4197
Studies on the Mechanism of Isomerization and Oxygen-18 Exchange of Glycerophosphoric Acid in Aqueous Solutions' William D. Fordham2 and Jui H. Wang Contributionf r o m Kline Chemistry Laboratory, Yale University, New Haven, Connecticut 06520. Received February 27, 1967
Abstract: The rate of acid-catalyzed isomerization of glycerophosphoric acid has been measured both by periodic acid oxidation and by nmr techniques as a function of acid and substrate concentrations, temperature, and deuterium atom in solvent water. The observed rates of isomerization are about lo3times the rates of hydrolysis of the phosphoglyceric acids. Most of the difference in rates of the two reactions can be accounted for by the difference in apparent activation energies. The rates of isomerization and hydrolysis increase on changing the solvent from H 9 0to DzO, indicating a fast protonation of glycerophosphoric acid prior to the rate-determining step. A kinetic study of 0 ' 8 exchange between water and glycerophosphoric acid indicate that the isomerization occurs both with and without the formation of a cyclic intermediate. A detailed kinetic treatment is given for the dual-path isomerization mechanism.
x
T
he isomerization of p-glycerophosphoric acid was discovered by Bailly3 who showed that in strong acid solutions the isomerization rate is much greater than that of hydrolysis. In the present work, the acidcatalyzed isomerization of glycerophosphoric acid has been chosen for detailed kinetic study both because of the biochemical importance of glycerophosphate itself and as a simplified model for more complex reactions such as the catalytic hydrolysis of ribonucleic acids. While a simple model can only suggest what may be possible in a more complex system, a knowledge of the basic chemistry involved may provide the foundation as well as the guideline for deeper understanding.j-' In this study the rate of isomerization of glycerophosphoric acid was measured by two methods. The first method involved measurements of the integrated nmr spectra of the mixed isomers. In the second method, a-glycerophosphate was oxidized by periodic acid t o a labile phosphate ester which was subsequently hydrolyzed and the concentration of the liberated inorganic phosphate determined. For comparison the rate of hydrolysis of glycerophosphoric acid was also determined under the same conditions as a function of hydrogen ion concentration and temperature. T o obtain detailed information regarding the isomerization reaction, measurements were also made in D,Oand HzOI8-enriched aqueous strong acid solutions. The rate of 0 I 8 incorporation into the glycerophosphates was also measured for a mixture of a- and pglycerophosphates a t isomerization equilibrium, when the kinetic treatment of 0 I 8 exchange between glycerophosphates and water is considerably simplified. The 0 18-incorporation data can be combined with the kinetic isomerization data t o demonstrate that the (1) This work was supported by a research grant from the National Institutes of Health (GM 04483-11,12). The authors want to thank Professor W. W. Watson for permission to use his Nuclide mass spectrometer. (2) National Institutes of Health Predoctoral Fellow, 1962-1966. (3) M. C. Bailly, Bull. SOC.Chim. Fi-mce, 9 , 340 (1942). (4) D. M. Brown and A. R. Todd, J . Chem. SOC.,52 (1952); 2040 (1953). (5) J. Kumamoto, J. R. Cox,Jr., and F. H. Westheimer, J . A m . Chem. SOC.,78, 4858 (1956). (6) P. C. Haake and F. H. Westheimer, ibid., 83, 1102 (1961). (7) F. H. Westheimer, Special Publication No. 8, The Chemical Society, London, 1953, p 1.
isomerization occurs via at least two reaction paths. In the first path, the isomerization proceeds via the formation of a cyclic phosphate diester which is subsequently hydrolyzed to give the other isomer with concomitant 0l8 exchange. In the other path, the cyclic intermediate is not formed and hence no 0 ' 8 exchange should occur. A kinetic treatment is developed which quantitatively correlates several kinds of rate data.
