Vol. 84
GORDON G. HA4Mh1ES.4ND DANIEL KOCHAVI
2078
MgATP and EG (6.2 X l o 3 M--l) is only about six times that for ATP and EG which indicates that although MgATP is the actual substrate rather than ATP, the role of the metal ion cannot he only to enhance the binding of ATP to the enzyme. This is contrary to the idea frequently brought forth that the metal ion acts as a strong structural cement between substrate and enzyme. Instead, a good deal of the binding seems to occur through the adenine and/or ribose portions of ATP which is consistent with the extended conformation of MgATP in solution proposed on the basis of nuclear magnetic resonance experiments6 The primary role of Mg++ is most likely to polarize the oxygen-phosphate bond being broken while anchoring the phosphate group of ATP to the enzyme. A more detailed discussion of the function of the metal ion will be presented elsewhere.' If the equilibrium constant were known, enough data is available to calculate all of the rate constants which are still unknown. Robbins and Boyer4 have determined the equilibrium constant under different conditions (pH 6, 30' and variable ionic strength) than those employed in our experiments, but a t least an approximate value of the desired constant can be obtained from their data. A reasonable estimate is that the desired equilibrium constant (as defined by equation 4) is about 300. Using this value and the r+!~ values in Table I, the rate constants can be calculated to within a factor of 2 or 3. Of course, kl, k-1, k2, k-2, kg and k-6 have all been determined independently and are known to about f 30%.1-3. A tabulation of all of the rate constants is (6) G. G. Hammes, G . E. Maciel and J . S. Waugh, J . A m . Chem. SOC., 83, 2394 (19Gl). ( 7 ) G. G. Hammes a n d D. Kochavi, ibid.. 84, 2076 (1962).
[COSTRIBUTIOS FROM
THE
DEPARTMENT
OF
'kl = 1.2 X 10' M-' set.-' * k _ , = 1.2 X los sec.-l k2 = 3.7 X lo6 M-'sec.-' k - ? = 1.5 >( loa sec.-l k k 3 = 6.5 X lo* set.-' ka = 4 X 106 M-l set.-' k . 4 = 2 X 1 0 6 M-l sec.-I k1 = 3 X lo3 set.-' k5 = 1 X l o 3 sec.-l k . 5 = 1 X 106 1W-l sec. I "ks = 2.5 X IO3 sec.-' * k - 6 = 3 x los df-' sec. '
The constants marked with * were determined at 25' and an ionic strength of 0.1 MKNOz. The magnitudes of k2 and k3 are fairly large but not nearly as large as many other enzyme-substrate reactions which approach the theoretical upper limit for a bimolecular rate constant (-J loy M-l S ~ C . - ~ ) . ~ , An ~ interesting point is that MgADP binds to both EG and EG6P (K = 3.3 X l o 2 M-' and 2 X l o 3 M-l, respectively); on the other hand no experimental evidence exists for the binding of MgATP and EG6P. This binding should be detectable if the binding constant is greater than about 50. This indicates that the phosphate group on GGP blocks the binding o f MgATP very effectively. Finally it should be pointed out that the procedure used for obtaining this rather detailed mechanism for the hexokinase system is applicable to phosphate transferring enzymes in general. This research was supported by a grant from the National Institutes of Health (RG-7803). Addendum.-Since this work was completed a kinetic study of the enzyme pyruvate kinase was carried out by Reynard, Hass, Jacobsen and Boyer. lo The mechanism involved is apparently somewhat different than that proposed for hexokinase. (8) L. Peller and R. A. Alberty, ibid., 81, 5907 (1959). (9) R. A. Alberty a n d G. G. Hammes, J . Phys. Chem., 62, 154 (1958). (10) A. M.Reynard, L. F. H a s , D. D. Jacobsen a n d P. D. Roye., J . Biol. Chem., 236, 2277 (1961).
CHEMISTRY, MASSACHUSETTS INSTITUTE MASSACHUSETTS]
OF
TECHNOLOGY, CAMBRIDGE,
Studies of the Enzyme Hexokinase. 111. The Role of the Metal Ion BY GORDON G. HAMMES AND DANIELKOCHAVI RECEIVED DECEMBER 22, 1961 Steady state kinetic experiments were carried out with hexokinase using C a + + as the metal ion activator. Although Ca+' is a much poorer activator than Mg++, both metals utilize the same mechanism. Comparison of the two metal ions as activators indicates that the rates of complex formation are not rate determining. I n fact, e a + +in general builds complexes about 100 times faster than M g + + . Furthermore, the equilibrium quotients involving the metal ions are approximately the same. However, the breakdown of the quaternary intermediate complex occurs over one hundred times faster for the M g + + system indicating that the rate controlling step involves polarization of the media (probably breaking of a chemical bond) since M g + + should be much more effective than C a + + for this purpose. Comparison of the rate constants for the two systems suggests that a t least two quaternary intermediates are necessary t o explain the results in a satisfactory manner.
