Eur. J. Biochem. 206,463-470 (1992) 0FEBS 1992

Two pathways of pyrophosphate hydrolysis and synthesis by yeast inorganic pyrophosphatase Alexander A. BAYKOV and Alexander S. SHESTAKOV A.N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Russia (Received October 29, 1991/February 4, 1992) - EJB 91 1454

Initial rates of pyrophosphate hydrolysis and synthesis by baker's yeast inorganic pyrophosphatase and equilibrium amounts of enzyme-bound and free pyrophosphate were measured over wide ranges of Mg2+ and respective substrate concentrations. Computer analysis of these data, in conjunction with those on phosphate/water oxygen exchange [Kasho, V. N. & Baykov, A. A. (1989) Biochem. Biophys. Res. Comm. 161, 475-4801, yielded values of the equilibrium constants for Mg2+ binding to free enzyme and central complexes and values of the forward and reverse rate constants for the four reaction steps, namely, PP, bindinglrelease, PPi hydrolysis/synthesis and two Pi bindinglrelease steps. All catalytic steps were found to proceed through two parallel pathways, involving 3 or 4 Mg2' 1 PPi or 2 Pi bound. Product release is the slowest catalytic event in both hydrolysis and synthesis of pyrophosphate, at least, for the four-metal pathway. In the hydrolytic reaction, magnesium pyrophosphate binding is faster for the four-metal pathway, dissociation of the second Pi is faster for the three-metal pathway, while PPi hydrolysis and the release of the first Pi may proceed with similar rates. Release of pyrophosphate formed on the enzyme is faster for the three-metal pathway. Both pathways are expected to operate in vivo, and their relative contributions will vary with changes in the Mg2 concentration, thus providing a means for pyrophosphatase-activity regulation. +

Inorganic pyrophosphatase is becoming an important model for enzymatic hydrolysis and synthesis of polyphosphates. This enzyme has been isolated from a variety of cells, but most mechanistic studies have been performed with baker's yeast pyrophosphatase (reviewed in [l - 31). The yeast enzyme is a dimer of identical subunits, each 32 kDa [4, 51, and its structure has been resolved to 0.3 nm [6]. The enzyme has an absolute requirement for a divalent metal activator, Mg2+being the best [7]. A striking feature ofpyrophosphatase catalysis is the high number of metal ions involved. Binding studies indicated the presence of two high-affinity and one low-affinity metal-binding sites on the enzyme [8 - 111. If one takes into consideration the metal ion associated with PPi, this gives a total number of four metal ions bound during the catalytic cycle. Kinetic analyses of PPi hydrolysis have revealed that three of the metal ions are absolutely required for activity [I1 - 151. The role of the fourth metal ion, which is presumably bound to the low-affinity site on the enzyme, is controversial. Springs et al. [14] and Welsh et al. [16] have determined the rate constants for the individual steps of the pyrophosphatase reaction at high metal-ion concentration and concluded that they are little changed by the binding of the fourth metal ion. On the contrary, Moe and Butler [17] have observed significant inhibition of PPi hydrolysis by excess Mg2+.Also, the kinetic pattern for the phosphatelwater ~-

Correspondence to A. A. Baykov, A. N. Belozersky Institute of Physico-Chemical Biology, Moscow State University, Moscow, Russia, 119899 Enzymes. Pyrophosphate phosphohydrolase (EC 3.6.1.1); ATPsulfurylase (EC 2.7.7.4).

oxygen exchange, which results from partial reversal of PPi synthesis in the active site, is considerably changed by the binding of the fourth metal ion [18], and Pi binding, as measured by difference spectroscopy, is stimulated [19]. In this work, we attempted to study the effects of Mg2+ on all individual steps of PPi synthesis and hydrolysis by yeast pyrophosphatase, basing on the approach used recently for Escherichia coli pyrophosphatase [20]. The results indicate that, in contrast to the E. coli enzyme, which uses only one reaction pathway, the yeast enzyme operates through two pathways involving 3 or 4 metal ions/PP, or 2 Pi bound. The two pathways have different kinetic characteristics and both can operate under physiological conditions.

EXPERIMENTAL PROCEDURES Highly purified pyrophosphatase, with a specific activity of 600 U/mg (pH 7.2,25"C), was prepared from baker's yeast using a modified procedure of Braga et al. [21] and stored as ammonium sulfate precipitate at - 25 "C. The enzyme was dissolved in 0.1 M Tris/HCl, pH 7.2, containing 1 mM MgC12 and freed from ammonium sulfate on a Sephadex G-50 column equilibrated with the same buffer. The pyrophosphatase concentration was estimated on the basis of a subunit molecular mass of 32 kDa [5] and A:& = 14.4 [7]. The time-course of PPi synthesis in solution was measured as described before [20], with the following modifications. The reaction medium contained Tris/HCl, 1- 50 mM Tris phosphate, pH 7.2, 0.35-55 mM MgC12, 10 pM adenosine5'-phosphosulfate, 20 pM EGTA, 0.3 - 1.2 U/ml ATP-

464

Time (min)

