Biochein. J. (1978) 169, 39-54 Printed in Great Britain
39
Kinetics and Mechanism of Action of Muscle Pyruvate Kinase By LEIGHTON G. DANN* and HUBERT G. BRITTON Department of Physiology, St. Mary's Hospital Medical School, London W2 1PG, U.K. (Received 29 March 1977)
1. The mechanism of rabbit muscle pyruvate kinase was investigated by measurements of fluxes, isotope trapping, steady-state velocity and binding of the substrates. All measurements were made at pH8.5 in Tris/HCl buffer and at 5mM-free Mg2+. 2. Methods of preparing [32P]phosphoenolpyruvate from [32P]pl in high yield and determining [32p]_ phosphoenolpyruvate and [8-14C]ADP are described. 3. The ratio Flux of ATP to ADP/ Flux of ATP to phosphoenolpyruvate (measured at equilibrium) increased hyperbolically with ADP concentration from unity to about 2.1 at 2mm-ADP, but was unaffected by phosphoenolpyruvate concentration. Since the ratio is greater than unity, one pathway for the addition of substrates must involve phosphoenolpyruvate adding first to the enzyme in a rate-limiting step. However, the substrates must also add in the alternative order, because of the non-linear increase in the ratio with ADP concentration and because the rate of increase is very much less than that predicted from the steady-state velocity data for an ordered addition. The lack of influence of phosphoenolpyruvate on the ratio is consistent with the rapid addition of ADP in the alternative pathway. At low ADP concentrations the alternative pathway contributes less than 33 % to the total reaction. 4. Isotope trapping was observed with [32P]phosphoenolpyruvate, confirming that when phosphoenolpyruvate adds first to the enzyme it is in a rate-limiting step. The release of phosphoenolpyruvate from the ternary complex must also be a slow step. Trapping was not observed with [8-14C]ADP, hence the addition of ADP to the free enzyme must be rapid unless its dissociation constant is very large (>20mM). 5. Binding studies showed that 4mol of [32P]phosphoenolpyruvate binds to 1 mol ofthe enzyme, probably unligated to Mg2+, with a dissociation constant appropriate to the mechanism indicated above. Binding of [8-14C]ADP could not be detected, and hence the binding of ADP occurs by a low-affinity step. The latter is also demanded by the steady-state velocity data. 6. The ratio Flux of phosphoenolpyruvate to ATP/Flux of phosphoenolpyruvate to pyruvate (determined from the incorporation of label into phosphoenolpyruvate from [3-14C]pyruvate or [y-32P]ATP during the forward reaction) did not differ significantly from unity. Steady-state velocity data predicted grossly different flux ratios for ordered dissociations of the products, and the results indicate that the dissociation must be rapid and random. The data also exclude a Ping-Pong mechanism. 7. Permissible rate constants for the above mechanism are calculated. The results indicate a high degree of cooperativity in binding, whatever the order of addition of substrate. Pyruvate kinase (EC 2.7.1.40) catalyses the formation of pyruvate and ATP from phosphoenolpyruvate and ADP and is an important enzyme in the regulation of glycolysis and gluconeogenesis (Llorente et al., 1970; Liao & Atkinson, 1971). The enzymes, which have been isolated from mammalian tissues (Tietz & Ochoa, 1958; Irving & Williams, 1973; Nicholas & Bachelard, 1974), require Mg2+ or Mn2+ and K+ for activity. They show hyperbolic or sigmoidal steady-state velocity kinetics with respect * Present address: Department of Chemical Pathology, Queen Charlotte's Hospital, London W6 OXG, U.K.
Vol. 169
to the substrate phosphoenolpyruvate and have been classified as M type, having hyperbolic kinetics, and L type, having sigmoidal kinetics and requiring fructose 1,6-bisphosphate for activation. The mechanisms of the mammalian and yeast enzymes have been investigated, but results do not support a single mechanism. Initial-velocity studies have been consistent with a rapid-equilibrium random mechanism for the muscle M-type enzyme (Reynard et al., 1961; Ainsworth & MacFarlane, 1973), an ordered addition of substrates and dissociation of products, for the yeast enzyme (MacFarlane & Ainsworth, 1972) and a Ping-Pong
40
mechanism involving a phosphoenzyme for the liver L-type enzyme (MacFarlane & Ainsworth, 1974). There are difficulties, however, in the interpretation of initial-velocity studies, and we are therefore studying the mechanism of these enzymes with a variety of techniques, including flux measurements with labelled substrates (Britton, 1966; Britton & Dann, 1978), isotope-trapping (Rose et al., 1974), binding and initial-velocity studies. The present paper describes the results obtained on the rabbit muscle enzyme. Materials and Methods
Materials Substrates and enzymes were obtained from Boehringer Corp. (London) Ltd. (London W.5, U.K.); ADP, ATP, NADH, NADP+ and pyruvate were sodium salts; phosphoenolpyruvate and glyceraldehyde 3-phosphate diethyl acetal were cyclohexylammonium salts. Scintillation chemicals were from Packard Instruments (Wembley, Middx., U.K.) and Rohm and Haas (U.K.) Ltd. (Croydon, Surrey, U.K.). All other chemicals were reagent grade or better and were obtained from BDH Chemicals (Poole, Dorset, U.K.). For the kinetic experiments enzyme suspensions were centrifuged and the sedimented enzymes dissolved to the original volume with water. [8-14C]ADP (ammonium salt), phospho[3-14C]enolpyruvate (cyclohexylammonium salt) and [32p]_ orthophosphate (in dilute HCI, pH 2-3) were obtained from The Radiochemical Centre (Amersham, Bucks., U.K.). Phospho[3-'4C]enolpyruvate was dissolved in water, and the solution divided into small portions and freeze-dried. All labelled compounds were stored at -20°C. [32P]Phosphoenolpyruvate was prepared from [32P]PI and glyceraldehyde 3-phosphate by an extension of the method of Schendel & Wells (1973). A 0.1 ml portion (1 mCi) of [32p]p1, pH2-3, in a conical centrifuge tube, was dried in a vacuum desiccator over NaOH. In a second tube, 95,1 of a solution containing (final concentrations) 26mMTris/HCl buffer, pH9.0, 1.05mM-MgCl2, 0.26mMKH2PO4, 0.53 mM-ADP, 1.27mM-NAD+, 0.25mg of Thiazolyl Blue/ml, 0.63mg of promethazine/ml and 10.5 mm-sodium pyruvate was prepared and transferred to the tube containing the [32p]pl with a Pasteur pipette. A 2,ul portion of pyruvate kinase [lOmg/ml in 3.2M-(NH4)2SO4] and 2,u1 of a mixed enzyme preparation [glyceraldehyde 3-phosphate dehydrogenase (1 mg/ml) and 3-phosphoglycerate kinase (5mg/ml) in 3.2 M-(NH4)2SO4] were added. A
20,u1lportionofglyceraldehyde3-phosphate(16.3 mM), prepared immediately before use by dissolving 3.26gmol of the diacetal in 100jl l of 0.2M-HCI,
L. G. DANN AND H. G. BRITTON heating the solution at 80°C for 2min, and, after cooling, neutralization with 100,ul of 0.2M-KHCO3, was added and the solution was incubated in the dark at room temperature (24°C) for 3-4h. A 10,l portion of EDTA (50mM) was added to stop the reaction. To isolate [32P]phosphoenolpyruvate, 101 of the incubation mixture was applied as a 5cm strip on a thin-layer cellulose plate and chromatographed with di-isopropyl ether/formic acid (3 :2, v/v) (Eggleston & Hems, 1952). The labelled phosphoenolpyruvate was identified with a Geiger-Muller tube and the strip cut out of the plate. The phosphoenolpyruvate was chromatographed to the margin of the strip with water and then extracted with 1 ml of 0.2mmphosphoenolpyruvate. The reaction proceeded to completion with little [32P]Pi remaining ( 1.3 mM.
