Structural aspects of manganese-pyruvate kinase substrate and inhibitor complexes deduced from proton magnetic relaxation rates of pyruvate and a phosphoenolpyruvate analog.

Abstract The distance between enzyme-bound Mn(II) at the active site of rabbit muscle pyruvate kinase and the protons of bound substrate or inhibitor was determined in ternary and quaternary enzyme complexes. In particular, the NMR relaxation rates of pyruvate protons effected by bound Mn(II) were measured for (a) the ternary pyruvate kinase-Mn(II)-pyruvate complex; (b) the abortive quaternary complex containing ADP as the fourth component; and (c) the quaternary complex containing ATP as the fourth component, i.e. the equilibrium mixture. The relaxation rates of the three proton resonances of the inhibitor, α-(dihydroxyphosphinylmethyl)acrylate, the methylene analog of P-enolpyruvate, were measured for the ternary enzyme-Mn(II)-inhibitor complex. Longitudinal (T1) and transverse (T2) NMR relaxation times were measured as a function of temperature and of Mn(II) concentration. Relaxation times were measured at two frequencies, 220 and 60 MHz, so that the correlation time and subsequently the distance of the substrate or inhibitor protons from the paramagnetic Mn(II) could be determined. The correlation time for all the pyruvate ternary and quaternary complexes was found to be 3.5 ± 1.2 x 10-9 s when determined from the T1:T2 ratio for the pyruvate resonance, and to be 2.7 x 10-9 s when determined from the frequency dependence of T1. The Mn(II) to pyruvate-proton distance of 8.2 ± 0.5 A is too large to accommodate a structure with direct Mn(II) coordination to pyruvate. The calculated distance is consistent with a structure in which the pyruvate is in the second coordination sphere of the Mn(II) bound to the enzyme. The correlation time for the ternary complex with the inhibitor, α-(dihydroxyphosphinylmethyl)acrylate, was found to be 1.0 x 10-9 s from the frequency dependence of T1. The distance from Mn(II), determined to be 5.3 A to the methylene protons, 6.5 A to one vinyl proton, and 6.2 A to the other vinyl proton, provides evidence that the ternary P-enolpyruvate analog complex involves coordination of the phosphinyl group to Mn(II) bound to the enzyme. Although binding experiments indicate that P-enolpyruvate and α-(dihydroxyphosphinylmethyl)acrylate compete for the same site on pyruvate kinase in the ternary complex, water proton relaxation rate data and EPR spectra show that the methylene analog of P-enolpyruvate forms a very different ternary complex than P-enolpyruvate. Consequently an extrapolation from the structure of the inhibitor complex to that of the substrate P-enolpyruvate is questionable.

The correlation time for the ternary complex with the inhibitor, cu-(dihydroxyphosphinylmethyl)acrylate, was found to be 1.0 >( lop9 s from the frequency dependence of T1. The distance from Mn(II), determined to be 5.3 A to the methylene protons, 6.5 A to one vinyl proton, and 6.2 A to the other vinyl proton, provides evidence that the ternary P-enolpyruvate analog complex involves coordination of the phosphinyl group to Mn(I1) bound to the enzyme. Although binding experiments indicate that P-enolpyruvate and cr-(dihydroxyphosphinylmethyl)acrylate compete for the same site on pyruvate kinase in the ternary complex, water proton relaxation rate data and EPR spectra show that the methylene analog of P-enolpyruvate forms a very different ternary complex than P-enolpyruvate. Consequently an extrapolation from the structure of the inhibitor complex to that of the substrate P-enolpyruvate is questionable. has a monovalent and a divalent metal ion requirement. Mn(I1) satisfies the divalent metal ion requirement and may function as a paramagnetic probe of the enzyme's active site (1). The equilibrium strongly favors formation of pyruvate and ATP (2).
