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Stereoselectivity in the metal complex catalyzed hydrolysis of amino acid esters — III Distribution equilibria
I. iaorg, nucl.Chem., 1973,VoL 35, pp. 1605-1620. PergamonPress. Printedin GreatBritain
STEREOSELECTIVITY IN THE METAL COMPLEX CATALYZED HYDROLYSIS OF AMINO ACID ESTERSIII DISTRIBUTION EQUILIBRIA J O H N R. B L A C K B U R N and M A R K M. J O N E S Department of Chemistry Vanderbilt University, Nashville, Tennessee 37203 ( R e c e i v e d 1 A u g u s t 1972)
A b s t r a c t - A study of the equilibria involving nickel(II) and equimolar amounts of different optically active amino acids shows that in such systems the mixed complexes, MAB, are favored to a greater extent than would be predicted from statistical considerations alone. Insofar as mixtures of optical isomers of a given amino acid are concerned, stereosdectivity in the stability constants of nickel(II) complexes was found only in the case of histidine. When optical isomers of a pair of amono acids were involved, no stereoselectivity was observed for the stability constants of any of the mixtures examined. These results correlate rather closely with most stereoselectivity studies involving the metal-complex catalyzed hydrolysis of amino acid esters. An anomaly exists, however, in the case of the tryptophan-histidine data, that suggests a more complicated relationship between the thermodynamic and kinetic stereoselectivities. INTRODUCTION
IN PREVIOUS papers in this series we have shown the stereoselective action of the mono (D (--) -- or L(+)-)histidinatonickel(II) as a catalyst in the hydrolysis of D ( - ) - o r L ( + ) - h i s t i d i n e methyl ester[l] and also that such behavior is apparently of limited occurrence in the nickel(II)-amino acid-amino acid ester systems [2]. The question then arose as to the origin of these effects. Do they arise from differences in stability constants or differences in rate constants? The present study describes a search for differences in equilibrium constants in systems containing enantiomeric amino acids. Thermodynamic data on amino acid-transition metal ion interactions is plentiful. However, few studies have involved systems in which two different amino acids were present. For this reason, potentiometric titrations were carded out on the systems studied here to (1) provide evidence for the existence of the mixed complexes, (2) provide a qualitative estimate of the degree of mixed complex formation as opposed to simple binary complex formation, and (3) determine whether stereoselective effects are present in equilibrium constants for these mixed complexes. A very few thermodynamic studies have been done on ternary complexes, in which the complex contains two different amino acids or amino acid derivatives (e.g. [Ni(histidine)(threonine)][3-5]. In these studies, it has been found that the 1. 2. 3. 4. 5.
J. E. Hix, Jr. and M. M. Jones, J. A m. chem. Soc. 90, 1723 (1968). J. R. Blackburn and M. M. Jones, Paper II, J. inorg, nucl. Chem. 35, 1597 (1973). R.-P. Martin and R. A. Paris, C. r. hebd. Sdanc. Acad. Sci. Paris 3932 (1963). B. E. Leach and R. J. Angelici, J. A m. chem. Soc. 90, 2504 (1968). H. C. Freeman and R.-P. Martin, J. biol. C h e m . 244, 4823 (1969). 1605
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J . R . BLACKBURN and M. M. JONES
mixed complexes are favored more than would be expected on a purely statistical basis over the complex containing only one type of amino acid chelate. One rate study of bidentate amino acid ester hydrolysis in ternary systems has been reported [6] in which stereoselectivity was observed, but no causal relationship could be determined. This study involved not a simple amino acid, but a polydentate amino acid derivative with which the complex structure was uncertain. EXPERIMENTAL Stability constant titrations As one means of determining whether mixed complex formation was occuring, each combination of amino acids used in the study was titrated with a standard sodium hydroxide solution and the pH vs. base added profile was recorded. This included 2 : 1 (amino acid "A" : Ni(II)) solution and 1 : 1 : 1 (amino acid "A" : amino acid "B" : Ni(lI) solutions). For the titrations of the amino acids in the various conbinations used were prepared from freshly boiled doubly distilled water. Stock solutions of the amino acids were prepared (0.10 F for histidine, lysine, and methionine; 0.020 F for aspartic acid, glutamic acid and tryptophan, the latter three more dilute for solubility considerations) and used for all titrations. Freshly prepared 4.0 F sodium nitrate was used to adjust the ionic strength of the reaction media, and carbonate free 0.1 N sodium hydroxide (1 = 1.0 with sodium nitrate) was used for the titrations. One miiliequivalent each of amino acid "A," amino acid "B" and nickel(II) was pipetted into a 200 ml jacketed beaker equipped with a magnetic stirrer a n d maintained at 25-0°C +0"I°C. This was followed by the appropriate amount of 4-0F sodium nitrate and doubly distilled water to give an initial volume of 120 ml and a final ionic strength of 1.0. For a period of approximately 30 rain prior to titration, dry nitrogen was bubbled through the solutions to degas them. The jacketed beaker was fitted with a polyethylene cover to protect against ambient air currents, and to help maintain a nitrogen atmosphere. Throughout the titrations, nitrogen was bubbled slowly through the mixture to prevent absorption of oxygen or carbon dioxide by the reaction mixture. This was necessary since any differences in the titration curves of non-mirror image systems would be expected to be very slight, and thus all possible external variables had to be minimized. Titrations were carried out manually with a Beckman research pH meter to a final pH greater than 10.5, at which point all ionizable protons from the amino acids had been neutralized. Each amino acid solution was also titrated in the 1 -- 1.0 medium in the absence of nickel(II) in order to standardize the solutions and to compare the titration curves with curves from the literature to determine the ionic strength effects. The titration curves for the amino acids only, in the presence and in the absence of NO3- were superimposable, and matched the literature curves closely. Thus, the literature values for the p K ' s of the amino acids were used in all calculations. The stability constants for complexes containing only one specific amino acid (/31,/32 and 133 where necessary) were estimated from the pH vs base added data using approximations derived by Albert [7]. These estimated constants were used in a computer program published previously [8] in order to calculate theoretical titration curves for the systems. The constants were varied until the calculated titration curves matched the experimentally observed curves within experimental error. The stability constants thus obtained were in general agreement with literature values for similar systems. By using the calculated values of the stability constants for the binary systems and estimating values for the stability constants of ternary complexes, it was again possible to calculate theoretical titration curves for systems containing two different amino acids. In this manner the stability constants for the mixed complexes could be determined. Configurational stability of free and complexed amino acids As in our previous studies on these systems [ 1,2] solutions of the amino acids both in the presence and absence of nickel(II) were observed over extended periods of time in order to demonstrate that racemization was not a factor in the results. Visible spectra and optical rotations were examined at intervals, and compared with the spectra and rotations of the freshly prepared solutions. In all cases, no changes were noted in either the visible spectra or the rotational data for at least one week. 6. B. E. Leach and R. J. Angelici, J. A m. chem. Soc. 91, 6296 (1969). 7. A. Albert, Biochem. 47, 531 (1950); ibidSO, 690 (1952). 8. J. E. Hix, Jr., Ph.D. Thesis, Vanderbilt University, Nashville, Tenn., 1967.
The metal complexcatalyzedhydrolysisof amino acid esters- III
1607
RESULTS
Stability and disproportionation constants for N i( I I )-amino acid complexes Since any investigation on the rates of hydrolysis of coordinated amino acid esters in the presence of varying catalysts are predicated on the assumption that whenever two different amino acids are present in a solution containing nickel(II) ion, appreciable amounts of the mixed complex MAB (as opposed to MA2 + MB2) are formed, it is necessary to justify that assumption. However, the metal ion catalyzes the hydrolysis of the ester linkage to such an extent that the results of the analytical methods for determing the solution composition-potentiometric titrations, specific rotations, and visible s p e c t r a - a r e affected during the time required for the measurements, with the result that the values obtained for the solution composition and for the various related constants are subject to rather large uncertainties. Thus, it would be very difficult to obtain precise values for the solution composition and the related constants for the systems containing the amino acid esters. It is possible, however, to examine solutions containing the amino acids themselves, since these solutions are quite stable, and undergo no reactions other than chelation under the conditions employed here. While these constants are accurate only for the amino acid systems, the trend which they establish can serve as qualitative, and to some extent quantitative evidence for similar trends for the ester systems if the amino acid solutions and the amino acid ester solutions can be shown to behave analogously. For this reason, similar analyses were performed on solutions of nickel(II) ion and the amino acids, which had been titrated to pH 8.0, and on solutions containing initially nickel(II) ion and the amino acid esters, which had been allowed to hydrolyze to completion at pH 8.0. The specific rotations and spectroscopic data for the two different solutions were identical when a hydrolyzed solution of the ester of an amino acid was compared with a freshly prepared solution of the amino acid itself. This, along with potentiometric data which will be presented in a later section, was taken as evidence that any trends noted for the solutions of the amino acids will be present to similar extents in the solutions of the amino acid esters.
Spectroscopic evidence for mixed complex formation Examination of the visible spectral region of the amino acid solutions provides obvious qualitative evidence for "the existence of the mixed complexes in solution. Figure 1 shows the observed spectra obtained from solutions containing nickel(II) and lysine, nickel(II) and histidine, and nickel(II), lysine and histidine. (A second absorbance maximum was observed in all nickel(II)-amino acid solutione near the short wave length end of the visible region (3500-4000 A) but the salt media (NO3-) contributed materially to the shape of the curve in this region, so only the higher wave length band was used for analysis). From the spectra of solutions containing only one amino acid, it was possible to calculate a composite spectrum that would be expected for a solution containing equal amounts of bis(histidinato)nickel(II) and bis(lysinato)nickel(II) and containing no histidinatolysinatonickel(II), from the Beer's law relationship A t = Xe~bci
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J.R.
