J. Phys. Chem. 1981, 85,3533-3540
3533
Phase Equilibrium Behavior of Certain Pairs of Amino Acids in Aqueous Solution Charles E. Messer,” Gary Malakoff, James Well, and Sherif Lablb Department of Chemistry, Tufts lJnlvers@, Medford, Massachusetts 02155 (Received: December 3 1, 1979; In Final Form: July 15, 1981)
The solubilities in water of the amino acids L-phenylalanine,L-methionine,L-leucine,L-norleucine, L-isoleucine, and Laspartic acid have been measured singly and in the pairs L-phenylalanine-L-leucine,L-methionine-cleucine, L-methionine-L-norleucine, L-methionine-L-isoleucine,L-leucine-L-isoleucine, and L-aspartic acid-L-leucine, as functions of temperature over various ranges between 20 and 140 O C . The method was a synthetic one, based on the temperature of disappearance of last crystals on slow heating of mixtures of known composition. The results show certain discrepancies with literature values for single amino acids, but give consistent information on the phase equilibrium nature of the pairs. The phenylalanine-leucine system shows quasieutectic behavior. The system aspartic acid-leucine shows evidence of complex formation. The other four systems, involving components of highly similar crystal as well as molecular structures, give evidence of extensive solid solution formation. The methionine systems show a singularity attributed to a known crystalline transition in Lmethionine. The leucine-isoleucine system shows evidence of an intermediate phase which either might be a complex or might be based on a second crystalline form of L-leucine or L-isoleucine. A limited thermodynamic treatment based on departures from ideal aqueous and solid solution behavior is presented. The results are discussed in terms of this treatment and in terms of models of interaction energies based on hydrophobic bonding energies and other treatments.
Introduction The direct determination of binary phase equilibrium by thermal analysis as a means of studying interactions between amino acids is not possible because of their decomposition on melting. Hence solubility determinations of mixtures in water must be used. Rather than the more customary analytical procedure, a synthetic method was chosen, based upon the techniques of heating sealed mixtures of known composition, with agitation by end-over-end tumbling, to the observed temperature of disappearance of the last crystals. This technique, first carried out by Benrath and co-workers’ in ampoules of about 3-mm diameter, was later developed by McLaughlin and co-workers2on a larger scale. The method is limited in the sense that it directly gives “liquidus” compositionsonly and does not give isothermal sets of data. It does seem to furnish the simplest way to ascertain the essential features of a binary amino acid system. It avoids sampling difficulties due to evaporation a t higher temperatures; it in fact enables measurements to be carried out above 100 “C on the aqueous solutions. A system could also readily be studied as a function of pH or salt concentration. The method is suitable for scarce substances, and it could readily be extended to at least the shorter peptides. Where the solubilities of the two individual amino acids are not very different, as is the case in the systems in this research, the total molal concentration of amino acid may be kept fixed, so that the system becomes pseudo-binary. The liquidus or mixed solubility curves then strongly resemble the usual binary solid-liquid phase equilibrium curves. The properties of the amino acids in aqueous solution, rather than in the liquid state, contribute to this type of phase diagram. The systems here investigated were the nonpolar pairs methionine-leucine, methionine-isoleucine, methionine(1)A. Benrath, F.Gjedebo, B. Schiffers, and H. Wunderlich, 2.Anorg. Chern., 231, 285 (1937). (2)E. McLaughlin and H. A. Zainal, J. Chern. Soc., 863 (1959);2485, 3854 (1960);E. McLaughlin and C. E. Messer, ibid., 1106 (1966).
norleucine, leucine-isoleucine, and phenylalanine-leucine, as well as the polar-nonpolar pair aspartic acid-leucine. Only the L isomers were used. The crystal structures of all except phenylalanine and aspartic acid are very similar, as shown in Table I. The special similarity between methionine and leucine was brought out by the early recognition of several workers3-’ that commercial L-leucine contained significant quantities of methionine as an impurity. Su and Shafer? incidental to a study of specific amino acid interactions by means of pairwise solubilities, found that several pairs of nonpolar amino acids formed “mixed solid phases of low solubility”, including isoleucine-leucine, leucine-methionine, isoleucine-methionine, and phenylalanine-methionine. They did not give quantitative data or classify these phases as solid solutions or solid compounds. Experimental Section Materials. The L-phenylalanine and L-aspartic acid were obtained from J. T. Baker Chemical Co. The L-leucine, L-isoleucine, and L-norleucine were obtained from the Aldrich Chemical Co., with a stated purity of 99%. These amino acids were analyzed in a Beckman amino acid analyzer, Model 119 CL, with a standard acid hydrolysis program. The concentration of each sample was 100 nmol mL-l. Norleucine was used as an internal standard. The samples were run through the cation-exchange column in citrate buffer at sequential pH values of 3.25,3.97, and 6.40, all components except aspartic acid coming through at pH 3.97. Detection was optical, following ninhydrin injection. (3)J. H.Mueller, Science, 81, 50 (1935). (4)S. W. Fox, Science, 84,163 (1936). (5)H.D. Baernstein, J. Biol. Chern., 115,25 (1936). (6)A. L. Demain, J. Bacteriol., 89, 1162 (1965). (7)M. S. Dunn and M. P. Stoddard, unpublished data; I. Hlynka, Thesis, California Institute of Technology, 1939;cited in R.C. Weast, Ed., “Handbook of Chemistry and Physics”, 53rd ed, Chemical Rubber Publishing Co., Cleveland, OH, 1972-3, p C-743. (8)S. K. C. Su and J. A. Shafer, J. Am. Chem. Soc., 90, 3861 (1968).
