1488
THOMAS C. BRUICEAND RICHARD M. TOPPING
imine formation is much more rapid than prototropy. Convincing evidence that 24 does not represent the reaction path is obtained from experiments in which the morpholine imine of PCHO (S) is used in place of P C H 0 . 2 0 Thus the catalytic rate-constants for the imidazole-catalyzed formation of ketimine (S”) from the morpholine imine of PCHO (S) (26) are similar to those for the reaction involving PCHO. This result
would not be predicted on the basis of 24 since it is well established that imines react a t a greater rate with general reagents of type R-NHz than do the corresponding aldehydes or k e t o n e ~ . ~ l Recently, -~~ Cordes and JencksZ5have shown that S reacts with semicarbazide a t a greater rate than does PCHO. I t may be noted that morpholine, which is a stronger base than imidazole, does not alone catalyze the transamination reaction between PCHO and a-aminophenylacetic acid under conditions (e.g., M reactants) which provide a facile transamination using imidazole buffers. This observation lends support to the suggestion that the catalytic activity of imid(20) Details of this study are reported separately in part 111, J . A m Chem. Soc., 86, 1493 (1963). (21) E. H. Cordes and W. P . Jencks, ibid.,8 4 , 826 (1962). (22) hlme. Bruzau, A v w . Chim., [ l l ] 1, 332 (1934). (23) E. A . Brodhag and C. R. Hauser, J . A m . Chem. Soc., 77, 3024 (1955). ( 2 4 ) C. R. Hauser and D. S. Hoffenberg, ibid.,‘7’7, 4886 (1955). (25) E. H. Cordes and W. P. Jencks, Biockem., 1, 773 (1962).
[CONTRIBUTION FROM
THE
Vol. 85
azole buffer arises from its ability to form a complex with a reactant. The catalysis would, therefore, appear to be best expressed by the path of 23 in which a complex of S’ with two molecules of an imidazole species is followed by a rate-controlling intracomplex catalysis of the prototropic shift converting S‘ to S”. Only 23 is compatible with the determined kinetic scheme (1018). Thus, the kinetic treatment is based upon the assumption of a rate-determining prototropic shift following a rapidly established low steady-state in S‘, and is found not only to provide a rate equation which accommodates the rate data to SO-SO% completion but also predicts the somewhat unusual rate variation caused by variation of the initial reactant concentrations (see Table 11). In the kinetic considerations of this paper we have treated PCHO, S’, and S” as discrete chemical entities. Of course they are not. Pyridoxal can exist in several ionic forms in both the free aldehyde and internal hemiacetal forms.26 Much the same is true of S’ and S”. The consideration of these complications was unessential to the arguments presented herein since the reactions were studied under restricted conditions of acidity, ionic strength, solvent composition and temperature. The present study suffices to establish the catalysis to occur through a complex of one or more of the aldimine species formed from PCHO and A with two neutral, two acidic or one neutral and one acidic imidazole species. Acknowledgments.-The authors express their gratitude to Mrs. Patricia Benkovic for performing many of the rate measurements necessary to the completion of this study. This work was supported by grants from the National Institutes of Health and from the National Science Foundation. For this support we are deeply grateful. (26) D. E. hletzler and E. E. Snell, J . A m . Chem. Soc., 77, 2131 (1955)
DEPARTMENT OF CHEMISTRY, CORNELL UNIVERSITY, ITHACA, S. Y . ]
Catalytic Reactions Involving Azomethines. 11. The pH Dependence of the Imidazole Catalysis of the Transamination of Pyridoxal by a-Aminophenylacetic Acid BY THOMAS C. BRUICEAND RICHARD TOPPING’ RECEIVED DECEMBER 21, 1962 The p H dependence of the catalysis of the transamination of pyridoxal by a-aminophenylacetic acid has amino acid ?=? aldimine been investigated. The first phase of the reaction ( i . e , ,pyridoxal ketimine) has been shown to occur via pre-equilibrium complexing of aldimine and ketimine with one molecule of imidazole free base and one ion of the conjugate acid of imidazole. The essential prototropic shift has been suggested to take place via an intracomplex general acid, general base mechanism in which imidazole acts as the general base and imidazolium ion as the general acid. Since the final equilibrium concentration of ketirnine is not influenced by the catalyst concentration (nor the p H ) it is essential for the proposed mechanism that either pyridoxal or amino acid also be complexed by imidazole. It has been established that a-aminophenylacetic acid forms a complex in aqueous solution with imidazole and imidazolium ion and that the formation constant for this complex is comparable to that determined kinetically for the imines.