B L A C K B U R N and M. M. JONES
0.40
0.30
--
~=0.20
~
8
0"10
0 = 4500
I
5000
I
5500
1
6000
I
6500
I
7000
Fig. I. Observed spectra for solutions containing 5"0 x 10-3 F Ni(NO3)~, and (a) 1-0 × 10 -= F L(+)-histidine ( - O - ) ; (b) 5.0 × 10-3 F L(+)-histidine and 5.0 × 10-3F L(+)-lysine (----);and(c) l - 0 X 10-2 F L(+)-lysine ( );all a t p H 8.0and 25°C.
equals the total abosrbance of the solution, Ei equals the extinction coefficient for component (i), b is the cell length in centimeters and ci is the concentration of component (i) in moles per liter. The calculated spectra thus obtained is compared in Fig. 2 with the observed spectra for a solution of equal concentrations of nickel(II), lysine, and histidine that had been titrated to pH 8.0. As can readily be seen, both the wavelength of maximum absorbance (Xma~)and the absorbance at Xmaxdiffer for the two spectra. In addition, the calculated spectrum is skewed to the left, due to the higher extinction coefficient of the bis(histidinato)nickel(II) species. The observed curve, on the other hand, is more symmetrical. These differences indicate the existence of
where A t
0"20
0"15
0'10
0,05
,~..~
I//"
~"
0
1
4500
5000
1
5500
I
6000
I
6.500
I
7000
Fig. 2. Spectrum observed for solution containing 5.0 × 10-3 F (each) Ni(NO3)2, L(+)lysine and L (+)-histidine (----); and spectrum calculated for the same solution and assuming no ternary complex formation ( - O - ) .
The metal complex catalyzed hydrolysis of amino acid esters-III
1609
a third species in the solution-the histidinatolysinatonickel(II) complex-which, if present in only small amounts must have a much higher extinction coefficient than the binary complexes in order to effect the shape of the curve in this manner; or in turn, must be present in large relative concentration if the extinction coefficient is of the same order of magnitude as those of the binary complexes. By using the above relationship, and spectra for the binary complexes, such as Fig. 4 (a) and (c), it is possible to calculate extinction coefficients for the MA ~ and MB~ species at any wavelength. By using these extinction coefficients, the observed spectra for the solutions containing two amino acids and the metal ion, and the concentrations of the various species in the mixed amino acid solutions (calculated from potentiometric titration data), it is possible to obtain values for the extinction coefficients for the mixed complexes of the type MAB. The results of calculations of this sort on several systems containing histidine in combination with other potentially tridentate amino acids are presented in Table 1. The spectra of the solutions of the pure MA z-type complexes differ appreciably both with respect to the position of the absorbance maximum and the extinction coefficient. For solutions containing (primarily) the MA2, MB2 and MAB complexes, a hmax is found that falls in all cases between the hm~x'S for the pure MA2-type complexes. This is not at all surprising, since an averaging of the electronic effects of each of the amino acids on the metal ion is to be expected in the MAB-type complexes. It is somewhat surprising to note, however, that the extinction coefficient for the mixed complexes are not simple averages of those for the pure complexes, indicating Table 1. Spectral data for bis complexes of Ni(lI) with histidine (A), methionine (B), lysine (C) and aspartic acid (D), a t p H = 8"0, a n d t = 25°C
Species
hmax(A)
Ex~ax
MA2 MB2 MCz MD2
5500 6010 6190 6000
4"20 2'90 2"70 2"50
Species
MA2 MB2 MAB MA2 MC2 MAC MA2 MD2 MAD
hmax*
5800
5850
5800
Conct 1.21 1.28 5.22 1-37 9.33 4.84 1 "01 4"35 5"73
× × x X x x × × ×
10 -3 10 -4 10 2 10 -3 10 -.~ 10 -.~ 10 -3 10 -4 10 3
E}~max 3-50 2.40 3-85 3.30 3.24 3-99 3'50 2" 10 2"90
Eave~
2.95
3.27
2'80
*Observed for solution containing initially equimolar concentrations (5 × 10 -~ F ) ofM, A a n d B, C o r D . tCalculated from potentiometric titration data. SAverage of e~ Maxfor MA.~and MB2 species.
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J.R. BLACKBURN and M. M. JONES
possibly differing degrees of interaction of the amino acids with the metal ion depending on the nature of the adjacent chelate. It should be noted here, that constants calculated in this manner hold only for these systems under the specific conditions of analysis-that is at pH = 8.0 and t = 25 °. Both hmax and the extinction coefficients for the solutions of transition metal ions with amino acids are very dependent upon pH. Figure 3 shows the results of varying the pH in the nickel(II)-histidine-lysine system between 2.5 and 7.5. Below pH 2.5 (actually about 3.0), the absorbance is due only to the aquated nickel(II) ion, since no complex forms with the completely protonated amino acids. As the pH is raised, the complex begins to form and the spectral changes begin to occur. The shift to shorter wave length hmax'S and higher emax'S continues as the pH is raised and complexation becomes more complete. At higher pH's (above 8.5) other complexes (MA3-type and hydroxy complexes) begin to become important and affect the shape of the spectral curve. Therefore, data of the type in Table 1, while providing valuable insights into trends in systems of this nature, is not specific enough in scope to apply to a wide range of mixed amino acid solutions as reference systems. In addition, the proximity of the ~.max'sfor the bis(methioninato)nickel(II), bis(lysinate)nickel(II) and bis(aspartate)nickel(II) complexes would make graphical resolution of the mixed solution spectra for these amino acids difficult and subject to a high degree of uncertainty. For these reasons, data on the mixed systems involving only histidine in combination with other potentially tridentate amino acids has been presented here. For each combination of amino acids studied, all possible permutations of D ( - ) - and L (+)-entiomers of each amino acid in combination with the metal ion and other amino acids were examined. In every case, the spectra were superimposible when the only differences in the systems were the configurations of the amino acids. Thus, for a system of the sort MAB, no differences were noted in the spectra, whether the complex was [ M ( L ( + ) --,4) (L(+) --B)], [M(L +) - - A ) ( D ( - ) - B ) ] , or their respective mirror images. Likewise in M`4z-type 0.40
0"30 0-20 -
J L
~
B 040
0
--
- -
I
5000
I
~00
I
6000
I
6500
r 7000
Fig. 3. The pH dependence of the visible spectra of a solution containing Ni(NO3)2, L(+)-lysine and L(+)-histidine, all 1.0×10-2F: (a) p H = 7 - 3 9 ; (b) p H = 4 0 0 ; (c) pH = 4.28; (d)pH = 3.64; (e) pH = 2.41.
The metal complexcatalyzed hydrolysisof amino acid esters- I 11
1611
systems, spectral changes were not observed when data for the optically pure [M(L(+)--A)z] and for the racemic [ M ( L ( + ) - - A ) ( D ( - ) - - A ) ] complexes were examined. Thus, the data presented in Table 1 and Figs. 1-3 are representative of any permutations of the optically active forms of the amino acids being discussed. This is not necessarily an indication that differences would not be expected due to the optical activity of the species i n v o l v e d - o n l y that these differences are not manifested by the visible spectra.
Stability and disproportionation constants for the mbced amino acid complexes Data of the type needed for the determination of the stability constants for these systems are available from the titration curves for the amino acids in the absence and presence of the metal ions. From the base added vs pH plots for the amino acids alone, it is possible to obtain values for the hydrolysis constants for the amino acids. These hydrolysis constants can them be combined with the titration data for the solutions containing the metal ion and the various amino acids, in order to obtain the stability constants associated with the systems. When the solution contains two (or more) different amino acids, the analysis must include all possible complexes of each individual amino acid with the metal ion, plus the additional unknown, the mixed complex MAB (and its protonated forms). For this reason, data on mixed systems is at present quite limited. Sample titration curves of the types discussed above are shown in Fig. 4 for the bis(histidinato)-
8"0
~-
6-0
f
4"0
/
- -
/
z.o
L 0
I
2"0
Equivolenfs
4"0
of bose
Fig. 4. Titration curves for solutions containing 1 equivalent of Ni(NOa)2, and (a), 2 equivalents of L(+)-histidine. HC1 (--O--); (b), 2 equivalents of L(+)-lysine. 2HCI ( ); and (c), 1 equivalentof each of the above aminoacids (----).
1612
J.R. BLACKBURN and M. M. JONES
nickel(II) system, the bis(lysinato)nickel(II) system, and the histidinatolysinatonickel(II) system. From curves of the type (a) and (b) (binary systems), all the stability constants for the nickel-lysine and nickel-histidine systems can be obtained. The stability constants for the ternary nickel-histidine-lysine system can be calculated from curve (c), and the values obtained from curves (a) and (b). Using the assumption (based on the potentiometric data) that only the species M, A and B are of importance in the present study, it is possible to construct a series of equations that illustrate the interrelationships between the constants for the systems. When the two polydentate ligands are allowed to interact with a metal ion, the following equilibria are expected to occur: M + A ~ MA + A ~ MA2
(1)
M + B ~ M B + B ~-- MBz
(2)
MA + B , ~ MAB MB+A @
(3)
where [MA] K ~ = [M] [A]
[MB] K 2 = [M][B]
(4a, b)
[MA~] KI~= [MA][A]
[MB2] K22= [MB][B]
(5a, b)
[MAB] K,2 = [MA] [B]
K,2
_
[MAB] [MB] [.4]
(6 a, b)
and the stability constants for the possible bis complexes are: flA : KIKll
(7)
fib = K2K22
(8)
tim = K1K12 = K2K21-
(9)
The tendency for the complex M A B to disproportionate as shown in Eqn (10) is given by Kdis, the constant for equilibrium (1 1). 2 MAB
MA2 + MB2
K.~ = [MA2] [MB2] [MAB]2
(10) (l 1)
Substituting Eqn (4-6) into (1 1) gives the expression for the disproportionation constant in terms of the equilibrium and stability constants. Petit et al. [9] have derived the statistical relationship between flA, fib and tim for the random distribution of A and B on the coordination center M to give a value for Kdis of 0.25. This is the value one would expect if no selectivity of coordination were 9. R. D. Gilland, H. M. Irvingand L. D. Petit, J. chem. Soc. (A),673 (1968).
