kinetic and magnetic resonance studies of the py ruvate ... · kinetic and magnetic resonance...

THE JOURNAL OF BIOLOGICAL CHEMI~TRV Vol. 241, No. 5, Issue of March 10, 1966

Printed in U.S.A.

Kinetic and Magnetic Resonance Studies of the

PY ruvate Kinase Reaction

II. COMPLEXES OF ENZYME, METAL, AND SUBSTRATES*

(Received for publication, August 2, 1965)

ALBERT S. MILDVAN? AND MILDRED COHNI

From the Johnson Research Foundation, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104

SUMMARY

A correlation between the kinetics of the pyruvate kinase reaction and the enhancements of the relaxation rate of the nuclear spins of water protons in the ternary enzyme- manganese-substrate (E-Mn-S) complexes, et, has revealed certain salient features of the pathway of the reaction and the structure of the ternary intermediates. The rate equation for initial velocities of the forward reaction was derived by assuming (a) rapid simultaneous equilibria of enzyme with divalent metal ion, adenosine diphosphate, manganese adenosine diphosphate, and phosphoenolpyruvate, (b) random order of combination, and (c) phosphoryl transfer as the rate-determining step. This formulation permitted the calculation of the dissociation constants KS of the ES complexes and KB of the EiWS complexes for ADP and phosphoenolpyruvate. The values of KS for E-Mn-ADP and E-Mn-phosphoenolpyruvate were determined directly by equilibrium experiments with proton relaxation rate (PRR) with the use of et as the parameter which characterized the ternary complexes. The values of KS for E- phosphoenolpyruvate and E-ADP were determined directly by equilibrium experiments with the use of the kinetic protection method with p-chloromercuribenzoate inactiva- tion. The agreement of the dissociation constants of the binary and ternary enzyme complexes determined by equilibrium methods with the kinetically calculated ones, taken in conjunction with the previously established agreement of the dissociation constant of EIM with its kinetically calculated activator constant, validates the assumed random binding of metal, ADP, MnADP, and phosphoenolpyruvate to the enzyme.

The inhibitor constant, KI, for ATP agreed well with its KS determined by PRR. In the ternary pyruvate complex, the results from PRR data differed from the kinetic data in

* A preliminary report of this work was published in the Ab- stracts of the 145th American Chemical Society Meetings, 1963, p. 82~. This work was sunnorted in oart bv United States Public Health Service Grant GM- 08320 and National Science Founda- tion Grant G 23384.

t This work was done during the tenure of an Advanced Re- search Fellowship of the American Heart Association.

$ This work was done during the tenure of a Career Investiga- torship of the American Heart Association.

two ways: pyruvate was not competitive with phosphoenol pyruvate, and K3 from PRR data was an order of magnitude lower than KI obtained kinetically. The value of KS was raised to the KI value when the PRR titration was performed in the presence of ADP or inorganic phosphate, suggesting that the breakdown of the product complex in the pyruvate kinase reaction proceeds by a preferred order in which pyruvate dissociates first.

The PRR enhancement values of all the ternary EMS complexes, tt, were found to be less than tb, the enhancement of the binary complex; this decrease may be ascribed in part to the replacement of water ligands by groups on the substrate. The magnitude of the decrease of t,(ATP) with respect to E t(ADP) is consistent with a metal bridge structure in which the divalent cation is coordinated both to the enzyme and to the y-phosphoryl group of ATP in the active complex. No data have been found which contravene a metal bridge structure. Kinetic data which favor this structure may be adduced from the relative binding constants of substrates to the manganese- and magnesium-activated enzyme; changing the divalent activator from manganese to magnesium, which has a lower affinity for ligands, raised the KS of phosphoenolpyruvate and the KI of ATP and of pyruvate by factors of 2.6, 5.1, and 2.6, respectively, but it had little effect on the KS of ADP.

The structure of the E-M/In-phosphoenolpyruvate complex as reflected in the finding that tt(phosphoenolpyruvate) << tb requires a change in the environment of the manganese other than mere replacement of water ligands; such a change may be ascribed to a conformational change in the protein at the binding site.

In a previous paper (l), it has been shown that measurements of the enhancement of the proton relaxation rate of water, characteristic of a manganese-protein complex, could be used to determine the dissociation constants of the manganese and magnesium complexes of pyruvate kinase and to establish that the enzyme bound 2 metal ions per mole. Calcium, a competitive inhibitor with respect to manganese and magnesium, displaced

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Issue of March 10, 1966 A. S. Mildvan and M. Cohn 1179

manganese in the binary complex, and its dissociation constant could thus be determined. Dissociation constants determined by the PRRl and EPR techniques agreed with kinetically determined activator constants for manganese and magnesium and the inhibitor constant for calcium in the enzymatic reaction, This finding indicated that pyruvate kinase functions in combination with the activat.ing divalent cation as a metal enzyme.

The present paper extends the investigation by PRR and EPR methods to ternary complexes of enzyme, metal, and substrate. Analysis of PRR data permitted the determination of dissociation constants of those complexes which contained the paramagnetic manganous ion. Independent determinations of the dissociation constants of ES complexes can be obtained by measuring the alteration effected by substrate of the rate of in- activation of the enzyme by mercuribenzoate (2, 3).

In addition to the use of the enhancement value of complexes as a parameter to determine dissociation constants, the magnitude of the enhancement values of the various EMS complexes gives some insight into the conformat,ion of the active site. A comparison of the dissociation constants with those obtained by substrate kinetics permits the formulation of a kinetic scheme. The data obtained in this investigation thus illuminate some aspects of the mechanism of the pyruvate kinase reaction.

EXPERIMENTAL PROCEDURE

Materials

All compounds used were reagent grade or of the highest purity commercially available as previously described (1). Sodium pyruvate was purchased from Boehringer. To test for possible interference by the dimer of pyruvate (4), the experiments were repeated with potassium pyruvate prepared immediately before use from twice distilled pyruvic acid;2 identical results were obtained with both pyruvate samples. Tetramethylammonium ADP and ATP were prepared from the sodium salts of the nucleotides by ion exchange chromatography on Dowex 50.

Crystalline pyruvate kinase was prepared from rabbit muscle by the method of Tietz and Ochoa (5) and was found upon assay to have 80% of the maximum reported specific activity. For some binding experiments, crystalline pyruvate kinase purchased from Boehringer, which had 81% of the maximum reported activity, was used. No systematic differences in the kinetic or binding properties of the two preparations were detected. Some preparations of both kinds have sometimes been encountered which yield values of the enhancement of the manganese-pyruvate kinase complex as low as 24, and of the dissociation constant -0.3 X lop4 M outside the range of those previously reported. The source of these quantitative differences is not yet understood.

Methods

Kinetic Experiments-Rates of the reaction were measured by following the rate of appearance of pyruvate in the coupled assay with the use of the change in absorbance at 340 mM with lactic dehydrogenase and DPNH (1, 6). In kinetic experiments with pyruvate as inhibitor, the reaction was followed by the

1 The abbreviations used are: PRR, proton relaxation rate; T1, longitudinal relaxation time; EPR, electron paramagnetic resonance.

2 Frozen solutions of pyruvic acid are stable for months (R. W. Van Korff, personal communication).

rate of uptake of protons at constant pH by means of the Radi- ometer TTl pH-stat. In a total volume of 4.0 ml, the reaction mixture contained 0.1 M KCl, 2 mM ADP, 0.2 llZM MnCL, and 1 to 2 pg per ml of pyruvate kinase at pH 7.4. The temperature was 25”. The reaction was initiated with the tricyclohexyl- ammonium salt of phosphoenolpyruvate at a final concentration of 10 to 40 PM. The pH of the salt had been adjusted to 7.4 with HCl. The titrating agent was 0.5 m&r HCI.