Experimental Section Reagents. P-glycerophosphate, disodium salt pentahydrate, Grade I, and a-glycerophosphate, disodium salt hexahydrate, Grade X , Fiske and Subbarow Reducer were all from Sigma Chemical Co. Deuterium oxide (99.77 %) and 0'8-enriched (1.4%) water were from The Stuart Oxygen Co. Alkaline phosphatase (calf intestine), B grade, was supplied by CalBiochem. All the other chemicals were of reagent grade. Glycerophosphoric Acid Solutions. Solutions of glycerophosphoric acid (GPA) for isomerization experiments were prepared by dissolving disodium P-glycerophosphate pentahydrate in a known amount of water, cooling in an ice bath, and adding a calculated amount of concentrated acid. Solutions of GPA in sulfuric acid containing 95 % D 2 0 were prepared in the same way by dissolving the glycerophosphate in D 2 0 and adding the calculated amount of the concentrated acid. Since commercial concentrated perchloric acid contains 30 % H20, which cannot be removed by evaporation due to explosion hazard, solutions of GPA in perchloric acid and 99% D20 were prepared by dissolving the glycerophosphate, in which the exchangeable hydrogen atoms had been replaced by deuterium atoms, in D20 and adding the calculated amount of DCIOl in D 2 0 . The DClOa in D1O solution was prepared by passing a solution of NaCIOa in D 2 0 slowly through a cation-exchange column which had been converted to the D+ form by washing with 99.7% D 2 0 until the effluent contained less than 1 % H 2 0 as determined from the nuclear magnetic resonance (nmr) spectrum. The exchangeable hydrogen atoms in disodium glycerophosphate were replaced with deuterium atoms by repeated evaporation with 99.7% D 2 0 under reduced pressure. The solid sample was dried over phosphorus pentoxide in a vacuum dessicator (1 mm) for 2 days at room temperature before use. Kinetic Measurements of Isomerization. Since an equilibrium mixture of GPA at 50-100" was found in the present work to contain about 86% a-GPA and 14% P-GPA, the rate of isomerization was measured by starting from the P form. The sodium salt of P-glycerophosphate used in these measurements contained only 0.1 % a-glycerophosphate as an impurity. Both nmr and periodate oxidation analysis were employed to follow the progress of the reaction.
Fordham, Wang
01*Exchange of Glycerophosphoric Acid
4198 For kinetic runs followed by the nmr method, capped, thin-walled glass nmr tubes containing 0.5-ml samples of the reaction solution were kept at a constant temperature in a heat bath. These sample tubes were transferred one by one to an ice bath at regular intervals to quench the reaction and kept there until the nmrspectraweretaken in a Varian A-60 nmr spectrometer. The temperature in the nmr probe was kept at 5 ” by the Varian V-6040 variable-temperature controller. P-GPA in D20 has a doublet with 1.2-ppm chemical shift relative to water due to splitting of the four methylene hydrogens by the /?-hydrogen and/or the phosphate group and a complex multiplet between the water peak and the doublet. a-GPA in D 2 0 has two unequal doublets due to the four methylene hydrogen atoms. In a mixture of a- and /3-GPA, one of the a-GPA doublets is superposed on the /3-GPA doublet, but the other a-GPA doublet is farther downfield and can be distinguished from the other peaks in the nmr spectrum of a mixture of isomers. By taking the ratio of the area of the separate a-GPA doublet t o the total area of all peaks for both the a and p isomers, the fraction of GPA present in the a form in a mixture of both isomers can be determined. For kinetic runs followed by the periodate oxidation method, 0.5- or 1.0-ml samples of the reaction mixture were quenched in an ice bath, immediately neutralized with equivalent amounts of base, and diluted to the concentration required for analysis by the periodate method. The concentrations of a- and P-glycerophosphates were determined by a modification of Burmaster’s procedure.* a-Glycerophosphate can be quantitatively oxidized by periodic acid to glycolic aldehyde phosphate at pH below 3 and room temperature when the migration rate is negligible. The iodate formed and the excess of periodic acid were destroyed with sodium sulfite, and the glycolic aldehyde phosphate produced was hydrolyzed with hot acid in 1 hr. The resulting orthophosphate was then determined colorimetrically by a modification of the method of Fiske and Subbarow,Qin which the orthophosphate was converted to phosphomolybdic acid in 0.5 F H2SOasolution, reduced with l-amino-2-naphthol-4-sulfonic acid, and then assayed with a Cary Model 11 spectrophotometer. The /?