July 20, 1956
INFLUENCE OF HYDROLYSIS ON INITIAL VELOCITY OF CY-AMYLASE [CONTRIBUTION FROM THE
DEPARTMEENT O F CHEMISTRY,
3343
COLUMBIA UNIVERSITY]
Influence of the Extent of Hydrolysis upon the Determination of the Initial Velocity of a-Amylase Action1 BY JOHN W. VANDYK,*Jo-FEN TUNGKUNGAND M. L. CALDWELL RECEIVED DECEMBER 7, 1955 I n reactions catalyzed by a-amylases, the velocity depends markedly upon the extent of hydrolysis. If this fact is neglected in the treatment of kinetic data, erroneous conclusions will result. A simple method for treating kinetic data, which permits comparable and well defined initial velocities to be obtained with a-amylases, is presented.
Introduction In random or random-like depolymerization of condensation polymers, the molecular weight and usually the molecular weight distribution of the polymer changes during the reaction. In some cases, particularly in enzymatically catalyzed reactions where steric factors are important, the velocity of the reaction depends upon these molecular characteristics of the p01ymer.~ Such a dependence is marked with cr-amyla~es.~-~ The data reported here for the action of crystalline pancreatic amylase from swinelo on defatted waxy maize ~ t a r c l1h ~illustrate ~~~ the erroneous and ambiguous conclusions that are obtained when these molecular characteristics are neglected in kinetic studies. A simple method for obtaining comparable and well defined initial velocities for such complex systems is suggested.
iodometric procedure.le A modification of this method” was used for the lower substrate concentrations studied (0.03 to 0.01%).
Toralballa, ibid., 74, 4033 (1952). (11) T. J. Schoch, ibid., 64, 2954 (1942). (12) Courtesy of National Starch Products, Ioc., New York, New York. (13) T. J . Schoch. “Advances io Carbohydrate Chemistry,” Vol. I, Academic Press, Inc., New York, N. Y.,1945, pp. 247, 260. (14) S . Lansky, M . Kooi and T . J. Schoch, THIS JOURNAL, 71, 4066 (1949). (15) F. L. Bates, D. French and R. E. Rundle, ibid., 65, 142 (1943).
(16) M. L. Caldwell, S. E. Doebbeling and S. H. Manian, Ind. E n g . Chem., A n a l . Ed., 8 , 181 (1936). (17) John W. Van Dyk, Dissertation, Columbia University, New York, 1954. (181 John W. Van Dyk and M. L. Caldwell, THISJOURNAL, 78, 3343 (1956). (19) Louise L. Phillips and M. L. Caldwell, ibid., 73, 3563 (1951). (20) Virginia M. Hanrahan and M . L. Caldwell, z b i d , 76, 2191 (1953).
Results
As part of an investigationla of the hydrolysis of waxy maize starch by pancreatic amylase from swine, the authors were interested in determining the dependence of the velocity of hydrolysis upon the substrate concentration. Starch concentrations between 0.5 and 0.08% were investigated first, because previous studies with this and other ~ ~ - a m y l a s e had s ~ - indicated ~ ~ ~ ~ ~ a~ dependence ~ of velocity on substrate concentration within this range. Since previous work in this Laboratory had indicated that the velocity of hydrolysis by a-amylases is strongly dependent on the extent of reaction or on the molecular weight of the produ c t the ~ data ~ ~were ~ plotted ~ ~ in ~ a manner which permitted comparison of the velocities a t the same extent of reaction. This comparison was made by Experimental plotting the fraction of the bonds hydrolyzed Amylase .-Crystalline pancreatic amylase from swinelo versus the time divided by the initial substrate was used in this work. concentration. Since, in this type of plot the orSubstrate.-The substrate was waxy maize starch12 that dinate is the extent of reaction and the slope of the had been used in previous studies with this a m y l a ~ e . ~I,t~ curve is the rate, the desired comparison is made had been defatted exhaustively” and gave no evidence of easily. The single curve obtained for the four contamination by linear ~omponents.’~-~5It had been washed thoroughly with cold distilled water t o remove low substrate concentrations, Fig. 1, shows that the velocity of hydrolysis is independent of the submolecular weight impurities. Methods.