Determination of Binding Parameters of Binary Enzyme-Sub- strate Complexes-The dissociation constants of the ES complexes were measured by the kinetic protection method, which has previously been shown to give the correct value of the dissociation constant of the binary Mn-enzyme complex (3). This method depends upon the alteration by the substrate of an easily measured rate constant of the reaction between the enzyme and an irreversible inhibitor such as mercuribenzoate. As previously described (3), pyruvate kinase (0.027 PM enzyme sites) was incubated initially with excess (0.5 to 1.1 pM) mercuribenzoate for 3 min in a cuvette containing 0.1 M KCl, 0.05 M Tris-HCl buffer at pH 7.5, 100 PM DPNH, and varying concentrations of the substrate under investigation in a total volume of 3 ml. The residual pyruvate kinase activity was then assayed by rapid addition of 0.5 llZM MnC&, excess crystalline lactic dehydrogenase, 10 to 15 Mg per ml, and saturating levels of the two substrates (1.0 mM phosphoenolpyruvate and 1.7 mM ADP). The enzymatic reaction was followed by the rate of change of the absorbance at 340 mp. The dissociation constant of the ES complex was determined graphically from the effect of the concentration of the substrate in the initial incubation mixture on the second order rate constant of the inhibition reaction between mercuribenzoate and pyruvate kinase (3).

Determination of Binding and Enhancement Parameters of Binary Metal-Substrate ComplexesSolutions of 50 to 100 pM

MnC12 were titrated with the appropriate substrates; the free manganese was measured by EPR (7), and bound manganese by the PRR of water (8). The results were analyzed as previously described (9) to give the dissociation constant, Ki, of the 1:l complexes and the enhancement of the effect of manganese (when bound) on the PRR of water (ea) for each substrate.

Determination of Binding and Enhancement Parameters of Ternary Complexes-Binding experiments were carried out with preparations of pyruvate kinase which were separated from ammonium sulfate by the use of Sephadex G-25 as previously described (1). The EPR technique for measuring the concentration of free manganese in the presence of Dhe enzyme and the PRR method for determining the enhancement of the effect of manganese (when bound) on the proton relaxation rate of water have been described previously (9). Solutions containing 30 to 70 PM pyruvate kinase, 50 to 100 pM MnC12, in the presence of 0.03 to 0.05 M Tris-HCl buffer at pH 7.5, and 0.1 M KC1 were titrated with identical solutions which contained, in addition, a substrate or product of the pyruvate kinase reaction.

Each manganese species has a characteristic enhancement value (e) of the PRR of water; ef refers to the free manganous ion which equals 1 by definition, ea to the binary Mn-substrate complex, eb to the binary Mn-enzyme complex, and et to the ternary enzyme-Mn-substrate complex (10). The observed enhancement (e*) in any solution containing the three components-metal, enzyme, and substrate-is a weighted average (9) of the enhancements due to each complex of manganese (the subscripts f and T refer to free and total Mn, respectively).


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Ternary Complexes of Pyruvate Kinase Vol. 241, No. 5

E* _ [Mnlr ‘, + MnSl E -- - [MnlT Mnl,

+ [EMnl Eb + [EMnSl a Mnlr

- tt MnlT (1)

where Eb = 32.7 f 3.2 for manganese pyruvate kinase as previously determined (l), The e, for each manganese substrate complex may be determined independently. The enhancement, et, of the ternary complexes of enzyme, manganese, and each substrate, as well as the relevant dissociation constants, may be evaluated graphically from the values of E*, which are measured as a function of substrate and enzyme concentrations, by expressing Equation 1 in a form amenable to graphical solution of the desired parameters as outlined below.

Let us first define the equilibria in the system in terms of the dissociation constants of the various complexes as follows.

Kz = [EIMnSl [EMnSl

K 3

= [EMnl[Sl [EMniSI

(2c)

from which it follows that for each substrate

KlK2 = K3KD = KtAKs (3)

Inserting the dissociation constants from Equations 2a to 2d into Equation 1, one obtains the following equation relating the observed enhancement e* to the concentrations of free enzyme and substrate.

(4)

Because an exact solution of Equation 4 to extract the values of et and of K8 was not feasible, the evaluation of et and KS has been achieved by graphical methods which involve several types

TABLE I

Dissociation constants (K1) and enhancements (e,) of manganese-substrate complexes

Conditions were as follows: 0.05 M Tris-HCl buffer at pH 7.5, 0.1 M KCl, and 50 to 100 PM MnC12; substrate cohcentration 54 mix; temperature, 24” f 1”.

Substrate I

Kl I 6z

P x 104

ADP . 1.0 f 0.2 1.7 f 0.1

Phosphoenolpyruvate. 19.1 f 2.8 1.15 f 0.04

ATP . 0.14 & 0.06 1.7 f 0.1 Pyruvate. 32.2 f 8.7 1.0 zk 0.1

of approximations which simplify Equation 4 and yield linear functions of [S] and [E] which allow appropriate extrapolations. The development of the requisite equations (Equations 5 to 17) for analysis by four different procedures is presented in detail in the “Appendix.” The substrate phosphoenolpyruvate was the simplest to analyze since its dissociation constant in the ternary complex, KS, is small, and its dissociation constant in the binary manganese complex, K1, is large; consequently, Kz is small. At saturating levels of phosphoenolpyruvate, a negligible variation of e* with enzyme concentration was observed in the range of concentrations experimentally investigated. Therefore, the desired parameters, et and K3, could be evaluated from titrations with varying concentrations of substrate at a single enzyme concentration; for all other substrates, it was necessary to vary the concentrations of both enzyme and substrate.

In Procedure I, the value of E at a fixed enzyme concentration and infinite substrate concentration, denoted by Ebb, is obtained by extrapolating to infinite substrate concentration in a plot of E* against l/[S]* (cf. Equation 5). A secondary plot of l/e*, against 1 /[EIT yields the value of et at infinite enzyme concentration (cf. Equation 7). Now that et has been evaluated, Kt may be determined from Equation 8 by using the values of Bag. Because Kt and KD are known quantities, KS may be evaluated from Equation 3 above.

In Procedure II, the PRR titration data are analyzed by reversing the order of extrapolation. The value of e* at infinite enzyme concentration is obtained by plotting l/e* against l/[E], (cf. Equation 6); this value is denoted by e*d. The values of e*d at different substrate concentrations are then extrapolated to infinite substrate concentration (cf- Equation 9) to obtain et. With et evaluated, K3 may be determined from Equation 10 by using the values of e*d.

Procedure III leads only to an evaluation of KS which may be equated with the value of the concentration of free substrate which produces half-maximal enhancement at saturating enzyme concentrations (cJ Equation 12).

In Procedure IV, EPR data are used in conjunction with PRR data to set upper and lower limits on et and KS. Because the concentration of free manganese is directly determined from EPR data, the first term in Equation 1 is known, and the enhancement may then be expressed in terms of the bound manganese only (cf. Equation 13). The substrate concentration required to produce half-maximal enhancement of bound manganese yields a lower limit of KP (Equation 17) which in turn may be used to evaluate a lower limit of et (Equation 6). Upper limits on these parameters may be found by assuming the lowest possible value for the free enzyme concentration, i.e. [Elf = [E]T - [Mn],, as described in the “Appendix.”

Because approximations were made to permit linear extrapolations, several independent types of analyses of the data seemed warranted (cf. “Appendix”). Equal weight was given to each type of analysis in computing the averages.

RESULTS

Dissociation Constants and Enhancements of Metal-Substrate CompZemces-Table I summarizes the constants obtained by titrations of manganese with the four substrates of the pyruvate kinase reaction. The K1 values for the nucleotides and for phosphoenolpyruvate are in agreement with dissociation constants in the literature (11, 12). Values for the dissociation


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constant of the Mn-pyruvate complex are unavailable in the literature.

Dissociation Constants and Enhancements of Ternary Complexes with Manganese-In the presence of a constant concentration (50 PM) of manganese, pyruvate kinase was titrated with ADP and the relaxation rate, l/Tl, of the protons of water was measured. The data obtained at a series of enzyme concentrations were analyzed by Procedure I as shown in Fig. 1, A and B. In Fig. IA, the observed enhancement (E*) is plotted against the reciprocal of the substrate concentration according to Equation 5, which permits extrapolation of e* t’o infinite substrate concentration. In this extrapolation, the region of downward curvature at high ADP concentration was ignored. The curvature is ascribed to the formation of the binary complex MnADP as a predominating species in the solution, as evidenced by the fact that. e* approaches an enhancement value of -1.7, which

25

20

15

E’

IO

5

0 I I I I I I I I

0 0.5 1.0 I.5 2.0 2.5 3.0 3.5

0 1 I I I I 0 I 2 3 4 I

m x lo-’ M-’ FIG. 1. A, titration of MnClz (50 PM) and pyruvate kinase with

tetramethylammonium ADP at six enzyme concentrations. The observed enhancement, E*, is plotted against l/[ADP]t,,tni according to Equation 5 of the “Appendix,” for analysis by Pro- cedure I. The concentrations were 0.1 M KC1 and 0.05 M Tris-HCI buffer, pH 7.5. Micromolar concentrations of enzyme sites: Curve 1, 32.4; Curve 2, 51.7; Curve 3, 52.7; Curve 4, 84.4; Curve 6, 129; Curve 6, 163. Temperature, 24’ f lo. Total volume, 0.1 to 0.2 ml. B, secondary plot of the extrapolated enhancement at infinite ADP concentration, Ebb, against the enzyme concentration, in double reciprocal form, according to Equation 7 for analysis by Procedure I. From the intercept on the ordinate et is equal to 21.3.