The metal complex catalyzed hydrolysis of amino acid esters- III
1613
i n v o l v e d - t h a t is, if no one complex were preferred for kinetic, steric or thermodynamic reasons. In the cases where the mixed complex is preferred over the binary complexes, Kdi~ < 0.25, and when the binary complexes are preferred, Kdis > 0.25. This statement holds true anytime that A and B are physically distinguishable ligands. In the present study, two types of combinations meet the above requirement-when A and B are optical isomers of the same amino acid, and when they are totally different amino acids.
Optical isomers of the same amino acid It has been shown [9] that the observed stability constant for a solution containing a racemic ligand and a coordination center is related to the specific stability constants for the optically pure and racemic complexes as is shown in Eqn (13), where/32+ refers to the optically pure bis complex containing 2/3ob~ = /3',+ + 0"5/3+_
(13)
only one enantiomer, and/3+_ refers to the racemic bis-complex containing both enantiomers. It can be seen from Eqn (13) that when separate titrations are carried out on racemic and optically ligands in the presence of a transition metal ion, that if the two curves are superimposable, the observed stability constants must be equal, or/3obs = /32+- From Eqn (13), this can only be true if/3+_ = 2/3~+. Substitutions of these quantities into Eqn (12) yields Kois = 0.25 for the completely random case, which is the same value derived for the general case of differing ligands A and B. Thus, in the same fashion in which deviation from the value 0.25 in the case where A and B are totally different ligands is a measure of the selectivity for the mixed complex formation, deviation from 0.25 in the case where A and B are optical isomers of the same amino acid is a measure of the stereoselectivity of coordination of enantiomers to form either the optically pure or racemic complexes. Calculated and observed titration curves for the bis(histidinato)nickel(II) system are shown in Fig. 4. The values of/3~an were obtained by a trial-and-error computer fit of the data. The stability constants obtained and the ionization constants employed for the binary systems are listed in Table 2.
Optical isomers of different amino acids When A and B are two different amino acids, rather than enantiomers of the same amino acid, Eqns (1-9) still describe the system. However, the situation is complicated when, as in the present study, A and B each have optically active forms; L(+)- and D ( - ) - A and L(+)- and D(--)-B. When this occurs, the six equilibria of expressions 1-3 become the 20 equilibria shown in Fig. 6. As in the preceding section, the discussion can be simplified by noting that certain pairs of complexes are mirror images, hence their thermodynamic parameters are the same. For the equilibria shown in Fig. 12, there are I0 pairs of mirror image complexes, and thus 10 pairs of equilibrium constants that are equal (1 and 2, 3 and 4, 5 and 6 . . . . 19 and 20). This leaves a total of 10 potentially different equilibrium constants to be determined. The constants for complexes containing only the enantiomers of one amino acid (1-6 and 11-16) can be obtained from systems containing only that amino acid and the metal ion. These were dealt with in the
1614
J.R.
B L A C K B U R N and M. M. J O N E S
Table 2. Ionization constants for the amino acids studied, and stability constants for their binary complexes with Ni(II) (ionic strength = 1.0) pK*
Log ,82
Amino acid
Log ,81 pK,
pKz
pK3
Histidine
1.82
6.08
9.20
Aspartic acid
1.94
3.70
9-62
Glutamic acid
2.19
4-28
9.95
Lysine
2.18
8.95
10.53
Methionine
2.28
9-21
Trytophan
2.44
9.43
Log/32+
Log/~2b+~ Log/3~+'~ Log ,Ss
8.36 8-69T 8.65~: 6.81 7.18§ 7.14" 6.29 5.62§ 5.58* 5.47
15.40 15.58T 15.50~ 11.99 12.46§
5.41 4.7* 5.20" 5.47
10-81
15.65 15.84T 15.70¢ 11.99 12.46§ 12.34" 11-13 9.82§ 9.70* 9.00 8.8* 10-81 9.4* 9.84* 10.09
11.13 9.82§ 9.00
10.09
16.15 16.14T 16.14 12.29 12.76§ 11.43 10.12§ 9.30
10.98
11.11
13.43 11.7"
10.39
13.56
*L. G. Sillen and A. E. Martell, compilers, Stability Constants, Special Publication No. 17, (1964), and Stability Constants, Supplement No. 1, Special Publication No. 25 The Chemical Society, London ( 1971). tP. J. Morris and R. B. Martin, J. inorg, nucl. Chem. 32, 2891 (1970). -~I. H. Ritsma, J. C. van de Grampel and F. Jellinek, Rec. Tray. Chim. 88, 411 (1969). §J. H. Ritsma, G. A. Wiegers and F. Jellinek,Rec. Tray. Chim. 84, 1577 (1965).
preceding section. When the solution contains enantiomers of both amino acids, there are three possible bis complexes present (if only one enantiomer of each amino acid is present). M + L(+)-A + L(+)-B ~ M(L(+)-A)2 + M(L(+)-B)2 + M(L(+)-A) (L(+)-B).
(14) The relation between the three bis complexes is again represented by Kdis (Eqn (1 1)). The stability constants for the four mixed complexes can be expressed in terms of the constants for the specific equilibria involved. K1K7 = K12KI., = flLADS KIK9 ------KllK17 = flLALB
(15 a-d) K 2 K l o = K12K2o = flOADB
K2Ks = KIIK2o = floarB.
Since M(LA)(LB) is a mirror image of M ( D A ) ( D B ) , and M(LA)(DB) is a mirror image of M ( D A ) ( L B ) , it follows that /3LALB= /3OADBand ~LAOn = ~OALB. There are, then, four unique equilibrium constants that relate to the mixed com-
The metal complex catalyzed hydrolysis of amino acid e s t e r s - I I I
1615
6"50
6.00
Io. 5-50
i 5-00
-~
4.~
I
I
2"0
5.0
Equivolenl~
4"0
of bose
Fig. 5. Calculated and observed titration curves for the bis(histidinato) nickel(II) system. Solid triangles show calculated curve with 13M~,= 2-5 × 10~5; solid circles show calculated curve with /3MA,= 2"5 × 1015, BMaB= 5"0× 101~, open circles show calculated curve with /3MA,= 2"5 × 10~s, /3MAB= 1"4 × 10TM. The solid line is the observed curve for a 1 : 2 solution of Ni(II) and L (+)-histidine, and the broken line is the observed curve for a 1 : 2 solution of Ni(II) and D, L-histidine.
[M(LA)(DA)]
[
M(LA) 2 ]
xNXx~+DA + L ~ / ~ (3) 5)
M(LB)(DB) ["M(LAXLB)]_
[M(.LI~)2 ]
~ X + DB + L B / 05) (~3)
M
'"'
(2)'x~ _
"rL¢11~/ -"~
+De
[MibA) ]
"'J +DA
(19) "~'x~
//
~,=1
/_~M(DB)]
[M(OmCLm]
Fig. 6. Possible equilibria for the distribution of two optically active tridentate iigands on an octahedral center.
