
 
 ' A further attempt to render Invertase 8 abnormal was made by ex- 
 posing some of it for 2 hours, in a quartz flask, to the ultraviolet and other 
 radiation given by a mercury arc lamp. The result, Invertase 8F, had 
 about one-half the activity of Invertase 8, but was also found to be still 
 normal, as is shown by Expts. B52 and B53, Table XIII. 
 
 TABUS XIII. 
 
 ACTION OF NORMAL INVERTASE AFTER FURTHER DIALYSIS, HEATING, AND EXPOSURE 
 
 TO THE MERCURY ARC. 
 
 Expt. B46. 
 Invertase 8A, dialysed, 5 cc. per 100 cc. 
 
 Time, Amt. 
 t. Rotation, inverted, nX10 e . 
 Min. Degrees. p, %. 
 
 13.06 
 
 Expts. B50 and B51. 
 Invertase 8E, heated, 5 cc. per 100 cc. 
 
 Time, Rotation, Amt. 
 /. B50. B51. inverted nX10. 
 Min. Degrees. p, %. 
 
 13.10 13.10 
 
 15 
 
 11.27 
 
 10.62 505 
 
 15 10.94 10.94 12.82 
 
 612 
 
 30 
 
 9.56 
 
 20.77 504 
 
 30 8.88 8.89 25.04 
 
 614 
 
 60 
 
 6.44 
 
 39.29 501 
 
 50 6.37 6.38 39.94 
 
 612 
 
 90 
 
 3.78 
 
 55.07 499 
 
 70 4.18 4.19 52.94 
 
 610 
 
 120 
 
 1.66 
 
 67.66 497 
 
 90 2.30 2.35 63.98 
 
 610 
 
 180 
 
 -1.14 
 
 84.27 501 
 
 110 0.79 0.84 72.94 
 
 612 
 
 230 
 
 -2.34 
 
 91.39 502 
 
 140 -0.87 -0.85 82.85 
 
 618 
 
 270 
 
 -2.87 
 
 94.54 499 
 
 180 -2.20 -2.18 90.74 
 
 624 
 
 3 days 
 
 -3.79 
 
 Mean, 501 
 
 2-5 days -3.78 -3.78 Mean, 614 
 
 
 
 Av. dev., 0.40%. 
 
 Av. dev., 
 
 0.57%. 
 
 
 
 Expts. 
 
 B52 and B53. 
 
 
 Invertase 8F, exposed to mercury arc, 5 cc. per 100 cc. 
 
 
 Time, 
 
 Rotation, 
 
 Amt. 
 
 
 
 /. 
 
 B52. 
 
 B53. inverted, nXlO*. 
 
 
 
 Min. 
 
 Degrees. 
 
 P, % 
 
 
 
 
 
 13.09 
 
 13.09 
 
 
 
 15 
 
 10.33 
 
 10.35 16.32 785 
 
 
 
 25 
 
 8.61 
 
 8.63 26.53 783 
 
 
 
 35 
 
 6.99 
 
 7.04 36.08 781 
 
 
 
 45 
 
 5.51 
 
 5.53 44.92 779 
 
 
 
 65 
 
 2.93 
 
 2.99 60.12 775 
 
 
 
 85 
 
 0.94 
 
 0.97 "72.05 776 
 
 
 
 105 
 
 -0.54 
 
 -0.53 80.89 781 
 
 
 
 140 
 
 -2.12 
 
 -2.12 90.27 787 
 
 
 1 to 3 days 
 
 3.77 
 
 3 80 Mean, 781 
 
 
 
 
 Av. dev., 0.38%. 
 
 
27 
 
 Since the values of n in Table XIII are constant in each experiment, 
 having an average deviation from the mean in each case of less than 0.7%, 
 the results show that the invertase was still acting normally. Hence it 
 may be concluded that it is not possible by any of these three methods 
 of treatment to render a normal invertase preparation abnormal. 
 