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

* Ed I5

-I

IO

5

1

01 0 0.5 I.0 1.5 2.0 2.5 3.0 3.5

- x 10-q M“

[ .bPy

FIG. 2. A, analysis of the titration data of Fig. 1A by Procedure II. Double reciprocal plot of the enzyme site concentration against the observed enhancement according to Equation 6 at the following micromolar concentrations of ADP: Curve 1, 28.4; Curve 2, 56.8; Curve 9,32.1; Curve 4, 168; Curve 6, 319; Curve 6, 376. B, secondary plot of the extrapolated enhancements at infinite enzyme concentration, E*d, against the reciprocal of the ADP concentration according to Equation 9. From the intercept on the ordinate et is equal to 19.5.

is characteristic of MnADP (Table I). A secondary plot of l/a*, against l/[E]* (Fig. 1B) yields a value for et (ADP) of 21.3 and for Kz (ADP) of 0.15 x lo-’ M. With the latter value and KD equal to 0.75 X lo-’ M (I), Equation 3 yields a value for KS of 0.21 x lo-’ M. The same data are analyzed by Pro- cedure II in Fig. 2, A and B, in which the order of extrapolation is reversed. A secondary plot according to Equation 8 (Fig. 2B) yields a value for et (ADP) of 19.5 and for KP of 0.87 x lo-’ M. KS (ADP) values which were determined by Procedures I and II differ by a factor of 4.

The concentration of free ADP for half-maximal enhancement showed no significant variation with enzyme concentration, as predicted from the fact that Kz - KD (see Equation 12). There- fore, all values of (S)+ msx were averaged to give a value for Ka of 0.67 X lo-4 M (Procedure III).

The concentration of free manganese measured by EPR di- minished significantly during the course of a titration of manganese and pyruvate kinase with ADP. By measuring the concentration of free manganese and enhancement at each point of a titration, one may use Procedure IV (Equations 13 and 14) to obtain independent limiting values of et (15.6 5 et 5 22.2) and Ka (0.58 x lo-’ M $ KS S 1.32 X N-4 M). The average values of et, Kz, and KI determined by various procedures are presented in Table III, and the values obtained with each procedure of analysis are listed in Table VIII.


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1182 Ternary Complexes of Pyruvate Kinase Vol. 241, No. 5

TABLE II Titration of pyruvate kinase and manganous chloride with

phosphoenolpyruvate at various enzyme concentrations

The solutions contained 0.05 M Tris-HC1 buffer at pH 7.5, 0.1 M KCl, and 50 MM MnC12. Temperature was 25”.

[Enzyme sitesIr I

l *c

M x 101

0.64 2.26 0.715 2.08 1.02 2.22 1.13 2.05 1.57 2.34 1.67 2.56

Average / 2.3 zt 0.4 / 0.16 f 0.4

[Phos~phodyruv- m

M x 104

(0.78) 0.24 0.12 0.18 0.15 0.11

TABLE III Summary of enhancements and dissociaiion constants determined

by PRR method

KP and Ka were calculated by Procedures I through IV, and et was calculated by Procedures I, II, and IV.

Substrate KZ K1 et

db x 1oI &f x 10’

ADP . ..___.__..._._. 0.50 f 0.18 0.68 rt 0.24 19.9 f 1.7 Phosphoenolpyru-

vate.............. 0.0059 =k 0.0020~0.15 =t 0.05~ 2.2 =t 0.2 ATP . 1.6 =t 0.8 0.31 Z!Z 0.14 13.1 & 1.2 Pyruvate. . . . 0.14 f 0.04 5.8 f 1.7 11.0 f 1.1 Pyruvate + ADP,

0.8mnn 0.82 f 0.05b 35.1 & 2.2b >19.9 PyrUVate+Pi,0.1M. 0.91 f O.lkb 39.0 f 6.0b >19.9

Q Calculated by Procedures II, III, and IV as explained in “Ex- perimental Procedure.”

b Calculated only by Procedure III as explained in “Experi- mental Procedure.”

Similar titrations were carried out with the other substrates. The extrapolations for ATP and pyruvate are shown in Figs. 3 and 4, respectively, and the constants are summarized in Table III. As mentioned previously, no experimentally significant variation of E* at saturating levels of phosphoenolpyruvate was observed when the enzyme concentration was varied. The values of Ebb, which is in this case the same as et, are listed in Table II, and the average values of et and the dissociation constants obtained by the different procedures are summarized in Table III. The values of the dissociation constants and et from the four procedures of analysis of the data are presented in Table VIII of the “Appendix” with a discussion of the degree of validity of each procedure.

It should be noted that the enhancement values of all of the ternary EMS complexes (et) are lower (cf. Table III) than the enhancement of the binary E-Mn complex (eb = 32.7 f 3.2). Moreover, the phosphorylated form of the substrate gives a lower et value than the unphosphorylated form, i.e. et (ATP) < et (ADP) and et (phosphoenolpyruvate) < et (pyruvate).

Dissociation Constants of Abortive Quaternary Complexes-The value of Ka for pyruvate, 6 x 10e4 M, found for the E-Mn-pyruvate complex was lower than the kinetically determined Kr of

pyruvate. That this complex is not the kinetically active species was shown in two ways: (a) phosphoenolpyruvate does not compete for the pyruvate site which is characterized by this dissociation constant although, as shown later, phosphoenolpyruvate does compete for the pyruvate site in the kinetically active species; and (b) in the presence of saturating levels of ADP or Pi, a considerably larger dissociation constant for pyruvate is obtained, Kt E 40 x 10e4 M, which agrees in magnitude with the kinetically determined K, for pyruvate.

Pyruvate at 5 mM and 15 mM was found, by PRR titrations with Procedure III, to increase the apparent Kt (phosphoenolpyruvate) by factors of only 2.1 and 2.0, respectively, and it did not affect et (phosphoenolpyruvate). Factors of 9.6 and 27, respectively, would have been anticipated if phosphoenolpyruvate competed directly with pyruvate at the tight binding site for pyruvate. The data indicate that the binding sites for pyruvate and phosphoenolpyruvate do not overlap in the ternary complexes of these substrates.

5 4 3

” I

0 Ol5 II0 1.; 210

ypl, x IO” M”

0.30 B

1

o- 0 0.5 1.0 I.5 2.0

TfTf x 10'4 M"

FIG. 3. A, enhancement, e*, in a titration of MnClz (50 PM) and pyruvate kinase with tetramethylammonium ATP at five enzyme concentrations is plotted against l/[ATP]t,t,i for analysis by Procedure I. Micromolar concentrations of enzyme sites: Curve 1, 48.3; Curve 2, 62.0; Curve 3, 97.0; Curve 4, 129; Curve 6, 162. Other conditions were the same as described in the legend to Fig. 1A. B, secondary plot of l/~*~ for ATP against ~/[E]T for analysis by Procedure I. From the intercept on the ordinate et is equal to 14.3.