plexes: those for equilibria 7(--8), 9(--- 19), 17(= 18), and 19(= 20); and two unique/3's-those for the non-mirror image complexes. It follows from the above expressions (14, 15) that solutions containing optical isomers of two amino acids
1616
J.R. BLACKBURN and M. M. JONES
can show both stereoselectivity of coordination (between the non-mirror image complexes) and selectivity of coordination (between the binary and ternary complexes). (a) Stereoselectivity of coordination in ternary complexes. Only one of the previously mentioned studies of ternary complexes in solution reported attempts to examine stereoselective effects [5]. In that study titration curves for solutions containing optical isomers of both histidine and threonine in the presence of Cu(II) were superimposable, regardless of the combination of optical isomers present, hence thermodynamic effects due to stereoselectivity of coordination were absent from the system. The present work extends the study of these possible effects to combinations of the six potentially tridentate amino acid listed earlier. If stereoselectivity of coordination were present in any of the combinations studied, the titration curves for sets of solutions containing one enantiomer of A (or B) and either enantiomer of B (or A) would not be superimposable. If, however, stereoselectivity were not present for a given pair of amino acids, the titration curves for all solutions containing enantiomers of both amino acids would be superimposable. Since histidine had previously been shown to display stereoselectivity of coordination with itself, it was titrated with enantiomers of each of the other five amino acids. Other combinations examined were: aspartic acid with lysine and methionine; and lysine with glutamic acid and methionine. In all cases examined, the titration curves for all combinations of enantiomers of a given pair of amino acids were superimposable within experimental error, indicating a complete lack of thermodynamic effects due to stereoselectivity of coordination. Hence, from Fig. 6, F7 = K8 = K9 = g l 0 , K17 = K18 = Kaa = K~0 and t~LALB =/3OAOB= flL.4OB= flO.4L8for all combinations of amino acids studied. (b) Selectivity of coordination in ternary complexes. Since the four possible stability constants for the mixed complexes have been shown to be equal, it is now possible to discuss the selectivity of coordination simply in terms of the amino acids A and B, rather than in terms of their enantiomers. It is possible to arrive at the value for flMABthrough a trial-and-error procedure whereby known values for the stability constants for the species MA, MB, MA2 and MB2 are combined with estimated values for/3Man in order to calculate a titration curve. When the correct value for /3MABis attained, the calculated and experimental titration curves will match. Figure 7 shows an example of the curves calculated with four different values of fluaB, along with the experimentally obtained curve. When the value for fluAn has been obtained, it is then possible to calculate the composition of the solution at any given pH, and to note the change in percentage composition as the pH of the solution changes. Table 3 shows the percentage composition of a solution containing aspartic acid, histidine, and nickel(II) at pH's 4-9. It can be clearly seen that at pH values where appreciable amounts of each amino acid are coordinated to the metal ion, the mixed complex greatly predominates in solution. Values for flMABwere calculated in this manner for each of the combinations of amino acids studied. Using these /3's, and the known values for 131 and fie (from Eqn (6 a, b)), it is possible to calculate the equilibrium constants for the reaction of B with MA and A with MB to form the mixed complexes (Kle and K21 of Eqn (8)). In addition, using the calculated fluaB values with the previously determined/3MA, and flus, values, the disproportionation constant
The metal complex catalyzed hydrolysis of amino acid e s t e r s - III
1617
9,00
8,00
T 7'00
6"00
5.00
:-
t
I
3"0
3-5
4"0
Equivolenfs of base Fig. 7. Calculated and observed titration curves for the 1:1:1 nickel(ll)-histidineaspartic acid system: (a),/3UAB = 6"0 × 1013; (b), /3Man = 9"0 X 1013; (C), BMA~= 4"0 × 1014; (d),/3MAn = 6"0 × 1014. Circles show experimental points.
Kai~ can be calculated from Eqn (16). Table 4 lists the calculated values for [~MAB, K12, K21 Kd~s for the amino acid combinations studied and literature values for similar systems. As previously mentioned, deviations of Ka~s from 0.25 indicate selectivity of coordination; if Ka~ > 0.25, preference for the formation of mixed complexes is indicated, and if Ka~ < 0.25, preference for the binary complexes is indicated. As Table 4 shows, marked selectivity of coordination was observed in every case, with the mixed complex preferred each time over the binary complexes. DISCUSSION
We have dealt primarily with complexes of the type MA B, where A and B are the acidate anions of the different amino acids. In actual practice, a great many more complexes are present in solution varying concentrations, with different complexes being the predominant species at different pH's of the solution. In certain low pH ranges, mono complexes of the type MA or MB would be expected to predominate, with minor contributions from the protonated complexes MHA, MHB, MHAB, and from the previously mentioned bis complexes. At still lower pH's, complexes involving the anion of the amino acid would be expected to be unimportant, and the only complexes (other than the aquated metal ion) of any important would be the weakly bound protonated complexes. In the intermediate pH ranges, bis complexes of the type MA., and MB2 would be expected to predominate, and at very high pH's, the hydroxy complexes MA(OH), MB(OH), M(OH) and M(OH)2 might be expected to be important contributors to the solu-
1618
J. R. B L A C K B U R N and M. M. J O N E S
Table 3. Percentage composition of a solution containing equimolar amounts (initially 8-00 × 10-3 F in each) of Ni(ll), histidine, and aspartic acid at various pH's ( / = 1.0) pH
M
4"00 4"50 5"00 5"50 6"00 6"50 7"00 7"50 8"00 8"50 9"00
85"6 51"1 18'6 6"2 2"4 0"9 0"3
A
B
M(OH)
0"1 0"4 I'1 3"4
M(OH)2
HA
H~A
HB
0"2 1'0 2"9 5"3 6"9 7"8 8"7
0'8 1"7 2'2 1'3 1"0 0"5 0"3 0"2 0"2 0'2 0"2
91'5 63"1 26"8 6'8 1"2 0"2
62'1 71"8 68"9 58'1 43"5 30"3 21 '5 16"4 15"9 15"0 14"0
pH
MA
MA~
MB
4.00 4-50 5.00 5"50 6.00 6.50 7.00 7"50 8.00 8'50 9"00
7-5 3 I" 1 48"1 40"8 27-5 16-6 8"7 3"7 1-3 0"5 0.2
0"9 5"9 12"8 15-1 14.8 14"0 13'8 13"6 13-8 14.1
6.6 14"4 15-9 14.2 13" 1 10.6 6.9 3.3 1"2 0-4 0.1
MB,2
0"3 0.8 1-6 2.9 4-3 5"3 5"7 5"8 5"6
MB 3
H2B 31'1 11"4 3"5 0"9 0"2
MAB 0-2 2"4 11-I 25" 1 40.1 53"3 62.9 68"6 71"3 71-9 71 "5
tion composition. Thus, it is necessary to obtain a reasonable estimate of the concentrations of the various species discussed above in the pH ranges used in the present study in order to accurately assess the importance of each to the overall solution composition. H. C. Freeman and R.-P. Martin have laid a foundation for this type of work with their study on the copper-histidine-threonine system[5]. This study has greatly simplified the interpretation of titration data by dearly demonstrating the pH ranges in which the various possible complexes contribute materially to the experimental data. In a rigorous analysis of calculated and observed titration curves, they have considered the following complexes (A=histidinate, B~threoninate, M~Cu(II)): M, MHA, MA, MH_IA, MH~A2, MA2, MB, MB2, MH-1B2, MHAB, MAB and MH_IAB. The MAB complex was shown to greatly predominate the pH's above 4 and below 10. In the pH range of greatest interest in the present study (6-8.5) only the bis complexes of the acidate anion, MA2, MBz and MAB, contribute to the experimental data. Stereoselective effects in the stability constants for amino acid-transition metal complexes have previously been found to be absent in all studies involving only bidentate a-amino acids, and in the case of aspartic acid and glutamic acid, but are found to be present in the case ofhistidine. These effects have been confirmed in the present study, and the study extended in include other potentially tridentate
The metal complex catalyzed hydrolysis of amino acid esters- 1 II
1619
Table 4. Stability constants for ternary amino acid complexes with Ni(II) A
Histidine Histidine Histidine Histidine Histidine Aspartic acid Aspartic acid Lysine Lysine Histidine Histidine Glycine Glycine Alanine
B
Aspanic acid Glutamic acid Methionine Tryptophan Lysine Lysine Methionine Glutamic acid Methionine Methyl histidinate Threonine Alanine Tyrosine Tyrosine
Log/3uaB
Log Klz
Log K21
Kai~
14.60
6.24
7-79
0.0153
13.78 13.40 13.20 10.00
5-42 5.04 4.84 1.64
7.49 7.99 7.73 4.53
0.0975 0.0769 0.0250 0.0258
*
*
*
*
11.95
5-14
6-54
0.0176
* 10.00
* 4-53
* 4-59
* 0.0646
13"40t 17.52, 15.60§ 15.55 § 15.84§
5'90t 7.30*
7-38t 9.56
0.051* 0.0178, 0.141 § 0-105 § 0.0251 §
* C u r v e fit not possible. fRef. [8]. *Ref. [5], M = Cu(ll). §Ref. [3], M = Cu(II).
amino acids. Titrations and calculations were performed on solutions of histidine, glutamic acid, tryptophan, methionine, and lysine, all with nickel(II) present. The only case in which stereoselectivity was observed was in the case of histidine. For all other amino acids studied, flobs=/32+ and 3+_ = 2/32+. In the case of histidine, as seen in Table 2, however, 3+_ # 232+. When the solution contained nickel(II) and enantiomers of two different amino acids, no stereoselective effects on the stability constants were found with any combination of amino acids. This is particularly striking when compared with the rate data presented earlier [2] that showed marked kinetic stereoselectivity with combinations of tryptophane and histidine methyl ester on the nickel(II) center. Similar effects were indicated in the first paper [ 1] when the kinetic stereoselectivity observed with combinations of histidine and histidine methylester was reported, but titration curves of the non-mirror image systems containing one equivalent each of nickel(II), the amino acid and the ester were superimposable. Titration curves with the ester present are subject to some uncertainty, due to the hydrolysis of the ester, but comparisions of the rate and thermodynamic data with the tryptophan-methyl histidinate solution indicate strongly that the appearance of thermodynamic stereoselective effects is n o t an indication that kinetic stereoselective effects will be seen, and vice versa; rather, the data points strongly to the conclusion that the kinetic and thermodynamic stereoselectivity arise from different sources. Since the ease with which the esters hydrolyze prevents their being studied
1620
J.R.
B L A C K B U R N and M. M. J O N E S
potentiometrically, and the mixed complexes with the esters have not been isolated for solid state study, the most appropriate method for studying the kinetic stereoselective effects seems to be the systematic variation of the catalyst used in Paper II in this series [2], and further variation of the ester itself to examine other amino acid esters in addition to histidine methylester under the same conditions. The validity of this method is clearly indicated by Table 4, when it can be seen that in all cases involving ternary systems that have been reported, the mixed complexes are found preferentially in solution (the Kdis for the dissociation31 of the MAB complex into M.42 and MB2 is in all cases a factor of 5-25 smaller than the statistical value), so the MAB-type complex can be assumed to greatly predominate in solution, and thus the characteristics of the system will be the characteristics of the mixed complexes themselves.