+
Introduction In the preceding paper3the imidazole-catalyzed transamination of pyridoxal by a-aminophenylacetic acid a t pH 8.6 (30’ in water a t p = 0.05 .IT) was described. (1) Post-doctoral Fellow of The Ilepartment of Chemistry. Cornell University. (2) Abbreviations employed in this paper are: pyridoxal, P C H O . pyridoxamine, PCH2NH2; or-aminophenylacetic acid, A ; phenylglyoxylic acid, P G ; t h e aldimine formed between pyridoxal and a-aminophenylacetic acid, S’; the ketimine formed between pyridoxamine and phenylglyoxylic acid, S ” ; the complex of S‘ with one molecule of imidazole and one molecule of the conjugate acid of imidazole, Sc’; like complexes of S” and A are similarly abbreviated as SC” and A,, respectively; total imidazole ISIT, where IMT = I M IXIH’. ( 3 ) T. C. Bruice and R . X I . Topping, J. Awz. Cheiiz. Soc., 86, 1. 80 il9fi:3),
+
I t was established that the reaction occurred in two distinct stages, the first leading to the formation of an equilibrium mixture of pyridoxal, amino acid, aldimine (at low steady state) and ketimine, and the second stage of the reaction to a final equilibrium mixture of pyridoxal, amino acid, aldimine (low steady state), ketimine. pyridoxamine and phenylglyoxylic acid. PCHO
+ A z(S’)zS” Kl
K2
fast
slow
Phase one
Phase two
PCHlNH2 f PG
(1)
pH DEPENDENCE OF CATALYSIS OF TRANSAMINATION OF PYRIDOXAL
20, 1963
"-":
1489
0-
0
2 I
0
0 (.I1M ) ( I M0.2 H ~ ( m o0.3 l r s 2 / l i t0.4 r ~ 2,) A 0.5
5-
/"
0
D 1
I
1
I
1
1
( I M) ( I M H q (mo Ier2/ I i t e r 2 ) , Fig. 1.-Plots of the observed first order rate constants ( k o b s L ) for the appearance of S" vs. the product of the concentrations of imidazole and imidazolium ion. The points are experimental and the curves are those obtained from equation 3 employing the constants provided in Table I : ( A ) pH, 7 . 8 ; ( B ) pH, 8.3; (C) pH, 8.6; ( D ) pH, 9.3.
Though the reactions of (1) could be shown to occur in imidazole buffer a t both very low (spectrophotometric) and high (isolation procedures) concentrations of PCHO and A, the reaction was found to occur a t measurable rates in morpholine or carbonate buffers only a t high reactant concentrations. The efficiency of imidazole buffer as catalyst was ascribed to its ability to form complexes with reactants and intermediates. In accord with this supposition, i t was found that the rate of approach to equilibrium in phase one was dependent upon the second power of the total imidazole concentration a t low concentrations of imidazole buffer and to be independent of imidazole concentration a t higher concentrations of the buffer. The apparent first order rate of approach to equilib-
rium in phase one,,therefore, allowed the well known Michaelis-Menten form
In order to determine the imidazole species involved in complex formation and catalysis and to shed further light on mechanism, we have extended our investigations to other acidities. The results of this study are reported herein. Results In Fig. 1 are presented plots of the observed firstorder rate constants for the approach to equilibrium in phase one (1) a t several pH values usus. the product of the concentrations of free imidazole (IM) and the
THOMAS C. BRUICEAND RICHARD M. TOPPING
1490
Vol. 85
Inspection of Table I shows that V m increases with increasing pH. The values of V m have been shown to follow equation 5.
where Vml and Vm2 are rate constants for approach to equilibrium of phase one a t saturation by catalyst species, as the hydrogen ion activity as determined by the glass electrode and K a ’ a kinetically apparent dissociation constant. Rearrangement of (5) provides (6). UU( Vm
0
1
I
1
I
2
I
1
3
4
I
I
5
6
7
I
8
l \ O I l
1
9
1
0
1
1
v, x IO?