Isotope trappintg Isotope trapping was carried out at room temperature (23-26°C) at pH8.5 in 50mM-Tris/HCl buffer containing 50mM-KCI and 5 mM free Mg2+. Virtually all of the [32P]phosphoenolpyruvate bound to the enzyme (calculated by using a binding constant of 65 pM) was trapped as [y-32P]ATP, but no trapping of [8-14C]ATP was detected (Table 2). If ADP were bound by the enzyme in a rate-limiting step, significant trapping should have been observed, provided that the dissociation constant for ADP is less than 20mM. Further, the relatively low ionic strength of 1978
47
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
1600 (a)
0
E
T 1200 'a
0
CD
0 0
ciC8
_
U
P4
0
Bound/free ratio
t
0
0. 261
0 0
0 0
0
4. 15 rmM 4.5
t 0. 307
m
m
0 0
400 _
0.154
0
00
0000
2
mM
t 0. 0471m
0
0
10
20
30
40
50
Fraction no. 0
0
(b)
800
0 0
600 _ 0
'a ci
0
400 _ 0. >4-
0.14tmM
0
0 0 244
10..362
t
mM
0.048 mM
0 0
200 _ 0
0
0
20
30
40
50
60
Fraction no. Fig. 5. Binding of [32P]phosphoenolpyruvate and [8-14C]ADP to pyruvate kinase Measurements were made by using a rapid-equilibrium-dialysis cell. At intervals, unlabelled substrate was added to give the concentration shown. Mg2+ was added with the substrates to maintain the free Mg2+ concentration constant. Tetraethylammonium chloride was added to give I 0.2. The abscissa represents 2m1 fractions; 0.5ml samples were withdrawn and their radioactivities counted. The points illustrated were corrected as described in the text. (a) 3.9pM[32P]Phosphoenolpyruvate and 27puM-pyruvate kinase in 5OmM-Tris/HCI buffer, pH8.5, containing 50mM-KCI and 5mM-free Mg2+. A Scatchard plot is shown inset. (b) 8.6puM-[8-'4C]ADP and 17pM-pyruvate kinase in the buffer system described above. At fraction number 50 a further portion of [8-14C]ADP was added. The doubling of the radioactivity in the diffusate indicates that the kinetics of diffusion of [8-14C]ADP did not change during the experiment.
Vol. 169
L. G. DANN AND H. G. BRITTON
48
Table 2. Isotope-trapping experiments A 0.1 ml portion of a 'pulse' solution containing pyruvate kinase, 50 mM-Tris/HCI buffer, pH 8.5, 50 mM-KCI, 5 mMMgCl2 and either [32P]phosphoenolpyruvate or [8-'4CqADP was rapidly added at room temperature (23-26°C) to 1 ml of a 'chase' solution of unlabelled phosphoenolpyruvate and ADP and sufficient MgCl2 to give a free Mg2+ concentration of S mm. After approx. I s 1 ml of 1 M-HCI04 was added, and after 5 min 1 ml of this solution was neutralized with 0.5 ml of 1 M-KHCO3, The solution was centrifuged to remove KC104, ATP, [32P]phosphoenolpyruvate, [y-32P]ATP, [8-14C]ADP and [8-14C]ATP were determined as described in the Materials and Methods section. The amount of labelled substrate bound to the enzyme in the 'pulse' solution was calculated by usinga binding constant of 65AM for phosphoenolpyruvate and 2mM for ADP (see Fig. 5 and the text), and assuming four active sites per enzyme molecule (Cottam et al., 1969). Pyruvate kinase Substrate bound Quantity of Labelled substrate ATP trapped to enzyme (active sites) trapped (nmol) (nmol) (nmol) (as Y% bound) 1.37 1.50 4.29 109 L--r jmollspnoenuipyruviuc 1.30 4.26 1.37 95 0 -0.08 6.2 0.6 [8-14C]ADP 0 -0.09 6.12 0.6
the 'pulse' solution (0.09 mol/l) might have been expected to increase any binding of ADP. Discussion Interpretation of results Addition of substrates. A ratio Flux of ATP to ADP/Flux of ATP to phosphoenolpyruvate greater than unity (Fig. la) is unequivocal evidence that one pathway for the enzyme reaction involves the addition of phosphoenolpyruvate to the free enzyme in a rate-limiting step. Isotope effects may cause errors in the determination of the fluxes, but with 14C and 32p such effects would seem to be far too small to influence the results significantly. The hyperbolic rise in the ratio towards a plateau as the ADP concentration was increased also indicates that the substrates can add in reverse order. The ratio was unaffected by phosphoenolpyruvate concentration, and it follows that (a) the release and addition of ADP from the free enzyme is rapid and/or (b) the ratio kL7/(kL2+k-7) is very small (Scheme 2 of Fig. 1 in Britton & Dann, 1978). There is evidence from the isotope-trapping data (see below) that condition (a) applies. For a random addition and if the phosphoenolpyruvate concentration does not affect the flux ratio, from eqn. (3) of Britton & Dann (1978): 1 + a[ADP] Flux of ATP to ADP Flux of ATP to phosphoenolpyruvate 1 + IJ[ADP] (3) where a and ,B are constants depending on the rate constants. Further, if the addition of ADP is rapid as in Scheme 3 (of Fig. 1 in Britton & Dann, 1978): 1 OA §5AB KB where KB is the dissociation constant of the [E-ADP] binary complex. Assuming KB = 2mM (see below) and
with the values of qA and qAB in Table 1, a value of 1.78mM-1 is obtained for a. Line I in Fig. l(a) represents eqn. (3) with this value and a value of of 0.588mM. The latter value was arbitrarily taken to give a flux ratio of 2.1 at an ADP concentration of 2mM. The theoretical line fits reasonably with the experimental points and yields a plateau value for RB of 3.04. From eqn. (17) of Britton & Dann (1978) (d= y =0 and RA = 1) it follows that at low ADP concentrations at least 67% of the reaction follows the upper pathway in Scheme 3 (of Fig. 1 in Britton & Dann, 1978). At higher ADP concentrations the proportion following the lower pathway increases. For example, at an ADP concentration of 1 mm the proportion following this pathway will lie between 37 and 47 %. An ordered addition with phosphoenolpyruvate adding first to the enzyme would yield a flux ratio independent of phosphoenolpyruvate concentration, as observed (Fig. lb), but rising linearly with the concentration of ADP. Although the latter condition appeared not to be fulfilled (Fig. la), the experimental points show a considerable scatter. Further evidence to exclude an ordered addition may be obtained by calculating the slope of the theoretical line for this mechanism from the steady-state velocity data [eqn. (23) of Britton & Dann, 1978)]. From the [3-14C]pyruvate experiments (see the Results section) and eqn. (24) of Britton & Dann (1978):
(s
-A
20mM, the binding of ADP by the enzyme need not be rapid to explain the isotope-trapping data. Alternative mechanisms. For simplicity it has been assumed in Scheme 3 (of Fig. 1 in Britton & Dann, 1978) that the dissociations of EPQ into EQ and EP are rapid steps. However, the same kinetics would be obtained if these steps were rate-limiting, provided that the dissociations of the binary complexes EQ and EP are rapid. Similarly the same kinetics will be obtained if the complex EAB dissociates directly into EQ and EP by rate-limiting steps. In these cases the rate constants for the addition of substrates will still be in Fig. 6(b). General discussion Mechanism of muscle pyruvate kinase. In initialvelocity studies on rabbit muscle pyruvate kinase at pH8.5 in glycylglycine buffer, Reynard et al. (1961) found that the enzyme obeyed hyperbolic steadystate kinetics. ATP was a competitive inhibitor with respect to both phosphoenolpyruvate and ADP. They concluded that the mechanism was rapid random. Ainsworth & MacFarlane (1973) madeinitial-velocity studies at pH6.2 in sodium cacodylate buffer at an ionic strength of 0.2mol/I while the free Mg2+ was 1978
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