Attempts to obtain quantitative structural information, i.e. interatomic distances in enzyme-substrate or product complexes from measurements of the paramagnetic relaxation effect of Mn(I1) on substrate nuclei have been hampered by the relative magnitude of the various rate processes of this particular system. The complex formed with excess substrate, P-enolpyruvate, is not amenable to this approach because the rate-limiting step in the observed nuclear relaxation rate is the rate of chemical exchange between free and tightly bound substrate rather than the rate of the Mn(II)-induced nuclear relaxation process.
Therefore, more weakly bound substrates or inhibitors which do not suffer from this limitation have been substituted, including fluorophosphate (3), P-glycolate and P-lactate (4), and in the current investigation the methylene analog of I'-enolpyruvate, cr-(dihydroxyphosphinylmethyl)acrylate.
The relevance of the structure of the substrate analog complexes to that of P-enolpyruvate will be considered.
The product, pyruvate, in its Mn(II)-enzyme complex enolizes if the phosphate site of the enzyme is occupied (5). In the active form of the complex, e.g. in the presence of ATP, enolization occurs and, at high enzyme concentrations, the methyl protons become rapidly deuterated when the solvent is the usual D&I, and proton NMR is no longer feasible. This report describes pyruvate 'H NMR investigations of (a) the ternary pyruvate kinase-Mn(II)-pyruvate complex in DzO; (b) the abortive quaternary complex in DSO including ADP as the fourth component; and (c) the reactive quaternary complex in 10% H&90% DzO including ATP as the fourth component; this complex is the major species at equilibrium in the reaction. For valid distance calculations between a paramagnetic ion and a nucleus to be obtained from the paramagnetic effect on the nuclear relaxation rate, several conditions must be met. (a) The binding of the paramagnetic ion must be specific for one site on the enzyme or. enzyme-substrate complex. This prerequisite has been shown to be satisfied for pyruvate kinase (6). (5) The complex must exist in one structure.
This requirement is also satisfied for the complexes described in this paper as evidenced by EPR experiments (7). (c) The nucleus under observation must undergo rapid chemical exchange between diamagnetic and paramagnetic environments. Experiments on frequency and temperature dependence of the relaxation rates will be described which bear on this point.
(d) Data must be available to determine 7c, a parameter needed in the calculation of the distance r from the experimentally determined relaxation rates (cf. Equation 4). In some earlier investigations with rabbit muscle pyruvate kinase (3, 4), approximations were used to estimate the correlation time, rc. The approximation, which consists of estimating 7c from the PRR' enhancement of water in the same complex, may not hold. In particular it does not hold for the ternary pyruvate kinase-Mn(II)-P-enolpyruvate complex where it was found by a detailed study of the PRR dependence on temperature and frequency that, on an average, only 0.5 water molecule from the first coordination sphere of Mn(I1) contributes to the proton relaxation rate of water (8). More confidence can be placed in distance determinations using correlation times estimated directly from the frequency dependence of the relaxation rates of nuclei on the substrate or inhibitor as, for example, in the NMR studies of [*%]pyruvate in complexes with Mn(II)-pyruvate kinase and pyruvate carboxylase (9). The variation of both temperature and frequency as detailed in the current investigation of proton relaxation rates are often needed to assign an unambiguous value for rc (1).
The NMR longitudinal (T1) and transverse (!I',) relaxation times of the proton resonances of the substrate pyruvate, or of the inhibitor, methylene analog of P-enolpyruvate, bound to pyruvate kinase were measured as a function of Mn(I1) concentration and temperature.
NMR measurements were made at two frequencies, 220 MHz and 60 MHz, so that the correlation time could be determined and the distance of paramagnetic Mn(I1) from protons of pyruvate or of the P-enolpyruvate methylene analog could be calculated.
1 The abbreviations used are: PRR, water proton longitudinal relaxation rate; DSS, 2,2-dimethyl-2-silapentane-5-sulfonate. MATERIALS AND METHODS Sample Preparation-Pyruvate kinase was isolated from rabbit muscle according to the procedure of Tietz and Ochoa (10) with a final ammonium sulfate fractionation.