 X. Experimental Details. 
 
 Preparation of materials. The invertase used was all obtained from 
 yeast by the method of Nelson and Born, 19 with slight modifications as 
 described below. Preparations 6 and 7 had been made by previous workers 
 in this laboratory and had been kept for several years in solution, saturated 
 with toluene, in an ice-box. Preparations 1, 2 and 3 were made from 
 yeast which had been permitted to autolyze for about a month and then 
 filtered, and the filtrate had been treated with toluene and kept in stoppered 
 bottles at room temperature for three years or more. During this time 
 more solid matter had separated, and this was filtered off and the filtrate 
 treated according to the method described by Nelson and Born 19 with the 
 following modifications. Only one precipitation with alcohol was used 
 and the kaolin treatment was omitted. After treatment with lead acetate 
 and potassium oxalate, the filtrate was dialyzed for from 4 to 6 days in 
 collodion bags against running tap water. The solutions become colorless 
 and nearly clear during the dialysis. The dialyzed solutions were not 
 precipitated again, but were preserved with toluene and kept in the ice-box 
 until needed for the experiments. Preparation No. 8 was prepared by 
 the same method from a new lot of 100 pounds of pressed yeast. 2Q The 
 preparation of Invertase No. 2 was carried out by Nelson and Simons, 21 
 who modified the treatment further by nearly neutralizing the solution 
 with ammonia before the alcohol precipitation. No differences in the 
 method of preparation are known which might account for the abnor- 
 mality of invertase preparations Nos. 3 and 6. 
 
 Two lots of sucrose were used. In each case the starting point was the best com- 
 mercial sugar, which was dissolved in distilled water and clarified with charcoal. The 
 first lot was precipitated by alcohol by the method of Cohen and Commelin. 22 Its 
 rotation was found to agree within 0.1% with that calculated from the formulas of 
 Landolt and Schonrock. 23 The second lot was recrystallized from water by a procedure 
 similar to that of Bates and Jackson. 24 Its rotation agreed with the calculated value 
 within 0.04%. 
 
 Other chemicals were c. p. grades, used without further purification. 
 
 19 Nelson and Born, J. Am. Chem. Soc., 36, 393 (1914). 
 
 20 Kindly furnished by the Jacob Ruppert Brewery of New York City. 
 
 21 Simons, Dissertation, Columbia University, 1921; Nelson and Simons, J. Am. 
 Chem. Soc., (to be published later). 
 
 22 Cohen and Commelin, Z. physik. Chem., 64, 29 (1908). 
 
 23 Browne, "A Handbook of Sugar Analysis," John Wiley and Sons, New York, 
 1912, pp. 177-8. 
 
 24 Bates and Jackson, Bur. of Standards Sci. Papers, No. 268, 75 (1916). 
 
28 
 
 Apparatus. Constant temperature was obtained by the use of an 
 electrically controlled water-bath which remained at 25 0.01. 
 
 The progress of the inversion was followed by means of a Schmidt and 
 Haensch polarimeter reading to 0.01. The tubes used were 200 mm. 
 long, and were proved to be of the same length by observing the rotation 
 of the same 10% sugar solution in each tube. The temperature of the 
 tubes was kept constant by the. thermostat described by Nelson and 
 Beegle, 25 which maintained a temperature of 25 0.05. 
 
 Monochromatic light of wave length 546.1 /*// was obtained from a 
 mercury vapor arc by purification through two Wratten filters, one a 
 No. 77, and the other a No. 77 which had been re-cemented with a green 
 film in place of the yellow one. Thanks are due to Dr. C. B. K. Mees of 
 the Eastman Kodak Company for preparing these filters. This light 
 made it possible to use the polariscope with a half -shadow angle of 0.5. 
 
 Nonsol bottles were used to contain the solutions undergoing hydrolysis. 
 All volumetric apparatus used in making up solutions was calibrated. 
 