STEREOSELECTIVITY IN THE METAL COMPLEX CATALYZED HYDROLYSIS OF AMINO ACID ESTERSIII DISTRIBUTION EQUILIBRIA J O H N R. B L A C K B U R N and M A R K M. J O N E S Department of Chemistry Vanderbilt University, Nashville, Tennessee 37203 ( R e c e i v e d 1 A u g u s t 1972)
A b s t r a c t - A study of the equilibria involving nickel(II) and equimolar amounts of different optically active amino acids shows that in such systems the mixed complexes, MAB, are favored to a greater extent than would be predicted from statistical considerations alone. Insofar as mixtures of optical isomers of a given amino acid are concerned, stereosdectivity in the stability constants of nickel(II) complexes was found only in the case of histidine. When optical isomers of a pair of amono acids were involved, no stereoselectivity was observed for the stability constants of any of the mixtures examined. These results correlate rather closely with most stereoselectivity studies involving the metal-complex catalyzed hydrolysis of amino acid esters. An anomaly exists, however, in the case of the tryptophan-histidine data, that suggests a more complicated relationship between the thermodynamic and kinetic stereoselectivities. INTRODUCTION
IN PREVIOUS papers in this series we have shown the stereoselective action of the mono (D (--) -- or L(+)-)histidinatonickel(II) as a catalyst in the hydrolysis of D ( - ) - o r L ( + ) - h i s t i d i n e methyl ester[l] and also that such behavior is apparently of limited occurrence in the nickel(II)-amino acid-amino acid ester systems [2]. The question then arose as to the origin of these effects. Do they arise from differences in stability constants or differences in rate constants? The present study describes a search for differences in equilibrium constants in systems containing enantiomeric amino acids. Thermodynamic data on amino acid-transition metal ion interactions is plentiful. However, few studies have involved systems in which two different amino acids were present. For this reason, potentiometric titrations were carded out on the systems studied here to (1) provide evidence for the existence of the mixed complexes, (2) provide a qualitative estimate of the degree of mixed complex formation as opposed to simple binary complex formation, and (3) determine whether stereoselective effects are present in equilibrium constants for these mixed complexes. A very few thermodynamic studies have been done on ternary complexes, in which the complex contains two different amino acids or amino acid derivatives (e.g. [Ni(histidine)(threonine)][3-5]. In these studies, it has been found that the 1. 2. 3. 4. 5.
J. E. Hix, Jr. and M. M. Jones, J. A m. chem. Soc. 90, 1723 (1968). J. R. Blackburn and M. M. Jones, Paper II, J. inorg, nucl. Chem. 35, 1597 (1973). R.-P. Martin and R. A. Paris, C. r. hebd. Sdanc. Acad. Sci. Paris 3932 (1963). B. E. Leach and R. J. Angelici, J. A m. chem. Soc. 90, 2504 (1968). H. C. Freeman and R.-P. Martin, J. biol. C h e m . 244, 4823 (1969). 1605
1606
J . R . BLACKBURN and M. M. JONES
mixed complexes are favored more than would be expected on a purely statistical basis over the complex containing only one type of amino acid chelate. One rate study of bidentate amino acid ester hydrolysis in ternary systems has been reported [6] in which stereoselectivity was observed, but no causal relationship could be determined. This study involved not a simple amino acid, but a polydentate amino acid derivative with which the complex structure was uncertain. EXPERIMENTAL Stability constant titrations As one means of determining whether mixed complex formation was occuring, each combination of amino acids used in the study was titrated with a standard sodium hydroxide solution and the pH vs. base added profile was recorded. This included 2 : 1 (amino acid "A" : Ni(II)) solution and 1 : 1 : 1 (amino acid "A" : amino acid "B" : Ni(lI) solutions). For the titrations of the amino acids in the various conbinations used were prepared from freshly boiled doubly distilled water. Stock solutions of the amino acids were prepared (0.10 F for histidine, lysine, and methionine; 0.020 F for aspartic acid, glutamic acid and tryptophan, the latter three more dilute for solubility considerations) and used for all titrations. Freshly prepared 4.0 F sodium nitrate was used to adjust the ionic strength of the reaction media, and carbonate free 0.1 N sodium hydroxide (1 = 1.0 with sodium nitrate) was used for the titrations. One miiliequivalent each of amino acid "A," amino acid "B" and nickel(II) was pipetted into a 200 ml jacketed beaker equipped with a magnetic stirrer a n d maintained at 25-0°C +0"I°C. This was followed by the appropriate amount of 4-0F sodium nitrate and doubly distilled water to give an initial volume of 120 ml and a final ionic strength of 1.0. For a period of approximately 30 rain prior to titration, dry nitrogen was bubbled through the solutions to degas them. The jacketed beaker was fitted with a polyethylene cover to protect against ambient air currents, and to help maintain a nitrogen atmosphere. Throughout the titrations, nitrogen was bubbled slowly through the mixture to prevent absorption of oxygen or carbon dioxide by the reaction mixture. This was necessary since any differences in the titration curves of non-mirror image systems would be expected to be very slight, and thus all possible external variables had to be minimized. Titrations were carried out manually with a Beckman research pH meter to a final pH greater than 10.5, at which point all ionizable protons from the amino acids had been neutralized. Each amino acid solution was also titrated in the 1 -- 1.0 medium in the absence of nickel(II) in order to standardize the solutions and to compare the titration curves with curves from the literature to determine the ionic strength effects. The titration curves for the amino acids only, in the presence and in the absence of NO3- were superimposable, and matched the literature curves closely. Thus, the literature values for the p K ' s of the amino acids were used in all calculations. The stability constants for complexes containing only one specific amino acid (/31,/32 and 133 where necessary) were estimated from the pH vs base added data using approximations derived by Albert [7]. These estimated constants were used in a computer program published previously [8] in order to calculate theoretical titration curves for the systems. The constants were varied until the calculated titration curves matched the experimentally observed curves within experimental error. The stability constants thus obtained were in general agreement with literature values for similar systems. By using the calculated values of the stability constants for the binary systems and estimating values for the stability constants of ternary complexes, it was again possible to calculate theoretical titration curves for systems containing two different amino acids. In this manner the stability constants for the mixed complexes could be determined. Configurational stability of free and complexed amino acids As in our previous studies on these systems [ 1,2] solutions of the amino acids both in the presence and absence of nickel(II) were observed over extended periods of time in order to demonstrate that racemization was not a factor in the results. Visible spectra and optical rotations were examined at intervals, and compared with the spectra and rotations of the freshly prepared solutions. In all cases, no changes were noted in either the visible spectra or the rotational data for at least one week. 6. B. E. Leach and R. J. Angelici, J. A m. chem. Soc. 91, 6296 (1969). 7. A. Albert, Biochem. 47, 531 (1950); ibidSO, 690 (1952). 8. J. E. Hix, Jr., Ph.D. Thesis, Vanderbilt University, Nashville, Tenn., 1967.
The metal complexcatalyzedhydrolysisof amino acid esters- III
1607
RESULTS
Stability and disproportionation constants for N i( I I )-amino acid complexes Since any investigation on the rates of hydrolysis of coordinated amino acid esters in the presence of varying catalysts are predicated on the assumption that whenever two different amino acids are present in a solution containing nickel(II) ion, appreciable amounts of the mixed complex MAB (as opposed to MA2 + MB2) are formed, it is necessary to justify that assumption. However, the metal ion catalyzes the hydrolysis of the ester linkage to such an extent that the results of the analytical methods for determing the solution composition-potentiometric titrations, specific rotations, and visible s p e c t r a - a r e affected during the time required for the measurements, with the result that the values obtained for the solution composition and for the various related constants are subject to rather large uncertainties. Thus, it would be very difficult to obtain precise values for the solution composition and the related constants for the systems containing the amino acid esters. It is possible, however, to examine solutions containing the amino acids themselves, since these solutions are quite stable, and undergo no reactions other than chelation under the conditions employed here. While these constants are accurate only for the amino acid systems, the trend which they establish can serve as qualitative, and to some extent quantitative evidence for similar trends for the ester systems if the amino acid solutions and the amino acid ester solutions can be shown to behave analogously. For this reason, similar analyses were performed on solutions of nickel(II) ion and the amino acids, which had been titrated to pH 8.0, and on solutions containing initially nickel(II) ion and the amino acid esters, which had been allowed to hydrolyze to completion at pH 8.0. The specific rotations and spectroscopic data for the two different solutions were identical when a hydrolyzed solution of the ester of an amino acid was compared with a freshly prepared solution of the amino acid itself. This, along with potentiometric data which will be presented in a later section, was taken as evidence that any trends noted for the solutions of the amino acids will be present to similar extents in the solutions of the amino acid esters.
Spectroscopic evidence for mixed complex formation Examination of the visible spectral region of the amino acid solutions provides obvious qualitative evidence for "the existence of the mixed complexes in solution. Figure 1 shows the observed spectra obtained from solutions containing nickel(II) and lysine, nickel(II) and histidine, and nickel(II), lysine and histidine. (A second absorbance maximum was observed in all nickel(II)-amino acid solutione near the short wave length end of the visible region (3500-4000 A) but the salt media (NO3-) contributed materially to the shape of the curve in this region, so only the higher wave length band was used for analysis). From the spectra of solutions containing only one amino acid, it was possible to calculate a composite spectrum that would be expected for a solution containing equal amounts of bis(histidinato)nickel(II) and bis(lysinato)nickel(II) and containing no histidinatolysinatonickel(II), from the Beer's law relationship A t = Xe~bci
1608
J.R.