maintained constant and also found that the enzyme conformed to hyperbolic kinetics. They concluded that the mechanism was rapid random, since the products gave the appropriate competitive inhibition patterns, apart from pyruvate, which showed noncompetitive inhibition with respect to ADP. The last was attributed to the formation of a dead-end complex E-ADP-pyruvate. In contrast, Melchior (1965), in a careful study at pH 7.0 and I 0.5, found that the initial velocities did not obey hyperbolic kinetics at high ADP concentrations and suggested that the reaction was random but not rapid. Robinson & Rose (1972) also suggested, from experiments on the incorporation of 3H from water into phosphoenolpyruvate, that addition of substrates might not be rapid, but there are alternative interpretations of their findings. The intersection close to or on the abscissa of the reciprocal plots of velocity against substrate concentrations in the experiments of Reynard et al. (1961) and Ainsworth & MacFarlane (1973), together with the assumption of a rapid random mechanism, imply that the binding of one substrate does not greatly affect the binding of the other. Our steady-state data would lead to the same conclusions if the addition is assumed to be rapid and random. Reynard et al. (1961), Mildvan & Cohn (1966) and James et al. (1973) found that the free enzyme bound phosphoenolpyruvate with a dissociation constant similar to the Ki, as required by the assumption of a rapid random mechanism. However, Reynard et al. (1961) found little binding of ADP and were unable to determine a dissociation constant, although they concluded that it must lie within an order of magnitude of the Km. In contrast, Mildvan & Cohn (1966) found a dissociation constant for ADP of 0.0680.2mM at pH7.5 from magnetic-resonance measurements and protection studies with mercuribenzoate. Giles et al. (1976) have described measurement of equilibrium exchanges between ATP and phosphoenolpyruvate, ATP and ADP and pyruvate and phosphoenolpyruvate at pH7.4 and 25°C. All the exchange rates were the same within the statistical error, apart from that for the exchange between phosphoenolpyruvate and pyruvate, which was lower. The exchange rates between phosphoenolpyruvate, ADP and ATP are consistent with our own findings at pH 8.5. However, the maximum ADP concentration used by Giles et al. (1976) was only 0.05mM, and thus, on the basis of the steady-state data for the forward reaction reported in the present paper, such measurement will not distinguish between an ordered or random addition of substrates. The slower exchanges between phosphoenolpyruvate and pyruvate are not consistent with our finding, since they imply that the ratio Flux of phosphoenolpyruvate to ATP/Flux of phosphoenolpyruvate to pyruvate must be substantially greater than unity at ATP Vol. 169
51
concentrations of 1 mm and 7.65 mm. Measurements of this ratio at pH7.4 may therefore be valuable. Our study at pH8.5 has shown by two unequivocal methods that one pathway for the enzyme involves phosphoenolpyruvate adding first to the enzyme in a rate-limiting step. The substrates can also add in alternative order (although this pathway is a relatively minor one at low ADP concentrations), and there is strong evidence that the dissociation of products is rapid and random (Fig. 6). With the rate constants indicated in Fig. 6, the enzyme will obey hyperbolic kinetics, except at very high ADP concentrations. This mechanism predicts non-competitive inhibition by both pyruvate and ATP with ADP as the varied substrate [eqn. (1) in Appendix I], whereas both Reynard et al. (1961) and Ainsworth & MacFarlane (1973) reported competitive inhibition between ATP and ADP. Exact comparisons cannot be made, but both small variations in the concentration of free Mg2+ and the non-linearities predicted by eqn. (1) (in Appendix I) may have minimized the noncompetitive element in these experiments. Our binding studies have confirmed the binding of phosphoenolpyruvate and have shown that it is probably the unligated species that is bound to the enzyme. However, our observations indicate that the dissociation constant (65pM) is larger than the Km determined under the same conditions (32.5pM), as required if the addition of phosphoenolpyruvate to the free enzyme is a rate-limiting step. We have been unable to demonstrate binding of ADP either in the presence or in the absence of Mg2+, despite a Km for ADP of 170guM, and we are unable to confirm the findings obtained by Mildvan & Cohn (1966). Although binding of ADP would have been expected if the mechanism were rapid and random, a large dissociation constant is a necessary requirement if a non-rapid random mechanism is to exhibit hyperbolic steady-state kinetics. Our binding data are therefore in complete accord with our kinetic data, and lead to the conclusion that the binding of either substrate increases the affinity of the enzyme for the other substrate by a very large factor. With the rate constants indicated in Fig. 6 the increase is 7.5-8.5 times, and the increase may be larger because a KADP of 2mm represents a minimum value. Such large changes clearly have considerable implications for the molecular mechanism of the enzyme. We thank the Science Research Council for financial support, and Dr. Geoffrey Franglen of St. George's Hospital Medical School, London, U.K., for computer facilities in the calculation of weighted linear regressions.
References Ainsworth, S. & MacFarlane, N. (1973) Biochein. J. 131, 223-236 Britton, H. G. (1966)Arch. Biochem. Biophys. 117,167-183
52
L. G. DANN AND H. G. BRITTON
Britton, H. G. & Clarke, J. B. (1968) Biochem. J. 110, 161179 Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Colowick, S. P. & Womack, F. C. (1969) J. Biol. Chem. 244, 774-777 Cottam, G. L., Hollenberg, P. F. & Coon, M. J. (1969) J. Biol. Chem. 244, 1481-1486 Dalziel, K. (1957) Acta Chem. Scand. 11, 1706-1723 Dann, L. G. & Britton, H. G. (1974) Biochem. J. 137, 405407 Dann, L. G. & Britton, H. G. (1977) Biochem. J. 161,445448 Dyson, R. D., Cardenas, J. M. & Barsotti, R. J. (1975) J. Biol. Chem. 250, 3316-3321 Eggleston, L. V. & Hems, R. (1952) Biochem. J. 52, 156160 Garland, P. B., Newsholme, E. A. & Randle, P. J. (1964) Biochem. J. 93, 665-678 Giles, I. G., Poat, P. C. & Munday, K. A. (1976) Biochem. J. 157, 577-589 Irving, M. G. & Williams, J. F. (1973) Biochem. J. 131, 287-301 James, T. L., Reuben, J. & Cohn, M. (1973)J. Biol. Chem. 248,6443-6449 Liao, C. L. & Atkinson, D. E. (1971) J. Bacteriol. 106, 37-44
Llorente, P., Marco, R. & Sols, A. (1970) Eur. J. Biochem. 13,45-54 Lowry, 0. H., Rosebrough, N. J., Fair, A. L. & Randall, R. J. (1951) J. Biol. Chem. 193, 265-275 MacFarlane, N. & Ainsworth, S. (1972) Biochem. J. 129, 1035-1047 MacFarlane, N. & Ainsworth, S. (1974) Biochem. J. 139, 499-508 Melchior, J. B. (1965) Biochemistry 4, 1518-1525 Mildvan, A. S. & Cohn, M. (1966) J. Biol. Chem. 241, 1178-1193 Nicholas, P. C. & Bachelard, H. S. (1974) Biochem. J. 141, 165-171 Phillips, R. C., George, S. J. P. & Rutman, R. J. (1966) J. Am. Chem. Soc. 88, 2631-2640 Reynard, A. M., Hass, L. F., Jacobsen, D. D. & Boyer, P. D. (1961) J. Biol. Chem. 236, 2277-2283 Robinson, J. L. & Rose, I. A. (1972) J. Biol. Chem. 247, 1096-1105 Rose, I. A., O'Connell, E. L., Litwin, S. & Tana, J. B. (1974) J. Biol. Chem. 249, 5163-5168 Schendel, P. F. & Wells, R. D. (1973) J. Biol. Chem. 248, 8319-8321 Sugino, Y. & Miyoshi, Y. (1964)J. Biol. Chem. 239, 23602364 Tietz, A. & Ochoa, S. (1958) Arch. Biochem. Biophys. 78, 477-493 Wilkinson, G. N. (1961) Biochem. J. 80, 324-332 Wold,F. &Ballou, C. E. (1957)J. Biot. Chem.227,301-312
APPENDIX I Kinetics of a Branched Pathway, Conditions for observed, and the coefficients can be related to the q Approximating to Hyperbolic Steady-State Velocity values [Table 1 of the main paper (Dann & Britton, Kinetics and Calculation of Rate Constants and Flux 1978)] and the inhibition data as follows: Ratios For Scheme 3 (of Fig. 1 in Britton & Dann, 1978), the velocity v of the reaction in the absence of Q is given by the expression: 1 V
(1l/k+3)(1+ k-7/k-2[D]) = q0 (k+3 +k_7)/k+lk+3[D] = OA- AB/KB (k-2 +k+3 + k7)/k+3k+2[D] = qB
(5) (6) (7)
1 1 + k_7 + (k+3+ k-7)k+2+k-L(k-2+ k+3+ k-7)/KB+ (k+3+k_7)[P] (ET) [k+3 k+3k-2[D] k+1k+2k+3[A][D] k+lk+3[A][D]KP / [P]\] Lk-(k-2+k+3+k-7) (k_2+k+3+k_7) +
(k+3+k_7)[B]+ k+2k+3[B][D] k+lk+3[A]KB k+lk+2k+3[A][B][D] V Kp(1)
where
[D]
=
1 + (k-7/kI2) + (k-7k+2/k_j1k2[B])
and (ET) represents the amount of enzyme. Also: k+lk+2k+3KpQ/k-lk-2k-3 = Keq. and
k+lk+2k-7KO = k-lk-2k+7
(2) (3)
(4) where Keq. is the equilibrium constant for the reaction. Provided that the [B]/[A] term is small in eqn. (1) and that the [B] term is small in eqn. (2), Scheme 3 (of Fig. 1 in Britton & Dann, 1978) will approximate to hyperbolic steady-state velocity kinetics, as
k-1(k-2 +k+3 + k7)/k+lk+2k+3D] = OAB KP = [OA+ OlAB(1/[B] -/KB)]/mp
(8) (9)
where mp is the slope of the replot for ATP [Fig. 4(b) and Table 1 of the main paper (Dann & Britton, 1978)]. Since a similar expression to eqn. (1) holds for the reaction in the presence of Q but in the absence of P:
KQ = [0A+ OAB(1/[B]-1/KB)]/mQ
(10)
where mQ is the slope of the replot for pyruvate [Fig. 4(a) and Table 1 of the main paper (Dann & Britton, 1978)]. The values of KP and KQ given in Fig. 6 of the main paper (Dann & Britton, 1978) were calculated from these values and assuming KB = 2mM.
