1118
Biochemistry
DILIP RAVAL AND R. G. WOLFE
Malic Dehydrogenase.
IV. pH Dependence of the Kinetic Parameters* DILIPN. RAv&t
AND
R. G. WOLFE
From the Chemistry Department, University of Oregon, Eugene, Oregon Received May 23, 1962
The pH dependence of the kinetic parameters of the reaction catalyzed by pig heart malic dehydrogenase has been investigated. The kinetic behavior of the system is explained through a model in which groups on the enzyme surface which have p K values of approximately 7 and 10 are involved in the catalytic function, and the proton generated during the oxidation of malate is taken up by the enzyme and not by the solvent. Calculated values of the individual rate constants for the reaction between various charged forms of the enzyme and the coenzyme are given. A compulsory substrate binding order mechanism involving one or more ternary complexes is compatible with the experimental data at every p H value studied. The dissociation of the coenzymeproduct from the enzyme-coenzyme complex appears to be the rate limiting reaction in both forward and reverse reactions. Detailed kinetic studies of pig heart malic dehydrogenase involving initial rate measurements at p H 8.0 and 25" have been reported in paper I1 (Raval and Wulfe, 1962a) of this series. Product inhibition studies have been reported in paper I11 (Raval and Wolfe, 1962b) of this series. The most plausible mechanism, the compulsory binding order mechanism given below, is supported by three types of evidence: 1. The over-all thermodynamic equilibrium constant is in agreement with that obtained with use of kinetic constants on the basis of the compulsory binding order mechanism. 2. Experimental values are in good agreement with theoretically predicted relationships between kinetic constants, assuming the compulsory binding order mechanism with a rapidly dissociating ternary complex. 3. Product inhibition studies indicate the presence of a ternary complex. The compulsory binding order mechanism, which may contain one or more ternary complexes, can be represented as follows: ki E
+ DPN
E.DPN
k? E-DPN
+M
kr EXY . eE.DPNH ke,
K, EXY
h
+ OAA + H +
k7
E.DPNH
+ E + DPNH ks
Previous kinetic studies have not considered the role of the proton generated as' a product or ab-
* This investigation was supported in part by Public Health Service Grant H 3226 from the National Heart Institute. t T a k e n from a thesis submitted in partial fulfillment of the requirements for the Ph.D. degree, University of Oregon, 1962, by Dilip N. R a d .
sorbed as a reactant in the above reaction. Moreover, Dalziel (1957) and Theorell (1958) have reported an apparent change in the reaction mechanism with pH in the case of yeast alcohol dehydrogenase. Variation in the values of kinetic parameters with p H has been interpreted in terms of ionizable groups on the enzyme by Alberty (1953). The above considerations have led to the p H dependence studies reported here. METHODS The enzyme isolation and assay methods used were identical to those described previously (Raval and Wolfe, 1962a) except that a Cary model 11 recording spectrophotometer was used at acid pH values. Tris acetate buffer, 0.05 M with respect to acetate, was used in all experiments. The ionic strength was therefore constant at 0.05 except for a small decrease in the extreme acid range because of the association of protons to form acetic acid. The pH of all solutions was adjusted with Tris (Sigma 121) so that the concentration of uncharged Tris increased at the higher pH values. The stability of the reagents was studied at each p H , and experimental conditions were carefully controlled to avoid decomposition. Substrate inhibition or activation (rates less than or in excess of that predicted by simple Michaelis-Menten theory) occurred at concentrations which were a function of p H . It was found possible to avoid concentration ranges where such effects were observed though velocity measurements were made over substrate concentration ranges which bracketed the Michaelis constant value in each experiment. The temperature was maintained constant at 25" by circulating water from a thermostated The following abbreviations are used throughout this paper: DPN = oxidized coenzyme, DPNH = reduced coenzyme, M = malate, OAA = oxalacetate, E = free enzyme, EXY = the ternary complex, and Tris = tris(hydroxymethy1)aminomethane.
Vol. 1, No.6,November, 1962
MALIC DEHYDROGENASE IV,PH DEPENDENCE KINETIC STUDIES
water bath through thermospacers in the spectrophotometer. All experimental parameters reported in this paper were obtained by extrapolation to conditions which were zero order with resped to both substrates. The reader is referred to previous work (Dalziel, 1957, or Raval and Wolfe, 1962a) for the details of extrapolation methods and methods of evaluating the experimental parameters. RESULTS
In the following discussion the reaction in the direction of malate oxidation will be referred to as the forward and that in the direction of oxalacetate reduction as the reverse reaction. Table I summarizea the values of various kinetic parameters a t a series of p H values in the range between pH 5.5 and 10.25.