-The hydrolyses were carried out a t 40” as de- strate concentration for the range studied. The scribed previously.1° T h e extent of hydrolysis of the higher curvature of the line shows the previously mensubstrate concentrations investigated was measured by an tioned dependence of the rate on the extent of reaction. (1) This investigation was supported, io part, by a research grant from The conclusion that the velocity of hydrolysis of the National Institutes of Health, Public Health Service; io part, by a research grant from the Corn Industries Research Foundation. waxy maize starch by swine pancreatic amylase is (2) The data reported here are taken, in part, from a dissertation independent of the substrate concentration within submitted by John W. Van Dyk in partial fulfillment of the requirethe range of substrate concentrations studied ments for the degree of Doctor of Philosophy io Chemistry under the Faculty of Pure Science of Columbia University. (0.5 to 0.08%) does not agree with the findings of (3) P. A. Flory, “Polymer Chemistry,” Cornell University Press, Bernfeld and Studer-P&ha5 for the action of swine Ithaca, N. Y.,1953, pp, 83-87. pancreatic amylase with substrate concentrations (4) K. Myrback and N. 0. Johansson, Arkio. K e m i , Mineral Ceol., within the same range. The reason for this dis2OA, No. 6 (1945). crepancy is shown in Fig. 2 where the data given ( 5 ) P. Bernfeld and H. Studer-PCcha, H e h . Chim. Acta, 30, 1895, 1904 (1947). in Fig. 1 are plotted as amount of products formed (6) S. Schwimmer, J. B i d . Chem., 186, 181 (1950). versus time of hydrolysis, the form employed by (7) Florence M. Mindell, Dissertation, Columbia University, New Bernfeld and Studer-P6cha6 and by other previous York, 1946. ( 8 ) Florence M. Mindell, A. Louise Agoew and M. L. Caldwell, investigator^.^,^,^^,^^ In this case, Fig. 2 , four THIS JOURNAL, 7 1 , 1779 (1949). different curves are obtained, and from these one (9) Roslyn B. Alfio and M. L. Caldwell, ibid., 70, 2534 (1948). can calculate four apparently different ‘‘initial (IO) M . L. Caldwell, Mildred Adams, Jo-fen Tung Kuog and Gloria
J. W. VAN DYK,J. T. K u N G
3344
AND
Vol. 78
from the single curve shown in Fig. 1. The dependence of “initial velocity” on substrate concentration, obtained above, in Fig. 2, is an artifact which arises from neglecting the dependence of the velocity on the extent of the reaction. A true dependence of velocity on substrate concentration is observed with this amylase and substrate only when more dilute substrate solutions (0.03 and O . O 1 ~ o )are used, as shown in Fig. 3.
u .20 a
N
2 W
5 .I5 v)
W
u
r
3
0
-a
0
-0
c
I
t
U
m * .I 0
*I0
2
.-0 0 0
M. L. CALDWELL
In c
2
.OS
.OS
+ 0
c
0 .. I -
x O
2
LL
O,
40
120
80
Time/Substra te Concentration ( M inute s / Per Cent. ). Fig. 1.-Hydrolysis of waxy maize starch by swine pancreatic amylase in the presence of excess substrate; substrate concentration: 0,0 . 5 7 ~ ;0 , O.ZSyo; C), 0.1%; 0 ,0.087,.
0
0
100 2 00 300 400 T i m e / S u b s t r a t e Concentration (Minutes/ P e r Cent.).
Fig. 3.-Influence of substrate concentration on the rate of the hydrolysis of waxy maize starch by swine pancreatic amylase.
Discussion Accurate and comparable initial velocities as a function of substrate concentration are essential to a kinetic study. They can be obtained conveniently by defining the “initial” velocity ( Vo) in terms of the reaction time ( t ) necessary for the hydrolysis of a given small fraction of the bonds
(F)
v o = -Fa-
0
t
0
2
4
6
8
1
0
Time (minutes). Fig. Z.--lpparent influence of substrate concentration on the rate of the hydrolysis of waxy maize starch by swine pancreatic amylase.
velocities” by an estimation of the slopes of the curves a t zero time. That the “initial velocities” calculated in this manner are incorrect is evident
where a0 is the initial substrate concentration. I n addition to being comparable, the velocities obtained by the above equation can be reproduced or used by investigators in different laboratories since the vagaries associated with the estimation of the slope a t zero time are not involved. I t should be noted, however, that VOequals the velocity a t zero time only if F is infinitesimally small, therefore F should be chosen as small as possible. Since choice of F will be limited by the precision of the measurements, a sensitive method should be used. In the case of the hydrolysis of starch fractions, spectrophotometric measurements are useful for this The procedure outlined here has been employed in an extensive investigation of the kinetics of the action of swine pancreatic amylase. This work is reported in a subsequent communication.1s NEWYORK,9.Y. JOURNAL, 66, 1154 (21) K . 31. McCready and W.2. Hassid, THIS (1443). ( 2 2 ) J o h n W. Van D y k and hf. L. Caldwell, A d . C h c n . , 28 (No. 31, 318 (1956).