1978
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
Since [B] ([ADP]) was 1OAM and 50pM respectively, Kp and KQ will be affected only negligibly if KB has a larger value. From eqn. (5) (Britton & Dann, 1978): (11) k+2k_71k_j(k-2+k-7) = f At chemical equilibrium the flux of A to P (Britton, 1966) is given by the expression:
(Flux of A to P]-1 =
1
(k___k_7
(E) [k+lk+3[A][D] + k.1(k-2+k-7 +k+3)] k+lk+2k+3[A][B][D]
(12)
and I 1 r k+,[A] k-1 (E) (ELT)
[B] +[P] [LQ] KB KP KQ
+ klk2 Q +
k_3) [A][B]]
(13)
where (E) represents the amount of free enzyme. The coefficients in eqn. (12) are given by eqns. (6) and (7). Further, from eqns. (7) and (8) k+11k-1 = qB/OAB, and, if a value for KB of 2mm is assumed, all of the coefficients except the last in eqn. (13) are known. Defining this coefficient as E:
OE = k+lk+2(1 +k+3/k.3)/lklk.2
(14)
in three experiments the rate of exchange between phosphoenolpyruvate and ATP was measured with enzyme that had been freshly assayed. With these results and the values of q in Table 1 of the main paper (Dann & Britton, 1978) a mean value (±S.E.M.) for E of 622 ± 87 was obtained. Eqns. (3)-(1 1) and (14) relate the rate and equilibrium constants to measured parameters [see Table 1 and Results section ofthe main paper (Dann & Britton, 1978)]. The range of solutions in Fig. 6 of the main paper (Dann & Britton, 1978) was obtained as follows. KB was assumed to be 2mM, and to a first approximation k+3==o-1. From eqns. (7), (8) and
(14): k_2 > k+lk+2/1k-1E > 1/bABOE (15) With the minimum value for k-2 given by eqn. (15) and the approximate value for k+3, a quadratic equation in k7 was derived from eqns. (6), (8) and (11). These values for k_2, k_7 and k+3 were then used to derive solutions for the other rate constants, assuming [D] = 1. A revised value for k2 was then taken, based on eqn. (15). Finally, a value for k+3 calculated from eqn. (5), and similarly values for the other rate constants, were obtained by inserting values for the rate constants in the expression for [D]. Iterations of the whole procedure led to the solution given in Fig. 6(b) of the main paper (Dann & Britton, 1978). To obtain the solutions shown in Fig. 6(a) of the Vol. 169
53
main paper (Dann & Britton, 1978), a similar procedure was used, but in this case the quadratic equation in k7 does not contain k2. Since KB> 1.3mm and in the initial-velocity experiments the maximum ADP concentration (substrate B in Scheme 3 of Fig. 1 in Britton & Dann, 1978) was 0.2mM, it follows from eqn. (1) that, even at the maximum ADP concentration, the [B]/[A] term in eqn. (1) will be less than one-fifth of the 1/IA] term. The 1/[A] term becomes most important at low phosphoenolpyruvate concentrations (substrate A), but, even then, with the values from Table 1 of the main paper (Dann & Britton, 1978), the [B]/[A] term contributes less than 5 % to the velocity. The contribution of the [B]/[A] term is thus negligible, as is required if Scheme 3 (of Fig. 1 in Britton & Dann, 1978) is to obey hyperbolic steady-state velocity. The [B] term in the expression for [D] (eqn. 2) should also be small. With the values in Figs. 6(a) and 6(b) of the main paper (Dann & Britton, 1978), the maximum contribution of the B term is about 10 %. Further, the contributions of the [B]/[A] term and the [D] term will be in opposite directions and will tend to cancel each other. If the [B] term were the major term in the expression for [D], the identification of the q terms with the coefficients in eqn. (1) would be incorrect. This possibility can be excluded on the following grounds. (1) From eqn. (10) of Britton & Dann (1978), and since RB = 3.04, k_7/k2 < 0.5. The [B] term in the expression for [D] could therefore only be large if k+2[B] > k-1, this corresponding to measurements at near-saturating concentrations of B. (2) Terms containing [B]-2 would appear in eqn. (1) and the plots of v-1 versus [B]-1 should be non-linear. (3) Even if the [B]-2 terms in eqn. (1) should be small, and, provided that KB> 1.3mmi, AB should be greater than A, contrary to observation. Flux Ratio for an Ordered Dissociation of Products If the addition of substrates is as in Scheme 3 (of Fig. 1 in Britton & Dann, 1978), but the dissociation of products is ordered with P dissociating first from the ternary complex, then with the rate constants as defined in Schemes 2 and 3 (of Fig. 1 in Britton & Dann, 1978): Flux of A to P= I + k-4Z[P] (16) Flux of A to Q k+5(Z+k+4) and k-3(k-1(k2 + k7) + k7k+2[B]) k_l(k2 + k7 + k+3) + (k7 + k+3)k+3[B] Further: OAB = k-1[(k3 + k+4)(k-2 + k-7) + k+3k+4]/k+3k+4[D]
(18)
OA
=
k-lk-3k-4(k-2 + k7)/k+3k+4k+5[D] (19)
L. G. DANN AND H. G. BRITTON
54
OA= {k+2[k-2(k3 +k+4) +k+3k+4] + kL[(k-2
References Britton, H. G. (1966) Arch. Biochem. Biophys. 117, 167-
+k-7)(k-3 +k+4) +k+3k+4]/KB}/k+3k+4[D] (20) Inspection of eqns. (16)-(20) indicates that the coefficient for [P] in eqn. (16) will be intermediate in value between those given by eqn. (28) and eqn. (29) of Britton & Dann (1978).
183 Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (1978) Biochem. J. 169, 3952
and
APPENDIX II substrates of the type shown in Scheme 3 (of Fig. 1 in Calculation of the Incorporation of Radioactivity into Britton & Dann, 1978) gives an intermediate value a Substrate from a Labelled Product for r (see Appendix I). Consider the experiment illustrated in Fig. 2(b) of To solve eqns. (2) and (3), eqns. (28) and (29) of the main paper (Dann & Britton, 1978), in which the Britton & Dann (1978) and the values of q given in reaction was carried out in the presence of labelled Table 1 of the main paper (Dann & Britton, 1978) ATP. Let A be phosphoenolpyruvate, B be ADP, were used to determine r. Eqns. (2) and (3) were then P be ATP and Q be pyruvate, and let: solved numerically by stepwise integration. In the () Flux of A toP initial calculations iterative procedure was used to determine dna and dn,g, but with the particular Flux of A to Q conditions iteration was found to be unnecessary. Then from eqn. (37) of Britton & Dann (1978): In the experiment illustrated in Fig. 4(a) of the main Flux of P to A = (r-1)x Net flux of A to Q paper (Dann & Britton, 1978) the reaction was carried out in the presence of labelled pyruvate. In this If N is total radioactivity, na is radioactivity in A, case radioactivity can only enter phosphoenolpyrunfl is radioactivity in glucose 6-phosphate and vate, and n2 = 0. Eqn. (2) can be integrated to give: is radioactivity in ATP, then:
N-(na+fng)
dna= [A]
-d(r-1)
(n.