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TABLE I1 THERMODYNAMIC AND KINETICOVER-ALL EQUILIBRIUM CONSTANTS FOR THE REACTION CATALYZED BY MALICDEHYDROGENASE AT VARIOUSp H VALUES PH 5.5 6.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.25
aPP.a Ke, 3.1 1 1 3.1 I 3.1 1 3.1 1 1.7
Vf.Knmri .OM V ~ . K D PM N .
x lo-’ 1 . 0 x x 106 1 . 5 x x 10-5 1 . 2 x x 10-5 3 x x 10-4 1 . 0x x 10-4 2 . 0 x x 10-3 1 . 0x x 10-3 4 . 0 x x 1.0 x x lo-% 1 . 7 x
lo-’ 10-6
10-5 10-5 10-4
10-4 10-3 10-3
10-2 10-2
vf3.Knp~~.Ko.4 4 VT’.KDPN.KM
x lo-’ x 10-6 1.8x 10-5 3 . 5 x 10-5 1 . 0 x 10-4 2 . 3 x 10-4 0 . 8 x 10-8 2 . 4 x 10-3 0 . 6 x 10-2 1 . 2 x 10-2 6.6 3.0
Thermodynamic equilibrium constant (Raval and Wolfe, 1962a). * The over-all equilibrium constant in terms of kinetic constants assuming a compulsory substrate binding order mechanism involving TABLE I one or more kinetically signiticant ternary complexes KINETICPARAMETERS FOR MALICDEHYDROGENASE The over-all equilibrium constant (Alberty, 1953). AT 25‘ AS A FUNCTION OF p H IN TRISACETATE in terms of kinetic constants assuming a compulsory BUFFER, IONIC STRENGTH 0.05 substrate binding order mechanism involving a kinetically insignificant ternary complex. KDPN Kr KDPN.II V / x 104 x 104 x 106 x io-‘ ous kinetic parameters and their experimental PH M M M~ M.A: 5.5 6.0 7.0, 7.5 8.0 8.5 9.0 9.5 10.0 10.25
8.0 3.0 2.2 1.4 2.0 1.3 2.5 4.8 17.0 22.0
120 0 55.0 12.0 8.0 8.0 7.0 10.0 20.0 65.0 82.0
40.0 5.0 1.0 0.6 0.6 0.4 0.7 1.5 4.5 6.0
0.3 0.3 0.5 0.6 1.0 1. o 1.6 2.5 5.0 6.3
5.5
0.5 1.2 1.5 1.8 1.8 2.1 2.0 2.2 3.5 3.0
0.2 0.8 2.0 3.0 4.0 6.0 10.0 25.0 40.0 56.0
0.06 0.2 0.5 0.9 1.9 3.4 7.6 32 0 210.0 400.0
0.4 0.8 2.0 3.0 3.5 4.0 3.8 3.6 3.0 2.7
6.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.25 a
values for a mechanism involving a kinetically insignificant ternary complex (Table IV). I t appears, therefore, that the compulsory binding order mechanism involving a kinetically insignificant ternary complex (one with a very short half life) applies over the broad p H range included in this study, and also that the ternary c o m p h becomes kinetically significant at acidic p H . The existence of a ternary complex has been suggested previously (Raval and Wolfe, 1962a), and experimental evidence of its presence was given subsequently (Raval and Wolfe, 1962b). Figure 1 represents the variation of the pre-
M.A. is t h o molecular activity of the enzyme.
TabIe I1 presents the over-all equilibrium constant as calculated from kinetic parameters at each p H studied. The thermodynamic equilibrium constant is also included in this table to facilitate comparison with kinetic values. It is apparent that there is reasonably good agreement between thermodynamic and kinetically determined values of the over-all equilibrium constant except at very acidic p H values. There is also very good agreement, except at acidic p H values, between the expeded relationships between vari-
FIG. 1.-A plot of molecular activity (M.A.) as a function of p H for both reaction directions. The open circles represent experimental points obtained with a reaction mixture containing 5 X M malate, 2 x 10-5~ DPN, and 2.4 X g/ml of malic dehydrogenase. Solid circles represent experimental points obtained with 1 X M oxalacetate, 1 X M DPNH, and 2.4 X 10-8 g/ml of malic dehydrogenase. The continuous curves represent calculated values from equations (1)and (2) using the values of kinetic parameters given in Table I.
1120
Biochemistry
DILIP RAVAL AND R. G. WOLEE
vailing initial velocity with pH in both reaction directions. The p H optimum for the forward reaction is approximately 8.9, whereas the p H optimum for the reverse reaction is approximately 7.5. The solid lines represent theoretical curves calculated from the following rate law equations by use of the values of the kinetic parameters given in Table I: V,/U
