KINETICS OF HEXOKINASE ENZYME AT pH 8
June 5 , 1962
2069
[CONTRIBUTION FROM THE DEPARTMEST OF CHEMISTRY, MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS]
Studies of the Enzyme Hexokinase.
I. Steady State Kinetics at pH 8
BY GORDON G. HAMMES AND DANIELKOCHAVI RECEIVED OCTOBER 5, 1961
A steady state kinetic study of t h e transfer of a phosphate group from ATP t o u-glucose as catalyzed by the enzyrnc hexokinase was carried o u t a t p H 8 and 25.0'. The necessary divalent metal ion used was MgCt and t h e ionic strength was 0.3 ;M in (CH3)4NC1. T h e results indicate t h a t t h e most probable mechanism is the combination of MgATP and an enzyme-glucose complex t o form a quaternary intermediate which in turn decomposes t o MgADP and a dissociable enzymeglucose-6-phosphate complex. Several rate constants and lower bounds of rate constants were calculated, and it was found t h a t all of t h e bimolecular rate constants in the forward direction are greater than lo5 1V-l set.-' and the first order constants are greater than i o 0 set.?. I n addition the binding constant of D-glucose to hexokinase was found t o be 2.5 X IO3 -1I-l.
Introduction Although hexokinase was first crystallized a number of years ago, 1 , 2 surprisingly little is known about its mechanism of action. The hexokinase catalyzed transfer of a phosphate group from adenosine triphosphate (ATP) to the 6 position of various six carbon sugars is well known to require the presence of a divalent metal ion, usually Mg++, but few of the details o f a t h e mechanism have been firmly established. Agren and Engstrom3 reported the isolation of an enzyme phosphate intermediate, but this finding is in conflict with recent exchange studies where labelled glucose was found not to exchange with glucose-6-phosphate in the presence of the e n ~ y m e . These ~ latter results were explained by postulating a mechanism involving a glucosyl enzyme. Several kinetic studies have been carried out previously with rather inconclusive results. Slein, Cori and Corij studied the effect on the reaction rate of varying the sugar concentration. Since they worked a t constant and quite high ATP and Mg++ concentrations, no detailed mechanistic information was obtained. Melchoir and Melchoir6 attempted to clarify the situation by studying the initial velocity as a function of the various ionic species present (i.e. ,%TP,MgATP, Mg++); however because the role of the sugar was not taken into account, their studies could not distinguish between several plausible mechanisms. The investigation reported here will make it manifestly clear that it is not only desirable but necessary to consider simultaneous concentration variation of all of the possible reactants if a meaningful interpretation of steady state kinetics is to be made. In this study the initial velocity of the transfer of a phosphate group from ATP to D-glucose was determined over a wide range of ATP, Mg++, MgATP and glucose concentrations. At pH 8, each mole of ATP reacting is accompanied by formation of an equivalent of H f , so that a pH stat could be used to determine these rates. In order to determine the concentration of all species present in the reaction mixture, the equilibrium quotient for MgATP formation was also determined. (1) ?JKunitz a n d 51.K . McDonald, J . Ciii. P h y s . , 2 9 , 393 (1946). ( 2 ) L. Berger, Rf Slein, S. P , Culowick and C. F. Cori, ibid., 29,
379 (1916). (3) G. Agren and L. Engstrom, Acia Chem. Scand., 10, 481) (19%). (4) V. A. S a j j a r and E. E. McKay, Federation Pvoc., 17, 1141 (1958). Slein, (J) > W ' I G . T . Cor? and C. F. Cori, J . Rid Chem.. 186,703 ) S . C . Melclioir
and J D hlelchoir, zbzd., 231, (io9 [1!%5Sj
The results obtained favor a mechanism proceeding through formation of a quaternary intermediate complex produced by reaction of an enzyme-glucose complex with MgATP. In addition, many of the rate constants (or lower bounds thereof) were obtained.