)d[A]
(2)
and
dn2= N(fa+fng)d[A] [Q]
(3)
If the dissociation of products is ordered with P dissociating first from the ternary complex, then the minimum value of r is given by eqn. (28) of Britton & Dann (1978). This corresponds to an ordered addition, with A adding first to the enzyme. The maximum value of r is given by eqn. (29) of Britton & Dann (1978), corresponding to an ordered addition with the substrate last to add to the enzyme or to a rapid random addition. A random addition of
k(A] Inn[ exp(-k[A]) [ [A]- ik([Ao ]-[A]) k2([Ao]2 - [A]2) k3([Ao]3- [A]3) ... )] 4 + I] 2.2! 3.3! where [AO] is the initial concentration of A, and k is (1 -r)/r[P]. r was calculated as above but assuming that P is pyruvate. na
N
References Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (1978) Biochem. J. 169, 3952
APPENDIX III Flux Ratios for a Ping-Pong Mechanism From eqn. (31) of Britton & Dann (1978) and the values in Table 1 of the main paper (Dann & Britton, 1978) at 2mM-ADP: Flux of P to B 1.75 Flux of P to A The measured values for this ratio therefore fall within the allowed range. However, in the expression for the ratio Flux of A to Q/Flux of A to P [eqn. (32) Q of Britton & D4nn (1978)] (p2+ a/QB]) CQrrespondS
to the slope replot mQ. With this value and the value for A [Table 1 of the main paper (Dann & Britton, 1978)] the calculated incorporation of label into phosphoenolpyruvate is very large, and a Ping-Pong mechanism is therefore excluded. References Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (I97$) Biochem. J. 169, 3952
1978
39
Kinetics and Mechanism of Action of Muscle Pyruvate Kinase By LEIGHTON G. DANN* and HUBERT G. BRITTON Department of Physiology, St. Mary's Hospital Medical School, London W2 1PG, U.K. (Received 29 March 1977)
1. The mechanism of rabbit muscle pyruvate kinase was investigated by measurements of fluxes, isotope trapping, steady-state velocity and binding of the substrates. All measurements were made at pH8.5 in Tris/HCl buffer and at 5mM-free Mg2+. 2. Methods of preparing [32P]phosphoenolpyruvate from [32P]pl in high yield and determining [32p]_ phosphoenolpyruvate and [8-14C]ADP are described. 3. The ratio Flux of ATP to ADP/ Flux of ATP to phosphoenolpyruvate (measured at equilibrium) increased hyperbolically with ADP concentration from unity to about 2.1 at 2mm-ADP, but was unaffected by phosphoenolpyruvate concentration. Since the ratio is greater than unity, one pathway for the addition of substrates must involve phosphoenolpyruvate adding first to the enzyme in a rate-limiting step. However, the substrates must also add in the alternative order, because of the non-linear increase in the ratio with ADP concentration and because the rate of increase is very much less than that predicted from the steady-state velocity data for an ordered addition. The lack of influence of phosphoenolpyruvate on the ratio is consistent with the rapid addition of ADP in the alternative pathway. At low ADP concentrations the alternative pathway contributes less than 33 % to the total reaction. 4. Isotope trapping was observed with [32P]phosphoenolpyruvate, confirming that when phosphoenolpyruvate adds first to the enzyme it is in a rate-limiting step. The release of phosphoenolpyruvate from the ternary complex must also be a slow step. Trapping was not observed with [8-14C]ADP, hence the addition of ADP to the free enzyme must be rapid unless its dissociation constant is very large (>20mM). 5. Binding studies showed that 4mol of [32P]phosphoenolpyruvate binds to 1 mol ofthe enzyme, probably unligated to Mg2+, with a dissociation constant appropriate to the mechanism indicated above. Binding of [8-14C]ADP could not be detected, and hence the binding of ADP occurs by a low-affinity step. The latter is also demanded by the steady-state velocity data. 6. The ratio Flux of phosphoenolpyruvate to ATP/Flux of phosphoenolpyruvate to pyruvate (determined from the incorporation of label into phosphoenolpyruvate from [3-14C]pyruvate or [y-32P]ATP during the forward reaction) did not differ significantly from unity. Steady-state velocity data predicted grossly different flux ratios for ordered dissociations of the products, and the results indicate that the dissociation must be rapid and random. The data also exclude a Ping-Pong mechanism. 7. Permissible rate constants for the above mechanism are calculated. The results indicate a high degree of cooperativity in binding, whatever the order of addition of substrate. Pyruvate kinase (EC 2.7.1.40) catalyses the formation of pyruvate and ATP from phosphoenolpyruvate and ADP and is an important enzyme in the regulation of glycolysis and gluconeogenesis (Llorente et al., 1970; Liao & Atkinson, 1971). The enzymes, which have been isolated from mammalian tissues (Tietz & Ochoa, 1958; Irving & Williams, 1973; Nicholas & Bachelard, 1974), require Mg2+ or Mn2+ and K+ for activity. They show hyperbolic or sigmoidal steady-state velocity kinetics with respect * Present address: Department of Chemical Pathology, Queen Charlotte's Hospital, London W6 OXG, U.K.
Vol. 169
to the substrate phosphoenolpyruvate and have been classified as M type, having hyperbolic kinetics, and L type, having sigmoidal kinetics and requiring fructose 1,6-bisphosphate for activation. The mechanisms of the mammalian and yeast enzymes have been investigated, but results do not support a single mechanism. Initial-velocity studies have been consistent with a rapid-equilibrium random mechanism for the muscle M-type enzyme (Reynard et al., 1961; Ainsworth & MacFarlane, 1973), an ordered addition of substrates and dissociation of products, for the yeast enzyme (MacFarlane & Ainsworth, 1972) and a Ping-Pong
40
mechanism involving a phosphoenzyme for the liver L-type enzyme (MacFarlane & Ainsworth, 1974). There are difficulties, however, in the interpretation of initial-velocity studies, and we are therefore studying the mechanism of these enzymes with a variety of techniques, including flux measurements with labelled substrates (Britton, 1966; Britton & Dann, 1978), isotope-trapping (Rose et al., 1974), binding and initial-velocity studies. The present paper describes the results obtained on the rabbit muscle enzyme. Materials and Methods
Materials Substrates and enzymes were obtained from Boehringer Corp. (London) Ltd. (London W.5, U.K.); ADP, ATP, NADH, NADP+ and pyruvate were sodium salts; phosphoenolpyruvate and glyceraldehyde 3-phosphate diethyl acetal were cyclohexylammonium salts. Scintillation chemicals were from Packard Instruments (Wembley, Middx., U.K.) and Rohm and Haas (U.K.) Ltd. (Croydon, Surrey, U.K.). All other chemicals were reagent grade or better and were obtained from BDH Chemicals (Poole, Dorset, U.K.). For the kinetic experiments enzyme suspensions were centrifuged and the sedimented enzymes dissolved to the original volume with water. [8-14C]ADP (ammonium salt), phospho[3-14C]enolpyruvate (cyclohexylammonium salt) and [32p]_ orthophosphate (in dilute HCI, pH 2-3) were obtained from The Radiochemical Centre (Amersham, Bucks., U.K.). Phospho[3-'4C]enolpyruvate was dissolved in water, and the solution divided into small portions and freeze-dried. All labelled compounds were stored at -20°C. [32P]Phosphoenolpyruvate was prepared from [32P]PI and glyceraldehyde 3-phosphate by an extension of the method of Schendel & Wells (1973). A 0.1 ml portion (1 mCi) of [32p]p1, pH2-3, in a conical centrifuge tube, was dried in a vacuum desiccator over NaOH. In a second tube, 95,1 of a solution containing (final concentrations) 26mMTris/HCl buffer, pH9.0, 1.05mM-MgCl2, 0.26mMKH2PO4, 0.53 mM-ADP, 1.27mM-NAD+, 0.25mg of Thiazolyl Blue/ml, 0.63mg of promethazine/ml and 10.5 mm-sodium pyruvate was prepared and transferred to the tube containing the [32p]pl with a Pasteur pipette. A 2,ul portion of pyruvate kinase [lOmg/ml in 3.2M-(NH4)2SO4] and 2,u1 of a mixed enzyme preparation [glyceraldehyde 3-phosphate dehydrogenase (1 mg/ml) and 3-phosphoglycerate kinase (5mg/ml) in 3.2 M-(NH4)2SO4] were added. A
20,u1lportionofglyceraldehyde3-phosphate(16.3 mM), prepared immediately before use by dissolving 3.26gmol of the diacetal in 100jl l of 0.2M-HCI,
L. G. DANN AND H. G. BRITTON heating the solution at 80°C for 2min, and, after cooling, neutralization with 100,ul of 0.2M-KHCO3, was added and the solution was incubated in the dark at room temperature (24°C) for 3-4h. A 10,l portion of EDTA (50mM) was added to stop the reaction. To isolate [32P]phosphoenolpyruvate, 101 of the incubation mixture was applied as a 5cm strip on a thin-layer cellulose plate and chromatographed with di-isopropyl ether/formic acid (3 :2, v/v) (Eggleston & Hems, 1952). The labelled phosphoenolpyruvate was identified with a Geiger-Muller tube and the strip cut out of the plate. The phosphoenolpyruvate was chromatographed to the margin of the strip with water and then extracted with 1 ml of 0.2mmphosphoenolpyruvate. The reaction proceeded to completion with little [32P]Pi remaining ( 1.3 mM.