Fig. 2.-Plot of equation 6. The slope provides the value of -K.’ and the intercept a t UH( V, - V,I) = 0 is Vmz.
conjugate acid of imidazole (IMH@). The points represent experimental values and the lines are theoretical having been calculated from equation 3. (3)
In Table I are recorded the values of Vm and K m so determined for each pH. Also recorded in Table I are the final equilibrium concentrations of S”for phase one (1) a t t,. The latter values have been calculated in the manner previously outlined in part I of this study (see ref. 3). TABLEI FROM EQUATION 3 AND VALUESOF K , AND V,,, CALCULATED FINALEQUILIBRIUM CONCENTRATIONS OF S“ AT t , FOR IMIDAZOLE CATALYSIS OF PHASE ONE^ pH
Buffer
7.06
Imidazole
7 . 8 0 Imidazole 8.30 8.00 9.30 10.20
Imidazole Imidazole Carbonate Carbonate
IM IMH@ Mole fraction 0.406 ,827 ,938 ,968 ,993
0.534 ,173 ,002 ,032 ,0066
v, x
108, mh-1
K,, mole? I . - ?
2.46 , . . 6,5 7 . 1 6 X 10-1 8 . 0 7 . 0 X 10-3 9.5 6 . 2 X 10-1 10.5 8 . 5 X 10-2 >11 ...
THE THE
S” a t I , , .M 5.2 X 5.3 X 5.6 X 8.3 X 4.8 X
10-6
10-8 10-8 10-5 10-5
Initial concentration of pyridoxal and amino acid was X , temperature 30”, ionic strength 1.0 M and solvent water. a
In part I3of this study it was established kinetically that the only satisfactory mechanism, proceeding through the formation of imines, was one in which S‘ was a t a low steady state concentration and the rate determining step was the prototropic shift leading to the reversible conversion of S,’ to S,”. If S’ must be complexed prior to conversion to S” then from microscopic reversibility s’’ must be complexed prior to conversion to S‘. The constancy of the values of K,, calculated on the basis of the involvement of one neutral and one acidic species of imidazole (Table I), is convincing evidence that the complexes of S’ and S” which partake in the reversible prototropic shift have one of the compositions of (4). It is of course not possible to differentiate kinetically between (4a), (4b) and (4c). S,’= S’, I M , I M H e or S’, IMH@,IMH@,OHe or S”
=
S’, I M , IM, H e S”, IM, IMHa or S”, IMHe, I M H a , OHe or S“, IM, IM, H @ ( 4 ) (a) (b) (c)
The catalytic complex as represented by (4a) would appear to be the most likely, however, only three species, rather than four, as in (4b) and (4c), being involved.
-
Vml)
Ka’( Vmz
-
Vm)
(6)
The value of Vml was determined to be 9 X low4min.-’ by the fitting of a theoretical dissociation curve to a plot of I‘m US. pH. In Fig. 2 is plotted a H ( V m - V m l ) os. Vm and from the slope of the line the value of Ka’ has been determined to be 1.64 X lo-* ( P K ’ a p p = 7.78) while from the intercept a t a H ( V m - V m l ) = 0, the value of Vmz was determined to be 10.2 X min.-’. Examination of the values of S” a t t , (Table I ) , calculated from experiments carried out under saturation conditions of imidazole buffer, reveals that the over-all equilibrium of phase one of the transamination reaction is not p H dependent. In like manner the final .equilibrium position of the reaction (determined by the absorbance of ketimine a t 246 mp) is not influenced unduly a t constant pH by alteration in the concentration of catalyst (Table 11). TABLE I1 INFLUENCEOF IMIDAZOLE O N POSITION OF EQUILIBRIUMOF PHASEONE AT t m ( p H 9.3; p = 1.0 M ; T = 30’) O.d.?as mfi IMT C W 0.400 0.6 1. 0 ,386 1.3 .420 1.8 .400 2.1 ,482 2.5 ,477 ,440 3.0 Av. 0.430 f.0.030
As shown in part I 3 of this study, S’is a t steady state and a t completion of phase one and a t saturation concentrations of catalyst, considerable PCHO remains. It is required, therefore, that PCHO or A also be complexed by imidazole and imidazolium ion and that the dissociation constant for the complex with the reactant be of the same magnitude as Km. The formation of a complex between a-aminophenylacetic acid and imidazole was suspected on the basis of the greater solubility of he amino acid in aqueous solutions containing imi azole buffers than in aqueous solutions containing bor te, morpholine or carbonate buffers a t the same p€ I (see ! Experimental section of part 13). The formation constant for complex formation between amino acid and imidazole buffer was approximately determined by means of solubility studies a t pH 8.6 and pH 7.06 and calculated using equation 12. The formation constants were found to be quite similar if calculated on the basis of the formation of a complex composed of one imidazole molecule, one imidazolium ion and one amino acid molecule in the form of the ~ w i t t e r i o n . ~ ( 4 ) Essentially the same formation constants are obtained if i t is considered t h a t the imidazole species complex with both t h e zwitterion and anionic species of t h e amino acid b u t are not a t all similar if i t is assumed t h a t only the anionic species of the amino acid forms the complex. Differentiation between these possibilities could n o t be made since at p H values of 9.0 and above the mole fraction of imidazolium ion is a n exceedingly small number and the resultant solubility of t h e amino acid i n imidazole buffersin t h i s p H r a n g e i s too smallto determine with any degree of accuracy (see Experimental).