Fig. 1. Time-courses of medium PPi synthesis by pyrophosphatase as measured using the coupled-enzyme assay. Pyrophosphatase (1 5 nM) was incubated for the indicated time with 5 mM total Pi and 5 mM free Mg2+ in the presence of 10 pM adenosine-5'-phosphosulfate and 0.05 (0). 0.1 ( O ) ,0.5 ( A ) , 0.75 ( A ) or 1.2 (0) U/ml ATP-sulfurylase and the ATP formed was assayed with luciferase [18]. 1 U luminescence corresponds to 1 FM ATP in the incubation medium for PP, synthesis.

sulfurylase and 0.24 mg/ml (7.5 nM) pyrophosphatase. The concentration of the Tris/HCl was varied over 0.03 -0.09 M in order to partly compensate for the increase in ionic strength at high levels of Pi and Mg2'. At suitable time points, 30 pl aliquots were withdrawn and quenched by mixing with 30 p1 1 M HC104. The mixture was allowed to stand for 5 min at room temperature, neutralized by the addition of 30 pl 1 M Tris, and the ATP formed was assayed using 10 pl of the resulting solution and 200 p1 luciferase/luciferin mixture. Stock solutions of ATP-sulfurylase (1.3 mg/ml, 8 Ujml) were passed through a Sephadex G-50 column, equilibrated with 0.1 M Tris/HCl, pH 7.2, and were stored for up to 1 month at 4' C without any loss in activity. All quoted values of ATPsulfurylase activity refer to pH 7.2 and 25°C and were about one third of those measured at pH 8 and 30"C, under the standard conditions for this enzyme. The incubation media used for the measurements of enzyme-bound and free PP, at equilibrium were formulated in the same manner and contained Tris/HCl, 1.2 - 50 mM Tris phosphate, pH 7.2, 2.5-55 mM MgCI2, 0.1 mM dithiothreitol and indicated concentrations of pyrophosphatase. All data reported in this paper were collected at pH 7.2 and 25 C. Mg2+ concentrations mentioned in the text refer to free, uncomplexed Mg2' in solution. Other materials and details of the experimental procedures have been described in the preceding paper [20]. RESULTS Initial rates of pyrophosphate synthesis

The equilibrium concentration of PPi in the system 2 Pi + PPi is quite low (for instance, 0.03 pM in the presence of 5 mM of both Pi and MgC12; see below). Under these circumstances, initial rates of PPi synthesis can hardly be measured using conventional approaches. Nyren and Lundin [22] have recently developed a highly sensitive procedure to continuously monitor PPi synthesis using ATP-sulfurylase and

Total P,

(mM

Fig. 2. Dependence of the initial velocity of the medium PPi synthesis on the total Pi Concentration. The free Mg2+ concentration was fixed 0.2 ( O ) ,0.5 (A), 1 ( A ) , 2 (O), 5 (m), 10 (V) at 0.05 (+), 0.1 (C), or 20 (V)mM. The pyrophosphatase concentration was 7.5 nM. The lines represent the best fit of Eqn (16).

luciferase as coupling enzymes. Their procedure, however, requires the addition of many reagents that may interact with pyrophosphatase and, besides, cannot be used with partly purified luciferase because of the instability of luminescence. Therefore, we developed a two-step procedure utilizing the same enzymes. The application of this procedure has recently been briefly described [20]. The incubation of pyrophosphalase with Pi and Mg2+was performed in the presence of ATPsulfurylase and adenosine-5'-phosphosulfate. Due to the verylow value of AGO for the ATP-sulfurylase reaction in the direction of ATP formation (-48 kJ/mol) [23],virtually all PPi formed could be converted into ATP in the presence of sufficient ATP-sulfurylase. In the second incubation step, the ATP formed was assayed using the luciferase/luciferin system. This approach allowed one to accumulate much more ATP compared to the equilibrium concentration of PPi and in this way increase the sensitivity of the PPi-synthesis assay. The amount of ATP-sulfurylase added must be high enough to keep the steady-state concentration of PPi at a low level at which product inhibition can be neglected. Fig. 1 shows typical kinetic curves obtained at different concentrations of ATP-sulfurylase. It is seen that the luminescence intensity, and hence ATP concentration, increased linearly with the time of incubation with pyrophosphatase. The measured rate of the reaction reached a limiting value at a high level of ATP-sulfurylase. Fig. 2 shows part of the rate data obtained using 150 mM total Pi and nine fixed levels of free Mg2+. For each point, measurements were performed at two concentrations of ATP-sulfurylase, which differed by a factor of two. If the difference between the two measured rates was less than 20%, the rate obtained at the higher level of the coupling enzyme was taken as the true rate of PPi synthesis. Otherwise, the amount of ATP-sulfurylase was further doubled. The final concentrations of the enzyme were in the range 0.3 - 1.2 U/ ml. The concentration of pyrophosphatiise was kept constant (7.5 nM), and the decrease in the activity of synthesis at