B L A C K B U R N and M. M. JONES
0.40
0.30
--
~=0.20
~
8
0"10
0 = 4500
I
5000
I
5500
1
6000
I
6500
I
7000
Fig. I. Observed spectra for solutions containing 5"0 x 10-3 F Ni(NO3)~, and (a) 1-0 × 10 -= F L(+)-histidine ( - O - ) ; (b) 5.0 × 10-3 F L(+)-histidine and 5.0 × 10-3F L(+)-lysine (----);and(c) l - 0 X 10-2 F L(+)-lysine ( );all a t p H 8.0and 25°C.
equals the total abosrbance of the solution, Ei equals the extinction coefficient for component (i), b is the cell length in centimeters and ci is the concentration of component (i) in moles per liter. The calculated spectra thus obtained is compared in Fig. 2 with the observed spectra for a solution of equal concentrations of nickel(II), lysine, and histidine that had been titrated to pH 8.0. As can readily be seen, both the wavelength of maximum absorbance (Xma~)and the absorbance at Xmaxdiffer for the two spectra. In addition, the calculated spectrum is skewed to the left, due to the higher extinction coefficient of the bis(histidinato)nickel(II) species. The observed curve, on the other hand, is more symmetrical. These differences indicate the existence of
where A t
0"20
0"15
0'10
0,05
,~..~
I//"
~"
0
1
4500
5000
1
5500
I
6000
I
6.500
I
7000
Fig. 2. Spectrum observed for solution containing 5.0 × 10-3 F (each) Ni(NO3)2, L(+)lysine and L (+)-histidine (----); and spectrum calculated for the same solution and assuming no ternary complex formation ( - O - ) .
The metal complex catalyzed hydrolysis of amino acid esters-III
1609
a third species in the solution-the histidinatolysinatonickel(II) complex-which, if present in only small amounts must have a much higher extinction coefficient than the binary complexes in order to effect the shape of the curve in this manner; or in turn, must be present in large relative concentration if the extinction coefficient is of the same order of magnitude as those of the binary complexes. By using the above relationship, and spectra for the binary complexes, such as Fig. 4 (a) and (c), it is possible to calculate extinction coefficients for the MA ~ and MB~ species at any wavelength. By using these extinction coefficients, the observed spectra for the solutions containing two amino acids and the metal ion, and the concentrations of the various species in the mixed amino acid solutions (calculated from potentiometric titration data), it is possible to obtain values for the extinction coefficients for the mixed complexes of the type MAB. The results of calculations of this sort on several systems containing histidine in combination with other potentially tridentate amino acids are presented in Table 1. The spectra of the solutions of the pure MA z-type complexes differ appreciably both with respect to the position of the absorbance maximum and the extinction coefficient. For solutions containing (primarily) the MA2, MB2 and MAB complexes, a hmax is found that falls in all cases between the hm~x'S for the pure MA2-type complexes. This is not at all surprising, since an averaging of the electronic effects of each of the amino acids on the metal ion is to be expected in the MAB-type complexes. It is somewhat surprising to note, however, that the extinction coefficient for the mixed complexes are not simple averages of those for the pure complexes, indicating Table 1. Spectral data for bis complexes of Ni(lI) with histidine (A), methionine (B), lysine (C) and aspartic acid (D), a t p H = 8"0, a n d t = 25°C
Species
hmax(A)
Ex~ax
MA2 MB2 MCz MD2
5500 6010 6190 6000
4"20 2'90 2"70 2"50
Species
MA2 MB2 MAB MA2 MC2 MAC MA2 MD2 MAD
hmax*
5800
5850
5800
Conct 1.21 1.28 5.22 1-37 9.33 4.84 1 "01 4"35 5"73
× × x X x x × × ×
10 -3 10 -4 10 2 10 -3 10 -.~ 10 -.~ 10 -3 10 -4 10 3
E}~max 3-50 2.40 3-85 3.30 3.24 3-99 3'50 2" 10 2"90
Eave~
2.95
3.27
2'80
*Observed for solution containing initially equimolar concentrations (5 × 10 -~ F ) ofM, A a n d B, C o r D . tCalculated from potentiometric titration data. SAverage of e~ Maxfor MA.~and MB2 species.
1610
J.R. BLACKBURN and M. M. JONES
possibly differing degrees of interaction of the amino acids with the metal ion depending on the nature of the adjacent chelate. It should be noted here, that constants calculated in this manner hold only for these systems under the specific conditions of analysis-that is at pH = 8.0 and t = 25 °. Both hmax and the extinction coefficients for the solutions of transition metal ions with amino acids are very dependent upon pH. Figure 3 shows the results of varying the pH in the nickel(II)-histidine-lysine system between 2.5 and 7.5. Below pH 2.5 (actually about 3.0), the absorbance is due only to the aquated nickel(II) ion, since no complex forms with the completely protonated amino acids. As the pH is raised, the complex begins to form and the spectral changes begin to occur. The shift to shorter wave length hmax'S and higher emax'S continues as the pH is raised and complexation becomes more complete. At higher pH's (above 8.5) other complexes (MA3-type and hydroxy complexes) begin to become important and affect the shape of the spectral curve. Therefore, data of the type in Table 1, while providing valuable insights into trends in systems of this nature, is not specific enough in scope to apply to a wide range of mixed amino acid solutions as reference systems. In addition, the proximity of the ~.max'sfor the bis(methioninato)nickel(II), bis(lysinate)nickel(II) and bis(aspartate)nickel(II) complexes would make graphical resolution of the mixed solution spectra for these amino acids difficult and subject to a high degree of uncertainty. For these reasons, data on the mixed systems involving only histidine in combination with other potentially tridentate amino acids has been presented here. For each combination of amino acids studied, all possible permutations of D ( - ) - and L (+)-entiomers of each amino acid in combination with the metal ion and other amino acids were examined. In every case, the spectra were superimposible when the only differences in the systems were the configurations of the amino acids. Thus, for a system of the sort MAB, no differences were noted in the spectra, whether the complex was [ M ( L ( + ) --,4) (L(+) --B)], [M(L +) - - A ) ( D ( - ) - B ) ] , or their respective mirror images. Likewise in M`4z-type 0.40
0"30 0-20 -
J L
~
B 040
0
--
- -
I
5000
I
~00
I
6000
I
6500
r 7000
Fig. 3. The pH dependence of the visible spectra of a solution containing Ni(NO3)2, L(+)-lysine and L(+)-histidine, all 1.0×10-2F: (a) p H = 7 - 3 9 ; (b) p H = 4 0 0 ; (c) pH = 4.28; (d)pH = 3.64; (e) pH = 2.41.
The metal complexcatalyzed hydrolysisof amino acid esters- I 11
1611
systems, spectral changes were not observed when data for the optically pure [M(L(+)--A)z] and for the racemic [ M ( L ( + ) - - A ) ( D ( - ) - - A ) ] complexes were examined. Thus, the data presented in Table 1 and Figs. 1-3 are representative of any permutations of the optically active forms of the amino acids being discussed. This is not necessarily an indication that differences would not be expected due to the optical activity of the species i n v o l v e d - o n l y that these differences are not manifested by the visible spectra.
Stability and disproportionation constants for the mbced amino acid complexes Data of the type needed for the determination of the stability constants for these systems are available from the titration curves for the amino acids in the absence and presence of the metal ions. From the base added vs pH plots for the amino acids alone, it is possible to obtain values for the hydrolysis constants for the amino acids. These hydrolysis constants can them be combined with the titration data for the solutions containing the metal ion and the various amino acids, in order to obtain the stability constants associated with the systems. When the solution contains two (or more) different amino acids, the analysis must include all possible complexes of each individual amino acid with the metal ion, plus the additional unknown, the mixed complex MAB (and its protonated forms). For this reason, data on mixed systems is at present quite limited. Sample titration curves of the types discussed above are shown in Fig. 4 for the bis(histidinato)-
8"0
~-
6-0
f
4"0
/
- -
/
z.o
L 0
I
2"0
Equivolenfs
4"0
of bose
Fig. 4. Titration curves for solutions containing 1 equivalent of Ni(NOa)2, and (a), 2 equivalents of L(+)-histidine. HC1 (--O--); (b), 2 equivalents of L(+)-lysine. 2HCI ( ); and (c), 1 equivalentof each of the above aminoacids (----).
1612
J.R. BLACKBURN and M. M. JONES
nickel(II) system, the bis(lysinato)nickel(II) system, and the histidinatolysinatonickel(II) system. From curves of the type (a) and (b) (binary systems), all the stability constants for the nickel-lysine and nickel-histidine systems can be obtained. The stability constants for the ternary nickel-histidine-lysine system can be calculated from curve (c), and the values obtained from curves (a) and (b). Using the assumption (based on the potentiometric data) that only the species M, A and B are of importance in the present study, it is possible to construct a series of equations that illustrate the interrelationships between the constants for the systems. When the two polydentate ligands are allowed to interact with a metal ion, the following equilibria are expected to occur: M + A ~ MA + A ~ MA2
(1)
M + B ~ M B + B ~-- MBz
(2)
MA + B , ~ MAB MB+A @
(3)
where [MA] K ~ = [M] [A]
[MB] K 2 = [M][B]
(4a, b)
[MA~] KI~= [MA][A]
[MB2] K22= [MB][B]
(5a, b)
[MAB] K,2 = [MA] [B]
K,2
_
[MAB] [MB] [.4]
(6 a, b)
and the stability constants for the possible bis complexes are: flA : KIKll
(7)
fib = K2K22
(8)
tim = K1K12 = K2K21-
(9)
The tendency for the complex M A B to disproportionate as shown in Eqn (10) is given by Kdis, the constant for equilibrium (1 1). 2 MAB
MA2 + MB2
K.~ = [MA2] [MB2] [MAB]2
(10) (l 1)
Substituting Eqn (4-6) into (1 1) gives the expression for the disproportionation constant in terms of the equilibrium and stability constants. Petit et al. [9] have derived the statistical relationship between flA, fib and tim for the random distribution of A and B on the coordination center M to give a value for Kdis of 0.25. This is the value one would expect if no selectivity of coordination were 9. R. D. Gilland, H. M. Irvingand L. D. Petit, J. chem. Soc. (A),673 (1968).