-glycerophosphate was not affected by periodic acid and was not appreciably hydrolyzed during the above hydrolysis of the glycolic aldehyde phosphate. The total glycerophosphate ( a and p forms) was determined in a separate sample by reacting with periodic acid in hot acid solution in which the isomerization, oxidation by periodic acid, and the hydrolysis of glycolic aldehyde phosphate formed all took place at the same time to give 100% conversion to orthophosphate. The amount of P-glycerophosphate was then obtained by subtracting the previously determined value for a-glycerophosphate from the total phosphate. Kinetic Measurements of Hydrolysis. The rate of acid-catalyzed hydrolysis of glycerophosphoric acid was determined under similar conditions to those used for the isomerization of the phosphoryl group, except that longer periods at high temperatures were required. At successive time intervals, measured aliquots, usually 0.05 to 0.1 ml, of the reaction mixture were taken with a pipet and transferred to volumetric flasks. These samples were diluted and analyzed for inorganic phosphate by the procedure described above. Synthesis of Glycerol Cyclic Phosphate. The barium salt of glycerol 1,?.-cyclic phosphate was synthesized by dehydrating glycerolphosphoric acid with dicyclohexylcarbodiimide (DCC) by a modification of the method of Ukita and co-workers.1° Disodium glycerophosphate ( 5 g) was dissolved in 100 ml of water and converted to the free-acid form (GPA) by ion exchange on an Amberlite IR-120 column. The eluate was lyophilyzed and the residue redissolved in a liquid mixture of 50 ml of acetonitrile 5 ml of pyridine 50 ml of dioxane 9.5 ml of tri-,i-butylamine. DCC (6.0 g) was dissolved in this solution, and the mixture was left standing for 2 days at room temperature. Then 30 ml of water was added to react with the excess DCC, and the precipitated dicyclohexylurea was removed by filtration. By adjusting the “pH” of the filtrate to 9 with aqueous Ba(OH)2 solution, the insoluble barium glycerophosphate was precipitated and centrifuged off. The supernatant was saturated with C 0 2 to precipitate the excess Ba(OH), as BaC03 which was removed by centrifugation. After removing the organic solvents, the solution was lyophilized t o give a glassy viscous liquid. This glassy liquid was redissolved in
+
+
+
(8) C. F. Burmaster, J . Bid. Chenz., 164, 233 (1946). (9) C. H. Fiske and Y.Subbarow, ibid., 66, 375 (1925). (10) T. Ukita, K. Nagasawa, and M. Irie, Pharm. Bull. (Tokyo), 5,
121, 127 (1957).
Journal of the American Chemical Society
89:16
water, adjusted to pH 9 with Ba(OH),, repeatedly extracted with ether, again saturated with C02 and filtered to remove the excess Ba(OH),, and lyophilized to give a white powder of barium glycerol cyclic phosphate which was further purified by recrystallization from aqueous ethanol and dried in a desiccator over Drierite. The purity of the barium glycerol cyclic phosphate was checked by ascending chromatography on Whatman No. 1 filter paper. The organic phosphates were detected by spraying the chromatograms with Hanes-Isherwood reagent, drying for 1 hr in a cool air stream, and exposing the dried chromatogram to ultraviolet radiaTwo tion for 2 min. The phosphates appear as blue different solvent systems were used: (1) 2-propanol-H20 (1 : 1); (2) 2-propanol-5 N NH3 solution (as) (2:l). The first solvent system is convenient to check the barium glycerol 1,2-cyclic phosphate for possible contamination by barium glycerophosphate, since the latter does not travel on paper with this solvent.ld It was found that no phosphate remained at the origin of the above chromatogram. In the second solvent system, the observed R f values were 0.64 for barium glycerol cyclic phosphate and 0.26 for disodium glycerophosphate. The literature values for the second solvent system were 0.6 and 0.25-0.35, respectively.l0,13 Although both systems could detect an impurity of less than 2 % noncyclic glycerophosphate, none was detected in the barium glycerol 1,2-cyclic phosphate prepared by the above procedure. Hydrolysis of Glycerol 1,2-Cyclic Phosphate. At room temperatures, glycerol I ,2-cyclic phosphate is not hydrolyzed for at least 24 hr if the pH is between 3.5 and 9.5. lo For