465 low Pi and Mg2+ levels was compensated by increasing the reaction time between points on the kinetic curves over 0.25 5 min. As a result, the amounts of ATP finally measured were comparable for different sets of Pi and Mg2 concentrations. Control experiments indicated that the rate values obtained in this way were proportional to the pyrophosphatase concentration. The curves in Fig. 2 are clearly sigmoidal, in accordance with the requirements for two Pi molecules for PPi synthesis. The rate of the synthesis increased with increasing Mg2+ concentration in the range 0.05 - 20 mM. +

Initial rates of pyrophosphate hydrolysis Initial rates of the hydrolytic reaction were measured as a function of magnesium pyrophosphate concentration at several levels of free Mg2' in the range 0.02-50 mM, using a highly sensitive continuous photometric method [24]. The reaction followed the Michaelis-Menten kinetics as shown in Fig. 3 for several concentrations of Mg2+. It should be mentioned in this regard that yeast pyrophosphatase can exist in two functionally different forms. One of them displays nonMichaelis-Menten kinetics for hydrolysis with respect to the substrate magnesium pyrophosphate [25],which seems to be

caused by the presence of a regulatory site with affinity for PPi , Pi and ATP [26]. In this work, we used a different form of the enzyme, which obeys the Michaelis-Menten kinetics probably, due to an altered affinity of the regulatory site, and is more suitable for mechanistic studies since its kinetics can be analyzed in a straight-forward manner. The values of the apparent catalytic constant (kdPP) and of the ratio of the apparent Michaelis constant to it (Ka$p/kapp) are shown in Table 1. It is seen that kappwas virtually constant at 0.05-0.5 mM Mg2+,but decreased significantly at higher levels of the activator. The value of Ka,PP/kaPPwas a linear function of the reciprocal Mg2' concentration in the range 0.02- 1 mM, but significant downward deviations were observed at higher Mg2+levels (Fig. 4). The equilibrium of pyrophosphate synthesis in the active site of the enzyme The synthesis of PPi in solutions involves the formation of enzyme-bound PPi. Due to favorable thermodynamic parameters for the 2 Pi 4 PPi reaction on pyrophosphatase, the total

0.08

VI

1

-z5

0.06

W

Y

004

0.02

0

2

1

I/CMPPl

3 (pM-'l

Fig. 3. Lineweaver-Burk plots for the hydrolysis of magnesium pyrophosphate (MPP). The free MgZ concentration was fixed at 0.05 (0),0.1 ( A ) , 2 (1) or 50 ( 0 )mM. The lines represent the best fit of the Michaelis-Menten equation. +

Fig. 4. Dependence of the slopes of the lines in Fig. 3 on the reciprocal Mgz+ concentration. The inset shows the data at high Mg2+ concentrations. The values of r z p / k " P P were determined for each Mg2+ concentration using the Michaelis-Menten equation. The solid line represents the best fit of Eqn (6). The broken line on the inset is the extrapolation of the solid line on the main plot to high Mgz+ concentrations.

Table 1. Michaelis-Menten parameters for the hydrolysis of magnesium pyrophosphate at different Mgz+ concentrations. Values in parenthesis refer to the theoretical values predicted for the mechanism shown in Fig. 7.

Free Mg'+ concentration

Magnesium pyrophosphate concentration

in M

PM 0.3-100 0.3 - 100 0.3-100 0.3 - 100 0.3-100 0.3-100 0.2-100 0.1- 50 0.1- 10 0.1- 10

0.05 0.1 0.2 0.5 1 2 5 10 20 50

Number of rate measurements

pmPPPP/PPP

k"PP

nM.s-'

S-'

10 11 9 11 21 9 11 10 8 8

354 345 355 349 312 295 259 244 245 205

f 32(367) f 35 (353) f 27 (343) f 14(325) f 20 (311) f 12(294) f 7(268) f 8 (245) f 7 (215) f 5 (206)

2.4 (44.4) 47.2 1.9 (25.2) 21.3 1.2 (15.1) 15.4 7.2 f 0.32 (8.38) 7.34 f 0.49 (5.73) 3.8 & 0.28 (3.76) 1.86 f 0.08 (2.04) 1.18 'I 0.08 (1.28) 0.81 0.05 (0.84) 0.69 0.04 (0.58)

466

Total Pi

Total Pi

(mM)

Fig. 5. Dependence of the amount of enzyme-bound PPi on the total Pi concentration.The free Mgz+concentration was fixed at 2 (0),5 (a), 10 (A)or 20 (A)mM. The enzyme concentration was 47-62 pM. The lines represent the best fits of Eqn (17).

equilibrium concentration for PPi can significantly exceed the amount of PPi free in solution [14, 271. Earlier measurements of enzyme-bound PPi were carried out in the presence of 5 20 mM Mg2' using a radioisotopic technique [14, 271. We extended these measurements to lower concentrations of Mg2+,using the highly sensitive luminometric PPi assay of Nyren and Lundin [22], as modified previously [20]. Fig. 5 shows the dependencies of the amount of enzyme-bound PPi on the total Pi concentration at four fixed concentrations of Mg". The maximal level of PPi was about 0.16 mol/mol enzyme in agreement with the earlier data [14, 271. The equilibrium of pyrophosphate synthesis in solution

Mixtures of Pi, MgC12 and 0.3 pM pyrophosphatase were equilibrated for 10 min, quenched with 0.8 M HC104, and the PPi present was measured using the luminometric procedure. Enzyme-bound PPi was less than 2% of its total content at this concentration of pyrophosphatase and was therefore neglected. Part of the results are shown in Fig. 6 . The whole data (50 independent measurements) were analyzed in terms of the following equilibrium

MP

+ P+MPP.