May 20, 1963
1491
pH DEPENDENCE OF CATALYSIS OF TRANSAMINATION OF PYRIDOXAL
The similarity of the constant so determined to the value of l/Km derived from the Michaelis-Menten equations provides the necessary rationale to our experimental finding that the equilibrium position of phase one is independent of catalyst concentration, that measurable pyridoxal remains a t t ,and that aldimine species are a t steady state. The question as to the nature of the cohesive forces binding the complex remains a t this time open. It would appear that the portion of the aldimine and- ketimine which is complexed by the imidazole includes the benzene ring of the amino acid since the amino acid and the imines are complexed to about the same degree. The formation of complexes between aromatic, lyophobic compounds and heterocyclic compounds in water is a well established, if perhaps not well understood p h e n o m e n ~ n , though ~,~ catalysis proceeding through such complexes in aqueous solution has not been observed previously. Combining equations 3 and 5 with equation 14 of part I3of this series provides the experimentally derived differential equation which describes the kinetics for phase one a t various acidities and catalyst concentrations (7).
TABLE I11 A LIST OF THE KATE AND EQUILIBRIUM STEPS REQUIREDTO PROVIDE A FULLDESCRIPTION O F PHASE ONE OF THE IMIDAZOLE CATALYSIS OF THE TRANSAMINATION OF PYRIDOXAL BY WAMINOPHENYLACETIC ACID K.‘ (a) CeH5CH(NH1e)C00s CsH5CH(SH2)COOs H” (AH) (AS) Km’ ( b ) AH IM IMH@ Complex. AH KmII (c) AS IM IMH@J_ Complex. AS K.11 (d) Complex. AH Complex. As HJ
+
+ +
+
Jr
H 0-6-OH (f)
where PT = total concentration of all pyridoxal and aldimine species a t time t; AT = total concentration of all amino acid species a t time t ; ST” = total concentration of all ketimine species a t time t; K , is defined by equation 9. From (7) the apparent first order rate constant is given bv ( 8 )
+ +
e ‘’ K
Qr:
WQ+ H@
(PCHOO)
(PCHOi)
Kt? ( 9 ) PCHOi
PCHO
KhlI ( h ) PCHOie
PCHO’
K1
+ A 1_ s‘
(i)
PCHO
(j)
PCHO~ A
+
K1’
set K,”’
+ I M + IMH@ S,’ KmI” Ss’ + I M + I M H @_T &,e’
(k) S’
“=l
(1)
4
and K1K2 is d.efined by equation 1. A t t,, dST“/dt = 0 and K, is pH and catalyst invariant (9)
The second-order rate constant for the forward reaction (formation of S”) is provided approximately by
where kz is the first-order rate constant for the prototropic shift and K, is the formation constant for aldimine. If one initial reactant concentration (ie., PCHOOor Ao)remains constant, the other initial reactant concentration may vary from zero up to the initial concentration of the reactant a t constant concentration with only minor changes in c (8). However, if the initial concentration of both reactants vary, then c is markedly changed. Metzler’ has shown that the pH profile (log Keq vs. pH) for the formation constant of pyridoxal aldimines from e-amino acids exhibits ( 5 ) T. Higuchi a n d D. A. Zuck, J . A m . Pharm. Assoc., Sci. E d . , XLII, 132 (1953); T. Higuchi a n d J. L. Lach, ibid., XLIII, 349 (1954); E. H. Gans and T. Higuchi, ibid., XLVI, 458 (1957); T. Higuchi a n d S. Bolton, ibid., XLVIII, 557 (1959); J. W. Poole a n d T. Higuchi, ibid., XLVIII, 692 (1959). ( G ) H. A. Harbury and K. A. Foley, Proc. Narl. A c a d . Sci.,G. S., 44, 662 (1958); H. A . Harbury, K. F. L a X o u e . P. A. Loach and R . M. Amick, ibid., 46, 1708 (1959). (7) U. E. Xet7’er, J . Ant. Chern. SOL.,79, 485 (1957).