Isotope trappintg Isotope trapping was carried out at room temperature (23-26°C) at pH8.5 in 50mM-Tris/HCl buffer containing 50mM-KCI and 5 mM free Mg2+. Virtually all of the [32P]phosphoenolpyruvate bound to the enzyme (calculated by using a binding constant of 65 pM) was trapped as [y-32P]ATP, but no trapping of [8-14C]ATP was detected (Table 2). If ADP were bound by the enzyme in a rate-limiting step, significant trapping should have been observed, provided that the dissociation constant for ADP is less than 20mM. Further, the relatively low ionic strength of 1978
47
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
1600 (a)
0
E
T 1200 'a
0
CD
0 0
ciC8
_
U
P4
0
Bound/free ratio
t
0
0. 261
0 0
0 0
0
4. 15 rmM 4.5
t 0. 307
m
m
0 0
400 _
0.154
0
00
0000
2
mM
t 0. 0471m
0
0
10
20
30
40
50
Fraction no. 0
0
(b)
800
0 0
600 _ 0
'a ci
0
400 _ 0. >4-
0.14tmM
0
0 0 244
10..362
t
mM
0.048 mM
0 0
200 _ 0
0
0
20
30
40
50
60
Fraction no. Fig. 5. Binding of [32P]phosphoenolpyruvate and [8-14C]ADP to pyruvate kinase Measurements were made by using a rapid-equilibrium-dialysis cell. At intervals, unlabelled substrate was added to give the concentration shown. Mg2+ was added with the substrates to maintain the free Mg2+ concentration constant. Tetraethylammonium chloride was added to give I 0.2. The abscissa represents 2m1 fractions; 0.5ml samples were withdrawn and their radioactivities counted. The points illustrated were corrected as described in the text. (a) 3.9pM[32P]Phosphoenolpyruvate and 27puM-pyruvate kinase in 5OmM-Tris/HCI buffer, pH8.5, containing 50mM-KCI and 5mM-free Mg2+. A Scatchard plot is shown inset. (b) 8.6puM-[8-'4C]ADP and 17pM-pyruvate kinase in the buffer system described above. At fraction number 50 a further portion of [8-14C]ADP was added. The doubling of the radioactivity in the diffusate indicates that the kinetics of diffusion of [8-14C]ADP did not change during the experiment.
Vol. 169
L. G. DANN AND H. G. BRITTON
48
Table 2. Isotope-trapping experiments A 0.1 ml portion of a 'pulse' solution containing pyruvate kinase, 50 mM-Tris/HCI buffer, pH 8.5, 50 mM-KCI, 5 mMMgCl2 and either [32P]phosphoenolpyruvate or [8-'4CqADP was rapidly added at room temperature (23-26°C) to 1 ml of a 'chase' solution of unlabelled phosphoenolpyruvate and ADP and sufficient MgCl2 to give a free Mg2+ concentration of S mm. After approx. I s 1 ml of 1 M-HCI04 was added, and after 5 min 1 ml of this solution was neutralized with 0.5 ml of 1 M-KHCO3, The solution was centrifuged to remove KC104, ATP, [32P]phosphoenolpyruvate, [y-32P]ATP, [8-14C]ADP and [8-14C]ATP were determined as described in the Materials and Methods section. The amount of labelled substrate bound to the enzyme in the 'pulse' solution was calculated by usinga binding constant of 65AM for phosphoenolpyruvate and 2mM for ADP (see Fig. 5 and the text), and assuming four active sites per enzyme molecule (Cottam et al., 1969). Pyruvate kinase Substrate bound Quantity of Labelled substrate ATP trapped to enzyme (active sites) trapped (nmol) (nmol) (nmol) (as Y% bound) 1.37 1.50 4.29 109 L--r jmollspnoenuipyruviuc 1.30 4.26 1.37 95 0 -0.08 6.2 0.6 [8-14C]ADP 0 -0.09 6.12 0.6
the 'pulse' solution (0.09 mol/l) might have been expected to increase any binding of ADP. Discussion Interpretation of results Addition of substrates. A ratio Flux of ATP to ADP/Flux of ATP to phosphoenolpyruvate greater than unity (Fig. la) is unequivocal evidence that one pathway for the enzyme reaction involves the addition of phosphoenolpyruvate to the free enzyme in a rate-limiting step. Isotope effects may cause errors in the determination of the fluxes, but with 14C and 32p such effects would seem to be far too small to influence the results significantly. The hyperbolic rise in the ratio towards a plateau as the ADP concentration was increased also indicates that the substrates can add in reverse order. The ratio was unaffected by phosphoenolpyruvate concentration, and it follows that (a) the release and addition of ADP from the free enzyme is rapid and/or (b) the ratio kL7/(kL2+k-7) is very small (Scheme 2 of Fig. 1 in Britton & Dann, 1978). There is evidence from the isotope-trapping data (see below) that condition (a) applies. For a random addition and if the phosphoenolpyruvate concentration does not affect the flux ratio, from eqn. (3) of Britton & Dann (1978): 1 + a[ADP] Flux of ATP to ADP Flux of ATP to phosphoenolpyruvate 1 + IJ[ADP] (3) where a and ,B are constants depending on the rate constants. Further, if the addition of ADP is rapid as in Scheme 3 (of Fig. 1 in Britton & Dann, 1978): 1 OA §5AB KB where KB is the dissociation constant of the [E-ADP] binary complex. Assuming KB = 2mM (see below) and
with the values of qA and qAB in Table 1, a value of 1.78mM-1 is obtained for a. Line I in Fig. l(a) represents eqn. (3) with this value and a value of of 0.588mM. The latter value was arbitrarily taken to give a flux ratio of 2.1 at an ADP concentration of 2mM. The theoretical line fits reasonably with the experimental points and yields a plateau value for RB of 3.04. From eqn. (17) of Britton & Dann (1978) (d= y =0 and RA = 1) it follows that at low ADP concentrations at least 67% of the reaction follows the upper pathway in Scheme 3 (of Fig. 1 in Britton & Dann, 1978). At higher ADP concentrations the proportion following the lower pathway increases. For example, at an ADP concentration of 1 mm the proportion following this pathway will lie between 37 and 47 %. An ordered addition with phosphoenolpyruvate adding first to the enzyme would yield a flux ratio independent of phosphoenolpyruvate concentration, as observed (Fig. lb), but rising linearly with the concentration of ADP. Although the latter condition appeared not to be fulfilled (Fig. la), the experimental points show a considerable scatter. Further evidence to exclude an ordered addition may be obtained by calculating the slope of the theoretical line for this mechanism from the steady-state velocity data [eqn. (23) of Britton & Dann, 1978)]. From the [3-14C]pyruvate experiments (see the Results section) and eqn. (24) of Britton & Dann (1978):
(s
-A
20mM, the binding of ADP by the enzyme need not be rapid to explain the isotope-trapping data. Alternative mechanisms. For simplicity it has been assumed in Scheme 3 (of Fig. 1 in Britton & Dann, 1978) that the dissociations of EPQ into EQ and EP are rapid steps. However, the same kinetics would be obtained if these steps were rate-limiting, provided that the dissociations of the binary complexes EQ and EP are rapid. Similarly the same kinetics will be obtained if the complex EAB dissociates directly into EQ and EP by rate-limiting steps. In these cases the rate constants for the addition of substrates will still be in Fig. 6(b). General discussion Mechanism of muscle pyruvate kinase. In initialvelocity studies on rabbit muscle pyruvate kinase at pH8.5 in glycylglycine buffer, Reynard et al. (1961) found that the enzyme obeyed hyperbolic steadystate kinetics. ATP was a competitive inhibitor with respect to both phosphoenolpyruvate and ADP. They concluded that the mechanism was rapid random. Ainsworth & MacFarlane (1973) madeinitial-velocity studies at pH6.2 in sodium cacodylate buffer at an ionic strength of 0.2mol/I while the free Mg2+ was 1978
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