Here, P, MP and MPP stand for phosphate, magnesium phosphate and magnesium pyrophosphate, respectively. The equilibrium constant for PPi hydrolysis, K,, which is defined as [MP][P]/[MPP], was computed using the dissociation constants for magnesium phosphate, magnesium pyrophosphate and dimagnesium pyrophosphate listed in Table 2 and was found to be 440 20 M.

The overall scheme of catalysis by yeast pyrophosphatase The data obtained in this work and reported previously for this enzyme can be explained in terms of the two-pathway scheme shown in Fig. 7. Each pathway involves, in the direction of synthesis, stepwise binding of phosphate and magnesium phosphate, formation of magnesium pyrophosphate and its dissociation into solution. The interaction of Mg2+ with the substrates in solution is characterized by dissociation constants Kpp, Kmppand K, which have been measured previously [19, 281. The reaction can involve as many as 3 or 4

(mM)

Fig.6. Dependence of the equilibrium amount of medium PPi on the total Pi concentration. The free Mg2+ concentration was fixed at 2 (0),10 (A)or 20 (0)mM. The lines were constructed using K, = 440 M (see text).

Fig. 7. Kinetic scheme for yeast pyrophosphatase catalysis in both directions. M, P and PP refer to magnesium, phosphate and pyrophosphate, respectively. K,,, Km2.etc. are the dissociation constants for Mg2+ binding, while k;,k'Ll, k ', etc. are rate constants.

Mg2+/PPior 2 Pi molecules in both directions. Three Mg2+ ions are shown to bind to the enzyme in the absence of any substrate [9,14], and the fourth one comes with the substrates. The second pathway requires only three Mg2+ ions. The linearity of the plot in Fig. 4, down to a concentration of 0.02 mM Mg2+,indicated, in accordance with previous estimates [9], that Kml is far below 0.05 mM, the lowest concentration of Mg2' used in subsequent calculations. Hence, the concentration of free enzyme (E) could be neglected. Values of the constants shown in Fig. 7 were calculated from the above data using the previously reported parameters for P i / H 2 0oxygen exchange catalyzed by yeast pyrophosphatase [18]. The oxygen-exchange studies yielded values of four useful parameters ;partition coefficients for the two pathways (PL and Pi),the catalytic constant for the exchange through the four-metal pathway (k;J and A . The equations relating them to the constants in Fig. 7 are given below [14, 18,291. Pc =

k-2 k-2

+ k;

467 The numerical values of these parameters are [18]: Pb,0.16 0.02; Pi, 0.37 f 0.015; klx, 226 f 21 s-'; A , 0.32 0.14 mM. The overall calculation strategy has been outlined recently for E. coli pyrophosphatase [20], but in the case of the yeast enzyme the iterative procedure has been realized in a somewhat different way, as described below. First, the PPi-hydrolysis data were analyzed according to Eqns (1) and (9 - 15) (see Supplement). This analysis, however, required, at least an approximate value of several parameters. Two constants referring to the four-metal pathway, kL and K ! could be estimated from the PPi synthesis data (Figs 2 and 5, respectively) obtained at saturating concentrations of Mg2+ and Pi. Kj was used to calculate kLzfrom Eqn (3). Parameter kl and the ratio k- 4 / k L 4 were assigned provisional values. The analysis of the hydrolysis data yielded initial estimates of k l , Pi, L 2 , k4, k l , Km2 and Km3,which were further used to determine refined estimates of k - l , k L l , k-4, k N 4 and k L 2 , as well as initial estimates of k- and kl from the data on medium and enzyme-bound PPi formation. The dependencies of the amount of the enzyme-bound PPi (61 separate PPi measurements) and of the rate of medium PPi formation (143 separate PPi measurements) on Mg2+ and Pi concentrations were treated simultaneously because these data were obtained in experiments of the same kind and by the same method. In this case, the following function was minimized