 Control of the Hydrogen-ion Concentration. The desired hydrogen-ion 
 concentration was obtained by the use of a buffer mixture of 0.1 M acetic 
 acid and 0.1 M sodium acetate in the proportions given by Michaelis. 26 
 One hundred cc. of the final solution always contained 10 cc. of this buffer, 
 making the total concentration 0.01 M. This concentration was low 
 enough so that any salt effect on the invertase action was negligible, espec- 
 ially at the optimum hydrogen-ion concentration. 18 In the experiments 
 of Nelson and Vosburgh 1 the desired hydrogen-ion concentration was 
 obtained by the use of diluted hydrochloric acid. In the experiments of 
 Vosburgh and Nelson 14 a buffer of citric acid and secondary sodium citrate 
 was used at a total citrate concentration of 0.01 M. 
 
 The hydrogen-ion concentration was measured during or after each 
 inversion by the colorimetric method of Sorensen, 15 using a-naphthyl- 
 amino-azo-^-benzene sulfonic acid as indicator with citrate standards. 
 The latter were standardized electrometrically with the hydrogen electrode 
 and the saturated potassium chloride calomel cell 27 using a salt bridge of 
 saturated potassium chloride solution. The hydrogen-ion concentrations 
 were based on 0.1000 M hydrochloric acid as a standard, its ionization 28 
 being taken as 92.04% at 25, the temperature at which the present deter- 
 minations were made. 
 
 Procedure. In general the procedure followed was that recommended 
 by Vosburgh. 16 Duplicate experiments were run on different days with 
 freshly prepared sugar solutions. A solution was made up containing 
 
 25 Nelson and Beegle, /. Am. Chem. Soc., 41, 559 (1919). 
 
 26 Michaelis, "Die Wasserstoffionenkonzentration," Springer, Berlin, 1914, p. 184. 
 
 27 Kales and Mudge, /. Am. Chem. Soc., 42, 2434 (1920). 
 28 Fales and Vosburgh, ibid., 40, 1295 (1918). 
 
29 
 
 sucrose and buffer in such concentrations that when a certain volume of 
 this had been measured out it would be possible to add from a pipet a 
 round number of cubic centimeters of invertase to start the reaction. For ex- 
 ample, in Bxpt. Bl 32.680 g. of sucrose and 32.68 cc. of buffer were diluted to 
 500 cc. at 25 . Of this solution 321.80 cc. was pipetted into a Nonsol bottle, 
 and 5 cc. of invertase was added to start the reaction. This produced 
 the initial concentrations given in Table I A. The solutions were stirred 
 by a current of filtered air while being mixed, and. samples were taken 
 by pipets delivering in 10 seconds or less. 21 The time of mixing or of 
 sampling was taken as the mean time of delivery of the pipet used. The 
 reaction was stopped and mutarotation hastened by the use of sodium 
 carbonate as recommended by Hudson, 29 a 25cc. sample being added to 
 5 cc. of 0.1 M sodium carbonate solution. The initial rotation of each 
 solution was determined by preparing samples of identical composition 
 in which the sodium carbonate was added to the sugar before the addition 
 of the invertase, thus rendering the invertase entirely inactive. The 
 rotation of each solution was determined by taking the mean of at least 
 four concordant readings, the tube being rotated slightly after each reading 
 to ensure the detection of any strain in the cover glasses. 30 The zero point 
 of the polariscope was similarly determined by the use of a tube filled with 
 distilled water. The final rotations were obtained by taking samples 2 
 days or more after the start of the reaction. Samples taken on the second 
 and third days usually had the same rotation. In calculating the per- 
 centage inverted, the total change in rotation was always taken as 16.85, 
 since this value was obtained in all the experiments of Vosburgh and 
 Nelson 14 as well as in the majority of the present experiments. 
 
 Since in several experiments the total change in rotation appeared to 
 be a few hundredths of a degree more than 16.85, it was thought ad- 
 visable to test the effect of such differences on the values of n as obtained 
 by the use of Equation 12. A sample calculation was made for Expt. 
 B46, Table XIII, with the following results. 
 
 Using 16.85, Using 16.89, 
 
 nX10. nXlO*. 
 