maintained constant and also found that the enzyme conformed to hyperbolic kinetics. They concluded that the mechanism was rapid random, since the products gave the appropriate competitive inhibition patterns, apart from pyruvate, which showed noncompetitive inhibition with respect to ADP. The last was attributed to the formation of a dead-end complex E-ADP-pyruvate. In contrast, Melchior (1965), in a careful study at pH 7.0 and I 0.5, found that the initial velocities did not obey hyperbolic kinetics at high ADP concentrations and suggested that the reaction was random but not rapid. Robinson & Rose (1972) also suggested, from experiments on the incorporation of 3H from water into phosphoenolpyruvate, that addition of substrates might not be rapid, but there are alternative interpretations of their findings. The intersection close to or on the abscissa of the reciprocal plots of velocity against substrate concentrations in the experiments of Reynard et al. (1961) and Ainsworth & MacFarlane (1973), together with the assumption of a rapid random mechanism, imply that the binding of one substrate does not greatly affect the binding of the other. Our steady-state data would lead to the same conclusions if the addition is assumed to be rapid and random. Reynard et al. (1961), Mildvan & Cohn (1966) and James et al. (1973) found that the free enzyme bound phosphoenolpyruvate with a dissociation constant similar to the Ki, as required by the assumption of a rapid random mechanism. However, Reynard et al. (1961) found little binding of ADP and were unable to determine a dissociation constant, although they concluded that it must lie within an order of magnitude of the Km. In contrast, Mildvan & Cohn (1966) found a dissociation constant for ADP of 0.0680.2mM at pH7.5 from magnetic-resonance measurements and protection studies with mercuribenzoate. Giles et al. (1976) have described measurement of equilibrium exchanges between ATP and phosphoenolpyruvate, ATP and ADP and pyruvate and phosphoenolpyruvate at pH7.4 and 25°C. All the exchange rates were the same within the statistical error, apart from that for the exchange between phosphoenolpyruvate and pyruvate, which was lower. The exchange rates between phosphoenolpyruvate, ADP and ATP are consistent with our own findings at pH 8.5. However, the maximum ADP concentration used by Giles et al. (1976) was only 0.05mM, and thus, on the basis of the steady-state data for the forward reaction reported in the present paper, such measurement will not distinguish between an ordered or random addition of substrates. The slower exchanges between phosphoenolpyruvate and pyruvate are not consistent with our finding, since they imply that the ratio Flux of phosphoenolpyruvate to ATP/Flux of phosphoenolpyruvate to pyruvate must be substantially greater than unity at ATP Vol. 169
51
concentrations of 1 mm and 7.65 mm. Measurements of this ratio at pH7.4 may therefore be valuable. Our study at pH8.5 has shown by two unequivocal methods that one pathway for the enzyme involves phosphoenolpyruvate adding first to the enzyme in a rate-limiting step. The substrates can also add in alternative order (although this pathway is a relatively minor one at low ADP concentrations), and there is strong evidence that the dissociation of products is rapid and random (Fig. 6). With the rate constants indicated in Fig. 6, the enzyme will obey hyperbolic kinetics, except at very high ADP concentrations. This mechanism predicts non-competitive inhibition by both pyruvate and ATP with ADP as the varied substrate [eqn. (1) in Appendix I], whereas both Reynard et al. (1961) and Ainsworth & MacFarlane (1973) reported competitive inhibition between ATP and ADP. Exact comparisons cannot be made, but both small variations in the concentration of free Mg2+ and the non-linearities predicted by eqn. (1) (in Appendix I) may have minimized the noncompetitive element in these experiments. Our binding studies have confirmed the binding of phosphoenolpyruvate and have shown that it is probably the unligated species that is bound to the enzyme. However, our observations indicate that the dissociation constant (65pM) is larger than the Km determined under the same conditions (32.5pM), as required if the addition of phosphoenolpyruvate to the free enzyme is a rate-limiting step. We have been unable to demonstrate binding of ADP either in the presence or in the absence of Mg2+, despite a Km for ADP of 170guM, and we are unable to confirm the findings obtained by Mildvan & Cohn (1966). Although binding of ADP would have been expected if the mechanism were rapid and random, a large dissociation constant is a necessary requirement if a non-rapid random mechanism is to exhibit hyperbolic steady-state kinetics. Our binding data are therefore in complete accord with our kinetic data, and lead to the conclusion that the binding of either substrate increases the affinity of the enzyme for the other substrate by a very large factor. With the rate constants indicated in Fig. 6 the increase is 7.5-8.5 times, and the increase may be larger because a KADP of 2mm represents a minimum value. Such large changes clearly have considerable implications for the molecular mechanism of the enzyme. We thank the Science Research Council for financial support, and Dr. Geoffrey Franglen of St. George's Hospital Medical School, London, U.K., for computer facilities in the calculation of weighted linear regressions.
References Ainsworth, S. & MacFarlane, N. (1973) Biochein. J. 131, 223-236 Britton, H. G. (1966)Arch. Biochem. Biophys. 117,167-183
52
L. G. DANN AND H. G. BRITTON
Britton, H. G. & Clarke, J. B. (1968) Biochem. J. 110, 161179 Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Colowick, S. P. & Womack, F. C. (1969) J. Biol. Chem. 244, 774-777 Cottam, G. L., Hollenberg, P. F. & Coon, M. J. (1969) J. Biol. Chem. 244, 1481-1486 Dalziel, K. (1957) Acta Chem. Scand. 11, 1706-1723 Dann, L. G. & Britton, H. G. (1974) Biochem. J. 137, 405407 Dann, L. G. & Britton, H. G. (1977) Biochem. J. 161,445448 Dyson, R. D., Cardenas, J. M. & Barsotti, R. J. (1975) J. Biol. Chem. 250, 3316-3321 Eggleston, L. V. & Hems, R. (1952) Biochem. J. 52, 156160 Garland, P. B., Newsholme, E. A. & Randle, P. J. (1964) Biochem. J. 93, 665-678 Giles, I. G., Poat, P. C. & Munday, K. A. (1976) Biochem. J. 157, 577-589 Irving, M. G. & Williams, J. F. (1973) Biochem. J. 131, 287-301 James, T. L., Reuben, J. & Cohn, M. (1973)J. Biol. Chem. 248,6443-6449 Liao, C. L. & Atkinson, D. E. (1971) J. Bacteriol. 106, 37-44
Llorente, P., Marco, R. & Sols, A. (1970) Eur. J. Biochem. 13,45-54 Lowry, 0. H., Rosebrough, N. J., Fair, A. L. & Randall, R. J. (1951) J. Biol. Chem. 193, 265-275 MacFarlane, N. & Ainsworth, S. (1972) Biochem. J. 129, 1035-1047 MacFarlane, N. & Ainsworth, S. (1974) Biochem. J. 139, 499-508 Melchior, J. B. (1965) Biochemistry 4, 1518-1525 Mildvan, A. S. & Cohn, M. (1966) J. Biol. Chem. 241, 1178-1193 Nicholas, P. C. & Bachelard, H. S. (1974) Biochem. J. 141, 165-171 Phillips, R. C., George, S. J. P. & Rutman, R. J. (1966) J. Am. Chem. Soc. 88, 2631-2640 Reynard, A. M., Hass, L. F., Jacobsen, D. D. & Boyer, P. D. (1961) J. Biol. Chem. 236, 2277-2283 Robinson, J. L. & Rose, I. A. (1972) J. Biol. Chem. 247, 1096-1105 Rose, I. A., O'Connell, E. L., Litwin, S. & Tana, J. B. (1974) J. Biol. Chem. 249, 5163-5168 Schendel, P. F. & Wells, R. D. (1973) J. Biol. Chem. 248, 8319-8321 Sugino, Y. & Miyoshi, Y. (1964)J. Biol. Chem. 239, 23602364 Tietz, A. & Ochoa, S. (1958) Arch. Biochem. Biophys. 78, 477-493 Wilkinson, G. N. (1961) Biochem. J. 80, 324-332 Wold,F. &Ballou, C. E. (1957)J. Biot. Chem.227,301-312
APPENDIX I Kinetics of a Branched Pathway, Conditions for observed, and the coefficients can be related to the q Approximating to Hyperbolic Steady-State Velocity values [Table 1 of the main paper (Dann & Britton, Kinetics and Calculation of Rate Constants and Flux 1978)] and the inhibition data as follows: Ratios For Scheme 3 (of Fig. 1 in Britton & Dann, 1978), the velocity v of the reaction in the absence of Q is given by the expression: 1 V
(1l/k+3)(1+ k-7/k-2[D]) = q0 (k+3 +k_7)/k+lk+3[D] = OA- AB/KB (k-2 +k+3 + k7)/k+3k+2[D] = qB
(5) (6) (7)
1 1 + k_7 + (k+3+ k-7)k+2+k-L(k-2+ k+3+ k-7)/KB+ (k+3+k_7)[P] (ET) [k+3 k+3k-2[D] k+1k+2k+3[A][D] k+lk+3[A][D]KP / [P]\] Lk-(k-2+k+3+k-7) (k_2+k+3+k_7) +
(k+3+k_7)[B]+ k+2k+3[B][D] k+lk+3[A]KB k+lk+2k+3[A][B][D] V Kp(1)
where
[D]
=
1 + (k-7/kI2) + (k-7k+2/k_j1k2[B])
and (ET) represents the amount of enzyme. Also: k+lk+2k+3KpQ/k-lk-2k-3 = Keq. and
k+lk+2k-7KO = k-lk-2k+7
(2) (3)
(4) where Keq. is the equilibrium constant for the reaction. Provided that the [B]/[A] term is small in eqn. (1) and that the [B] term is small in eqn. (2), Scheme 3 (of Fig. 1 in Britton & Dann, 1978) will approximate to hyperbolic steady-state velocity kinetics, as
k-1(k-2 +k+3 + k7)/k+lk+2k+3D] = OAB KP = [OA+ OlAB(1/[B] -/KB)]/mp
(8) (9)
where mp is the slope of the replot for ATP [Fig. 4(b) and Table 1 of the main paper (Dann & Britton, 1978)]. Since a similar expression to eqn. (1) holds for the reaction in the presence of Q but in the absence of P:
KQ = [0A+ OAB(1/[B]-1/KB)]/mQ
(10)
where mQ is the slope of the replot for pyruvate [Fig. 4(a) and Table 1 of the main paper (Dann & Britton, 1978)]. The values of KP and KQ given in Fig. 6 of the main paper (Dann & Britton, 1978) were calculated from these values and assuming KB = 2mM.