where wi and wj are statistical weights, t is the incubation time in the rate measurements for thejth point and A([PP]/[E]Ji and ~l(v,t/[E],)~ are differences between measured and calculated values of respective functions for each point. The values of w i and wj were taken to be proportional to the respective values of [PP]/[E], and v,t/[E], and were further scaled in such a way that the total contributions of the enzyme-bound PPi and medium PPi synthesis data sets into F were proportional to the numbers of separate measurements in them. The refined values of k- l , kL1 , k L and k-4/kN4 were substituted into Eqns (9 - 14) and the whole calculation cycle was repeated. The iterations were performed until the results converged. The final values of all parameters estimated in this way with their standard errors are given in Table 2. For two rate constants referring to the three-metal pathway ( k - l and L 2 )this , treatment could only give lower estimates. These constants were found to be highly correlated with each other. As a result, the value of k- could be varied in the range 100 - 10000 s-' without significantly affecting the fit for Eqn ( 5 ) (Results) and Eqn (15) (Supplement). For k- = 50 s- ', the minimum value of F increased by 24%, and for k- = k L the increase was 13-fold. The computed estimate of K 2 was 100 s - l at high fixed k P l values, but increased to lo9 sC1 at k - l = 50 s-'. Based on these calculations, one could conclude that k- 2 50 s- and k- 2 100 s- '. Since k 2 ,k3 and K,, are all expressed via k- 1, they could be also estimated from only one side. The ratios k;/k; and k 3 / k - 2 were 10 and 5.3, respectively, at all fixed values of k-l. The theoretical curves in Figs 2, 4 and 5 were constructed using the constants listed in Table 2. The dependence of the slope of the Lineweaver-Burk plot on the Mg2 concentration +

Table 2. Summary of the kinetic and thermodynamic parameters for baker's yeast pyrophosphatase (25OC and pH 7.2). The values in square brackets are for dimagnesium pyrophosphate and magnesium phosphate as the binding species. The values of Kpp,Kmppand K, were taken from [19] and [28]. Rate or equilibrium constant

Value

k;

(1.4 f 0.24) x 10' (I .7 x lo9] 2 50 2 470 > 100 2 530 (8.5 t- 9 ) x lo4 2400 _+ 900 (2.3 +. 0.5) x 105 ~ 6 . 5x lo3] 2 3 . 6 x 10-7 ? 26.2~ 10 - z (2.4 _+ 0 . 4 ) ~I O - ~ (3.3 f 1.4) x 5 4 . 5 x 10-4 4.4x 30-4 (3.0 & 0 . 9 ) ~lo9 [2.6 x lo8] 20.5 f 0.6 1490 230 310 30 540 +_ 100 (4.0 0.9) x lo5 380 & 80 (3.7 f 1.2) x 105 [9.5 x 1041 6.8 x

Unit

M M M M M M M M-1.

s-l

**

M

4.65

1.35x 10-3 10-3 2.3 x 8 . 6 lo-' ~ 2.83 x 8.5 x 10-3

M M M M M M

(Fig. 3) was obtained from Eqn (6), where rate constants are defined as shown in the supplement.

Several comments on the procedure for data analysis are appropriate at this point. Derivation of the rate equations for PPi hydrolysis and synthesis in solution is based on a combined steady-state and equilibrium approach which assumes that substrate conversion is a steady-state process, while Mg2 binding to free enzyme and various central complexes is a rapid equilibrium process. This assumption is based on the premise that each reaction cycle does not necessarily involve metal-ion addition to and dissociation from the enzyme. Besides, formation and breakdown of the magnesium complexes of PPi and Pi in solution are rapid reactions [30] compared to enzyme-bound PPi conversions (Fig. 7). +

468

DISCUSSION The primary objective of this study was to define the reaction sequence for Mg2+-activated pyrophosphatase with sufficient accuracy to determine the requirements for Mg2 in all four reaction steps, namely PPi binding/release, PPi hydrolysis/synthesis and successive bindinglrelease of Pi. Since pyrophosphatase can bind up to 4 Mg2+, 2 Pi and 1 PPi, the total number of enzyme species formed in their presence is as high as 20 [lo]. Most of these species, however, are stoichiometrically insignificant, and the minimum number of species which are required to explain the data of this work is nine. These species are shown in Fig. 7, which also contains free enzyme (E), although, as discussed above, K,, is too low for E to be present in significant amounts. All enzyme/substrate complexes shown contain two or three Mg2 in addition to the metal associated with PPi or Pi. The absence of species with lower Mg2+ contents is explained by the fact that the enzyme affinity for metal ions increases markedly in the presence of the substrates [lo, 111. The M2EMP2/M3EMP2pair is required to explain the effect of Mg2+ concentration on P, for P i / H 2 0oxygen exchange [16]. The existence of this pair, as well as M2EP/M3EP,also agrees with the scheme of Mg2+ and Pi binding with pyrophosphatase deduced from their effects on the rate of Pi/H20oxygen exchange [16] and on the protein spectrum [17]. It should be remembered that kinetic experiments of this kind can only define the stoichiometric composition of intermediates, but not the pathways of their formation. One cannot therefore exclude the possibility that M3EMPP or M2EMPP results from M2PP and M2E or ME, as discussed previously in connection with the E. coli pyrophosphatase [20]. Alternatively, both MPP and M2PP may be active substrate species that combine with M2E. The same considerations apply to the reverse reaction, in which M3EP may originate from M2E and MP rather than from M3E and P. Rate constants for the alternative substrate forms are also listed in Table 2. The principal feature of the scheme in Fig. 7 is the existence of two parallel reaction pathways for the hydrolysis and synthesis of PPi. The idea of two pathways is supported by two important observations. First, the value of P, for the exchange of oxygens between Pi and H 2 0 was found to depend on the Mg2+concentration [18, 311. An alteration in this parameter is a very sensitive indicator of reaction taking another route [31,32], and in the case of inorganic pyrophosphatase it shows that the diphosphate complexes of the enzyme which differ in Mg2+ content undergo reactions at different rates [38]. Second, the maximal velocity of PPi hydrolysis goes through a maximum, then drops to a constant non-zero level 1171 when the Mg2+concentration is increased. This means that at least one of the three steps involved in PPi hydrolysis following its binding is reduced in rate upon Mg2+ binding. With other metal activators, these effects are even more pronounced. Thus, the value of P , for Co2+-supported P i / H 2 0 oxygen exchange increases from 0.13 to 0.54 at increasing Co2+ concentrations 1161. Rates of Zn2+-supported and Mn2+-supported hydrolysis of PPi, which are at least 200 s- at optimal concentrations of the metal ions, drop to less than 10 s - l at high concentrations [33, 341. Although minimal, the scheme in Fig. 7 contains as high as 14 independent parameters. A natural question is to what extent one can rely on the values of these parameters, obtained by computer fitting. Without doubt, the number of parameters is too high to be estimated from a single set ofdata. Therefore, we used four independent sets of data which were collected in +