the measurement of hydrolysis, the barium glycerol cyclic phosphate was dissolved in cold water, brought up to the temperature for the reaction, and mixed with the calculated amount of perchloric acid to start the hydrolysis. After the reaction, the solution was neutralized by adding sodium hydroxide and analyzed for a-glycerophosphate as well as the total GPA by the periodic acid oxidation method described above Kinetic Measurements of Oxygen-18 Exchange. In the preliminary experiments, disodium P-glycerophosphate pentahydrate was mixed with the dissolved in water containing 1.36 atoms % 0l8, required amount of perchloric acid in an ice bath, and brought up to the temperature for the isomerization and OI8 exchange to take place simultaneously. For the simplicity of interpretation, most of the 018-exchange rate measurements were carried out at isomerization equilibrium by dissolving the equilibrium amounts (86 a-GPA and 14% P-GPA at 60‘) of a- and 8-glycerophosphates in 0 ’8-enriched aqueous perchloric acid solution and keeping the reaction mixture in glass-stoppered flasks immersed in a heated constant-temperature bath. At predetermined intervals, the reaction was quenched by placing one of the flasks in an ice bath and immediately neutralizing the solution with 10 N KOH (aq). Each of the solutions was filtered to remove the precipitated KC104 and the 0 1 8 content of the phosphoryl group in glycerophosphate was determined by a modification of the procedure of Cohn.14 The above filtrate (0.6 ml) was mixed with 8 rnl of 0.1 F NH3NH&I buffer, pH 9.3, 1 ml of 0.6 F MgCl?, and 3 mg of alkaline phosphatase, After incubation for 2 hr at 37’, the mixture was transferred to a refrigerator at 0 ” and left there overnight to complete the precipitation of MgNH4P04. The white precipitate was redissolved in 5 trichloroacetic acid and centrifuged to remove the denatured enzyme. The MgZTin the supernatant was removed by an Amberlite IR-120 column in the H+ form. The eluate was concentrated by vacuum evaporation and adjusted to pH 4.4 with KOH (aq). The phosphate was reprecipitated as KH2PO:by adding absolute ethanol, washed, and dried 01 U N C ~ K Jfor 16 lir at 100”. Very little hydrolysis of GPA took place at the temperature and acidity of the above-described Ol*-exchange experiments. As a check, the above procedure was repeated without alkaline phosphatase. No precipitate of MgNHIPOl was formed. The oxygen of K H 2 P 0 4was converted to COP by heating with dry guanidine hydrochloride according to the method of Boyer l5 and analyzed in either a Consolidated Engineering 21-401 mass
(11) R. S. Bandurski, J . Biol. Cheni., 193, 405 (1951). (12) R. L. Bielski, h a l . Biochem., 6, 54 (1963). (13) T. Ukita, N. A . Bates, and H. E. Carter, J . Biol. Chenz., 216, 867 (1955). (14) M. Cohn in “Methods in Enzymology,” Vol. 4, S. P. Colowick and 0. M. Kaplan, Ed., Academic Press Inc., New York, X. Y . , 1957, p 905.
(15) P. D. Boyer, D. J. Graves, C. H. Suelter, and M. E. Dempsey, Anal. Chem., 33, 1906 (1961).
August 2, 1967
4199 spectrometer or a Nuclide mass spectrometer by the isotope ratio method. The 0 ' 8 content of enriched water was determined by the same procedure as that used for KH2P0d, except that it is necessary t o heat the sealed tube containing water and guanidine hydrochloride for 2 min for satisfactory yields of CO2. The experimentally determined values of 0l8a t o m z in CO2 are equal to the corresponding values of 0 ' 8 atom in the KH2P04 obtained by enzymatic hydrolysis of glycerophosphate. In order to use these data in the rate equations for Ole exchange, it is necessary to make two corrections. First, it is necessary to subtract the excess of OI8 abundance introduced into the phosphate group during enzymatic hydrolysis of the glycerophosphate in 10 ml of buffer solution containing 0.6 ml of the neutralized reaction mixture in 018-enriched solution. The amount of this 0 18-enrichment correction was determined from the 0 ' 8 content of the phosphate from an unheated sample of the reaction solution. The only Ole incorporation which could occur in this blank experiment is that during enzymatic hydrolysis. Secondly, it is also necessary to multiply the excess 0 1 8 concentration found in the KH2P04 by four-thirds, since only three of the oxygen atoms were from GPA,; the fourth oxygen atom was introduced into the phosphate group during the hydrolysis by alkaline phosphatase.