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Issue of March 10, 1966 A. X. Mildvan and M. Cohn 1183

0 : I I t I

0 0.1 0.2 0.3 0.4

I

[Pyr”“ate]T x 10-4 M-1

0 I I I I t 0 I 2 3 4 I LEA x 1o-4 M-’

FIG. 4. A, enhancement, B*, in a titration of MnClz (50 PM) and pyruvate kinase with potassium pyruvate at three enzyme concentrations is plotted against l/[pyruvateltotal for analysis by Procedure I. Micromolar concentrations of enzyme sites: Curve 1, 47.5; Curve 2, 71.4; Curve 8, 95.4. Other conditions were the same as described in Fig. IA. B, secondary plot of l/~*~ for pyruvate against l/[EIT for analysis by Procedure I. From the intercept on the ordinate et is equal to 11.9,

In the presence of saturating levels of ADP, the dissociation constant of pyruvate from the E-Mn-ADP-pyruvate complex was determined from the concentration of pyruvate at half- maximal enhancement in the titration curve, of Fig. 5 (Proce- dure III). These conditions, namely the inclusion of a nucleotide as a component of the system, more closely parallel the conditions of the kinetic experiment. A similar titration curve for pyruvate was observed when 0.1 M inorganic phsophate replaced ADP. The dissociation constant of pyruvate, therefore, is also increased by the presence of inorganic phosphate, a condition under which Rose (13) observed detritiation of labeled pyruvate catalyzed by pyruvate kinase, a reaction with a high Km for pyruvate.

From Fig. 5, it may also be seen that titration of the ternary E-Mn-ADP complex with pyruvate causes an increase in e*. A similar increase in e* was observed on titrating the E-Mn-Pi complex with pyruvate, which suggests that theenhancements, eq, of the quaternary E-Mn-ADP-pyruvate and E-Mn-Pi-pyruvate complexes are higher than et of the ternary E-Mn-ADP and

E-Mn-Pi complexes. To extract the value of the enhancement of the quaternary complexes would require extrapolation of E* to infinite concentrations of pyruvate, ADP, and enzyme.

Kinetic Constants of the SubstratesFig. 6 shows the results of a kinetic experiment in which the concentrations of ADP and manganese were varied at a saturating concentration of phosphoenolpyruvate. The concentrations of free substrates were calculated from the simultaneous equations given by the dissociation constants of the manganese-substrate complexes (Table I). The resulting cubic equations were solved by successive approximations (1). The data fit the general equation derived by Dixon and Webb for a metal-activated enzyme with the assumption of equilibrium kinetics and random order combination of metal and substrate with enzyme (16).

v v=

KsK’a ’ ’ [Mnl[Sl

l I [Mnl I H (18)

k’~ KS

in which KD; K’,, and K8 have been defined (Equations Za, Ze, and 2f).

The intersection of lines gives Ky, as may be seen by setting [S] = -KS. The resulting equation shows 2, to be independent of [Mn], a condition which exists only at the intersection.

v v=-

l-- KD

(19)

K& is found by the intercept on the abscissa of the secondary plot of l/V([S] -+ m) against l/[Mn]. KD is found by plotting the data in the alternative manner, i.e. l/[Mn] against l/v at various levels of [X] (1). KS can be evaluated from Equation 3.

Plotting l/[MnADP] against l/v yields points which lie on a straight line with a K,(MnADP) equal to 1.1 f 0.4 x 10e4 M,

E* (No ADP)

15

IO E*

(+ ADP)

[ Pyruvate ] x IOJ T

FIG. 5. The enhancement, E*, in titrations with pyruvate of the E-Mn-ADP complex and of the E-Mn complex, respectively. To a solution containing 791 I.~M ADP, 40.4 PM pyruvate kinase sites, 50 PM MnCl2, 0.1 M KCl, and 0.03 M Tris-HCI at pH 7.5, aliquots of an identical solution which also contained 0.058 M potassium pyruvate were added. Ka (pyruvate), obtained from the concentration of free pyruvate required to produce half-maximal enhancement (Procedure III), is 3.9 X 10-S M; temperature, 19”. As shown, a similar titration was performed with ADP omitted from the solutions in which K, (pyruvate) was.equal to 3.4 X 1V M (Procedure III).


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Ternary Complexes of Pyruvate Kinase Vol. 241, No. 5

which suggests that the E + MnADP --f EMnADP pathway those of Reynard et al. that ATP is competitive with respect to can also operate to form the active complex (15, 17, 1). The phosphoenolpyruvate. With both magnesium and manganese, various kinetically determined dissociation constants are sum- additional inhibition occurs at high concentrations of ATP which marized in Table IV. may be due to the removal of the divalent activator by the for-

Fig. 7 gives the results of an experiment in which phosphoenolpyruvate and manganese were varied at a saturating level of ADP. The dissociation constants derived from the kinetic data are summarized in Table IV.

40

Inhibitor Constants of Pro&c&--Product inhibition by ATP was discovered by Meyerhof and Oesper (18) and studied in detail in magnesium-activated pyruvate kinase at pH 8.0 and 0” by Reynard et al. (15). The results with manganese-activated pyruvate kinase are shown in Fig. 8 and are in agreement with

0 2 C E30

* 2 x

T TZO x E

s

I I I I

5 IO 15 20

[*h‘ x 10-4 M-’

FIG. 6. Double reciprocal plot of free ADP concentration against initial velocity of the pyruvate kinase reaction at a saturating concentration of phosphoenolpyruvate (1 mM) and at varying levels of manganese. Total micromolar concentrations of manganese: Curve 1, 66.7; Curve 2, 100; Curve S, 133; Curve 4, 200; Curve 6, 300; Curve 6, 500. Each cuvette contained, in addition, 0.05 M Tris-HCl buffer (pH 7.4), 0.1 M KCl, 150 PM DPNH, and 25 pg of crystalline lactic dehydrogenase in a total volume of 3.0 ml. The reaction was started by adding 2.7 rg of pyruvate kinase. Temperature, 29”. The reaction was followed spectro- photometrically at 340 rnp (1, 6). Free ADP was calculated as described in “Results.” The turnover number is defined as the number of molecules of pyruvate formed per active site per min, with the assumption that the molecular weight of pyruvate kinase is 237,000 (14) and the enzyme has two active sites per mole (1, 15).

; b IO E ; .

/’ Lf

2 -5 0

I I I I

5 IO 15 20

[ 4, x IO-’ M-1

FIG. 7. Double reciprocal plot of free phosphoenolpyruvate (PEP) concentration with respect to the initial velocity of the pyruvate kinase reaction at a saturating concentration of 2.0 mM ADP and the following micromolar concentrations of manganese: Curve 1, 50; Curve 2, 100; Curve S, 200. Temperature, 29”. Other components of the reaction mixture are the same as described in Fig. IA. Free phosphoenolpyruvate was calculated as described in “Results.”

FIG. 8. Double reciprocal plot of free phosphoenolpyruvate (PEP) concentration with respect to the initial velocity at three ATP concentrations which shows competition between ATP and phosphoenolpyruvate in the manganese-activated pyruvate kinase reaction. The concentrations were 2.0 mM ADP, 4.0 rnM MnC12, and as follows for tetramethylammonium ATP: Curve 1, 2.5 mM; Curve 2, 1.25 mM; Curve d, 0. Other components are the same as described in Fig. IA. Temperature, 29”.

TABLE IV

Dissociation constants of substrates from manganese-activated pyruvate kinase determined by substrate kinetics

Conditions were as stated in legends to Figs. 6 to 9.

Substrate

ADP . . Phosphoenolpyruvate ATP Pyruvate....................

K’ A

KS K3 KI

2z x 104 di x 10’ M x 104 &%I x 104

0.210 f 0.074 1.48 f 0.20 0.44 f 0.06 0.48 f 0.09 0.41 f 0.05 0.27 i 0.05

0.66 f 0.08 40 f 14


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mation of the binary metal-ATP complex under these conditions. The KI of ATP was calculated with the assumption that ATP was also competitive against ADP (15).

Fig. 9 shows pyruvate to be a competitive inhibitor with respect to phosphoenolpyruvate with a KI equal to 4 x 10-s M.

In an experiment not shown, pyruvate had very little effect on the K, of ADP. This observation was taken into account in calculating the KT of pyruvate. The inhibitor constants of the products of the manganese-activated pyruvate kinase reaction are summarized in Table IV.