+

wide ranges of Mg2+ and respective substrate concentrations, rates of PPi hydrolysis, rates of PPi synthesis, rates of oxygen exchange and equilibrium amounts of enzyme PPi intermediate. In total, the data contain enough information for estimating all parameters. The fact that only lower estimates were obtained for two rate constants (k-l and k P 2 )and related parameters is explained by the lower values of K,, and Km5 compared to Kp. Consequently, the concentrations of MP at low levels of Mg2+,when the three-metal pathway prevails, are not high enough to saturate the enzyme even at the highest concentration of Pi used. This is an intrinsic problem that cannot be cured by performing measurements at different Mg2+ and Pi concentrations. The validity of the present analysis is supported by a comparison of the values of some parameters obtained with previous estimates obtained using different approaches. The value of Km2is close to the dissociation constant of 0.15 mM for the binding of the second Mg2+ to the enzyme, as measured using difference spectroscopy [8]. The dissociation constants for successive binding of two magnesium phosphate molecules to EM2 (3.9 mM and 1.35 mM, as estimated in this work) are in satisfactory agreement with the values of 3.4 mM and 2.7 mM obtained from spectral studies of enzyme/phosphate interactions [19]. Our estimate of Km4 agrees with a dissociation constant of 0.21 mM for the binding of Mg2+ to the fluoride-stabilized complex of the enzyme with PPi [9]. Besides, the equilibrium constant for PFi formation in solution, calculated as K ' ~ K ' ~ K ' ~ (920 / K ' ~ M) do not differ significantly from the value of 440 M measured directly. Springs et al. [I41 were the first to proposed the idea of determining individual rate constants for pyrophosphatase catalysis from steady-state and equilibrium measurements. They assumed, however, that the catalytic properties of pyrophosphatase are not affected by the binding of the fourth M g 2 + .In fact, their analysis was carried out using 5 - 100 mM Mg2+, i. e. under conditions where the four-metal pathway predominates. Accordingly, their estimates of the rate constants agree quite well with the values of the double-primed constants in Table 2 (note that they expressed k , in terms of total PPi Concentration). The value of k:. quoted by Springs et al. is, however, only 6 s-l compared to the value of 20.5 sdetermined in the present work. This discrepancy may result from the fact that they estimated this constant from PPihydrolysis data rather than from direct measurements of PPi synthesis. One can see from Table 2 that hydrolysis of PPi by pyrophosphatase and release of two molecules of the product proceed with similar rate constants, at least for the fourmetal pathway, in accordance with previous data [14]. On the contrary, PPi release is much slower compared to its synthesis in the active site (KLl 6 kL2). The rate constant for PPi binding is considerably higher for the four-metal pathway (k; > k i ) , while the rate constant for the second Pi release is smaller (ki< kk). This means that, although less effective in PPi hydrolysis at saturating PPi concentrations, the four-metal pathway will become more effective at low PPi concentration when substrate binding is rate-limiting. Theoretically, the same is true for PPi synthesis, since k - > k" and ki.3 > K 3 .It is, however, impossible to saturate the enzyme with magnesium phosphate in the three-metal pathway, as discussed above. Interestingly, the rate constants for the binding of PPi to the pyrophosphatase active site are higher by several orders of magnitude than those for the binding of Pi, a simpler compound. We interpret this result as showing that filling up