P-GPA in various acid solutions in HzO and D,O at different temperatures are summarized in Table I. The values of the apparent activation energy E, and the frequency factor k o are calculated from the slopes of the linear plots of log k p us. 1/T, assuming that k, - koe-E"/(RT), and are also included in Table I. In order to examine the effect of hydrogen ion concentration on the isomerization rate, a series of 0.5 M GPA solutions of constant ionic strength but increasing [NaC104] perchloric acid concentration ([HCIO,] = 4.0 F ) was studied at a chosen temperature. The k,) are also listed in Table I. measured values of ( k , A plot of these values of log ( k , k,) us. log [H+]
+
+
2,o
Results
+
f
Acid-Catalyzed Isomerization. Consider the isomerization reaction
where for simplicity of notation a and P represent either the isomeric molecular species a-GPA and 0-GPA or their molar concentrations, k , and k, the corresponding first-order rate constants. The net isomerization rate is
+
is the total molar concentration of where a = a GPA. Integration of (1) gives In
ao - ba a - ba ~
=
(k,
+ k&
Figure 1. Isomerization of 0.5 M @-glycerophosphoric acid in 1 N HCIOa(as).
gives a straight line up to [HC104] = 2.0 M with a slope of 0.9, which indicates that the isomerization reaction is approximately first order with respect to [H+]. Acid-Catalyzed Hydrolysis of a- and 0-GPA. The acid-catalyzed hydrolysis of GPA was also found to follow strictly first-order kinetics. If the reactions are represented by
where a0 denotes the initial concentration of a-GPA and b = k p / ( k , kp). At isomerization equilibrium the concentrations am and Pm satisfy the requirement kea, = ksPm; hence
+
Pi.
+
glycerol
where h, and h, represent the rate constants for the hydrolysis of a- and P-GPA, respectively, to inorganic phosphate and glycerol, we have and (2) becomes
(3)
+
Thus ( k , k,) can be determined from the slope of the linear plot of In [(am- ao)/(a,- a)]us. t; k, was then ks. All plots of this calculated from a,/Pm and k, kind were found in the present work to be strictly linear. A typical example is given in Figure 1. The experimentally determined values of the apparent first-order rate constants for phosphoryl group migration of 0.5 M
+
Since the rate of isomerization is much faster than the rate of hydrolysis, the ratio fila remains at the isomerization equilibrium value throughout the hydrolysis reaction, and consequently we may write the isomerization equilibrium constant K as
Fordham, Wang
Exchange of Glycerophosphoric Acid
0l8
4200 Table I. Rate of Acid-Catalyzed Isomerization of Glycerophosphoric Acid (k,
Solvent
Catalyzing acid 1.85 N HzS04 1.85 N DzSOa 1 . 4 N D2S04 1 N HC10, 1 NDC!Gd 1 N HClO, 3 FNaC104 1 . 5 NHCIOl 2 . 5 FNaC10, 2.ONHClOa 2.0FNaC104 2.5NHC104+1.5FNaC104 3 . 0 N H C 1 0 4 l.OFNaC10,
+
+ + +
50'
2"
Hz0 95 Z DzO 95 Z DzO HzO 99zD~20 65 Z DzO 65 D,O 6jzDz0 65zDz0 65zDz0
0.00075 0.0017
+ kp) X lo3,sec-' 60"
0.29 0.405 0.31 0.53 0.925 1.06 1.5 1.9 2.2 2.45
0.22
z
70"
0.685 1.3
-
80"
100"
1.38 1.99 1.46
5.4 8.2 4.94
E, for k p , kcal/mole 18.2 15.7 17.5 19.7 19.2
ko, sec-1
2 X 108 8 X 108 9 . 1 x 107 3 . 5 x 109 3 x 109
Table 11. Kinetic Data for the Hydrolysis of Glycerophosphoric Acid Initial concn of. GPA,
4
h
a
+ Kha)/(l + IC)-X 106, sec-1
Catalyzing acid
Solvent
M
80
looo
120"
Ea!, kcal/mole