0022-365418112085-3533$01.25/0 0 1981 American Chemical Society
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The Journal of Physical Chemistry, Vol. 85,No. 23, 1981
Messer et al.
TABLE I: Crystal Structures of Amino Acids amino acid
space group
bo, a
a,, 2%
eo, 2%
P , deg
z
ref
L-phenylalanine P2 13.13 6.59 10.28 104.63 4 a L-leucine p21 9.618 5.318 14.728 86.2 4 b 9.75 5.32 14.12 95.8 4 c L -isoleucine p21 L -isoleucine P222, 13.896 20.175 5.539 8 d L -norleucine c2 9.550 5.260 15.377 95.60 4 e L -valine p21 9.71 5.27 12.06 90.8 4 f L -methionine p21 9.498 5.189 15.318 97.69 4 e L -methionine p21 15.49 3.84 14.11 103.9 4 a WDL -methionine P 2 1 la 9.76 4.70 16.70 102 4 g W D L -methionine P 2 la 9.89 4.70 16.74 102.3 4 h aspartic acid p2I 7.617 6.982 5.142 99.84 2 i a V. Khawas, A c t a Crystallogr., Sect. B, 26, 1919 (1970). M. M. Harding and R. Howieson, ibid., 32, 633 (1976). K. Torii and Y. Iitaka, ibid., 27, 2237 (1971). V. Khawas, ibid., 26, 1 3 8 5 (1970). e K. Torii and Y. Iitaka, ibid., 29, 2799 (1973). f K. Torii and Y. Iitaka, ibid., 26, 1317 (1970). g A. McL. Mathieson, A c t a Crystallogr., 5, 332 (1952). T. Taniguchi, Y. Takaki, and K. Sakurai, Bull. Chem. SOC.Jpn., 53, 803 (1980). J. Derissen, H. J. Endemann, and A. F. Peerdeman, A c t a Crystallogr., Sect. B , 24, 1349 (1968).
*
Several minor chromatographic peaks were present in each sample, of the order of 1% or less of the corresponding principal peaks in area and height. All were present in both blank and laboratory norleucine standard as well, and were equal to or less than the corresponding peaks in both blank and standard, in all cases. The L-methionine was Aldrich Chemical Co., 98+%. Measurements of optical rotation of this sample were made on a Rudolph Model 62 polarimeter. The results and literature comparisons are as follows: [.]25D = +24.2", 8 g/100 mL in 6 N HC1 (this research); [ci]25D = +24.3", 8 g/100 mL in 6 N HC1 (manufacturer); [.I2'D = +24.2", 4 g/100 mL in 6 N HCl (K. Hayashi et al., Agr. Biol. Chem. (Tokyo), 30, 1221-32 (1966); Chem. Abstr., 66, 61887 (1967)); [ciI2OD = +24.0°, 10 g/100 mL, 6.3 N HC1 (K. Vogler and F. Hunziger, Helu. Chim. Acta, 30, 2013-18 (1947)). All samples were dried in a desiccator over anhydrous calcium sulfate at room temperature for at least 1 week before use, and stored in the desiccator. All solids remained white, and all aqueous solution samples remained colorless and clear after they were run. Temperature Measurements. All measurements were made with an ordinary laboratory thermometer, 0-260 "C X 1 "C. This thermometer was calibrated against the ice point and the melting points of naphthalene (80 "C), benzoic acid (122 "C), and anthracene (218 "C). The last three were run in the apparatus of this research and following the usual procedure at a heating rate of the order of 0.1 "C/min. No corrections were larger than 1 "C. Preparation of Samples. Sample size was adjusted to contain about 1 g of H20. The samples were sealed into Pyrex ampules of 9-mm tubing, 6-7 cm long. The desired amount(s) of amino acid(s) was weighed to f0.1 mg, and the water added by syringe and weighed to &lmg, before sealing off at -78 "C. Apparatus. Two ampules were mounted on a rotor which enabled them to be rotated in a vertical plane at 2 revolutions per minute, using a chain and pulley operated by an external motor. The rotor was immersed in a 1.5-L beaker, filled with cottonseed oil, and resting on a hot plate provided with a magnetic stirrer. The thermometer was mounted so that the bulb was at the same level as the rotor axis, as close to the rotor as possible and midway between the ampules. A small auxiliary heater, adjustable by a variable transformer, was provided in the bath, to enable better control of the final heating rate. Procedure. The apparatus was rapidly heated (1-2 "C mi&) until the amount of remaining crystals was relatively small. The heating rate was then reduced to about 0.25 "C min-l until solution was complete. The temperature
of disappearance of the last crystal(s) was usually definite to f l "C. If the last crystal dissolved a t a temperature 3 "C or more higher than the next-to-last, the run was repeated. Every sample was repeated until the solution temperature was definite to &l"C, or until the average deviation could not be reduced by further runs. Reproducibility was always to f 2 "C except where stated. Often but not always the first run of a sample was abnormally high and could be rejected presumably because the initial sample crystals were large or otherwise atypical. In some cases, the samples on cooling did not form crystals at room temperature or formed only large crystals. Such samples had to be seeded by plunging into ice water to produce the desired small crystals. Samples containing only one amino acid were particularly prone to cause seeding problems; those containing two amino acids gave finer crystals and also results of higher precision. Some aspartic acid-leucine mixtures had to be seeded by chilling to -78 "C. The method was very sensitive to any lack of scrupulous cleanliness of the glass ampule surface, such areas encouraging both the sticking of crystals to glass and the formation of large crystals. The phenylalanine was especially prone to show this type of behavior; aspartic acid and methionine showed it least. The phenomenon is presumably related to the highly hydrophobic nature of the particular amino acid side chains.