Experimental Materials.-Crystalline hexokinase was prepared according to the procedure of Darrow and Colowick.' All hexokinase used in the kinetic experiments was crystallized three times; such enzyme is substantially free of all enzymatic impurities except for a small residual amount of ATPase activity.8 The specific activity of the enzyme was from 200-500 Kunitz-McDonald units/mg.' Since the specific activity usually decreases with time, denatured hexokinase is probably always present. The disodium salt of ATP (Pabst) was freed of sodium ion by shaking with an excess of the hydrogen ion form of Dowex 50 resin. T h e concentration of -1TP was then determined spectrophotometrically. The pH was adjusted to the desired value with (CH3)&OH (Eastman Kodak Co.). This base was standardized with potassium acid phthalate in the usual manner. The ( CH3)4SC1(Eastman Kodak Co.) was recrystallized from isopropyl alcohol and dried in vacuo. The MgCL and dextrose were C P grade and were used without further purification. All solutions were made from COn free conductivity water. Determination of MgATP Binding Constants.-Fifteen nil. of a solution 0.3 M-in (CH3)cXCi, ,If in ATP and in ,MgCIS were titrated inside a thermostatted cell a t 25.0" (i.0.1) C with standardized (CHJj4XOH (approximately 0.1 ;\-). X similar titration without Mg'- was also performed. Errors due to COS absorption were prevented by working under a CO? free atmosphere of water saturated Nr. Titration curves were obtained using a n automatic titrator manufactured by Radiometer of Copenhagen (SBR-BC and TTT lb). Both titrations were made in triplicate. Kinetic Measurements.-Solutions were prepared containing all possible combinations of the following total condl, 2 X centrations: (.ITP)T= 5 X M, 1 X X,5 X I I ; iMg),r = same as (ATP)T; and dextrose = 1 x 10-3 A I , 5 x io-' M ,2 x 10-4 -11, 1 x 10-4 AI. This resulted in 61 different solutions. The ionic strength was kept constant with 0.3 :?! (CH3)rSCl. I Monovalent metal ions were avoided because they have been shown to inhibit the enzymatic reaction.6 For each kinetic run, 14 tnl. of solution were put into a thermostatted cell a t 25.0" (i0.1): the solution was then adjusted t o approximately p H 8 with strong acid or base and a known amount of enzyme solution (- 0.02 ml.) was added with a pipet. The rate of H + formation was then measured a t PH 8.0 ( + 0.05) using the Radiometer apparatus as a pH stat. Since the reaction produces H+ and the buret injects base into the solution, a n y initial deviation from pH 8 is compensated for quite quickly. T h e volume of base used was always less than 0.2 ml. The glass electrode was soaked in a solution containing ( 7 ) R . A. Darrow and S. P. Colowick, in "Methods in Enzymology" (S. P. Colowick and N. 0 . Kaplan, eds.), 5'01. V,Academic Press, Inc., Piew York, N . Y . , l9ti1, p . 226. (8) K . A. Trayser and S P. Colowick, A r c h . Biocheni Biophys., 94, 1111 ( I W j I j .
GORDON C. HAMMES A N D DANIEL KOCHAVI
2070 1.2
1
-
0-
0
s4
I
01
0.1
VOl
t-
I I .-:_ I.. .L, i ..
.
L.
~
. L~
..
.. ..
10~3/[MgATP) ( M - ' ) ,
Fig. 2.-The
slopes of (Eo)/v - l / ( G ) plots ( e . g Fig. 1) veysus l/(MgATP).
The enzyme solution was prepared by centrifuging down the crystals, decanting the liquid and dissolving them in a n appropriate amount of ice cold water. The concentration was adjusted to give conveniently measurable initial velocities (- 1 0 - 9 hl). Although the enzyme was kept in a n ice bath, it was found to slowly lose activity. This effect was corrected for by referring all rates to t h a t of a standard solution [(ATP)T = (Dextrose) = M , (Mg++)T = 5 X lo-* MI whose initial velocity was determined every hour. The decay of activity seldom amounted to more than 10% a day. The actual concentration of pure enzyme in the standard solution was found by using the Kunitz-McDonald assay together with their data for the specific activity of the pure enzyme and a molecular weight of 96,600.' This assumes one active site per molecule. T h e release of 1 X lo-' M/sec. of H C in the standard solution was found to correspond to an enzyme concentration of 2.06 X 10 -lo J l f . Since this work was completed Trayser and Colon-ickg have shown that crystalline hexokinase can be resolved into (9) K. Trayser and S. P. Colowick, Arch. Biockem. Biophys., 94,
177 (1961).