1978
MUSCLE PYRUVATE KINASE: KINETICS AND MECHANISM
Since [B] ([ADP]) was 1OAM and 50pM respectively, Kp and KQ will be affected only negligibly if KB has a larger value. From eqn. (5) (Britton & Dann, 1978): (11) k+2k_71k_j(k-2+k-7) = f At chemical equilibrium the flux of A to P (Britton, 1966) is given by the expression:
(Flux of A to P]-1 =
1
(k___k_7
(E) [k+lk+3[A][D] + k.1(k-2+k-7 +k+3)] k+lk+2k+3[A][B][D]
(12)
and I 1 r k+,[A] k-1 (E) (ELT)
[B] +[P] [LQ] KB KP KQ
+ klk2 Q +
k_3) [A][B]]
(13)
where (E) represents the amount of free enzyme. The coefficients in eqn. (12) are given by eqns. (6) and (7). Further, from eqns. (7) and (8) k+11k-1 = qB/OAB, and, if a value for KB of 2mm is assumed, all of the coefficients except the last in eqn. (13) are known. Defining this coefficient as E:
OE = k+lk+2(1 +k+3/k.3)/lklk.2
(14)
in three experiments the rate of exchange between phosphoenolpyruvate and ATP was measured with enzyme that had been freshly assayed. With these results and the values of q in Table 1 of the main paper (Dann & Britton, 1978) a mean value (±S.E.M.) for E of 622 ± 87 was obtained. Eqns. (3)-(1 1) and (14) relate the rate and equilibrium constants to measured parameters [see Table 1 and Results section ofthe main paper (Dann & Britton, 1978)]. The range of solutions in Fig. 6 of the main paper (Dann & Britton, 1978) was obtained as follows. KB was assumed to be 2mM, and to a first approximation k+3==o-1. From eqns. (7), (8) and
(14): k_2 > k+lk+2/1k-1E > 1/bABOE (15) With the minimum value for k-2 given by eqn. (15) and the approximate value for k+3, a quadratic equation in k7 was derived from eqns. (6), (8) and (11). These values for k_2, k_7 and k+3 were then used to derive solutions for the other rate constants, assuming [D] = 1. A revised value for k2 was then taken, based on eqn. (15). Finally, a value for k+3 calculated from eqn. (5), and similarly values for the other rate constants, were obtained by inserting values for the rate constants in the expression for [D]. Iterations of the whole procedure led to the solution given in Fig. 6(b) of the main paper (Dann & Britton, 1978). To obtain the solutions shown in Fig. 6(a) of the Vol. 169
53
main paper (Dann & Britton, 1978), a similar procedure was used, but in this case the quadratic equation in k7 does not contain k2. Since KB> 1.3mm and in the initial-velocity experiments the maximum ADP concentration (substrate B in Scheme 3 of Fig. 1 in Britton & Dann, 1978) was 0.2mM, it follows from eqn. (1) that, even at the maximum ADP concentration, the [B]/[A] term in eqn. (1) will be less than one-fifth of the 1/IA] term. The 1/[A] term becomes most important at low phosphoenolpyruvate concentrations (substrate A), but, even then, with the values from Table 1 of the main paper (Dann & Britton, 1978), the [B]/[A] term contributes less than 5 % to the velocity. The contribution of the [B]/[A] term is thus negligible, as is required if Scheme 3 (of Fig. 1 in Britton & Dann, 1978) is to obey hyperbolic steady-state velocity. The [B] term in the expression for [D] (eqn. 2) should also be small. With the values in Figs. 6(a) and 6(b) of the main paper (Dann & Britton, 1978), the maximum contribution of the B term is about 10 %. Further, the contributions of the [B]/[A] term and the [D] term will be in opposite directions and will tend to cancel each other. If the [B] term were the major term in the expression for [D], the identification of the q terms with the coefficients in eqn. (1) would be incorrect. This possibility can be excluded on the following grounds. (1) From eqn. (10) of Britton & Dann (1978), and since RB = 3.04, k_7/k2 < 0.5. The [B] term in the expression for [D] could therefore only be large if k+2[B] > k-1, this corresponding to measurements at near-saturating concentrations of B. (2) Terms containing [B]-2 would appear in eqn. (1) and the plots of v-1 versus [B]-1 should be non-linear. (3) Even if the [B]-2 terms in eqn. (1) should be small, and, provided that KB> 1.3mmi, AB should be greater than A, contrary to observation. Flux Ratio for an Ordered Dissociation of Products If the addition of substrates is as in Scheme 3 (of Fig. 1 in Britton & Dann, 1978), but the dissociation of products is ordered with P dissociating first from the ternary complex, then with the rate constants as defined in Schemes 2 and 3 (of Fig. 1 in Britton & Dann, 1978): Flux of A to P= I + k-4Z[P] (16) Flux of A to Q k+5(Z+k+4) and k-3(k-1(k2 + k7) + k7k+2[B]) k_l(k2 + k7 + k+3) + (k7 + k+3)k+3[B] Further: OAB = k-1[(k3 + k+4)(k-2 + k-7) + k+3k+4]/k+3k+4[D]
(18)
OA
=
k-lk-3k-4(k-2 + k7)/k+3k+4k+5[D] (19)
L. G. DANN AND H. G. BRITTON
54
OA= {k+2[k-2(k3 +k+4) +k+3k+4] + kL[(k-2
References Britton, H. G. (1966) Arch. Biochem. Biophys. 117, 167-
+k-7)(k-3 +k+4) +k+3k+4]/KB}/k+3k+4[D] (20) Inspection of eqns. (16)-(20) indicates that the coefficient for [P] in eqn. (16) will be intermediate in value between those given by eqn. (28) and eqn. (29) of Britton & Dann (1978).
183 Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (1978) Biochem. J. 169, 3952
and
APPENDIX II substrates of the type shown in Scheme 3 (of Fig. 1 in Calculation of the Incorporation of Radioactivity into Britton & Dann, 1978) gives an intermediate value a Substrate from a Labelled Product for r (see Appendix I). Consider the experiment illustrated in Fig. 2(b) of To solve eqns. (2) and (3), eqns. (28) and (29) of the main paper (Dann & Britton, 1978), in which the Britton & Dann (1978) and the values of q given in reaction was carried out in the presence of labelled Table 1 of the main paper (Dann & Britton, 1978) ATP. Let A be phosphoenolpyruvate, B be ADP, were used to determine r. Eqns. (2) and (3) were then P be ATP and Q be pyruvate, and let: solved numerically by stepwise integration. In the () Flux of A toP initial calculations iterative procedure was used to determine dna and dn,g, but with the particular Flux of A to Q conditions iteration was found to be unnecessary. Then from eqn. (37) of Britton & Dann (1978): In the experiment illustrated in Fig. 4(a) of the main Flux of P to A = (r-1)x Net flux of A to Q paper (Dann & Britton, 1978) the reaction was carried out in the presence of labelled pyruvate. In this If N is total radioactivity, na is radioactivity in A, case radioactivity can only enter phosphoenolpyrunfl is radioactivity in glucose 6-phosphate and vate, and n2 = 0. Eqn. (2) can be integrated to give: is radioactivity in ATP, then:
N-(na+fng)
dna= [A]
-d(r-1)
(n.
)d[A]
(2)
and
dn2= N(fa+fng)d[A] [Q]
(3)
If the dissociation of products is ordered with P dissociating first from the ternary complex, then the minimum value of r is given by eqn. (28) of Britton & Dann (1978). This corresponds to an ordered addition, with A adding first to the enzyme. The maximum value of r is given by eqn. (29) of Britton & Dann (1978), corresponding to an ordered addition with the substrate last to add to the enzyme or to a rapid random addition. A random addition of
k(A] Inn[ exp(-k[A]) [ [A]- ik([Ao ]-[A]) k2([Ao]2 - [A]2) k3([Ao]3- [A]3) ... )] 4 + I] 2.2! 3.3! where [AO] is the initial concentration of A, and k is (1 -r)/r[P]. r was calculated as above but assuming that P is pyruvate. na
N
References Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (1978) Biochem. J. 169, 3952
APPENDIX III Flux Ratios for a Ping-Pong Mechanism From eqn. (31) of Britton & Dann (1978) and the values in Table 1 of the main paper (Dann & Britton, 1978) at 2mM-ADP: Flux of P to B 1.75 Flux of P to A The measured values for this ratio therefore fall within the allowed range. However, in the expression for the ratio Flux of A to Q/Flux of A to P [eqn. (32) Q of Britton & D4nn (1978)] (p2+ a/QB]) CQrrespondS
to the slope replot mQ. With this value and the value for A [Table 1 of the main paper (Dann & Britton, 1978)] the calculated incorporation of label into phosphoenolpyruvate is very large, and a Ping-Pong mechanism is therefore excluded. References Britton, H. G. & Dann, L. G. (1978) Biochem. J. 169, 2937 Dann, L. G. & Britton, H. G. (I97$) Biochem. J. 169, 3952
1978