Results Solubilities of Single Amino Acids (Binary Systems). Table I1 shows the results of this research on the solubility temperatures of the individual amino acids other than methionine, in water, at those concentrations which were used in the two-amino-acidsystems. These are compared with the literature values of Dalton and Schmidt9 and others. Figure 1shows the results for L-leucine in the form of comparative solubility curves. Also included are values derived from the "phase diagrams" of the two-amino-acid systems, Figures 3-8, by extrapolation to the pure components. Additional measurements on single amino acids at other concentrations, all consistent with those of this research herein reported, are not shown. In all cases the solubility temperatures of this research obtained from individual amino acid measurements are higher than those from Dalton and Schmidt. Temperatures derived by extrapolation from the two-amino-acid systems agree more closely with Dalton and Schmidt. Above 110 "C, as shown in Table 11, solubility tempera(9)(a) J. B. Dalton and C. L. A. Schmidt, J. Biol. Chem., 103, 549 (1933); (b) ibid., 109,241 (1935).
The Journal of Physical Chemistty, Vol. 85, No. 23, 198 1 3535
Amino Acid Palrs in Solution
TABLE 11: Solubility Temperatures of Single Amino Acids ( t . '(2) ternary concn, mol kg-' of amino acid H,O L-phenylalanine L -leucine
L-isoleucine
binary this res
0.5
98
0.3 0.4
92 117
0.5 0.6 0.4
124 129 84
lit. 8ga
this res, other excomtrapo- polated nent 89
Leu
88 118 109 123 129 62 70 140d 88
Asp Met Ile Phe Met Leu Met Met Leu
O
E
o
r
070-
060-
m 0 50
77b1c 9SbsC
61a 97 i 7e
L-norleucine 0.4 140d L-aspartic 0.3 99 84b acid 87f a Reference 9b. Reference 9a. Hlynka, ref 7, reports results on methionine-free leucine which gave temperatures 10-12 "C higher than those of Dalton and Schmidt over the range 25-50 "C. Some runs gave values of 154 "C. See Figure 5. e Hade-Hutchens, ref 10. f J. W. Bressler, 2.Phys., 47, 611 (1904); from H. Stephen and C. Stephen, Ed., "Solubilities of Inorganic and Organic Compounds", Vol. 1, MacMillan, New York, 1963, Part 1, p 1188.
t" c Flgure 1. Solubility of L-leucine in water: (0)this research; (0) Hlynka, ref 7; (0)Dalton and Schmidt, ref 9b.
tures from the binary and ternary systems agree within 1 "C. It might be expected that the possible slow approach to equilibrium from a lower temperature in the method of this research would lead to high solubility temperatures. On the other hand, any effects of evaporation or incomplete filtration in the analytical method of Dalton and Schmidtgbat the higher temperatures might lead to high solubilities, hence to low solubility temperatures. The much smaller crystal size noted in the two-aminoacid systems, as compared with the single amino acid system, would favor better equilibrium. The additional tendency of the crystals to stick to glass caused even larger discrepancies with phenylalanine, both alone and with leucine. As shown in Figure 1, the results of this research on L-leucine are in qualitative agreement with those of
0 30
0 20
1
30
40
I 50
I
I
I
60
70
80
toc Flgure 2. Solubility of methionine in water: (0) this research, L isomer: (0)Dalton and Schmidt, ref 9, DL form: (0)Hade-Hutchens, ref 10, L form.
Hlynka,8 whose solubility values from a methionine-free sample were also considerably below those of Dalton and Schmidt. The values of Hlynka join consistently those of this research. For L-isoleucine, the results of Hade as reported by Hutchens,lo extrapolated well beyond the experimental range of 10-40 "C, indicate solubilities below those of this research as well as far below those of Dalton and Schmidt. The method of Hade is not stated. In ref 10, the results of Hade are indicated as agreeing with those of Dalton and Schmidt for L- and DL-alanine and for L-valine. The results on the solubility of pure L-methionine in water are shown in Figure 2. They show fair to good consistency at and above 0.5 m. However, for 0.4 m a total of 17 determinations were made on two samples, with results varying from 32 to 53 "C, and a mean of 41 f 6 "C. While there were several sequences of two and one sequence of four successive agreeing values, there seems to be no systematic direct interpretation of the sequential behavior. L-Methionine is known to undergo a crystalline transition of a gradual nature which is probably relevant to this behavior. Hutchens, Cole, and Stoutll have shown from heat capacity measurements that the transition is first detectable at ca. -93 "C, reaches its peak of heat capacity at 32 "C, and does not fully end until ca. 77 "C. If this is a relatively sluggish cooperative transition, the proportions of the two forms present, and hence the solubility, might vary from run to run, depending on the thermal treatment of the samples between runs, which was not controlled. For all three of the methionine ternary systems (Figures 4-6), the results of 0.4 m samples of mole fraction methionine 0.8 or lower extrapolate to about 50 "C for pure methionine. The results for higher mole fractions methionine extrapolate to about 40 "C. The results of HadelO at 20,30, and 40 "C are also shown in Figure 2. His solubilities are higher than those of this research, his solubility temperature at 0.4 m being about (10) Hade, Thesis, University of Chicago, 1962; from J. 0. Hutchens
in "Handbook of Biochemistry and Molecular Biology", Vol. 7, 3rd ed,
G. D. Fasman, Ed., Chemical Rubber Publishing Co., Cleveland, OH,
1976. (11) J. 0.Hutchens, A. G. Cole, and J. W. Stout, J. Biol. Chem., 239, 591 (1964).