 505 501 504 498 
 
 504 502 503 497 
 
 501 499 500 492 
 
 499 Mean, 501 497 Mean, 498 
 
 497 Av.dev.,0.40% 495 Av. dev.,0.60%. 
 
 These results show that an error of 0.04 in determining the total change 
 in rotation could not have caused sufficient error in the values of n to make 
 a normal invertase preparation appear abnormal. Since this was the 
 
 29 Hudson, /. Am. Chem. Soc., 30, 1564 (1908). 
 80 Browne, Ref. 23, p. 156. 
 
30 
 
 extreme deviation noticed from the value 16.85, the procedure adopted 
 of taking the total change as 16.85 in all calculations is quite justified. 
 A calculation of the possible error in determining the rotation of any 
 sample which might be due to errors in the various measurements of weight 
 and volume involved in this procedure has been made by Messrs. G. Bloom- 
 field and F. Hollander of this laboratory. Using estimates of these errors 
 based on the present authors' calibrations, this calculation gave a maxi- 
 mum error of about 0.01 in the determination of the rotation of a sample. 
 Since the duplicate experiments did not always agree so well as this, a 
 fairer estimate of the precision of the measurements may be obtained from 
 the agreement of the duplicates themselves. This would put the average 
 difference between duplicate measurements of a change in rotation at 
 about 0.02. The effect of such an error on the values of n obtained by 
 the use of Equation 12 has already been considered. 
 
 Summary. 
 
 1. It has been shown that not all preparations of yeast invertase are 
 alike in their action, but that some are abnormal in allowing the hydrolysis 
 of cane sugar to slow up more than others after the first 20% of the inver- 
 sion. 
 
 2. An empirical equation is given which fits the hydrolysis of cane sugar 
 by normal invertase over an extreme range of invertase concentration of 
 12 :1. By this means it has been shown that the hydrolysis-time curves 
 for normal invertase are of the same shape for these different invertase 
 concentrations and can be made to superimpose if the time scale be multi- 
 plied by the proper constant. 
 
 3. By the same method it has been shown that the hydrolysis curve 
 with normal invertase has the same shape at temperatures varying from 
 15 to 35, and at hydrogen-ion concentrations from 4.0 X 10~ 5 to 3.2 X 
 10~ 7 . 
 
 4. It was found that one abnormal invertase preparation could be ren- 
 dered normal by the presence of .boiled normal invertase or 0.1 M sodium 
 chloride, while another was not affected by either. The former preparation 
 also worked normally at a very high concentration. 
 
 5. It was found impossible to render a normal invertase preparation 
 abnormal by further dialysis or partial inactivation by heating or ultra- 
 violet light. 
 
VITA. 
 
 David Ingersoll Hitchcock was born in Detroit, Michigan, on June 26, 
 1893. In 1911 he was graduated from the Detroit Central High School. 
 In 1915 he was graduated from Dartmouth College with the degree of 
 Bachelor of Arts. From 1915 to 1917 he was Instructor in Chemistry at 
 Dartmouth College. He was a graduate student in Chemistry at Columbia 
 University during the summers of 1915, 1916, and 1917. In August, 1917, 
 he enlisted in the 101st Machine Gun Battalion of the 26th Division, 
 United States Army. In June, 1918, he was transferred to the Gas Service, 
 later the Chemical Warfare Service, and was assigned to the chemical 
 laboratory "at Hanlon Field, Chaumont, France. In January, 1919,' he was 
 discharged from the Army. Since February, 1919, he has continued his 
 studies at Columbia University, where he received the degree of Master 
 of Arts in 1919. He has been laboratory assistant in various courses in 
 the Department of Chemistry. Since February, 1920, he has been Harri- 
 man Research Assistant in the laboratory of Professor J. M. Nelson. He 
 is co-author with Professor Nelson of a paper on "The Activity of Ad- 
 sorbed Invertase," which has been accepted for publication in the Journal 
 of the American Chemical Society. For the year 1921-1922 he has been 
 appointed a Fellow of the Rockefeller Institute for Medical Research, 
 New York City. 
 
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