The metal complex catalyzed hydrolysis of amino acid esters- III
1613
i n v o l v e d - t h a t is, if no one complex were preferred for kinetic, steric or thermodynamic reasons. In the cases where the mixed complex is preferred over the binary complexes, Kdi~ < 0.25, and when the binary complexes are preferred, Kdis > 0.25. This statement holds true anytime that A and B are physically distinguishable ligands. In the present study, two types of combinations meet the above requirement-when A and B are optical isomers of the same amino acid, and when they are totally different amino acids.
Optical isomers of the same amino acid It has been shown [9] that the observed stability constant for a solution containing a racemic ligand and a coordination center is related to the specific stability constants for the optically pure and racemic complexes as is shown in Eqn (13), where/32+ refers to the optically pure bis complex containing 2/3ob~ = /3',+ + 0"5/3+_
(13)
only one enantiomer, and/3+_ refers to the racemic bis-complex containing both enantiomers. It can be seen from Eqn (13) that when separate titrations are carried out on racemic and optically ligands in the presence of a transition metal ion, that if the two curves are superimposable, the observed stability constants must be equal, or/3obs = /32+- From Eqn (13), this can only be true if/3+_ = 2/3~+. Substitutions of these quantities into Eqn (12) yields Kois = 0.25 for the completely random case, which is the same value derived for the general case of differing ligands A and B. Thus, in the same fashion in which deviation from the value 0.25 in the case where A and B are totally different ligands is a measure of the selectivity for the mixed complex formation, deviation from 0.25 in the case where A and B are optical isomers of the same amino acid is a measure of the stereoselectivity of coordination of enantiomers to form either the optically pure or racemic complexes. Calculated and observed titration curves for the bis(histidinato)nickel(II) system are shown in Fig. 4. The values of/3~an were obtained by a trial-and-error computer fit of the data. The stability constants obtained and the ionization constants employed for the binary systems are listed in Table 2.
Optical isomers of different amino acids When A and B are two different amino acids, rather than enantiomers of the same amino acid, Eqns (1-9) still describe the system. However, the situation is complicated when, as in the present study, A and B each have optically active forms; L(+)- and D ( - ) - A and L(+)- and D(--)-B. When this occurs, the six equilibria of expressions 1-3 become the 20 equilibria shown in Fig. 6. As in the preceding section, the discussion can be simplified by noting that certain pairs of complexes are mirror images, hence their thermodynamic parameters are the same. For the equilibria shown in Fig. 12, there are I0 pairs of mirror image complexes, and thus 10 pairs of equilibrium constants that are equal (1 and 2, 3 and 4, 5 and 6 . . . . 19 and 20). This leaves a total of 10 potentially different equilibrium constants to be determined. The constants for complexes containing only the enantiomers of one amino acid (1-6 and 11-16) can be obtained from systems containing only that amino acid and the metal ion. These were dealt with in the
1614
J.R.
B L A C K B U R N and M. M. J O N E S
Table 2. Ionization constants for the amino acids studied, and stability constants for their binary complexes with Ni(II) (ionic strength = 1.0) pK*
Log ,82
Amino acid
Log ,81 pK,
pKz
pK3
Histidine
1.82
6.08
9.20
Aspartic acid
1.94
3.70
9-62
Glutamic acid
2.19
4-28
9.95
Lysine
2.18
8.95
10.53
Methionine
2.28
9-21
Trytophan
2.44
9.43
Log/32+
Log/~2b+~ Log/3~+'~ Log ,Ss
8.36 8-69T 8.65~: 6.81 7.18§ 7.14" 6.29 5.62§ 5.58* 5.47
15.40 15.58T 15.50~ 11.99 12.46§
5.41 4.7* 5.20" 5.47
10-81
15.65 15.84T 15.70¢ 11.99 12.46§ 12.34" 11-13 9.82§ 9.70* 9.00 8.8* 10-81 9.4* 9.84* 10.09
11.13 9.82§ 9.00
10.09
16.15 16.14T 16.14 12.29 12.76§ 11.43 10.12§ 9.30
10.98
11.11
13.43 11.7"
10.39
13.56
*L. G. Sillen and A. E. Martell, compilers, Stability Constants, Special Publication No. 17, (1964), and Stability Constants, Supplement No. 1, Special Publication No. 25 The Chemical Society, London ( 1971). tP. J. Morris and R. B. Martin, J. inorg, nucl. Chem. 32, 2891 (1970). -~I. H. Ritsma, J. C. van de Grampel and F. Jellinek, Rec. Tray. Chim. 88, 411 (1969). §J. H. Ritsma, G. A. Wiegers and F. Jellinek,Rec. Tray. Chim. 84, 1577 (1965).
preceding section. When the solution contains enantiomers of both amino acids, there are three possible bis complexes present (if only one enantiomer of each amino acid is present). M + L(+)-A + L(+)-B ~ M(L(+)-A)2 + M(L(+)-B)2 + M(L(+)-A) (L(+)-B).
(14) The relation between the three bis complexes is again represented by Kdis (Eqn (1 1)). The stability constants for the four mixed complexes can be expressed in terms of the constants for the specific equilibria involved. K1K7 = K12KI., = flLADS KIK9 ------KllK17 = flLALB
(15 a-d) K 2 K l o = K12K2o = flOADB
K2Ks = KIIK2o = floarB.
Since M(LA)(LB) is a mirror image of M ( D A ) ( D B ) , and M(LA)(DB) is a mirror image of M ( D A ) ( L B ) , it follows that /3LALB= /3OADBand ~LAOn = ~OALB. There are, then, four unique equilibrium constants that relate to the mixed com-
The metal complex catalyzed hydrolysis of amino acid e s t e r s - I I I
1615
6"50
6.00
Io. 5-50
i 5-00
-~
4.~
I
I
2"0
5.0
Equivolenl~
4"0
of bose
Fig. 5. Calculated and observed titration curves for the bis(histidinato) nickel(II) system. Solid triangles show calculated curve with 13M~,= 2-5 × 10~5; solid circles show calculated curve with /3MA,= 2"5 × 1015, BMaB= 5"0× 101~, open circles show calculated curve with /3MA,= 2"5 × 10~s, /3MAB= 1"4 × 10TM. The solid line is the observed curve for a 1 : 2 solution of Ni(II) and L (+)-histidine, and the broken line is the observed curve for a 1 : 2 solution of Ni(II) and D, L-histidine.
[M(LA)(DA)]
[
M(LA) 2 ]
xNXx~+DA + L ~ / ~ (3) 5)
M(LB)(DB) ["M(LAXLB)]_
[M(.LI~)2 ]
~ X + DB + L B / 05) (~3)
M
'"'
(2)'x~ _
"rL¢11~/ -"~
+De
[MibA) ]
"'J +DA
(19) "~'x~
//
~,=1
/_~M(DB)]
[M(OmCLm]
Fig. 6. Possible equilibria for the distribution of two optically active tridentate iigands on an octahedral center.