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The Journal of Physical Chemistry, Vol. 85, No. 23, 198 1 I
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Messer et ai.
I
120 -
110-
100
-
t" c
boLf
1
40 1
0
1
I
PO
I
40
I
I 60
Phe
Mole %
I
I 80
I
Leucine
Figure 3. Solubility temperature t, (Oc) vs. mole fraction L-leucine for H20-0.5 m (L-leucine L-phenylalanine); (-) experimental, (- -) "ideal" assuming eutectic and no solid solutions.
+
1
1
--
29 "C. Hade's 40 "C result shows no evidence of the transition. A possible interpretation of these results is that the solubility temperature of the high temperature form of methionine is about 50 "C, that of i h e low temperature form is 29-32 "C, and that of the equilibrium mixture is about 40 "C. The results of Dalton and Schmidt on DL-methionine are also shown in Figure 2. They agree surprisingly closely with those of the L isomer of this research. It is to be noted that the crystal structure of a-DL-methionineis very similar to that of L-methionine (see Table I), while the crystal structures of DL-leucine and DL-iSOleUCine,both triclinic, are quite different from those of the L isomers.12 The solubilities of DL-leucine are considerablylower than those of the L formag DL-Methionine exists in a 0form as well as the CY (Table I, footnotes g and h), the unit cell of the former being double that of the latter in the c direction. Mathieson (footnote g) reports the forms as of almost equal stability, while Taniguchi, Takaki, and Sakurai (footnote h) refer to a reversible phase transition, 0 to a,at 53 "C. The solubility temperature of pure L-norleucine was determined as 140 f 2 "C at 0.4 m. Thre was one anomalous value of 154 "C; evidence for additional anomalously high values was also found at high norleucine contents in the system L-methionine-L-norleucine(Figure 5). Numerous references to discrepancies between various sets of solubility values of the same amino acid from different workers appear in the literature. Dalton and Schmidtg attribute most of the earlier ones to impurities, especially for the L forms. Nozaki13attributes several solubility discrepancies to the existence of more than one crystal form. Dalton and Schmidt14report separate solubility curves for two forms of L-valine, Sakata15for two forms of L-glutamic acid, and Abraham et a1.16for two forms of DL-a-aminobutyric acid. Sakata17 further reports that the presence of a second (12) B. Dawson and A. McL. Mathieson, Acta. Crystallogr., 4, 475 (1951). (13) Y. Nozaki, Methods Enzymol., 27, 491 (1973). (14) J. B. Dalton and C. L. A. Schmidt, J.Gen. Physiol., 19,767 (1936). (15) Y. Sakata, Agr. Biol.Chem., 25, 835 (1961). (16) M. H. Abraham, E. Ah-Sing, R. E. Marks, R. A. Schulz, and B. C. Stace, J. Chem. SOC.,Faraday Trans. 1, 73, 181 (1977). (17) Y. Sakata, Agr. Biol. Chem., 25, 829 (1961).
I
0 Met
IO0 Leu
I
I
I
I
I
40
20
I
I
Mole
%
I
1
100 Leu
BO
60
Leucine
+
Figure 4. t, (OC) vs. mole fraction L-leucine for H,O-(L-methlonlne L-leucine): (0)0.4 m in total amino acid; (0)0.6 m In total amino acM.
I
1
0 Met
I
I
I 20
I
I
I
I
I
40
Mole
%
I
I
1
I
I
I
I
1
80
60
I
100 Nle
Norleucine
Figure 5. t, (OC)vs. mole fraction L-norleucine for H2O-0.4 m (Lmethionine L-norleucine): (0)sample set 1; (0)sample set 2; (0) anomalous points.
+
I
l
l
I
I
I
I
(
t oc
20
40
60
80
100
Ile
Met
Mole
Yo
Isoleucine
Figure 6. t, ("C) vs. mole fraction L-Isoleucine for H20-0.4 m (Lmethionine iL-isoleucine): (0)sample set 1; (0)sample set 2.
solute can determine whether the a or form of glutamic acid will crystallize in a given case. Hirayama et a1.18 describe the conformations in the structures of a-and 0-glutamic acid in detail, and propose a mechanism for the a to 0 transformation in solution ~~
(18) N. Hirayama, Bull. Chem. SOC.Jpn., 53, 30 (1980).