The enzyme had a specific activity of 160 to 220 according to the assay of Tietz and Ochoa (10 were observed at the following chemical shifts from DSS: "a," 5.6 ppm; "b," 6.0 ppm; and "c," 2.8 ppm. The transverse relaxation time (Tz) for the pyruvate proton resonance was obtained from the linewidth at half-maximal amplitude, l/T2 = ?TW~,~, and represents the average of at least nine spectra.
Linewidths where r is the ion-proton internuclear distance, 01 is the angular precession frequency for the nucleus, and B is a product of physical constants determined by the electron spin of Mn(I1) and the magnetogyric ratio of the proton; the numerical value of B is 2.87 X lO+.
The correlation time 7e is given by: TC-1 = 7*-l + Ts-l + 7;l where 7r is the correlation time for rotational motion and 7g is the electron spin relaxation time.
Plots of fi (TV) and fz(~~), the terms in parentheses in Equations 4 and 5 versus 7c are shown in Fig. 2A for 220 and 60 MHz.
It has been found (13) that the correlation times 7, and 7~ may be described in terms of (Ea)i, activation energies: As the temperature decreases, 7I and TM will increase, but 711 may either increase or decrease The values for l/T, and l/T2 for the corresponding diamagnetic Mg(I1) complexes were subtracted from the observed values to yield the paramagnetic contribution to the relaxation rates, l/T1, and l/Tzp. The fraction of the diamagnetic contribution to the total relaxation rates ranged from 5 to 50% and 15 to 407& for l/T, and l/Tz, respectively, depending on Mn(I1) concentration. Table I lists the normalized values of the relaxation rates, l/pT1, and l/pTs,, where p is the ratio of the concentration of Mn(II) to pyruvate.
If l/TIP was determined by 7M only (cf. Equation 3), i.e. if limited by the rate of chemical exchange l/rM, then l/TIP and ~/TQ would not change with frequency.
It can be seen from Table I that the ratio of l/pT1, (60 MHz) to l/pT1, (220 MHz) is approximately 10, so the observed relaxation rate is not dominated by chemical exchange. To eliminate the possibility that 7M partially contributes to the relaxation rate, we can compare T1, and Tzp. Since T1, (or TIM) is considerably longer than Tzp (or TSM), one would expect TQ to be more affected by a TM contribution than T1,. Since 7.~ has a large temperature coefficient, the ratio of T1,/T2, should increase with temperature.
Examination of Table I reveals no such trend (Experiments 3 to 6). It is therefore concluded that 7~ < TIM, TZM, and the rate of chemical exchange l/~~ > lo3  The concentrations for the solutions are: pyruvate kinase binding sites, 0.60 to 0.75 mM; ATP, 1.0 mM; potassium pyruvate, 0.10 M for Experiments 1 to 9 and 0.25 M for Experiments 10 and 11; sodium cacodylate buffer, 50 mM (pD 7.0) in 9Oyc D20. Exceptions are cited in the footnotes.
The correlation time, TV, is calculated from the ratio of T,, to TzP using Equations 4 and 5 in the text, and the distances are calculated from Equation 4 Calculation of r,-The ratio T,,/T,, may be used to calculate 7C from Equations 4 and 5 as shown in Fig. 2B provided (a) ~z(T~) > jl(rC) (cf. Fig. 2A), i.e. 7C 2 l/wr; and (b) there is no hyperfine contribution to TQ,. The values of rC calculated from the TQ,/TQ ratio for several solutions with varying Mn(I1) concentration and temperature are given in Table I. It is apparent that there is no systematic temperature or concentration dependence of rc. It is also noteworthy that, within experimental error, the values of rC for the pyruvate kinase-Mn(II)-pyruvate ternary complex and pyruvate kinase-Mn(II)-ADP-pyruvate abortive quaternary complex are the same as rC for the reactive quaternary complex. The likely assumption that rM is also not limiting the relaxation rates for the ternary and abortive complexes was made in the calculations.
The average value for rC from all the Tl,,/Ttp calculations is 3.5 + 1.2 x 10-g s.