Introduction Recent studies's2 of the enzyme hexokinase have indicated that the most probable mechanism for the transfer of a phosphoryl group from ATP to glucose is Me
+ -4TP
ki
k5
MeXTP
k-
1
EG6P
If E + G6P k-
ks
k2 E+G,EG k- z
EG
MeADP
Me
kk3
k4
k--8
k-4
+ MeATP _c X I
EGGP
EG
+ ADP
6
+ MeADP
+ ATP I_ EGATP(inactive)
ir
(1) G. G. Hammes a n d D . Kochavi, .T. Am. Chem. Soc., 84, 2009 l9liZ). ( 2 ) I b i d . , 2073 (I'Jli2).
Here E respresents hexokinase, ATP is adenosine triphosphate, Me is the metal ion activator (Mg++ in previous studies), G is glucose, X1 is a quaternary
ROLEOF METALIONIN HEXOKINASE ACTIVITY
June 5 , 1962
2077
5l4
0
I
I
I
I
I
I
2
3
4
5
[I+
Fig. 1.-The
I . I X I03(ATP)]/(Ca
ATP)
I 6
7
(M-').
intercepts of ( & ) / a - l / ( G ) plots w s u s [ I f 1.1 X 103(ATP)]/(Ca ATP).
intermediate complex, G6P is glucose-6-phosphate and ADP is adenosine diphosphate. By coupling steady state kinetic studies'-* with equilibrium data3 and kinetic data obtained with the temperature jump m e t h ~ d ,all ~ of , ~the rate constants in the above mecharism were determined. From these results, the role of the metal ion, Mg++, seemed to be primarily connected with a bond breaking step in the mechanism rather than with enhancement of the binding between the enzyme-glucose complex and ATP. This finding is contrary to many previous speculations. Since the role of metal ions in enzyme catalysis is still not very well understood, it seemed worthwhile t o investigate further this aspect of the hexokinase mechanism. With this in mind, steady state kinetic studies have been carried out using Ca++ as the metal ion activator rather than Mg++. The reasons for choosing Ca++ over other divalent metals will become apparent in the discussion section. The results show that C a + + is a much poorer activator than Mg++ and that the main difference lies in their relative abilities to catalyze the step (probably bond breaking) characterized by the rate constant kq. The results also suggest that a t least one more intermediate Xz should be postulated if the kinetic data is to be consistent with results obtained from studies of model systems. Experimental The experimental procedure employed in determining the equilibrium binding constant for CaATP and in making the kinetic measurements was exactly as previously described.' The only notable difference was that a much higher enzyme concentration had to be used, namely, IO-' - lo-* M .
Results The equilibrium quotient for CaATP formation a t 25.0° and in 0.3 M (NH3)4NC1was found to be 3.7 X l o 3 M-I. The kinetic data was treated exactly as previously.'X2 The mechanism was (3) E. A . Robbins and P. D. Boyer, J. B i d Chem., 224, 121 (1957). (4) H. Diebler, M. Eigen and G. G. Hammes, 2. Naturforsch., ISB, 555 (1960). ( 5 ) ,21. Eisen and G. G. Hammes. J . A m . Chem. Soc., 82, RR51 (lY60); 83, 27813 (1961).
Fig. 2.-The slopes of ( B o ) / v- l/(G) plots versus l/(CaATP). The triangle represents the intercept found previously in the M g + + system.
assumed to be the same as that for the Mg++ activated system; therefore the expected rate law is
where (E)ois the total enzyme concentration, v is the initial steady state velocity, Ki is the equilibrium binding constant for EG and ATP, and the 4's are known functions of the rate constants 41= l / k r 41 = l/k?
+ Ilks
+
43 = (k--1 ka)/k-1ki 44 = k-?/kz
As predicted, (Eo)/v plotted versus 1/(G) a t constant total concentrations of Ca++ and ATP gives straight lines with intercepts of +3[1 Ki(ATP)]/(CaATP) and slopes of 42 -I- (P394./(CaATP). Figure 1 is a plot of the (Eo)/Y- 1/(G) intercepts obtained plotted against [l Ki(ATP) ]/(CaA.TP). The value of Ki is known to be 1.1 x l o 3 M f r o m the previous work with Mg++ as an activator and the line was fitted by the method of least squares. Figure 2 is a plot of the slopes of the (Eo)/n - l/(G) plots versus 1/ (CaATP). Again the line was drawn by using the method of least squares; the triangle is the intercept obtained in the Mg++ system. A.s is readily seen, the experimental results are in reasonably good agreement with equation 1. These data are not as abundant as those for h l g + + because 50-100 times as much enzyme had to be used for the Ca++ experiments. The relatively high enzyme concentration also caused a slight amount of buffering which made the kinetic measurements somewhat less precise. The relative error in the 4 ' s is about =k 20% except for 62 which the large error being due to the is 7.7 j= 5 X steepness of the slope and smallness of the intercept in Fig. 2. The values of the 4's found a t 25.0' p H 8.0 in 0.3 M (NH3)4NC1are
+
+
+
+2
= 6.0 X 10-2sec. = 7.7 x 10-7 M see.