Alteration of Kinetic Parameters with Magnesium as Divalent Activator-We have previously shown that manganese and magnesium (1) combine with pyruvate kinase and activate the enzyme in a similar manner with only quantitative differences in affinity and maximum velocity. The kinetic experiments with variation of substrates were repeated with magnesium as the activator and other conditions identical with the previous studies. The kinetic constants are summarized in Table V. As expected, the substitution of magnesium for manganese as the divalent cation had no effect on Ks, the dissociation constant of the ES complex. The kinetically determined dissociation constant of ADP from EM-ADP (and also the K&M-ADP)) were unaf-

-6 -6 -4 -2 0 i i 6 s

- x lo- M-1 &I‘

FIG. 9. Double reciprocal plot of free phosphoenolpyruvate (PEP) concentration with respect to the initial velocity at three pyruvate concentrations which shows competition between pyruvate and phosphoenolpyruvate in the pyruvate kinase reaction. The course of the reaction was followed in an autotitrator set to deliver 0.5 mM HCI to maintain the pH at 7.4. The concentrations were 0.1 M KCl, 0.2 mM MnC12, 2.0 mM ADP, and as follows for potassium pyruvate: Curve 1,O; Curve &2.2 mM; Curve S, 4.4 mM. Total volume was 4.0 ml. Temperature, 25”.

fected, but the Ka value of phosphoenolpyruvate increased as did the KI values of ATP and pyruvate. These increases, although small. are of the same order of magnitude as the relative values of the dissociation constants of the magnesium complexes and the manganese complexes of the substrates (see Table VI.

Determination of Dissociation Constants of ES Complexes (Ks) by Kinetic Protection Method-The kinetic results suggest that substrates can combine with pyruvate kinase in the absence of the divalent activator to form binary ES complexes. The existence of such ES complexes was demonstrated independently by studying the effect of each of the four substrates on the rate of inhibition of pyruvate kinase by mercuribenzoate (3). It was found that each substrate protected pyruvate kinase from loss of activity induced by reaction with mercuribenzoate, i.e. reduced the rate of formation of the inhibited enzyme. Halving of the

[ADP] X IO’ M

FIG. 10. The effect of ADP on the rate of inhibition of pyruvate kinase by mercuribenzoate. The reciprocal of the apparent rate constant is plotted against the concentration of the protector (3). The intercepts on the abscissa are the dissociation constants of the pyruvate kinase-ADP complexes: 2.0 X 1W4 M for Type I sites and 3.6 X 1OW M for Type II sites. Pyruvate kinase (1.5 pg per ml) was preincubated with excess (0.34 HM) mercuribenzoate in 0.05 M Tris-HCl buffer at pH 7.5, 0.1 M KU, 100 PM DPNH, and various concentrations of ADP for 3 min. The enzymatic reaction was started by adding the components to give a final concentration in the cuvette of 1 mM phosphoenolpyruvate, 5 mM ADP, 0.5 mM MnC12, and 15 pg per ml of lactic dehydrogenase. Temperature, 25”.

TABLE V Dissociation constants of substrates determined by substrate kinetics with magnesium-activated pyruvate kinase compared

with manganese-activated enzyme The solutions contained 0.05 M Tris-HCI buffer at pH 7.5 and 0.1 M KCI. Temperature was 27’ f 2’.

Substrate Kk (with Mg)

M x m

ADP . . . . . . . . . . . . . . . . . . . 2.67 f 0.62 Phosphoenolpyruvate . 1.92 f 0.23 ATP . . . . . . . . . . . . . . . . Pyruvate . . . . . .

KS (with W Ka (with Mg) RI (with Mg)

M x 104 M x 101 1.26 f 0.41 0.71 i 0.27 0.66 i 0.25 0.71 f 0.22

M x 104

3.39 i 0.38 105 i 45

Ks (with Mg)/ KS (with Mn)

1.6 3.4-6.3” 2.6 3.1*

5.1 3.2-8.Oa 2.6 3.7c

a See Reference 11. b See Reference 12. e Acetylacetone. See Reference 19. Data on Mg-pyruvate not available.


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1186 Ternary Complexes of Pyruvate Kinase

rate of reaction of pyruvate kinase with mercuribenzoate was effected by 3.1 mM ADP, 33 FM phosphoenolpyruvate, 2.8 mM ATP, and by 0.21 mM pyruvate.

Complete titrations of the effect of substrate concentration

1 I I I I I I I

-4 -2 0 2 4 6 6 IO

[PEP] X IO4 M

FIG. 11. The effect of phosphoenolpyruvate (PEP) on the rate of inhibition of pyruvate kinase by mercuribenzoate. The data are plotted as in Fig. 10. The intercepts on the abscissa are the dissociation constants of the pyruvate kinase-phosphoenolpyruvate complexes: 4.1 X 10Y6 M for Type I sites and 3.4 X 10m4 M for Type II sites. Pyruvate kinase, 3.2 rg per ml, was preincubated with excess (1.7 PM) mercuribenzoate in 0.05 M Tris-HCl buffer at pH 7.5,0.1 M KCl, 100 PM DPNH, and various concentrations of phosphoenolpyruvate for 3 min. The enzymatic reaction was started as described in Fig. 10 and in “Experimental Procedure.” Temperature, 25”.

TABLE VI Dissociation constants of binary ES complexes determined by kinetic

protection method

The solutions contained 0.05 M Tris-HCl buffer at pH 7.5 and 0.1 M KCl. Temperature was 25”.

Substrate K (Type I sites) K (Type II sites)

M x 104 M x loa

ADP . . . . . . . 1.4 * 0.2 31 f 8 Phosphoenolpyruvate . . 0.33 z!z 0.07 2.8 f 1.0

Vol. 241, No. 5

on the second order rate constant of the inhibition reaction were performed with ADP and phosphoenolpyruvate, and the results are shown in Figs. 10 and 11. This type of linear plot gives the dissociation constant of the ES complex by extrapolation to the abscissa (3).

For ADP and phosphoenolpyruvate, two types of sites were detected by the kinetic protection method as shown by the bi- phasic character of the curves in Figs. 10 and 11, respectively. Table VI summarizes the dissociation constants of these complexes. The smaller dissociation constants of ADP and phosphoenolpyruvate from one type of site (Type I) agree with the K,(ADP) and &(phosphoenolpyruvate), respectively, which were determined by substrate kinet.ics (cf. Table VII). The kinetic significance of the weaker binding sites (Type II) for both substrates is unknown. It may be noted that the dissociation constant of phosphoenolpyruvate from Type II sites is in good agreement with a dissociation constant (3.0 X 10e4 M) measured by Kayne and Suelter in the presence of 0.1 M tetramethylammonium chloride with the use of ultraviolet difference spec- troscopy (20).

The dissociation constants (K3, KI, and K,) from substrate kinetics are compared with those from the binding studies (KS and Ks) in Table VII. With the exception of pyruvate, the values of KS and KI from kinetics are in good agreement with KS, the dissociation constant of the ternary EMS complex to EM amd S. In the case of pyruvate, the value of KI derived from kinetic experiments is in agreement only with the value of KP from those binding experiments performed in the presence of saturating levels of ADP or inorganic phosphate. It should also be noted that the KS values of ADP and phosphoenolpyruvate agree with the dissociation constants of E-ADP and E-phosphoenolpyruvate obtained by the kinetic protection method.

DISCUSSION

The agreement of the dissociation constants of the ternary complexes from proton relaxation rate studies, with et as the parameter characteristic of the EMS complex, with the dissociation constants from kinetic studies suggests that the ternary complexes thus characterized are the enzymatically active complexes (with the exception of the pyruvate complex). The large differences between the enhancements of the ternary complexes (et) and the enhancement of the binary complex (Q) indicate that the binding of substrates to the manganese enzyme alters the environment in the coordination sphere of manganese.

Thus, in addition to the use of E for the evaluation of diseocia- tion constants, an examination of the parameters which deter-

TABLE VII Comparison of dissociation constants of ES and EMS complexes obtained from PRR, Michaelis-Menten kinetics, and

kinetic protection method

Proton relaxation rate Michaelis-Menten kinetics Kinetic protection method Substrate (Type I sites)

KS K8 KI KS KS

24 x 10’ 24 x 104 M x I04 M x 104 M x 104

ADP. . . . . . . . . 0.68 f 0.24 0.44 f 0.06 1.48 f 0.20 1.4 f 0.2 Phosphoenolpyruvate . . . . . . 0.15 f 0.05 0.27 f 0.05 0.41 f 0.05 0.33 f 0.07 ATP . . . . . . 0.31 i 0.14 0.66 f 0.08 Pyruvate . . , . . . . . . 5.8 f 1.7 Pyruvate + ADP . . . . . 35.1 f 2.2 40 f 14 Pyruvate + Pi.. . . . . . 39.0 f 6.0


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Issue of March 10, 1966 A. S. Mildvan and M. Cohn

mine T1 may yield some insight into the changes in molecular orientation or molecular motion, or both, which have occurred among the various ternary complexes and the binary complex and account for the observed differences in the enhancements.