The value of rc may also be determined from the frequency dependence of pTlp if rC >, l/(or)i where (wr)i is the lowest frequency used (cf. Fig. 2C). Using an average of the pT1, results at 220 and 60 MHz, 7C is determined to be 2.7 X lrg s in good agreement with the Tlp/Tzp calculations.
This result validates the assumption that the hyperfine contact contribution to pTzP is negligible.
These values of rC are also consistent with values of re of the order of lwg s estimated from the Mn(I1) EPR spectra of various pyruvate kinase-Mn(I1) complexes (7).
At the higher frequency, the temperature was varied over the range 5"-35".
In Fig. 3, the temperature dependence of l/T,, is shown for the experiments with Mn(I1) concentration equal to 0.15 mM. Under these conditions, more than 95% of Mn(I1) is bound in the quaternary complex, and consequently changes in the ratio of bound to unbound Mn(I1) need not be considered in analysis of the temperature dependence.
The small positive temperature dependence may be ascribed to the fact that wlrC > 1. We may consider which rate process dominates the correlation time in Equation 6. A Debye-Stokes law calculation for the rotational reorientation time of the entire enzyme gives T? = lo-' s. If the pyruvate is rigidly bound to the enzyme, rr is clearly too large to contribute to rC which is -3 x 10mg s. The very small temperature dependence lends further support to the choice of re as the pertinent correlation time since, as indicated earlier, rs is much less dependent on 0.8- temperature than rr or rM. The low temperature portion of the curve in Fig. 3 gives a calculated Z$, of < 1 Cal per mole. For ligand exchange processes, the activation energies are usually of the order of 10 Cal per mole (17). There is some possibility that rr is contributing to rc at high temperature. A maximum calculated E, of 3 Cal per mole can be obtained using the two higher temperature points. Calculation of Manganese to Pyruuate Proton Distances-The distance from Mn(I1) to the protons of pyruvate may be calculated using Equation 4 since rc is known.
Values for r are listed in Table I. Using rc values calculated from Tlp/Tzp for any particular solution, an average value r = 8.2 =t 0.5 A represents a relative deviation of only 6%. The rp6 functional dependence makes r relatively insensitive to uncertainties in TV. If rc is incorrect by a factor of 2, the maximum error in r is only 12%. The calculated values of r do not systematically depend upon concentration of Mn(I1) indicating that the small amount of Mn(I1) (< 5%) not bound in the quaternary complex has little influence on the calculated value of r.
Ternary Pyruvate Kinase-Mn(ZZ)-Inhibitor Complex-Since P-enolpyruvate exchanges so slowly on and off the Mn(II)enzyme that the rate of this exchange rather than TIM dominates the observed relaxation rate of its protons in the ternary enzyme complex,* it is not possible to use the relaxation rate to determine proton-Mn(I1) distances. A search among less tightly bound substrate analogs revealed that (Z)-P-enolfluoropyruvate was unsuitable because its proton NMR relaxation rate in the ternary complex with Mn(II)-enzyme was also exchange limited, i.e. no paramagnetic effect was observed on the proton relaxation rate and Tip = Tzp. The methylene analog of P-enolpyruvate, cr-(dihydroxyphosphinylmethyl)acrylic acid, which is a weak inhibitor,3 appeared suitable because the relaxation rates of the a and b vinyl protons and of the c methylene protons are not dominated by the chemical exchange rate l/rM. All three relaxation rates exhibit a frequency dependence indicating that the relaxation rates are dominated by TIM. The ratios of the relaxation rates at 60 to 220 MHz are 2.8, 2.7, and 2.3 for the a, b, and c protons, respectively, as listed in Table II. Calculation of r,-In this case, unlike the methyl protons of pyruvate, neither rM nor rc can be estimated from a comparison of 7'1, and TBp values because the apparent linewidth including 'H-'H and 31P-1H coupling is not necessarily a valid measure of * T. L. James, unpublished data. 3 F. J. Kayne, private communication. Tz. Consequently, TV must be estimated from the frequency dependence of Tl,.