a slope of ca. 1.0 in the pH range we have employed. This may be associated with the necessity to have the a-amino acid in the amino free base form for imine formation and suggests that the pKa‘ of pyridoxal of 8.6 has little influence upon the extent of pyridoxal aldimine formation ( i e . , both the protonated and unprotonated forms must react with the amino acid to about the same extent). We would anticipate then, that the c value of (10) would remain essentially constant and the pH dependence of V , must reflect the
THOMAS C. BRUICEA N D RICHARD M. TOPPING
1492 I
pk9.3.1MT*I.8M
I
I
1.2
9 0.8 I,Ot
Time (min.)
Fig. 3.-First order plots for the appearance of S" (as determined a t 246 mfi) in the presence of various concentrations of imidazole and a t various pH (pyridoxal and a-aminophenylacetic M; p = 1.0 M ; T = 30"). acid initially a t
pKa' of the a-amino acid and that of intermediates and final product. Listed in Table I11 are the various equilibrium and rate steps that must be taken into account in deriving any theoretical rate equation for phase one. Of the equilibrium and rate constants of Table 111,only a few can be determined separately, For this reason it is not possible to interpret meaningfully the pH dependence of V m . Less complex systems will have to be investigated for this purpose. We are a t present actively engaged in this endeavor.
Discussion In the transamination of pyridoxal by a-aminophenylacetic acid, the final equilibrium position for phase one (1) is independent of catalyst concentration, but the rate of approach t o equilibrium is catalyst dependent. This is so a t all pH values investigated (Table I). We are, therefore, dealing with a true catalysis. The constancy of Km (3), calculated on the basis of the formation of catalytic complexes involving one imidazole and one imidazolium species, suggests the possibility that the essential prototropic shift is catalyzed via the mechanism-of Chart I. The position of the critical transition state along the reaction coordinate cannot be specified from the data of this study, though it may be noted that Banks, Diamantis and Vernon8 have reported a feeble general acid catalysis in the transamination of pyruvic acid by pyridoxamine. The key experiments to resolve this issue will be the determination of the kinetic isotope effects when a-deuterioamino acid is employed and when the reaction is carried out with deuterioimidazolium ion in D20as solvent. The complete symmetry of the mechanism of Chart I is compelling and it may be noted CHARTI
coo-
\ '
cooI IV
C~H~-C H - N , ~
(8) B. E. C. Banks, A. 4235 (1961).
A.
UN-H
1)iamantis a n d C. A. V e r n o n , J , Chem. SOC.,
Vol. 85
that the mechanism is formally of the "push-pull" type as reported by Swain and Browngfor the catalysis of the mutarotation of tetramethylglucose by carboxylic acids and a-pyridone in benzene solution. Like the latter reaction, the imidazole catalysis of the transamination of pyridoxal by a-aminophenylacetic acid also involves a pre-equilibrium complex formation. Unlike the catalysis of Swain and Brown, however, the imidazole catalysis of the transamination reaction takes place in aqueous solution. The model reaction reported herein bears a close similarity to the enzymatic reaction. Hammes and Fasella have examined the kinetics of glutamic-aspartic transaminase by employing the temperature jump method.losll Six relaxation times were found for the over-all reaction a t high enzyme concentrations ( M ) . The measured rate constants were assigned as
+
EL AS-
>lo7 114-1 see.-'
80 set.-' + XI 1 >5 X lo3 sec.-I 26 set.-' 7 X lo7 M-1 sec.-I
xz
-
* EM + Oa
f
(11)
1.4 X lo* set.-' 30 sec.-l 2 X lo7 M-l set.-'
Kg
+ E M+
70 see.-' y1
r p
Y*
4
61 sec.-l 2.8 X lo3 sec.-l