According to the formulation of Luz and Meiboom (21),

1 1 1 P -=---= 2’1, TI* TKO, 7~ -I- TLU

(20)

where l/TIP equals the paramagnetic contribution to the observed relaxation rate (l/T1*); p is the ratio of the number of protons in the first coordination sphere of the manganese which can equilibrate with the bulk water to the total number of protons in the solvent; 7M is the lifetime of a water molecule in the coordination sphere, i.e. the reciprocal of the chemical exchange rate of water coordinated to the metal ion; and TIM is the relaxation time of a water molecule in the coordination sphere of the metal ion. The expression of TIM in terms of the molecular parameters of the system formulated by Bloembergen and Solomon reduces (Equation 21), in the case of the manganous ion under our experimental conditions, to

where r is the distance between the manganese and proton nuclei, p is the magnetic moment of the ion, and rC is the correlation time; in the case of the manganous aquocation, 7C is equal to TV, the rotational correlation time of water (-IO+ set). In the aquocation, rM is small compared to TIM, i.e. the rate of exchange of water is fast in comparison with the relaxation rate in the hydration sphere of the metal ion (22), and consequently, the observed relaxation rate is determined by rC (cf. Equations 20 and 21). To explain the enhancement in relaxation rate, l/Tr,, observed in the binary E-Mn complex over that of the Mn aquocation, Eb, one must invoke a decrease in TIM (Equat,ion 20) and, consequently, an increase in 7C (Equation 21). However, to explain the decrease in l/TIP in t.he ternary E-Mn-ADP complex (et < eb) and the further decrease in the ATP complex, it is unnecessary to invoke a change in rC; a change in p will suffice.

If we compare the enhancement values of the ternary complexes of Mn-pyruvate kinase with ATP and ADP, respectively, the ratio according to Equation 20 becomes

P (ATP) l t (ATP) l/Tl,(ATP) 4ATP) + TIM(ATP) 13.1 -= et (ADI l/T&ADP) = p(ADP) = G

= 0.658

.A&&) + Tl&ADP)

If we make the assumption that TM and TIM are equal for the ternary complexes of ATP and ADP, then the difference in r,(ATP) and e,(ADP) may be ascribed entirely to a change in p, and it follows that the number of water molecules, in the coordination sphere of the ion in the ATP complex is’ 3 of the number in the ADP complex. The ratio p(ATP):p(ADP) = 0.66, and with the assumption that the difference in p between E-Mn-ATP and E-Mn-ADP is 1 water molecule, the number of water molecules coordinated to manganese in the (E-Mn- ATP) complex equals 2 and in the (E-Mn-ADP) complex equals 3. Thus it is sufficient to invoke the replacement of one additional water ligand on the manganese in the ternary ATP complex relative to the ADP complex as the sole structural change to explain the experimentally determined ratio of et for these com-

plexes. It is tempting to identify the y-phosphate group as the replacing ligand on the manganese in the ternary complex which would establish a structure for the complex with the ion as a bridge between enzyme and ATP. One can only say, however, that the data are consistent with such a structure.

A similar calculation with the same assumption may be carried out for the binary E-Mn complex. The ratio e,(ATP) :eb = 0.40 and Q(ADP):E~ = 0.61; therefore, the number of water molecules coordinated to manganese in the E-Mn complex becomes 5.0. This number is of the right order of magnitude for the number of protons exchangeable with water remaining in the coordination sphere of the metal ion in the binary octahedral complex because the protein donates two ligands, one of which may be an a-amino group (1). The latter would be equivalent to a water molecule since it contains 2 protons exchangeable with the solvent water, and thus the number of water or equivalent ligands would change from six in the aquocation to five in the binary complex. Thus, the simplifying assumption in the interpretation of enhancement data, i.e. that only p changes in the formation of the ternary nucleotide complexes from the binary E-M complex, leads to the conclusion that ADP donates one or more ligands3 to the enzyme-bound metal ion and ATP donates an additional ligand to the metal ion. Such an interpretation of the data is consistent with the hypothesis that the divalent ion serves as a bridge between the enzyme and its nucleotide substrates. This hypothetical role of the metal ion as an activator in enzyme reactions was first suggested by Heller- man and Stock (23) and has since been extended to a number of enzyme systems (2426).

An analogous treatment of et dat,a for E-Mn-phosphoenolpyruvate (I) and E-Mn-pyruvate (II) leads to unreasonable values for p in the two ternary complexes.

P(I) 41) TMI(I) + Tld) 2.2 -= Et (II) p(D) = KG = o.20

4Ii+ TdII)

Again, if it is assumed that T,U and TIM remain unchanged, and that the difference between pcpyruvate) and p(phosphoenolpyruvate) is due to the replacement of 1 water molecule, the number of water molecules in the pyruvate and phosphoenolpyruvate complexes becomes 1.25 and 0.25, respectively. I f the value for the phosphoenolpyruvate complex were indeed correct and practically no water remained in the coordination sphere of the metal ion, its PRR would be less than that of the aquocation and et would be less than 1; however, the observed value of et is 2.2. In addition, if approximately 1 water molecule remains coordinated in the E-Mn-pyruvate complex, pyruvate must consequently have replaced 3 water molecules in the manganese coordination sphere; that pyruvate can serve as a tridentate ligand is highly unlikely. Therefore, it appears that the assumption that only p is different in the ternary complexes of phosphoenolpyruvate and pyruvate, respectively, is

3 Although the simplified treatment of the enhancement data indicates two ligands from ADP to the manganese in the ternary complex, the kinetically determined Kz for ADP, unlike that for ATP, is the same with magnesium and manganese. This finding would suggest that ADP is not a bidentateligand for the metal ion in the ternary E-M-ADP comnlex since the dissociation constants of the magnesium and manganese chelates of ADP differ (cf. Table V).


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1188 Ternary Complexes of Pyrwate Kinase Vol. 241, No. 5

M + S, ti MS,

M + S, e MS,

M + P, == MP,

FIG. 12. Tentative kinetic schema of the pyruvate kinase reaction. The solid arrows give the preferred pathways of the M, divalent activator; &, ADP; SZ, phosphoenolpyruvate; PI, ATP; Pp, pyruvate.

reaction.

untenable. Either rM or TIM; i.e. 7e, or both, must also be different.

By a similar comparison of the binary E-Mn complex, with the ternary complexes, it must also be concluded that a change solely in the number of water molecules remaining in the coordination sphere of the metal ion is insufficient to explain the observed differences in PRR when pyruvate or phosphoenolpyruvate is bound. Either the exchange rate of water in the coordination sphere of the metal ion, i.e. l/rM, has decreased, or l/TIN has decreased, and the rotational motion of the water in the coordination sphere is less hindered, i.e. 7C has decreased, or perhaps both. In any case a change in the environment of manganese bound to the enzyme must be invoked upon binding of phosphoenolpyruvate or pyruvate to explain the values of et for these substrates. Experiments are now in progress to determine whether the dominant change occurs in rM or in TIM; a change in TIM would necessitate a conformational change in the protein. It should be noted that Kayne and Suelter (20) observed the appearance of a tyrosine difference spectrum upon addition of phosphoenolpyruvate to the metal enzyme.

From the above discussion, it follows that the PRR data on the four substrates cannot be used to distinguish whether or not these substrates are coordinated to the metal ion in the ternary complexes. The PRR data on the nucleotide ternary complexes are consistent with a metal bridge structure. Inde- pendent evidence for the metal bridge concept comes from the fact that KS < KS for ADP and phosphoenolpyruvate and from the observation that the KS of phosphoenolpyruvate and the KI of pyruvate and of ATP increase by the expected amount when magnesium is substituted for manganese as the divalent activator.

Direct evidence for a metal ion with ligands from protein and a small molecule exists only in azide interaction with myoglobin crystals, in which case it has been demonstrated from x-ray analysis (27) that both azide and the protein provide ligands to the heme iron. There is, at present, no unequivocal evidence for an enzyme-metal-substrate bridge structure in solution. Such evidence is being sought in ternary pyruvate kinase complexes by investigating the nuclear magnetic resonance spectra of the substrates in such complexes.