469 of the first Pi-binding site is accompanied by a conformational change in the protein. The fact that the rates of pyrophosphatase-catalyzed hydrolysis of PPi and imidodiphosphate, whose spatial structures are practically identical [35],differ by a factor of 50000, while rates of non-enzymatic hydrolyses in solution are very close, led to the suggestion that enzyme catalysis involves interaction with the bridge oxygen atom of the substrate [15]. This hypothesis was corroborated by the observed dependence of enzyme affinity for a series of diphosphonate analogs of PPi on the nature of the substituent at the bridge carbon atom [36]. The fact that the substrate-binding constant, K[, is extremely low provides additional support for this hypothesis and indicates the size of this bond contribution to the total energy of substrate binding. The binding constant for imidodiphosphate measured in the presence of 1 mM free Mg2+ is 15 pM, which is altered to 0.44 pM after extrapolating to infinite Mg2 concentration using Km3.The ratio of the binding constants for PPi and imidodiphosphate is thus 65, which corresponds to a A G" of 10.5 kJ/mol. The results of the present work show that the mechanism of catalysis by baker's yeast pyrophosphatase is more complicated than that for E. coli pyrophosphatase. Using a similar approach, we recently found that the reaction catalyzed by the latter enzyme proceeds via one pathway which requires four metal ions in both directions [20]. Complexes containing three metal ions are also formed in this system, but they are dead-end species, as indicated by the constant value of P, and the maximal rate of PPi hydrolysis at increasing Mg2+ concentrations. The values of the rate constants characterizing the four-metal pathways are quite similar for the two enzymes. This may mean that the pyrophosphatase catalytic device has changed during evolution in a way which allows some protein groups to fulfill the function of the fourth metal ion under conditions where the Mg2+ concentration is low. The physiological significance of the two pathways in pyrophosphatase catalysis can only be guessed. A likely explanation is that they provide a mechanism for fine activity regulation in response to changes in the Mg2+concentration. Since yeast cells contain high concentrations of PPi [37], most of the pyrophosphatase is expected to exist in the form of a complexes with PPi and Pi. Therefore, the interaction of the enzyme with Mg2+ is governed by K,,, KmSand K,,, whose values are comparable with the reported cytosolic free Mg2+ concentration in a number of eucariotic cells other than yeast [38,39]. This means that both pathways of PPi hydrolysis may operate in the yeast cell. As a result, any decrease in the free Mg2+concentration, for instance due to increased production of PPi in biosynthetic reactions, will increase the fraction of the three-metal pathway in PPi hydrolysis and therefore its rate. +

The authors wish to thank Dr. B. S . Cooperman for helpful criticism, Dr. N . N. Ugarova and her colleagues for the gift of luciferase and luciferin and Dr. A. V. Vener for his hclp in pyrophosphatase isolation.

REFERENCES 1 . Bulter, L. G. (1971) in The enzymes, 3rd edn. (Boyer, P. D., ed.) vol. 4, pp. 529-541, Academic Press, New York. 2. Cooperman, B. S. (1982) Methods Enzymol. 87, 889-897. 3. Avaeva, S. M. & Nazarova, T. I. (1985) Usp. Biol. Khim. 26,4263.