1.85 N HzS04 3 . 2 NHClO4 3 . 2 NHClO, 2 . 2 NHC104
Hz.0 65 DzO H20 Ha0
0.5 0.4 0.4 0.4
0.478
2.89 6.95 6.37 4.53
1.69
24.5
ko', sec6 . 3 X lo8
which upon integration gives
or
+ (si)=( ) ha
In Substitution in (4) leads to dPi - _ -- a - Pi (ha dt l + K
+ &)
The kinetic data for hydrolysis of GPA are summarized in Table 11. A typical set of plots according to eq 5 is given in Figure 2 . Since the hydrolysis was followed by determining the concentration of Pi produced and isomerization equilibrium was essentially maintained throughout the hydrolysis reaction, it is not possible to compute h, and h, separately from the data in Table 11. However, comparison of these values with the data in Table I shows that in general the rate of isomerization of GPA is under the same experimental conditions about lo3 times faster than the rate of hydrolysis. The apparent activation energy E,' determined by plotting In [(ha Kh,)/( 1 K ) ] cs. 1/27 can be used to approximate the activation energy determined from a plot of In h, us. 1/T if the ratio, of the rate constants hp/haand the equilibrium constant K = k a / k , are independent of temperature. The approximation is supported by the observation that K is nearly independent of temperature. At loo", a factor of I O 3 in the rate of isomerization and hydrolysis reactions corresponds to a difference of 5.1 kcal/mole in activation energy if the two ko's are equal. Data in Tables I and I1 show that in 1.85 N HzS04 solution at loo", the apparent activation energy of hydrolysis exceeds that for isomerization by 6.3 kcal/mole, which indicates that the difference in rates is mainly due to the difference in activation energies.
+
Figure 2. Hydrolysis of 0.5 M glycerophosphoric acid in 1.85 N &SO4 (as).
Khp 1 f K
Journal of the American Chemical Society ] 89:16 J August 2, 1967
+
420 1
Table 111. Hydrogn-Isotope Effect on Acid-Catalyzed GPA Reactions
Reaction
Initial concn of GPA, M
Catalyzing acid
DzOin the solvent DzO solutions
Isomerization Isomerization Isomerization Hydrolysis
0.5 0.5 0.5 0.4
1 . 0 N HClO4 1.85 N HzS04 3.0 NHC104 3 . 2 N HC104
99 ,Z Dz0 95 ZDz0 65 ,Z Dz0 65 Z DzO
z
__
h.13
100"
2.1
1.75 1.4 1.15
1.44
1.5
Hydrelysis time, min
(cy
M (0.012) 0.198 0.192 0.198
5
20
0,495 0,495 0,495 0,495
OH
I
'0 O 'H
'0 O 'H H+
(c) -H+I
OH
OH
OH
0
$ !
[OHf
k'
0 POH
OPOH
I
OH
[gLi-O€I
+ $ -H+
OH 0 [O!OHI OH OH
OH
H+dH
(a)
and the time of hydrolysis is short enough so that the isomerization of the product CY- and ,L?-GPA is negligible, the following simple relationships hold daldt = k31~ dpldt = k32C where = concentration ofthe cyclic ester. Therefore, dCYlk31 = cdt
=
dp/k32
and hence =
0.67 0.64 0.67 AV e = si3
OH
l+H+
6
=e ...
OH I
O 'H
OH:
1;
=
kdk32
OH
!o/[.
OPOH
I.6
++E;- + ' + I,/gju,t
Scheme I. Mechanism of Isomerization and 0'8 Exchange between GPA and Water OH OH OH 10;
+M 61,
Acid-Catalyzed 0ls Exchange between GPA and Water. Since the isomerization of GPA involves intramolecular phosphoryl group migration, it may proceed via the formation of a cyclic phosphate diester (c), followed by hydrolysis, or via a concerted mechanism, with direct nucleophilic attack on the phosphorus atom by the oxygen of the neighboring hydroxyl group and simultaneous cleavage of one of the original P-0 bonds, or by a combination of both mechanisms. These two pathways for isomerization are shown in Scheme I.