The Journal of Physical Chemistry, Vol. 85, No. 23, 198 1 3537
Amino Acid Pairs In Solution I
I
I
I
I
I
I
I
I
It is possible that the transitions a t 0.4 m for methionine-leucine and methioninenorleucine are discontinuous, with a miscibility gap between two series of solid solutions, and a pseudo-peritectic type of phase diagram. At 0.6 m, the methionine-leucine system is more likely to be continuous, or, a t least, the miscibility gap is smaller. In the methionine-isoleucine system, Figure 6, the transition behavior was discontinuous. Two sets of samples were run. In. the first set, the transition appeared only a t 20% isoleucine, with one solubility temperature or the other appearing in any given run. In the second set only the lower temperatures appeared, even up to 80% isoleucine. Solid solution formation much closer to ideal than in the other methionine systems is indicated here a t all compositions. The isoleucine-leucine system, Figure 7, is characterized by nearly composition-independent solubility temperature behavior over the range from 20 to 50% leucine. Solid solubility of leucine in isoleucine up to 20% is definite; the extent of solid solubility of isoleucine in leucine is less certain, and could be quite small. It is not possible to judge whether the middle portion has gradual or sharp boundaries with the end portions. If the boundaries are gradual, there would be only one solid solution phase, with possible separation into two solid phases a t some temperature below 76 "C. If the boundaries are sharp, there must be a third solid phase capable of coexisting at equilibrium with the liquid solution from 20 to 50% isoleucine. This could be a complex, or it could be a series of solid solutions based on an alternate crystal form of L-leucine or L-isoleucine. Khawas (footnote d , Table I) has reported a structure of L-isoleucine different from the more general B1of Table I. Hade and Hutchenslo report a set of solubility values, from 10 to 40 "C, lower than those of either Dalton and Schmidt or of this research. Hutchens, Cole, and Stoutlg have measured the heat capacities of L-leucine and L-isoleucine up to 33 "C, with no evidence of any transition. The L-aspartic acid-L-leucine system is shown in Figure 8. The behavior would be pseudo-eutectic except for the anomalous points at 60 and 65 mol % leucine. The 65 mol % leucine point was verified on a second, independent sample. The solubility temperatures of these samples were about 10 and 5 "C, respectively, above values extrapolated from the two principal branches of the phase diagram; the uncertainties in the solubility temperatures were about f 2 "C. The solid phase obtained from cooling solutions of 5-55 mol % leucine settled very slowly, and on agitation appeared turbid rather than crystalline or microcrystalline. As the turbidity decreased on warming, it was seen that there were particles, although these were very fine. The final clearing temperature of each sample was clearly defined to f l "C, as shown in the aspartic acid branch of Figure 8. At and beyond 60 mol % leucine the solid phases were definitely crystalline. Dalton and Schmidtgbrefer to the early reference of Bayliss,maccording to which the presence of 1.25% leucine increased the solubility of aspartic acid 30-fold over that in water alone. No evidence for behavior of this sort was found in this research. Conceivably, Bayliss may not have considered the turbidity as jnsolubility. The behavior of the 60,65, and 70% samples is represented on the phase diagram as a horizontal liquidus a t 59 "C from 52 to 70% leucine. It might also be represented
6o 20
110
60
40
80
Leu
Mole % Leucine
Figure 7. fs ("C)vs. mole fraction L-ieucine for H,O-0.4 m (L-isoleucine L-leucine).
+
loo
1 1
500Ld 20
40
60
ASP
80
IO0
Leu
Mole
%
Leucine
Figure 8. t, ("C)vs. mole fraction L-leucine for H20-0.3 m(L-aspartic acid L-leuclne): (-) expermental; (----) "ideal" assuming no s o l i solutions.
+
involving three intermediate conformations. Abraham et al.16discuss the change of conformation in a-aminobutyric acid. These results suggest that metastability of a solution conformation may be possible, as well as metastability of a crystal structure. Pseudobinary (Ternary) Systems. The "phase diagrams" for the several systems are shown in Figures 3-8. The system methionine-leucine was run at both 0.4 and 0.6 m. The system phenylalanine-leucine was run at 0.5 m. The system aspartic acid-leucine was run at 0.3 m. All other systems were run a t 0.4 m. The phenylalanine-leucine system shows quasi-eutectic behavior, the kind normally expected where the crystal structures differ enough to preclude solid solutions. The large uncertainty in the solubility temperatures, found for pure phenylalanine, was also found in the mixtures of high phenylalanine content, as shown by the brackets in Figure 3. The systems methionine-leucine and methionine-norleucine, Figures 4 and 5, both show a "transition region" between 10 and 20% leucine or norleucine. The transition region is more gradual for the leucine system at 0.6 m, a t higher temperatures. This behavior is attributed to the previously discussed gradual transition in L-rnethionine.l1 The increases in temperature on adding leucine, norleucine, or isoleucine to methionine, and on adding leucine to isoleucine, in Figures 4-7, are indicative of solid solution formation. The low slopes at the opposite ends of Figures 4-7 are favorable to solid solution formation.
(19) J. 0.Hutchens, A. G. Cole, and J. W. Stout, J. Phys. Chem., 67, 1128 (1963). (20) W. M. Bayliss, J. Physiol., 36, 221 (1907).
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The Journal of Physical Chemistty, Vol. 85, No. 23, 1981
as a straight line running from (56 “C, 55%) to (61 “C, 75%). This behavior is best interpreted as indicating the presence of a crystalline complex. Solid 1:l complexes have been reported by Nishijo21for malonic acid and for glutaric and maleic acids with several DL nonpolar amino acids, and 2:l complexes for succinic acid. Bhat and Vijayan22 crystallized and determined the crystal structure of the hydrate L-histidine-L-aspartic acid.H20. Angelescu and Nicolau= prepared a 3:l tyrosine-glycine compound, which they have described as clathrate in nature. Some of the “low solubility mixed phases” of Su and Shafer8were also in systems where solid solutions are unlikely. The stoichiometry of the leucine-aspartic acid complex cannot be ascertained from the phase diagram. Since the “flat” portion includes the 66.6% leucine composition, 2:l Leu-Asp is favored over 1:l. If the liquidus were sloped from 55 to 70%, 3:l Leu-Asp would also be possible. Nishijo21 proposes that these complexes are based on carboxyl-to-carboxyl association. Such a complex could form in 2:l ratio since aspartic acid has two carboxyl groups. However, Bhat and Vijayan22find for 1:l histidine-aspartic acid a structure of alternating histidine and aspartic acid layers joined by hydrogen bonds. Such a structure, perhaps with charge transfer or van der Waals forces between layers contributing as well, would allow more favorable interaction of the polar carboxyl groups with the water.