43 = 1.13 X 10-5 M sec. Jf &4 = 5 2 x
Discussion The results for the Ca+f activated hexokinase system are consistent with the proposed mechanism,
2075
GORDON G. HAXMES AND DANIEL I
I:or h l g + + : 6 X lo3 M-' 3 k3/k--3 1.1 X lo3 A{-'; k4/ k-4 6 5; k'-4/k4' 6 5 X 102 M-';k3 3 3.3 x 106 M-I set.-'; k-3 3 550 sec.-l; k , 3 3 X 103sec.-l; k - 4 3 6 X 102sec.-'; k4' 3 3 X lO3sec.-'; k-4' 2 2 X lo5 M-' sec.
[CONTRIBUTION FROM
THE
For
ea++:5
2079
X lo3 M-' 3 k3lk-s 3 1.1 X l o 3 M - l ; k4k'r/k-4k'-r 4 X 10-3 M ; kAtc and k'=t, same as for Mg++; k4 = 17 sec.-l
>
It is obvious that the more complex mechanism only serves to strengthen the conclusions reached earlier concerning the role of the metal ion in the hexokinase system. It should be mentioned that the inequalities presented above are probably equalities within a factor of 2 or 3 in the case of Mg++. Work is now in progress to try and detect the proposed intermediates in a more direct manner. This research was supported by a grant from the National Institutes of Health (RG7803).
CALIFORMA RESEARCH CORPORATION, RICHMOND, CALIF.]
Inhibition of Cumene Oxidation by Tetralin Hydroperoxide BY J. R. THOMAS AND C. A. TOLMAN RECEIVEDJANUARY 25, 1962 Tetralin hydroperoxide is found to retard the rate of catalyzed oxidation of cumene at 57'. The retardation is explained in terms of tetralylperoxy radical formation by peroxidic hydrogen abstraction by cumylperoxy radicals and the more rapid termination reactions occurring between tetralylperoxy radicals with themselves and with cumylperoxy radicais than that TOzH + between cumylperoxy radicals. The data yield a rate constant of 12 liters/mole sec. for the reaction R02. R02H Top.. Possible reasons for the lack of a kinetic isotope effect, observed for this reaction, are discussed.
+
+
Russell' found that cumene solutions containing moderate concentrations of tetralin oxidize appreciably slower than either pure hydrocarbon alone. This behavior he showed to be due to the much faster termination reactions of tetralylperoxy radicals with themselves and with cumylperoxy radicals than that between cumylperoxy radicals alone. If the hydrogen exchange reaction between cumylperoxy radicals and tetralin hydroperoxide proceeds with sufficient speed, i t would be anticipated that tetralin hydroperoxide would retard the oxidation rate of cumene. We have observed that such an effect exists and find that as little as I 0-3 M tetralin hydroperoxide significantly retards the oxidation rate of 4 M cumene solutions initiated M azo-bis-isobutyronitrile (ABN) a t with 4 X 57'. Figure 1 shows the oxidation rate plotted as a function of tetralin hydroperoxide concentration. Utilizing the mechanism On ABN
+AOz.
ki
+ R H AOzH + ROz. kp + TOzH +AOzH + TOz. k.1 RO?. + R H ROpH + ROz. ROg. + T02H +R02H + TOz. ks TO2. + R H +T02H + ROp. ks TO2. + TOZ.+inactive products k, TO,. + RO2- +inactive products ks RO2. + ROZ. inactive products ks 0 2
AOz. AO?.
----f
0 2
----f
k4
0 2
--f
where R H is cumene and T02H is tetralin hydroperoxide, the conventional steady state approximation yields the rate equation (1) G.A. Russell, J . A m . Chem. Soc., 71, 4583 (1955).
kz [ R HI
I"'
It is assumed that kz = kd = ke and ks = kg. Using values of k7 = 2.3 x lo7 liters/mole sec. and kg = 3 X lo4liters/mole sec. as determined by Melville and Richards2 and ks = lo7 liters/mole sec. as determined by Russell, the value of the rate constant for the exchange reaction kb is 12 liters/ mole sec. The value of k l [ A B N ] was determined by use of diphenylnitric oxide as a radical trap (3.08 X lo-* mole/liter sec. for 4 X 10-*M ABN). This value is in good agreement with that determined by Hammond, et aL3 The best literature value2 of kz (0.45 liter/mole sec.) gives a calculated oxidation rate of cumene without tetralin hydroperoxide about 45% lower than observed. Consequently, k2 was adjusted to 0.64 liter/mole sec. to bring experiment and expectation into agreement. Using these values the solid line in Fig. 1 is calculated in accordance with eq. 1. Additional experiments were done with the following results : (1) Cumene hydroperoxide a t concentrations up to 5 x 1 0 - 2 M had no influence upon the oxidation rate with or without added tetralin hydroperoxide. ( 2 ) The addition of tetralin up to 0.03 M had no influence upon the rate, demonstrating that abstraction of "normal" tetralin hydrogens is not involved. ( 3 ) There is no measurable kinetic isotope effect observable when T02D (65%) is used in place of TOzH. These experiments were run a t (2) H. W. Melville and S. Richards, J . Chcm. SOC.,944 (1994).
(3) G.S. Hammond, J. N. Sen and C. E. Boozer, J . A m . Chem. SOL., 77, 3244 (1955).