8-GPA
the individual rate constants for the hydrolysis of glycerol 1,2-cyclic phosphate are experimentally rather difficult to determine by direct measurement. However, the ratio of rate constants k31/k32can be determined by simple measurements of the ratio of products formed by the hydrolysis of the cyclic ester. If the reaction is started from pure glycerol cyclic phosphate
-.+I
a,
0 1
(Blank) 60 23 23"
kia
kSl
80
1.09
Temp, "C
k32
glycerol 1,2-cyclic phosphate
7
60 O
Table IV. Hydrolysis of Barium Glycerol 1,2-Cyclic Phosphate in 1 N HClOa (as)
Hydrogen-Isotope Effect. The effect of replacing solvent H 2 0with D2O on the rates of both acid-catalyzed isomerization and hydrolysis of GPA is summarized in Table 111, in which kD/kH denotes the ratio of the corresponding rate constants in D20-enriched and ordinary aqueous solutions, respectively. In all cases studied, the rates are faster in solutions containing DzO, with the acceleration of rate greater near 100% D2O. Acid-Catalyzed Hydrolysis of Glycerol 1,2-Cyclic Phosphate to CY- and P-GPA. For the reaction wGPA
-kD/kH
2"
ku/k32
=
~./p
The experimental results are given in Table IV.
(6)
(8) Since the rate of hydrolysis of the cyclic phosphodiester to the noncyclic monoester is much faster than the isomerization reactions, the steady-state concentration of the cyclic diester during the isomerization reaction is very low. A study of the rate of 0 ' 8 exchange between GPA and water may provide information on the mechanism of isomerization. If the isomerization of GPA occurs via a cyclic phosphodiester intermediate, OI8 exchange between water and GPA will take place as was reported by Harrison, et al., based on a single experiment.l6 On the other hand, if the isomerization (16) W. Harrison, P. D. Boyer, and A. Falcone, J . B i d . Chem., 215, 303 (1955).
Fordham, Wang
Exchange of Glycerophosphoric Acid
0lg
4202
Knowing k13, the values of kZ3can be readily calculated by means of the relationship
from the experimental values of the over-all equilibrium constant K, and 6 obtained above. The rate constants k13 and k23, obtained from the slope of the linear plots of Figure 3, are listed in Table V. Table V. Oxygen-18 Exchange Rate Data at Isomerization Equilibrium 10.5 M GPA in 1 N HC10,(as)] k~ X lo4,sec-l k23 X lo4,sec-’
Figure 3. Oxygen-18 exchange between glycerophosphoric acid (0.5 M ) and water in 1 N HCIOasolution.
occurs exclusively uia a path without involving water as a reactant, no 0 l s exchange will take place. A kinetic study of the rate of 0 l 8 exchange was carried out under the same conditions that the rate of over-all isomerization had been measured, but these data were not adequately analyzed because of their complexity. A more thorough study was made on the rate of OIs exchange between water and GPA at isomerization equilibrium for which the quantitative treatment of the experimental data is greatly simplified. For the convenience of kinetic treatment the above reaction pathways may be replaced by the following scheme
g C & k12 3 z
k,,
where a, p, and c represent a-GPA, P-GPA and the cyclic diester, respectively, and k12andkzl are the apparent first-order isomerization rate constants for the lower reaction path without the formation of a cyclic intermediate. Let f, = atom-fraction of 01*in water, f, = atomfraction of 0 l 8 in the phosphoryl group of GPA, and a = a P ; then at isomerization equilibrium
+
-
P
= K = - -k13k32 -
a
k3ik23
Thus 3a(dfp/dt)
=
(kiaa
+
- kl2 kzi
k23P)(fw
- fp)
which gives upon integration
Since the ratio k3l/k32 = 6 was already determined from the above-described measurements of the hydrolysis of glycerol 1,2-cyclic phosphate, k I 3 can be calculated from the slope of the linear plot of In [(fw - f,”)/(fw - f,)]us. t. A typical example of such a plot is shown in Figure 3. Journal of the American Chemical Society
89.16
50 O
60
0.376 3.2
0.825 7.6
70 ’
O
1.83 18.4
Discussion The fact that the acid-catalyzed isomerization of GPA is faster in D 2 0 than in H 2 0 indicates a pretransitionstate fast protonation step as illustrated below. KBH+