Discussion Quantitative Interpretation. Quasi-binary phase equilibrium obtained by the methods of this research may be interpreted thermodynamically in ways analogous to those of standard solid-liquid phase diagrams. The lack of direct information on solid phase composition limits the scope of the information obtainable, especially when the solid phase is a solid solution. Two sets of conditions are amenable to thermodynamic analysis: (1)when the solid phase is a pure single amino acid; (2) when the solid phase is a solid solution, and it may be assumed that the aqueous phase is an ideal solution. An ideal solution would be here defined as one in which the interactions of the two amino acids with water would be highly similar, so that the enthalpy of mixing would be zero. In case (1) it may be shown by a method closely analogous to that used for ordinary binary solid-liquid equilibria that for any solute in a nonideal solution a = mo = y m where mo is the solubility of that component at the same temperature in the absence of the second solute component, and m is the solubility in the presence of the second component, from the quasi-binary phase diagram. The ratio mo/mmay be considered a form of activity coefficient y, m = moX, where X is mole fraction of first (major) solute component from the phase diagram, and mo is the constant total amino acid concentration used in that quasi-binary system. In case (2), if the aqueous solution of two amino acids is ideal as defined, it may be shown by analogy to the correspondingtreatment for binary solid-liquid equilibria, ~
~~
(21) J. Nishijo, Nippon Kaguku Kuishi, 224 (1975); Chern. Abstr., 82, 154952 (1975); J. Nishijo, Nippon Kaguku Kaishi, 1249 (1975); Chern. Abstr., 83, 114855 (1975). (22) T. N. Bhat and M. Vijayan, Acta. Crystatlogr., Sect. B, 34,2556 (1975). (23) E. Angelescu and G. Nicolau, An. Uniu. “C. I. Purhon” Bucuresti, Ser. Stiint. Nut., 10, 73 (1961); Chern. Abstr., 59, 76416 (1961).
Messer et al.
that for the major component of the solid solution phase at equilibrium
ass = y,,X, = m / m o = m o X / m o ss stands for solid solution; other symbols are as previously defined. This relation defines a hypothetical ideal solidus. Qualitative conclusions might be made from the position of this “solidus” relative to the liquidus curve and to the mo curve. But quantitative treatment could not be made unless yss or X,,were known, so this treatment is not further pursued. The treatment of case (1) has been applied to the system phenylalanine-leucine and to the end portions of the system aspartic acid-leucine. Curves of movs. temperature have been compared with the experimental phase diagrams. The precision of the calculations is limited by the uncertainties in the solubilities of the single amino acids. However, the necessary process of adjustment of the values of m and mo to coincide at the phase diagram terminal point should make the error in the ratio mo/m much less than the separate errors in m and m,,. For reference mo values, the Dalton and Schmidt curves for phenylalaninegband aspartic acidgawere used. For leucine, the composite curve of this research plus Hlynka,’ Figure 1, was used. A correction is necessary for the difference between the movalues (column 3 or 4 of Table 11)and the extrapolated ternary values (column 5 of Table 11). For phenylalanine at 0.5 m this is zero; for leucine at 0.5 m it is 1 “C. Accordingly the leucine values are shifted downward by 1 “C. For aspartic acid-leucine, Table I1 shows a 4 “C discrepancy for aspartic acid, and an opposite 6 “C discrepancy for leucine. It was felt that a uniform shift of 1 / T (K) would be better than a uniform shift of t (“C), so the mo reference curves were adjusted by A(l/K) = -0.030 X K-l for aspartic acid, and 0.046 X K-l for leucine. On the phenylalanine side of the system phenylalanine-leucine, Figure 3, it is seen that m < m,, Le., the experimental curve deviates positively from the ideal, the added leucine decreasing the solubility of phenylalanine. On the leucine side, the deviation shifts from negative at high leucine contents to positive at lower leucine contens near the eutectic. Despite the agreement of the solubilities of leucine between binary and ternary results of this research, the very steep slope of the solubility curve of Figure 1 above 110 “C suggests a possible experimental error at these higher temperatures common to both binary and ternary measurements. The Dalton and Schmidt curve for leucine, terminating at 100 “C, could not have been used at temperatures as high as 126 “C. In the system aspartic acid-leucine, Figure 8, the deviation is negative on the aspartic acid side and positive on the leucine side, consistently. The solubility of leucine is probably more reliable at these lower temperatures. A possible explanation for the shift in behavior is that most of the minor component is tied up in the complex in solution, so that the deviation pattern characteristic of the excess component is exhibited. In the nonpolar systems of this research, the ionization constants of the two amino acids of each pair are about the same, and all mixtures are close to the isoelectric point. In the aspartic acid-leucine system, both pH and ionic strength vary with composition. Thus the nature of the interaction could change with composition continuously without the influence of complex formation. However, the discontinuous nature of the change in interaction pattern suggests that complex formation is the primary factor involved.