The agreement between the dissociation constants of ES and EMS complexes, Ks and KD, of phosphoenolpyruvate and ADP from kinetic studies with their respective Ks and KS values from binding studies of the individual substrates confirms the proposed scheme of equilibrium kinetics (l), and the random

X-H

5-33

FIG. 13. The formation of the binary complex in the pyruvate kinase reaction. Y represents an or-amino group or an atypical -SH group (1). X-H represents an unidentified proton donor (13).

binding of metal and substrates to the enzyme (1) in the pyruvate kinase reaction. The existence of noncompetitive in- hibitors (1, 28) of the enzyme also supports this formulation. We have previously shown (1) that the order of combination of enzyme with the divalent activator, on the one hand, and with the substrate ADP, on the other, is random. We may now con- clude that the formation of the quaternary complex E-Mn- phosphoenolpyruvate-ADP is completely random. The kinetic data also permit the pathway involving the metal-nucleotide complex to combine with the free enzyme (15, 17) and therefore cannot be used for the unique determination of the structure of the true intermediates.

With respect to the products, although,KI of ATP agreed with its K, Kr of pyruvate was an order of magnitude higher


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P o--p -0 -P-O -Ribose -Adenine /

E, - 2

FIG. 14. Postulated ternary complexes in the pyruvate kinase reaction. A, ADP; and B, phosphoenolpyruvate

than its KS. Reynard et al. (15) have observed a similar dis- crepancy for pyruvate with the magnesium-activated enzyme. The tight binding site for pyruvate appears to be different from the phosphoenolpyruvate-binding site since binding studies of the ternary complexes reveal no direct competition between pyruvate and phosphoenolpyruvate. The ancillary binding site for pyruvate with a low dissociation constant exists even in the absence of the divalent activator as was revealed by the kinetic protection method. The presence of the nucleotide (ADP) is required to obtain competition between pyruvate and phosphoenolpyruvate and leads to agreement between KS (pyruvate) and Kr (pyruvate). The Km of pyruvate in the reverse reaction (29) and in the detritiation reaction (13) is also much higher than its KS. This suggests that the nucleotide.must be present for the proper binding of pyruvate. A tentative kinetic schema of the reaction (neglecting the monovalent ion) in which the product complex preferentially loses pyruvate is shown in Fig. 12. Preliminary simulation of this schema in a digital computer suggests that it is feasible; i.e. it does not require the assumption of unreasonable rate constants to fit the observed dissociation constants and kinetic parameters.4

The enzyme kinetics were carried out at -lo-* M enzyme, 4 L. Kerson and D. Garfinkel, unpublished observations.

and the PRR equilibrium studies involved enzyme concentrations in the range of lo-’ M; therefore, it is apparent that the dissociation constants hold over a wide range of protein concentrations. A second type of binding study by the kinetic protection method at 10-* M enzyme gratifyingly yielded the same KS values as those obtained by substrate kinetics.

We have attempted to restate all the experimental observations presented in this investigation as well as relevant data from other laboratories in terms of tentative structures of intermediates and a tentative reaction mechanism as illustrated schemati- cally in Figs. 13 to 15. Boyer was unable to detect a phosphorylated enzyme by three independent techniques (30). Hence a direct phosphoryl transfer from phosphoenolpyruvate to ADP was proposed. The feasibility of direct transfer follows from the observation (15) that product inhibition by ATP is competitive with respect to phosphoenolpyruvate. This is confirmed in the present investigation and implies that the phosphoryl group which undergoes transfer occupies the same site on the enzyme whether it is in phosphoenolpyruvate or in ATP. Rose showed (13) that pyruvate kinase also catalyzed a hydrogen exchange reaction in the methyl group of pyruvic acid which met the re- quirements of a true partial reaction of the over-all phosphoryl transfer reaction.


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-Ribose -Adenine

-Ribose -Adenine

FIG. 15. Mechanism of conversion of the substrate complex to the product complex in the pyruvate kinase reaction

In the first step, Fig. 13, the divalent activator is shown to phosphoenolpyruvate, converts it to a methyl group, and thus effects the keto-enol tautomerization (13). The product complex in Fig. 15 indicates that ATP donates two ligands to the bound manganese.

combine with an -imidazole ‘ligand and another ligand Y, which may be either an cr-amino group or an atypical sulfhydryl group (1). This combination results in a conformational change of the protein (1, 3, 20, 31) and yields a binary complex in which the rotational motion of water molecules remaining in the coordination sphere is considerably hindered (1). The substrate ADP combines with the Mn-enzyme complex (Fig. 14A), donates one ligand3 to the bound manganese, and reduces the enhancement to 19.9. The substrate phosphoenolpyruvate donates a ligand to the manganese (Fig. 14B) and also causes a further conformational change which may “open up” the site; this is inferred from the large decrease in the enhancement to 2.2. The group designated X-H in Fig. 14B is in a position to protonate the vinyl carbon atom of phosphoenolpyruvate. The structure of the quaternary E-Mn-ADP-phosphoenolpyruvate complex (Fig. 15) is merely the superposition of the structures of the two ternary complexes of Fig. 14. Preceding or during the phosphoryl transfer from phosphoenolpyruvate to ADP, the group X-H protonates the vinyl carbon atom of

These mechanistic speculations are designed as a working hypothesis to guide future experimentation. The role of the required monovalent activator has been omitted in the formulation; we have shown (32) that the monovalent ion controls the conformation of the ternary complexes although the chemical basis for this control is not clear at present.

Finally, despite the limited information at hand, it is clear that the mechanism of action of pyruvate kinase is different from that of creatine kinase (10). In creatine kinase, there is no evidence for a functional metal-enzyme complex (33, 34). Rather, the divalent activator combines with the nucleotide to form an active metal-substrate complex. It appears, therefore, that there are at least two types of mechanisms applicable to kinases: those in which the protein donates ligands to the divalent metal ion in the active complex (as in pyruvate kinase) and those in which the protein does not (as in creatine kinase).


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Issue of March 10, 1966 A. 8. Mildvan and ill. Cohn 1191

APPENDIX

Evaluation of et and KS

Glossary of Enhancbment Symbols

ef = enhancement’ of free Mn++ = 1. ea = enhancement of binary Mn-S complex. ~6 = enhancement of binary E-Mn complex. et = enhancement of ternary E-M&3 complex. e* = observed enhancement at finite [E] and [S]. Ebb = extrapolated enhancement at infinite [S] and finite [El. e*d = extrapolated enhancement at infinite [E] and finite [S]. e*(Mnb) = enhancement of bound Mn at finite [E] and [S]. ez-f = enhancement of bound Mn at infinite [S] and finite

[El. The details of the various procedures for obtaining values of

et and Ka from observed enhancements (E*) at variable concentrations of pyruvate kinase [E] and substrates [S] and at a constant concentration of manganous ion are given below. The equation relating 8 and the concentration of free enzyme and substrate is given by Equation 4.

For purposes of extrapolation, one may simplify Equation 4 by using the relationships at high levels of [El, and [SIT: [E] N WIT 1 KD, PI - [SIT > KS, eb >> 1 (Eb = 32.7 (I)), and Kz~,/[E] < et. These relationships permit one to neglect the first and second terms in the numerator and the first and third terms in the denominator of Equation 4, yielding the following approximate equations.

e* N -

which, in reciprocal form, becomes

(5)

+K1 2 (6) Ii317 a + et

Procedure I

Determination of et-Extrapolation of e* at constant [EIT to [S],: A linear extrapolation of a plot of E* against l/[S]r according to Equation 5 gives an enhancement value at [S],, denoted by Ebb, for each enzyme concentration. At [S], Equa- tion 6 becomes

(7)

Extrapolation of Cam to [El,: According to Equation 7, et may be found from a secondary plot of l/r*, against l/[E]7 by linear extrapolation to [El,.

Determination of KS-The value of Kz may be approximated from the slope (Kz/e,) of the linear plot of l/e*, against l/[EIT

(Equation 7). Since the enhancement of the manganese-substrate complex ea is known from an independent experiment (Table I), a more accurate determination of K2 may be obtained from the Ebb values by direct’ substitution of et and ea in the following exact equation for e*, obtained directly from Equation 4 by setting [S] = m.