plexes: those for equilibria 7(--8), 9(--- 19), 17(= 18), and 19(= 20); and two unique/3's-those for the non-mirror image complexes. It follows from the above expressions (14, 15) that solutions containing optical isomers of two amino acids
1616
J.R. BLACKBURN and M. M. JONES
can show both stereoselectivity of coordination (between the non-mirror image complexes) and selectivity of coordination (between the binary and ternary complexes). (a) Stereoselectivity of coordination in ternary complexes. Only one of the previously mentioned studies of ternary complexes in solution reported attempts to examine stereoselective effects [5]. In that study titration curves for solutions containing optical isomers of both histidine and threonine in the presence of Cu(II) were superimposable, regardless of the combination of optical isomers present, hence thermodynamic effects due to stereoselectivity of coordination were absent from the system. The present work extends the study of these possible effects to combinations of the six potentially tridentate amino acid listed earlier. If stereoselectivity of coordination were present in any of the combinations studied, the titration curves for sets of solutions containing one enantiomer of A (or B) and either enantiomer of B (or A) would not be superimposable. If, however, stereoselectivity were not present for a given pair of amino acids, the titration curves for all solutions containing enantiomers of both amino acids would be superimposable. Since histidine had previously been shown to display stereoselectivity of coordination with itself, it was titrated with enantiomers of each of the other five amino acids. Other combinations examined were: aspartic acid with lysine and methionine; and lysine with glutamic acid and methionine. In all cases examined, the titration curves for all combinations of enantiomers of a given pair of amino acids were superimposable within experimental error, indicating a complete lack of thermodynamic effects due to stereoselectivity of coordination. Hence, from Fig. 6, F7 = K8 = K9 = g l 0 , K17 = K18 = Kaa = K~0 and t~LALB =/3OAOB= flL.4OB= flO.4L8for all combinations of amino acids studied. (b) Selectivity of coordination in ternary complexes. Since the four possible stability constants for the mixed complexes have been shown to be equal, it is now possible to discuss the selectivity of coordination simply in terms of the amino acids A and B, rather than in terms of their enantiomers. It is possible to arrive at the value for flMABthrough a trial-and-error procedure whereby known values for the stability constants for the species MA, MB, MA2 and MB2 are combined with estimated values for/3Man in order to calculate a titration curve. When the correct value for /3MABis attained, the calculated and experimental titration curves will match. Figure 7 shows an example of the curves calculated with four different values of fluaB, along with the experimentally obtained curve. When the value for fluAn has been obtained, it is then possible to calculate the composition of the solution at any given pH, and to note the change in percentage composition as the pH of the solution changes. Table 3 shows the percentage composition of a solution containing aspartic acid, histidine, and nickel(II) at pH's 4-9. It can be clearly seen that at pH values where appreciable amounts of each amino acid are coordinated to the metal ion, the mixed complex greatly predominates in solution. Values for flMABwere calculated in this manner for each of the combinations of amino acids studied. Using these /3's, and the known values for 131 and fie (from Eqn (6 a, b)), it is possible to calculate the equilibrium constants for the reaction of B with MA and A with MB to form the mixed complexes (Kle and K21 of Eqn (8)). In addition, using the calculated fluaB values with the previously determined/3MA, and flus, values, the disproportionation constant
The metal complex catalyzed hydrolysis of amino acid e s t e r s - III
1617
9,00
8,00
T 7'00
6"00
5.00
:-
t
I
3"0
3-5
4"0
Equivolenfs of base Fig. 7. Calculated and observed titration curves for the 1:1:1 nickel(ll)-histidineaspartic acid system: (a),/3UAB = 6"0 × 1013; (b), /3Man = 9"0 X 1013; (C), BMA~= 4"0 × 1014; (d),/3MAn = 6"0 × 1014. Circles show experimental points.
Kai~ can be calculated from Eqn (16). Table 4 lists the calculated values for [~MAB, K12, K21 Kd~s for the amino acid combinations studied and literature values for similar systems. As previously mentioned, deviations of Ka~s from 0.25 indicate selectivity of coordination; if Ka~ > 0.25, preference for the formation of mixed complexes is indicated, and if Ka~ < 0.25, preference for the binary complexes is indicated. As Table 4 shows, marked selectivity of coordination was observed in every case, with the mixed complex preferred each time over the binary complexes. DISCUSSION
We have dealt primarily with complexes of the type MA B, where A and B are the acidate anions of the different amino acids. In actual practice, a great many more complexes are present in solution varying concentrations, with different complexes being the predominant species at different pH's of the solution. In certain low pH ranges, mono complexes of the type MA or MB would be expected to predominate, with minor contributions from the protonated complexes MHA, MHB, MHAB, and from the previously mentioned bis complexes. At still lower pH's, complexes involving the anion of the amino acid would be expected to be unimportant, and the only complexes (other than the aquated metal ion) of any important would be the weakly bound protonated complexes. In the intermediate pH ranges, bis complexes of the type MA., and MB2 would be expected to predominate, and at very high pH's, the hydroxy complexes MA(OH), MB(OH), M(OH) and M(OH)2 might be expected to be important contributors to the solu-
1618
J. R. B L A C K B U R N and M. M. J O N E S
Table 3. Percentage composition of a solution containing equimolar amounts (initially 8-00 × 10-3 F in each) of Ni(ll), histidine, and aspartic acid at various pH's ( / = 1.0) pH
M
4"00 4"50 5"00 5"50 6"00 6"50 7"00 7"50 8"00 8"50 9"00
85"6 51"1 18'6 6"2 2"4 0"9 0"3
A
B
M(OH)
0"1 0"4 I'1 3"4
M(OH)2
HA
H~A
HB
0"2 1'0 2"9 5"3 6"9 7"8 8"7
0'8 1"7 2'2 1'3 1"0 0"5 0"3 0"2 0"2 0'2 0"2
91'5 63"1 26"8 6'8 1"2 0"2
62'1 71"8 68"9 58'1 43"5 30"3 21 '5 16"4 15"9 15"0 14"0
pH
MA
MA~
MB
4.00 4-50 5.00 5"50 6.00 6.50 7.00 7"50 8.00 8'50 9"00
7-5 3 I" 1 48"1 40"8 27-5 16-6 8"7 3"7 1-3 0"5 0.2
0"9 5"9 12"8 15-1 14.8 14"0 13'8 13"6 13-8 14.1
6.6 14"4 15-9 14.2 13" 1 10.6 6.9 3.3 1"2 0-4 0.1
MB,2
0"3 0.8 1-6 2.9 4-3 5"3 5"7 5"8 5"6
MB 3
H2B 31'1 11"4 3"5 0"9 0"2
MAB 0-2 2"4 11-I 25" 1 40.1 53"3 62.9 68"6 71"3 71-9 71 "5
tion composition. Thus, it is necessary to obtain a reasonable estimate of the concentrations of the various species discussed above in the pH ranges used in the present study in order to accurately assess the importance of each to the overall solution composition. H. C. Freeman and R.-P. Martin have laid a foundation for this type of work with their study on the copper-histidine-threonine system[5]. This study has greatly simplified the interpretation of titration data by dearly demonstrating the pH ranges in which the various possible complexes contribute materially to the experimental data. In a rigorous analysis of calculated and observed titration curves, they have considered the following complexes (A=histidinate, B~threoninate, M~Cu(II)): M, MHA, MA, MH_IA, MH~A2, MA2, MB, MB2, MH-1B2, MHAB, MAB and MH_IAB. The MAB complex was shown to greatly predominate the pH's above 4 and below 10. In the pH range of greatest interest in the present study (6-8.5) only the bis complexes of the acidate anion, MA2, MBz and MAB, contribute to the experimental data. Stereoselective effects in the stability constants for amino acid-transition metal complexes have previously been found to be absent in all studies involving only bidentate a-amino acids, and in the case of aspartic acid and glutamic acid, but are found to be present in the case ofhistidine. These effects have been confirmed in the present study, and the study extended in include other potentially tridentate
The metal complex catalyzed hydrolysis of amino acid esters- 1 II
1619
Table 4. Stability constants for ternary amino acid complexes with Ni(II) A
Histidine Histidine Histidine Histidine Histidine Aspartic acid Aspartic acid Lysine Lysine Histidine Histidine Glycine Glycine Alanine
B
Aspanic acid Glutamic acid Methionine Tryptophan Lysine Lysine Methionine Glutamic acid Methionine Methyl histidinate Threonine Alanine Tyrosine Tyrosine
Log/3uaB
Log Klz
Log K21
Kai~
14.60
6.24
7-79
0.0153
13.78 13.40 13.20 10.00
5-42 5.04 4.84 1.64
7.49 7.99 7.73 4.53
0.0975 0.0769 0.0250 0.0258
*
*
*
*
11.95
5-14
6-54
0.0176
* 10.00
* 4-53
* 4-59
* 0.0646
13"40t 17.52, 15.60§ 15.55 § 15.84§
5'90t 7.30*
7-38t 9.56
0.051* 0.0178, 0.141 § 0-105 § 0.0251 §
* C u r v e fit not possible. fRef. [8]. *Ref. [5], M = Cu(ll). §Ref. [3], M = Cu(II).
amino acids. Titrations and calculations were performed on solutions of histidine, glutamic acid, tryptophan, methionine, and lysine, all with nickel(II) present. The only case in which stereoselectivity was observed was in the case of histidine. For all other amino acids studied, flobs=/32+ and 3+_ = 2/32+. In the case of histidine, as seen in Table 2, however, 3+_ # 232+. When the solution contained nickel(II) and enantiomers of two different amino acids, no stereoselective effects on the stability constants were found with any combination of amino acids. This is particularly striking when compared with the rate data presented earlier [2] that showed marked kinetic stereoselectivity with combinations of tryptophane and histidine methyl ester on the nickel(II) center. Similar effects were indicated in the first paper [ 1] when the kinetic stereoselectivity observed with combinations of histidine and histidine methylester was reported, but titration curves of the non-mirror image systems containing one equivalent each of nickel(II), the amino acid and the ester were superimposable. Titration curves with the ester present are subject to some uncertainty, due to the hydrolysis of the ester, but comparisions of the rate and thermodynamic data with the tryptophan-methyl histidinate solution indicate strongly that the appearance of thermodynamic stereoselective effects is n o t an indication that kinetic stereoselective effects will be seen, and vice versa; rather, the data points strongly to the conclusion that the kinetic and thermodynamic stereoselectivity arise from different sources. Since the ease with which the esters hydrolyze prevents their being studied
1620
J.R.
B L A C K B U R N and M. M. J O N E S
potentiometrically, and the mixed complexes with the esters have not been isolated for solid state study, the most appropriate method for studying the kinetic stereoselective effects seems to be the systematic variation of the catalyst used in Paper II in this series [2], and further variation of the ester itself to examine other amino acid esters in addition to histidine methylester under the same conditions. The validity of this method is clearly indicated by Table 4, when it can be seen that in all cases involving ternary systems that have been reported, the mixed complexes are found preferentially in solution (the Kdis for the dissociation31 of the MAB complex into M.42 and MB2 is in all cases a factor of 5-25 smaller than the statistical value), so the MAB-type complex can be assumed to greatly predominate in solution, and thus the characteristics of the system will be the characteristics of the mixed complexes themselves.