Amino Acid Pairs in Solution
From these limited results, it is indicated that a positive deviation is characteristic of nonpolar components and/or systems, and a negative deviation for the polar-ionic component case. Interaction Energy Models. The simplest models for deviations from ideal solution, like that of regular solution theory, depend upon a single parameter. This can be expressed as an interchange energy which is defined as the difference between the interaction energy of an unlike pair AB and the mean of the interaction energies of the like pairs A4 and BB. In a binary solution, this is derived most directly from the excess enthalpy as determined from measurements of enthalpies of mixing. For the mixing of dilute aqueous solutions, the enthalpy of mixing itself approaches zero as the concentration approaches zero. Hence the so-called pairwise enthalpy coefficients hAAand hm, in J kg moP, must be used instead. The actual excess enthalpy HEis equal to mhAB, in J mol-', where m is the molality. Such measurements have not been made for amino acids themselves, but Blackburn, Lilley, and W a l m ~ l e have y~~ measured enthalpies of dilution of the acetylamide derivatives of glycine, alanine, valine, and leucine. From these measurements, they have calculated the various pairwise coefficients. We may define and calculate a "disymmetry" parameter Amh = AB - l/z(hAA + ~ B B ) which would represent the interaction on mixing A and B in dilute solution. We find that for the valine-leucine but for alanine-valine A = pair A = -3 f 143 J kg molW2, -173 f 69 and for alanine-leucine A = -92 f 87. Blackburn, Lilley, and W a l m ~ l e yfound ~ ~ the individual parameters to be additive on the basis of group contributions to within 200 J kg mol-2, but the A values show that the small interaction between aliphatic amino acid pairs is likely to be negative, or attractive. The parent hydrocarbon molecules themselves are possible models for the interactions between the R groups of a pair of amino acids. Thus, the system toluene-isobutane would be a model for phenylalanine-leucine. This model would suffer the disadvantage that only the van der Waals contribution to the R group interactions are included, and no effects from the presence of water. It also cannot include any effect from the point of attachment of the R group, so for example could not distinguish between isoleucine and norleucine, where in both cases n-butane would be the parent hydrocarbon. However, results on certain pertinent systems are consistent with those found by other models. The excess enthalpy of mixing of benzene and n-hexane at mole , ~ ~values of this order of fraction 0.5 is +900 J m ~ l - land magnitude seem common to most aromatic-aliphatic pairs. This order of magnitude is not inconsistent with the results on phenylalanine-leucine presented in Table 111. The systems n-butane-isobutane, propane-isobutane, and propane-n-butane are said to show small negative deviations from Raoult's law,26and the system propane-isoThis agrees butane has also been said to be fully with the pattern of A values found for the acetylamino acid
derivative^.^^
A more direct model, although a more empirical one, would be based on the use of hydrophobic bonding energies (24) G. M. Blackburn, T. H. Lilley, and E. Walmsley, J.Chem. Soc., Faraday Trans. 1 , 76, 915 (1980). (25) H. V. Kehaian, Ber. Bunsenges. Phys. Chem., 81, 908 (1977). (26) S. Mitsuho, S. Suda, and T. Hakuta, Mem. Fuc. Technol., Tokyo Metrop. Uniu., No. 19, 103 (1969); Chem. Abstr., 74, 68337 (1971). (27) H. Hipkin, AIChE J., 12, 484 (1966).
The Journal of Physical Chemistry, Vol. 85, No. 23, 1981 3530
TABLE 111: Hydrophobic Interchange Parameters, Am, Calculated from Nemethy and Scheragau
AM^,
system Phe-Leu, 25 " C Phe-Leu, 7 0 "C Asp-Leu, CH, shielded, 25 "C Asp-Leu, CH, not shielded, 25 "C Ala-Val, 25 "C Ala-Leu, 25 " C Val-Leu, 25 "C
AAB~,
A&,
kcal mol-'
kcal mol-'
cal mol-' K-'
+0.55 +0.65 +0.10
-0.05 +0.45 -0.55
-2.05 -0.6 -3.0
+0.35
-0.20
-1.0
+0.2 +0.2 0.0
-0.2 -0.2 0.0
-1.3 -1.3 0.0
Reference 28.
such as those of Nemethy and Scheraga2*to define the A values. We may do so in terms of the parameters AGH," and AHH4"of Nemethy and Scheraga: A D G = AGAB" - '/(AGfi" + AGBB") AABH = AHAB" - l/,(AHU"+ AHBB")
Tables 11-IV of Nemethy and Scheraga may be used. The parameters of Nemethy and Scheraga include allowances for the attachment of the side chains to the peptide backbone, so that restrictions in rotation on hydrophobic bond formation are less than in the case of formation of such bonds from more freely mobile molecules in solution. These factors should largely cancel in the calculation of the A values. Since the total contributions of rotational changes to the parameters do not exceed 0.15 kcal mol-' or 600 J mol-l, the additional uncertainty in the A values resulting from this situation should not exceed 0.05 kcal mol-I. The values of A calculated for two systems of this research, and also for those systems treated by Blackburn, Lilley, and W a l m ~ l e yare , ~ ~shown in Table 111. Not shown in Table I11 are the systems methionineleucine, methionineisoleucine, and leucine-isoleucine. For these systems both AABGand AmH are -0.05 or 0.0 kcal mol-l at both 25 and 70 "C, so that the aqueous solutions are ideal within error of calculation. Phenylalanine-leucine was calculated at 70 "C because this temperature corresponded more closely to the conditions of the phase diagram of this research. Nemethy and Scheraga2s did not include values for aspartic acid, but these were approximated from their glutamic acid-leucine value in Table XI1 in two ways: (1) assuming the CH2 next to the peptide linkage to be shielded from contribution to hydrophobic bonding, A m = 0 for aspartic acid-leucine, and (2) assuming no shielding, AAB = one-half the value for glutamic acid-leucine. For aspartic acid-aspartic acid, AAAwas taken as zero. The free energy ADG for phenylalanine-leucine changes very little with temperature; the enthalpy increases and the negative entropy decreases significantly. The positive sign of AABHat 70 "C is in agreement with the behavior in Figure 3 for mole fraction leucine 0-0.65, but does not account for the reversed behavior beyond 0.65. Nemethy and ScheragaZshave discussed the nature of the aliphatic-aromatic side-chain interaction. Any restriction on the formation of bonds of maximum strength to be found in a protein would be removed in the aqueous solution of the amino acid. In the aspartic acid-leucine system, evaluation of the AAB factors is less certain because of the polarity of the aspartic acid. From Table XI1 of Nemethy and Scheraga, (28) G . Nemethy and H. A. Scheraga,J.Phys. Chem., 66,1773 (1962).