4. Heinrikson, R. L., Sterner, R., Noyes, C. & Cooperman, B. S. (1973) J . Biol. Chem. 28, 977-988. 5. Cohen, S . , Sterner, R., Keim, P. & Heinrickson, R. (1978) J . Bid. Chem. 253, 889- 893. 6. Terzian, S . S., Voronova, A. A., Smirnova, E. A,, Kurdnova, I. P., Nekrasov, Ju. V., Harutyunyan, E. G., Vainstein, B. K., Hohne, W. & Hansen, G. (1984) Bioorg. Khim. 10,1469-1481. 7. Kunitz, M. (1952) J . Gen. Physiol. 35,423 -449. 8. Rapoport, T. A., Hohne, W. E., Heitmann, P. & Rapoport, S. (1973) Eur. J . Biochem. 33, 341 -347. 9. Baykov, A. A., Tdm-villoslado, J. J. & Avaeva, S . M. (1979) Biochim. Biophys. Acta 569, 228 -238. 10. Cooperman, B. S., Panackal, A., Springs, B. & Hamm, D. (1981) Biochemistry 20, 6051 -6060. 11. Knight, W. B., Dunaway-Mariano, D., Ransom, S. C. & Villafranca, J. J. (1984) J . Biol. Chem. 259, 2886-2895. 12. Baykov, A. A. & Avaeva, S. M . (1973) Eur. J . Biochem. 32,136142. 13. Braga, E. A. & Avaeva, S. M. (1972) Biochem. Biophys. Res. Commun. 45, 528 - 535. 14. Springs, B., Welsh, K. M. & Cooperman, B. S. (1981) Biochemistry 20, 6384-6391. 15. Smirnova, I. N. & Baykov, A. A. (1986) FEBS Lett. 206, 121124. 16. Welsh, K. M., Jacobyansky, A., Springs, B. & Cooperman, B. S. (1983) Biochemistry 22, 2243-2248. 17. Moe, 0. A. & Butler, L. G. (1972) J . Biol. Chem. 247, 73087314. 18. Kasho, V. N., & Baykov, A. A. (1989) Biochem. Biophys. Res. Commun. 161,475 -480. 19. Smirnova, I . N., Shestakov, A. S., Dubnova, E. B. & Baykov, A. A. (1989) Eur. J . Biochem. 182,451 -456. 20. Baykov, A. A., Shestakov, A. S., Kasho, V. N., Vener, A. V. & Ivanov, A. H. (1990) Eur. J . Biochem. 194, 879-887. 21. Braga, E. A., Baykov, A. A. & Avaeva, S. M. (1973) Biokhimiya 38,344 - 359. 22. Nyren, P. & Lundin, A. (1985) Anal. Biochem. 151, 504-509. 23. Robbins, P. W. & Lipmann, F. (1958) J . Biol. Chem. 253, 686690. 24. Baykov, A. A. & Avaeva, S. M. (1981) Anal. Biochem. 116, 1 4. 25. Baykov, A. A., Pavlov, A. R., Kasho, V. N. & Avaeva, S . M. (1989) Arch. Biochem. Biophys. 273, 301 -308. 26. Bakuleva, N . P., Baykov, A. A., Kasho, V. N., Nazarova, T. I. & Avaeva, S. M. (1983) hi.J . Biochem. 15, 849-854. 27. Janson, C. A , , Degani, C. & Boyer, P. D. (1976) J . Biol. Chem. 254, 3743 - 3749. 28. Volk, S. E., Baykov, A. A., Duzhcnko, V. S. & Avacva, S. M. (1982) Eur. .I. Biochem. 125, 215-220. 29. Hackney, D. D. & Boyer, P. D. (1978) Pruc. Nut/ Acad. Sci. U S A 75, 3133-3137. 30. Frey, C. M., Bayasz, J. L. & Stuehr, J. E. (1972) J . Am. Chem. SUC.94,9198-9204. 31. Hackney, D. D. (1980).1. Biol. Chem. 255,5320-5328. 32. Hackney, D. D., Stempel, K. E. & Boyer, P. D. (1980) Methods Enzymol.64, 60-83. 33. Pavlov, A. R., Baykov, A. A. & Avaeva, S. M . (1986) Biokhimiya 51, 369 - 377. 34. Volk, S. E., Baykov, A. A. & Avaeva, S. M. (1981) Biokhimiya 46, 33 - 39. 35. Larsen,M., Willett,R.&Yount,R.G. (1969)Science166, 15101511. 36. Smirnova, I. N., Kudryavtseva, N . A., Komissarenko, S. V., Tarusova, N. B. & Baykov, A. A. (1988) Arch. Biochem. Biophys. 267, 280-2284, 37. Ermakova, S. A., Mansurova, S. E., Kalebina, T. S., Lobakova, E. S., Selyach, I. 0. & Kulaev, I . S. (1981) Arch. Microbiol. 128, 394 - 398. 38. Murphy, E., Stcenbergen, C., Levy, L. A,, Raju, B. & London, R. E. (1 989) J . Bid. Chem. 264, 5622- 5627. 39. Flatman, P. W. (1984) J. Memhr. Biol. 80, 1-14. 40. Huang, C. Y. (1979) Methods Enzymol. 63, 54-84.

470 Supplementary material to : (7)

Two pathways of pyrophosphate hydrolysis and synthesis by yeast inorganic pyrophosphatase Alexander A. BAYKOV and Alexander S. SHESTAKOV Rate equations for medium PP, hydrolysis and synthesis Assuming that metal-ion binding to all enzyme species is an equilibrium reaction and substrate binding and conversion proceed under steady-state conditions, the kinetic model shown in Fig. 7 can be simplified to the following form [40] ki

E S E(MPP) $ E(MP2) $ E(P) k-

I

2E, kL,

k-,

k-2

These equations contain a total of 21 parameters, but seven of them are dependent and can be therefore excluded. Thus, the dissociation constants K,,, K,, and Km6can be expressed via other parameters using Eqn (4) and the obvious relationships K,,,,k'- l/k'l = K,,,,kL ilk'{ and Km6k4/ki4= Km,ki/kL4.The rate constants e2,k;, k ; and k;' can all be expressed via kL2 with Eqns (1 -4) and the obvious relationship K,&'/k'L = K,,,k>/k'L2 One finally obtains

k L l =-

where the apparent rate constants are given by

+

(k"lklKm,/kY) k" 1 [MI ( k L , k ; K , , / k / k ' , ) +[MI

(9)

(3)

k-2 =

k'. 2 K,, Km,

+ k'L 2[M] + [MI

,

(4)

'

k-3

=

Km3k'-jk;h' 4 1 k i h ? 4 K,,k; k-,/kk k'L4

+ k"[M] --

+ [MI

(13)

+ kl;[M]_-

(14)

and (5)

k4

K,,k:k' =

4/k'L4

Kn,,k;k'-4/kkkL4 t [MI k-3

=

k - 3 K,,

+ k'i 3[M]

,

Km, + [MI

Initial rates of PP, hydrolysis (vh) and PP, synthesis (v,) are given by the following equations

'

1

vh

Enzyme-hound PPi formation The dependence of [PP]/[E],at equilibrium on medium phosphate concentration in terms of the apparent rate constants introduced above obeys the relationship [PPI

/=

[El1

1 .

(17)