I
I
,
I
,
I
,
I
I
I
I
Here a H designates the hydrogen ion activity as measured by the glass electrode, while all other species are given in concentration units. These results are in reasonable agreement with those in the literaturefitlO*ll and can be used to calculate the concentrations of the ionic species in solution. Kinetics.-Since the kinetic data are so nunierous, i t is not feasible to tabulate all of the results here; however, a summation of the 64 initial velocities and the concentrations of the individual species in solution are available.'? The concentration of free ATP was varied from 9.21 X M to 4.12 X M , that of MgATP from 3.26 X 10-4M to 4.36 X 10-3M and that of free Mg++ from 1.01 X 10-j M to 4.51 X M . (It should be mentioned that some of these initial velocities were measured under identical conditions ( I O ) A. E. hlarteil and G. Schwarzenbach. Helo. Chim. A d a . , 39, 653 (1956). (11) R. M. Smith and R. A. Alberty, J . Phys. Chem., 6 0 , 180 (1956). (12) These d a t a have been depusited a3 Document number 6919 with the AUI Auxiliary I'ublicatiuns k'rujcct, I'h,,LudIililiculic,ii S c r v ice, Library of Congress, Washington 2 5 , D . C. A copy may be secured by citing t h e Document number and by remitting $1.25 for photoprints, or $ 1 . 2 5 for 35 mm. microfilm. Advance payment is required. Make checks or money order payable to: Chief, Photoduplication Service, Library of Congress.
KINETICSOF HEXOKINASE ~ K ' L Y h l EAT pH 8
June 5, 1'362
2071
to those employed by Melchoir and Melchoir.6 In these cases agreement within experimental error ( 5 to 10%) was obtained if an appropriate normalization was used.) The rate law found to fit the data best will now be given and the adequacy of this representation will be demonstrated. The ratio of the total enzyme concentration to the initial velocity, (Eo)/v, can be represented within experimental error by the following equation:
phate intermediate and MgADP by a reaction between MgATP and enzyme, this step again being followed by reaction with glucose; formation of a quaternary Mg-ATP-enzyme-glucose complex preceded in order by the complexes (3) enzyme-Mg-ATP and enzyme-Mg, or (4) enzyme-Mg-ATP and enzyme-ATP, or ( 5 ) enzyme-ATP-glucose and enzyme-ATP; or (G) enzyme-ATP-glucose and enzyme-glucose ; and formation of a quaternary complex by (7) the reaction of MgATP with enzyme, the resulting intermediate combining with glucose, or (8) the reaction of MgATP with an enzyme-glucose com-3+4* plex. The reverse mechanisms are assumed to be (MgATP) $- K ' ( A T P ) l + ( G ) ( M g A T P ) symmetrical with the forward, ;.e., merely the substitution of ADP for A T P and glucose-6-phoswhere G represents D-glucose and 41 = 1.34 X phate for glucose. These mechanisms can be sec., t#~* = 2.71 X loF7Msec., qb8 = 3.02 X lO-'~11 represented by the reaction schemes sec., ( 6 4 * = 1.23 X lo-'" M 2 sec., and Ki = 1.1 X IO3 J-1-l. The estimated maximum error in the ki initial velocities is f 5y0,that in the 4's is 15% 1. E hlg EbIg and that in Ki is 20%. This assumes an error k- I of less than f 5y0in (Eo);actually the absolute kz k3 error in determining (Eo) is larger due to the Eblg ATP Xi E'Mg + ADP difficulty of obtaining great accuracy with the k--2 k-a Kunitz-McDonald assay. However, since all initial velocities were referred to a standard within k4 ks 5yo,the relative values of the 4's are correct E'Mg G Y1 I ' EMg + G6P k-4 k-s within the error limits cited. The above rate equation predicts that a t constant total concentrations of A T P and Mg++, 2 . ATP + hlg hlgATP (Eo)/v is a linear function of l/(G) with an inter#a[l Ki(ATP)]/(hlgATP) cept equal to $1 E' MghDP MgATP + E Xi and a slope equal to $* 44*/(MgATP). Figure E' + G I -1'1 E GBP 1 shows some typical plots of (Eo)/v versus 1/(G) a t various total concentrations of A T P and M g f + . hlgADP ADP Mg The slope of this plot should be a linear function of l/(XTgATP); Fig. 2 shows such a plot where the line was determined by the method of least squares. 3. E b l g z EMg Only one point deviates appreciably from the line, EMg ATP EMgATP i.e. greater than about loyo; this is a t the highest concentration of free ATP and probably indicates EMgATP 4- G SI EMgADP GOP the onset of some type of noncompetitive ATP inhibition. Therefore, this point was not included BMgADP EMg + ADP in the least squares treatment. Figure 3 shows Ki(ATP)]/ a plot of the intercept versus [l (MgATP); again the equation of the line was 4. E + .4TP EATP calculated using the method of least squares. EATP + Mg EATPMg The constant Ki was determined by using the value which minimized the average deviation of the exEATPhlg + G XI EADPMg GBP perimental points from the line. One point was omitted on the statistical basis that its deviation EADPhlg EADP + Mg from the line (-J 35yc)is greater than 4 times the average deviation. Including this point in the E ADP E.4DP least square calculations changed and 43by less than 27,. From these figures, it can be seen that EATP the proposed rate equation gives a good description 5. E + ATP of a large amount of data.