J. Phys. Chem. 1981, 85, 3540-3541
3540
an evaluation is possible at 25 "C only. structures, form extensive solid solutions. In particular, The polarity and ionic strength of the aspartic acid the solid solubility of methionine in leucine reported in should contribute very strongly to the total interaction the early literature has been confirmed. Phenylalanineenergy, especially on the aspartic acid side of Figure 8. leucine shows quasi-eutectic behavior. Leucine-isoleucine shows a third intermediate phase of unknown structure. This term should be negative, and the deviation on the Aspartic acid-leucine shows a complex. aspartic side is seen to be negative. The hydrophobic term AmH is shown to be negative at 25 "C according to either Ideality of a mixture of aqueous amino acid solutions assumption of CH2 shielding. However, if the variation has been defined thermodynamically, and departures of of AmH with temperature is in the positive direction as for the systems from ideality have been discussed in terms of phenylalanine-leucine, the positive deviation on the leucine interaction parameters based on hydrophobic bonding side is accounted for. enthalpies and other models. The increase of AmH with temperature is related to the All aqueous systems studied except phenylalanine-leurapid decrease in the hydrophobic interaction itself with cine and aspartic acid-leucine are indicated to be ideal temperature. This factor could preclude the use of a single within experimental error. Aspartic acid contributes a negative interaction energy, and phenylalanine a positive. interaction parameter to describe the behavior of aqueous Leucine shows a more complex behavior which may be amino acid solution systems at all temperatures. temperature dependent. The rapid decrease in the hyThe results for the systems alanine-valine, alaninedrophobic interaction with temperature may preclude the leucine, and alanine-isoleucine, for AmH,agree remarkably use of a single interaction parameter to describe these well with the pattern of AmH values previously calculated from the results of Blackburn, Lilley, and W a l m ~ l e y . ~ ~ systems.
Conclusion While the method does not give uniformly reliable data on the solubilities of individual amino acids in water as a function of temperature, it does give consistent information on the nature of binary systems of amino acids under the conditions of saturation equilibrium in aqueous solution. Most of the systems of two essential nonpolar aliphatic amino acids, of similar crystal and molecular
Acknowledgment. Acknowledgment is made to Messrs. Ronald Rosenberg, James Marino, and Peter Hagopian for earlier unpublished work which led to the final development of the apparatus and technique. Acknowledgment is also made to Dr. Barbara Furie and to Miss Margaret Dubois of the Department of Medicine, Division of Haematology and Oncology, Tufts New England Medical Center, Boston, MA for the amino acid analyses.
COMMENTS Reactive Contribution to the Apparent Translational Diffusion Coefflcient of a Micelle
Sir: Quasi-elastic light-scattering spectroscopy (QELSS) is a major tool for studying micelles.1*2 After correcting for intermicellar interactions: the translational diffusion coefficient DT determined by QELSS has been used to determine the average hydrodynamic radius ro and aggregation number4 n of a micelle. For a sphere, the diffusion coefficient for translation Brownian motion DH is given by6 DH = KBT/6avro (1) the usual analysis assumes DH = DR Equation 1has been tested extensively in studies on polystyrene latex spheres, proteins, and other macroparticles.6 For dilute monodisperse solutions, eq 1is in good agreement with experiment. The use of QELSS to determine ro for a micelle is thus a natural extension of earlier work. ~~
~
~
(1) D. McQueen and J. Hermans, J. Colloid Interface Sci., 39, 389 (1972). (2) N. A. Mazer, G. B. Benedek, and M. C. Carey, J.Phys. Chem., 80, 1075 (1976). (3) M. Corti and V. Degiorgio, J . Phys. Chem., 85, 711 (1981). (4) J. P. Kratohvil, J. Colloid Interface Sci., 75, 271 (1980), criticizes
the computation of n from ro on the grounds that the volume within ro may include water of hydration. (5) A. Einstein, Ann. Phys. (Leipzig) (IV),17, 649 (1905). (6) B. Chu, "Laser Light Scattering", Academic Press, New York, 1974.
One notes that a micelle is not a material object in the sense that a protein molecule is. A micelle is a dynamic assembly, constantly exchanging its component molecules with the free monomer molecules present in solution. Over sufficient time, the motion of a micelle and of the molecules it initially contained are unrelated. The exchange reaction is A i- A,-1
k+ k-
A,
A being a single amphiphile, and k+ and k- being the rate constants. For sodium dodecyl sulfate at 25 "C, k- = 1.0 X lo7 s-l, and n = 64, so every monomer in such a micelle is on the average replaced every 6.4 ps. By comparison, the diffusion time rDdetermined by QELSS for a micelle is expected to be (2DHq2)-l,q being the scattering vector. Assuming 6328-A illumination and 90" scattering, T D for such an SDS micelle is -16 ps. Over the relaxation time observed by QELSS, each surfactant monomer in an SDS micelle is therefore on the average replaced -2.5 times. While micelle motion appears to be continuous, after a time -TD the micelles in solution are composed of sets of monomers which are entirely different from those which were initially present. A micelle is like a wave, only its form being preserved in time. The monomer-micelle exchange reaction is now argued to contribute to the micelle's translational diffusion. After indicating why searches2for a chemical reactive component of the light-scattering line width I? do not see this effect,
0022-3654/81/2085-3540$01.25/00 1981 American Chemical Society