p
pH+ + H,O (fast equilibrium)
+ H30+
kp
PH+
cuH+ (rate-determining step) ka
The rate R can be written as
where KBH+is the ionization constant of the conjugate acid of P-GPA. From (9), it can be seen that the second-order rate constant kH for the reaction of P-GPA andhydrogen ion is given by(kpH,/K,HT),where the superscript H indicates the reaction in water as the solvent. For the same reaction in deuterium oxide as solvent, we have
Therefore the ratio of the rate constants for the two solvents is
kpD/kBH is usually close to unity if there is no kinetic isotope effect at the rate-determining step. For example, if the rate-determining step does not involve proton transfer, the only variation in rate due to the first ratio will be due to general medium effects which are usually small. But since acids are usually weaker the ratio KpH+/KpD+ can often be in D20 than in H20, greater than unity, which causes k D / k H> 1, as shown in Table 111. For the general case where the isomerization takes place through both of the reaction paths discussed above, the rate equations can be formulated in terms of k13, k31,k23, k32,k12,and k f l defined in the previous section. Thus we have
/ August 2, 1967
daldt = - ( k n
+ kl3)a + kz$ + k31~
dPjdt = ki2a -
+
(hi
+ k23)P + k32C
dc/dt = k i 3 ~ k23P - (k31
f k32)C
(1 1)
(12) (13)
4203
At steady state
k23P e = k13a k31 k32 Substitution of (14) into (1 1) gives
Rd = kiza - kz1P (20) The rates of isomerization by the two possible reaction paths can be conveniently compared at the initial steady state. For example, when the isomerization is started from pure a-GPA and the initial concentration of 0-GPA is approximately zero, we have
Since
Since 8 =
(1 5) may be written as
(3/j)(ki3/ki2) The values of k13, k12,k23, k21, K, and Rc/Rdare summarized in Table VI. These values are, within experimental error, consistent with the data in Table I.
+ +
2/3,
we have
Rc/&
(I+~k13 + k 1 2 )a( 7-- a
da =
+ +
where a = a P c =a gration of (16) gives
(l + , ')(*+ l + 8
+ P, and 8
- a) =
Table VI. Rate Constants for the Isomerization and 0l8Exchange of Glycerophosphoric Acid [ O S M GPA in 1 N HCIOa]
k31/k3~.
klz In a - (1 u - (1
+ K)ao = In + K)a
a m
- a0
____
am - a
(17)
- k31~= k32~- k23P
50 O
60 O
70 O
E a9 kcal/mole
kla X 104, sec-1 klz X lo4,sec-I
0.376 0.10
0.825 0.245
1.83 0.59
17.7 19.5
X 104, sec-1 X 104,sec-'
3.2 0.57 0.176
7.6 1.5 0.163
18.4 3.94 0.15
k23 k2l
Using K determined from equilibrium measurement, 0 determined from the hydrolysis of the cyclic phosphodiester, and k13 determined from 0's-exchange measurements, klz was then calculated from the slope of the - a)]us. t as shown in linear plots of In [(a, - ao)/(am Figure 1. kZ1was calculated from K and the so obtained k12. The rate of isomerization through the cyclic phosphodiester reaction path from a-GPA to P-GPA is
R, = ki3a
=
(18)
which because of (14) becomes
+ k23P - k23p= k32k13a - k31k23P + k32 ) k31 + k32
k13ff Rc = k32( k31
Meanwhile the rate of isomerization through the direct phosphoryl group transfer path without the formation of the cyclic intermediate is
K
The apparent activation energies for the direct isomerization of a-GPA and for the formation of the cyclic glycerol phosphate from a-GPA calculated from the temperature dependence of these rate constants are also listed in Table VI. It may be noticed that the activation energy for the hydrolysis of a-GPA is 6 kcal/mole more than the E, for isomerization by either reaction path. The data in Table VI show that acidcatalyzed isomerization occurs uia both reaction paths. Starting from a-GPA as the example, the rate constant k13 for the formation of the cyclic intermediate is more than three times the rate constant k12for direct isomerization uia a concerted mechanism with no 01*exchange. But since only a part of the cyclic intermediate formed results in isomerization, the initial rate of net isomerization proceeding via the cyclic intermediate is only about twice the rate of direct intramolecular phosphoryl group transfer.
Fordham, Wang 1
OI8
Exchange of Glycerophosphoric Acid