(8)

Initially one uses [E] = [KIT in Equation 8, and then one it- erates for the value of KP. Three iterations were sufficient to achieve a constant value of Kt. The dissociation constant of the manganese-substrate complex, K1, is also evaluated by an independent experiment (Table I) ; since K1, Kz, and K, are now known, K8 may be determined from the relationship

Procedure II

Determination of et-Extrapolation of e* to [El, at constant [SIT: The extrapolated value of e* at [El,, denoted by e*d, is evaluated graphically by plotting l/r* against l/[E], according to Equation 6. The value of e*d at [El- from Equa- tion 5 is

K3 e*a - [SIT Et + ft

Extrapolation of e*d to IS],: From the plot of e*d against l/[S], et is obtained from the intercept on the ordinate according to Equation 9.

Determination of KS-The value of KD may be approximated from the slope of the line (Equation 9). Alternatively, K8 may be more accurately determined by direct substitution and itera- tion in the following exact equation obtained from Equation 4 by setting [E] = m.

f*d = E ft + Et $+1

00)

Procedure III

Determination of KS-The value of KS may be obtained from the value of [S] which produces half-maximal enhancement. From Equation 4, the observed enhancement (e*) at [S] = 0 is

(11)

The enhancement at [S] = 00 and at finite [E], Ebb, is given by Equation 8. A general solution for the concentration of free substrate required to produce an enhancement halfway between c*([S] = 0) and e*,([S] = m), derived from Equation 4, is


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(15) (12)

From Equation 12, [S]+ msX approaches K3 as [E] approaches in- finity. IfAt max approximates KP at finite concentrations of [E] if Kz N Ko. In practice, a limiting value of [S]+ max was reached at high but finite concentrations of [E] for all the substrates. Thus, it was not necessary to devise any extrapolation procedures based on Equation 12.

Procedure IV

Since the concentration of free manganese is determined by K,, Kz, K3, and KD, an independent measurement of concentration of free manganese by EPR at each point of a titration of enzyme with substrates in conjunction with PRR data may be used to determine KS and et. One may subtract from the observed enhancement at each point of the titration the contribution of the concentration of free manganese to yield a value which is a weighted average of the enhancements of the bound manganese, i.e.

At infinite substrate concentration, Equations 14 and 15 both reduce to

KD&

e*c-f = [El Ea + K1 Et = El ea + et

KD&

/$+1 (16)

[El +K1

When [S] = 0, e*(Mnb) becomes equal to eb from Equation 14. The free substrate concentration which produces an enhancement halfway between eb and &([S]; ,,3 may be shown from Equation 14 to be

(17) [slfnl,x = K KK3 = - KG+1 g-1

A linear extrapolation of a plot of e*(Mnb) against l/IS], according to Equation 15 yields the value of 6,*-f (Equation 16); the value of St mrtx is obtained from the plot. By comparing Equa- tions 12 and 17, it may be seen that (13)

Mnlr

From Equation 1, c*(Mnb) may also be expressed as [Sl +msx = lSliln,X

( > %+1 (17a)

Since [S]; max was determined at only one enzyme concentration, we can use Procedure IV only to set limits on the constants. From Equation 17 it is seen that [S]; max is a lower limit of Ks. An approximate upper limit is found by evaluating Kz from the lower limit of KS, by assuming [E] = [BIT - [Mn]b, and inserting these values in Equation 17. Now that the limits on KI have been determined, one may find the corresponding limits on Kt from Equation 3. The value of KP given in Table VIII represents the midpoint between the limits, & the range. At infinite [S] one may evaluate [E] from these Kz values by assuming that all of the metal is bound to the substrate and that only the Kz equilibrium is significant. One may now use these values of [E] obtained from each of the limiting Kz values in Equation 16 to determine the limits on et. The values of et given in Table VIII represent the midpoints of these limit.s, i the range.

lMnS1 e*(Mnb) = [Mnlb 6 + ~

[EMnl 4 + WMniY [Mnlb

- Et tMnlb

(13a)

Using the dissociation constants defined in Equations 2a to 2d (see “Experimental Procedure”) in Equation 13a, one obtains

KDKS K3

~*(Mna) = KIWI ~ Ea + 8 eb + Et

04)

As the substrate concentration becomes high, [S] N [SIT > Ks and the second term in the denominat.or of Equation 14 may be neglected, the following linear relationship between e*(Mnb) and 1 /IS], is obtained.

TABLE VIII Comparison of constants calculated from PRR data by Procedures I, II, III, and IV -

I - I

-

.-

.-

K3 KZ

I II III IV Average II IV

19.5 18.9 zt 0.8 f 3.3 s2.5 2.1

* 0.1 14.4 10.7 * 1.2 i f 1.4 10.0 >6.3 * 0.1

Substrate

ADP

Phosphoenolpyruvate

ATP

Pyruvate

Pyruvate + [ADP]

Pyruvate + [Pj]

hwagl I

21.3 f 1.0 2.3 f 0.4 14.3 f 1.1 11.9 f 2.0

_-

e _-

I / II 1 III / IV 1 Average

M x 104

0.67 * 0.14 0.16 f 0.04 0.25 f 0.04 4.0 f 0.9 35.1 f 2.2 39 f.6

M x 104

0.50 f 0.11 0.0063 f 0.0016 1.34 f 0.21 0.093 f 0.021 0.82 f 0.05 0.91 f 0.14

19.9 f 1.7 2.2 * 0.2 13.1 f 1.2 11.0 f 1.1 219.9

>19.9

0.15 f 0.04

1.07 f 0.37 0.194 f 0.063

0.21 f 0.05

0.20 * 0.07 8.3 * 0.3

0.87 f 0.35 0.12 f 0.05 0.60 f 0.13 5.1 * 0.8

0.65 f 0.27 0.0047 * 0.0019 3.22 f 0.70 0.119 h 0.019

0.95 f 0.37 0.17 f 0.04 0.20 f 0.03 >1.7

0.72 ,. 0.27 0.0067 f 0.0016 0.82 f 0.26 0.040 f 0.020

0.50 f 0.18 0.0059 * 0.0020 1.61 f 0.80 0.135 f 0.040 0.82 * 0.05 0.91 32 0.14

0.68 f 0.24 0.16 f 0.05 0.31 f 0.14 5.80 f 1.7 35.1 f 2.2 39 f6

- -


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:Uagnitude of Errors Due to Approximations

A summary of the values of K2, KS, and Et obtained by each of t,he four procedures is given in Table VIII, from which it may be seen that the variation of the dissociation constants obtained by the,four procedures is not systematic. Agreement of dissociation constants within a factor of 4 is considered satisfactory.

The iMn-pyruvate kinase complex was found to have a high affinity for phosphoenolpyruvate. This high affinity (i.e. low KS and KJ permitted the direct measurement of e*c (phosphoenolpyruvate) but resulted in an insensitivity of this parameter to changes in [El. Hence KS for this system was determined only by Procedures II, III, and IV.

By inserting the average values of Kz, KS, ~6, et, and co into the appropriate equations, it is possible to estimate the magnitude of the total error introduced in various procedures by the approximations that have been used. In Procedures I and II, with the use of Equations 4,5, and 6, as [E] and [S] get large, the error in evaluating e* from Equations 5 and 6 becomes progressively smaller, and in the limiting case, i.e. infinit.e [S] and infinite [El, the total error is less than 13% for ADP. The results obtained by Procedure III are considered to be highly accurate, because no approximations were used in this procedure. In Procedure IV, the total error involved in deriving Equation 15 from Equation 14 does not exceed 3% for ADP in the limiting case at infinite levels of [E] and [S]. Thus, the total error introduced in the calculated values of c* by the mathematical approximations involved in Procedures I, II, and IV is sufficiently small that the errors introduced into the individual dissociation constants and et values obtained by these procedures are well wit,hin the experimental errors of these parameters (Table VIII).

Acknowledgments-The authors are indebted to Mr. John Leigh for his invaluable contribution to the instrumentation and to Mr. Alfred Achtert for his excellent technical assistance.

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Albert S. Mildvan and Mildred CohnCOMPLEXES OF ENZYME, METAL, AND SUBSTRATES

Kinetic and Magnetic Resonance Studies of the Pyruvate Kinase Reaction: II.

1966, 241:1178-1193.J. Biol. Chem.

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