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The correlation time, rE, determined from the ratio of the paramagnetic contributions to the longitudinal relaxation rate at 60 MHz and 220 MHz according to Equation 8, is given in Table II for each of the proton resonances of the analog.
In each case, rc is calculated to be 1 x 10eg s. Little temperature variation is observed at 220 MHz over the range of 6"-34" for the three proton resonances of the methylene analog in the ternary pyruvate kinase-Mn(II)-inhibitor complex as expected for a rc value of the order of 1 x lop9 s (cf. Fig. 1).
Calculation of Mn(ZZ) to Inhibitor Proton Distances-The distances from Mn(I1) to the various protons on cY-(dihydroxyphosphinylmethyl)acrylate in the ternary complex with pyruvate kinase-Mn(I1) were calculated from Equation 4 with the values of rc shown in Table II. The resulting values for the distance r are listed in Table II. Allowing a fairly large error in rc, distances were also calculated at the limits of the estimated range of rc. The estimated accuracy of the average distances is within +0.5 A.
Competition of P-enolpyruvate with a-(Dihydroxyphosphinylmethyl)acrylate in Ternary Pyruvate Kinuse-Mn(ZZ)-Ligand Complex-A titration of the ternary enzyme-Mn(II)-inhibitor complex with P-enolpyruvate was monitored by following the decrease in the paramagnetic contribution to the longitudinal relaxation rate of the methylene resonance of a-(dihydroxyphosphinylmethyl)acrylate.
The titration curve shown in Fig. 4 may be described by a simple competition between P-enolpyruvate and a-(dihydroxyphosphinylmethyl)acrylate with dissociation constants of 1.5 pM for the former and of 600 pM for the latter. DISCUSSION The reaction pathway for the binary metal-enzyme complex in the pyruvate kinase reaction is shown schematically below (Scheme 1). It is assumed in this scheme that the required monovalent cation potassium is present and that M(I1) is the activating divalent metal ion, Mn(I1) in the current investigation. Primary interest, of course, centers on the structure of the activated complex in the transition state between Complexes III and IV. Although the over-all equilibrium in this reaction favors the formation of ATP and pyruvate (2) (Keq -2000), there is insufficient data available under conditions with stoichiometric amounts of enzyme present to determine the relative amounts of enzyme-bound substrates at equilibrium, i.e. Complexes III, IV, and V. Our calculations of distances are based on the assumption that at equilibrium the enzyme is entirely in the form of Complex V. However, even if Complex V concentration were only 50% of the total enzyme concentration, it would change the calculated distance a maximum of only 12y0. paramagnetic contribution to the proton relaxation rate. From the molecular model of the structure in which Mn(I1) is complexed to the carboxyl group of pyruvate, the permissible values of Mn(II)-proton distance range from 2.5 to 4.8 A. In contrast the value derived from Experiment 1, Table I is 7.7 A unequivocally ruling out direct bonding between Mn(I1) and pyruvate in Complex VIA.
Similar conclusions have been reached from experiments on r3C relaxation rates in some [raC]pyruvate-pyruvate kinase complexes (9). On the basis of these results it is not possible to assign the position of the transferable phosphoryl group in the complex.
It has been suggested that the phosphoryl group is coordinated to Mn(I1) (9, 18). The experimentally derived values (Table I) of 8.2 & 0.5 A for the Mn(I1) to pyruvate proton distance in the equilibrium complex (predominantly Complex V) is certainly large enough to accommodate a phosphate group intervening between pyruvate and Mn(I1).
On the other hand, the Mn(I1) EPR spectra for the ternary pyruvate complex (Complex VIA) and the equilibrium complex are nearly identical, thus arguing against direct Mn(I1) coordination to the phosphoryl group (7). Possible modes of pyruvate bonding in Complexes V and VIA The structure of the Mn(II)-pyruvate kinase-P-enolpyruvate may be assessed by comparison of distances measured from complex is not yet established. Evidence for a metal-phosphoryl molecular models and those calculated in Table I from the bridge complex in pyruvate kinase-Mn(I1) complexes was