*
*
+
+
+
*
+
+
+
+
1-
+
+
+
+
+
+
+
+
+G EATPG EATPG + Mg I -SI1-EXDPGGP + hlg EXDPGGP EADP + GCjP EADP r'E + ADP
EATP
Discussion Eight mechanisms were examined to see if their initial velocities were consistent with the experirrieIitnl restilts. 111 brief, these iriecliniiisins are (1) formation of an enzyme-hlg complex followed by reaction with A T P to give ADP and an enzymehlg-phosphate intermediate which in turn reacts with glucose; ( 2 ) formation of an enzyme-phos-
6.
Same as 5 except ATP and ADP are interchanged with G and G6P respectively
GORDON G. HAMMES AND DANIEL KOCHAVI
2072 7.
ATP
Mg
0=
MgATP
+ E EMgATP EMgATP + G Jr XI EMgADP + G6P MgADP 8.
ATP
MgADP ADP
(GI
(2)
(MgATP)
o = 4421 + 43 - + p (GI
0
(.4TPj 4245
+E
+ Mg
(Ea!=
+-
V
+ Mg I-MgATP
(ATP)
E+G,'EG MgATP
+2 4 + .dL-
V
Mg.4TP
EMgADP
VOl. 54
+ EG
Xi
EGGP
EG6P
7 4 + .---+E?--
+ MgADP
(Mg)
I-E + G6P
MgADP
ADP
(Eo)=41+2L+_2k+*. (GI
21
+ Mg
(ATP)
&(Mg)
(Mg)
L (1 + 9(GI)
+
+ 7--4 +-?@!!--( 5) ( A4TP )( G j
Here E represents the free enzyme, XI and IT1 are enzyme intermediates, G6P is glucose-6-phosphate, and other symbols have their obvious meanings. Rate constants can be assigned to all the mechanisms in a manner similar to that employed in mechanism 1. The initial velocities can be written in terms of the rate constant^'^ and initial concentrations or alternatively the familiar maximum velocities, Michaelis constants and equilibrium constantsI4 may be used. Since this latter notation is rather combersome for such complicated mechanisms, the initial steady state velocities will be expressed in terms of experimentally determinable constants designated by +'s. These constants can be related to the rate constants of a given mechanism. Table I contains
(4)
(ATP)(G)(R.Zgj
( ATP )( G )( b f g )
Same as 5 except ATP and ADP are interchanged with G and G6P, respectively (6) (Gj
Z'
(Eo) V
=
_. + .--@1
+ .-z,4 +
(Eo) = ,$1
+ A. + (G)
(MgATP) ~
(MgATP)
+
(-
(G)(MgATP)
0
.--w(G)(MgATP)
(8)
In mechanisms 2 , 7 and 8, the first and last steps have been assumed rapid compared to the over-all reaction ; this is in accord with recent experimental results. 15,16 If equations 1-8 are examined carefully, i t will be seen that except f o r mechanisms 7 and 8 which have initial velocities that are identical functions of the various concentrations, all of the mechanisms are
TABLEI DEFINTIOSSOF STEADY STATEKINETICCONSTASTS Mechanism
+I
1
1
1
k,+h
2
G+L
3
&+&
4
k,+k,+k,
1
1
1
1
1
1
1
+ + + +
$2
k-a ks kdks k-4 ks kaks k-3 k4 kska k-3 ka k3k4
1 kz
.-
a tabulation giving the expressions for these steady state parameters in terms of the rate constants for each mechanism. The ratio of the total enzyme concentration, (Eo), to the initial velocities, v for these eight mechanism can be written as
(13) E . I,. King a n d C. Altman, J . P h y s . Chem., 6 0 , 1375 (1956) ( 1 4 ) R A Alherty. A d v in E B Z Y ~ O ~ O17, E Y1, (1956).
(in principle) experimentally distinguishable. The data obtained do not fit the first six mechanisms in even a qualitative manner. 0 1 1 the other hand, the initial velocity functions for Inechanisms 7 and 8 are identical to the experiniental rate law 1/43 =
ka kj
> l / d l = 750 sec.-l > 1/41 = 750 sec.-l
3.3 X 106 Af-1 sec.-1
Due to the difficulty of obtaining the absolute value of (Eo) accurately, the rate constants are probably certain to only f. 40%. From previous w ~ r k , ' ~ , ' ~ i t is also known that a t 25" and in 0.1 M KN03, k1 = 1.2 X loi i1l-l sec.-', k-1 = 1.2 x IO3 sec.-', kg = 3 X IO6 M-' set.-' and k-6 = 2.5 x 103 sec-l. 'The association constant for the enzymeglucose complex is 2.5 X 10a M-l ( + 25%). This is :!bout 60% smaller than the value found by Trayser and Colowick'* by an indirect method. The rate constants will be discussed more fully in the next paper of this seriesLg Acknowledgments.-The authors are inde ted to Dr. M. Kunitz and Dr. S. P. Colowick for samples of hexokinase and to the latter for advice regardic.g the preparation of crystalline hexokinase. Thanks are also due to Professor J. Buchanan and Dr. A. Larrabee of the M.I.T. Biochemistry Department for use of their facilities. This research was supported by a grant from the National Institutes of Health (RG-7803). (17) L. Peller and R. A . Alberty, J . Am. Chem. S o c . , 81,5907 (1959). (18) K . Trayser and S. P. Colowick, Arch. Biochem. Biophys., 94, 169 (1961). (19) G . G. Harnrnes and D . Kochavi, J. .4m Chem. Soc., 84, 2073 (1962).
DEPARTMEST O F CHEMISTRY, MASSACHUSETTS Ih'S'ITT'LJTE UP MASSACHUSETTS]
'hCHSOLUGS,
CAMRRIL)C;E,
Studies of the Enzyme Hexokinase. 11. Kinetic Inhibition by Products BY GORDON G. HAMMES AND DANIEL KOCHAVI RECEIVEDOCTOBER5 , 1961 The rate of transfer of a phosphate group from A T P t o D-glUCOSe is retarded by the presence of initial concentrations of the products, A4DPand glucose-6-phosphate. This inhibition is in quantitative agreement with the previously proposed mechanism of action for the enzyme hexokinase. From these studies, the binding constants for glucose-6-phosphate and free enzyme and for MgATP and a n enzyme-glucose complex were found t o be 1.1 X IO2 A f - l and 6.2 X lo3 A!-1, respectively. The latter constant is only about six times larger than the binding constant for the enzyme-glucose complex and free ATP. (1.1 X los This suggests t h a t M g is not a very important factor for binding of the substrate to the enzyme; instead the primary role.of M g is probably t o aid in the bond breaking step in t h e reaction. Combining all of the kinetic data available with the equilibrium constant for the over-all reaction permits all twelve of the rate constants in the mechanism to be determined.
Introduction The previous paper in this series' proposed the following mechanism for the hexokinase catalyzed
transfer of a phosphate group from adenosine triphosphate (AiTP)to D-glucose (1) G G H a m m e s a n d 1 ) Kochavi J chu,ji soc 8 4 , 2 0 (~I W )
