Hydrophilicity of Fructose, Glucose, Sucrose

Nov 22, 2007 - Dynamic light scattering study of aggregation in aqueous solutions of five amphiphiles. Jacobo Troncoso , Katerina Zem?nkov? , Aida Jov...
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J. Phys. Chem. B 2007, 111, 13943-13948

13943

Relative Hydrophobicity/Hydrophilicity of Fructose, Glucose, Sucrose, and Trehalose as Probed by 1-Propanol: A Differential Approach in Solution Thermodynamics Yoshikata Koga* Department of Chemistry, The UniVersity of British Columbia, and Suitekijuku (Water Drop Institute), VancouVer B. C., Canada V6T 1Z3

Keiko Nishikawa Graduate School of AdVanced Integration Sciences, Chiba UniVersity, Chiba, Japan 263-8522

Peter Westh NSM, Research Unit for Functional Biomaterials, Roskilde UniVersity, Roskilde, DK-4000 Denmark ReceiVed: June 1, 2007; In Final Form: October 10, 2007

Earlier, we developed the 1-propanol probing methodology that could separately evaluate the relative hydrophobicity and hydrophilicity scale of a given sample. We applied it here to fructose, glucose, sucrose, and trehalose and evaluated the same for these saccharides. We then construct a two-dimensional map with the hydrophobicity and the hydrophilicity axes and plot the above saccharides together with other nonelectrolytes subjected earlier to the same analysis. We point out that these saccharides together with other so-called “osmolytes” that accumulate in vivo under H2O stress occupy a small specific region near H2O in this map.

Introduction The importance of carbohydrates in aqueous solutions of biological significance requires no emphasis. In particular, trehalose and sucrose, together with other polyols are known as “osmolytes” that accumulate in vivo under the so-called “osmotic stress” to sustain function under conditions of variable water contents.1 While the name “osmolyte” may represent only a part of the overall effects, there is no doubt that the carbohydrates’ amphiphilic nature toward H2O plays a crucial role. They possess both hydrophobic and hydrophilic moieties which cooperatively or competitively interact with H2O. In so doing, the relative strength of hydrophobicity and hydrophilicity must be an important factor. We have introduced a differential approach to solution thermodynamics.2-4 Unlike conventional thermodynamic studies, we experimentally determine higher order derivative quantities without resorting to any fitting function. We showed by applying this methodology to aqueous solutions that there are in general three distinct composition regions in each of which the mixing scheme or the “solution structure” is qualitatively different from those in the other regions. It was only shown in the H2O-rich region that the aqueous solution retains the integrity of liquid H2O. Namely, within the limited H2O-rich region, the hydrogen bond network of bulk H2O remains fluctuating and bond-percolated or connected throughout the entire bulk at any given instance. We call the mixing scheme operative in this H2O-rich region “mixing Scheme 1”. In the intermediate and the solute-rich regions, there are no such characteristics pertaining to liquid H2O. Furthermore, it was shown that in “mixing Scheme 1”, the solute-solute interaction is mediated by the bulk H2O which is modified in a specific manner (yet retaining the integrity of liquid H2O) depending on the solute. This is * Corresponding author. E-mail: [email protected].

true for the interaction between both the identical and the different solute species. This led us to the 1-propanol (1P) probing methodology2,5 in which we experimentally determine the second-order derivative quantities pertaining only to 1P in a ternary 1P-sample-H2O system and evaluate graphically the E third-order derivative, H1P-1P , that provides information about the enthalpic interaction between 1P molecules. The x1P E dependence of H1P-1P shows a unique peak pattern reflecting how 1P modifies H2O, where x1P is the mole fraction of 1P. E The H1P-1P pattern for binary 1P-H2O is shown in Figure 1, as case [0]. When a third component “sample” is present, the E changes depending on the peak height and the locus of H1P-1P nature and the amount of sample present, still keeping the basic peak pattern as shown in Figure 1, if the amount of the sample is not so high as to destroy the integrity of H2O. If the sample is hydrophobic, its main effect is to shift the peak pattern to the left and the peak point X moves to a smaller value of x1P, case A in Figure 1. For hydrophilic samples, the x1P locus of point X remains unchanged, but the peak height decreases as in case B. Amphiphiles’ effects are between the above two cases as in case C in Figure 1. The mechanisms responsible for these behaviors are coming from the fact that the interaction among solutes, the same or different species, is operative via modified bulk H2O. We have discussed this issue at some length earlier.2,5 It follows then that the relative hydrophobicity and hydrophilicity can be evaluated even within an amphiphile by the degree of the left and the downward shifts of point X, respectively. Namely, the extent of the left shift with a unit amount of the sample would represent the strength of hydrophobicity and that of the downward shift may show the strength of hydrophilic moiety in the sample amphiphile relative to the behavior of E H1P-1P pattern changes. We applied this 1P-probing methodology for fructose,6 glucose, sucrose, and trehalose; in this work, for the latter three

10.1021/jp074273t CCC: $37.00 © 2007 American Chemical Society Published on Web 11/22/2007

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Koga et al.

E Figure 1. Induced changes in the H1P-1P pattern by the presence of a E sample S, in 1P-S-H2O. [0] is the H1P-1P pattern for the binary 1PH2O; [A] shows that for hydrophobic S; [B] is that with hydrophilic S, and [C] that with an amphiphile.

saccharides. We would like to map their relative hydrophobicity/ hydrphilicity and learn their roles in aqueous solutions in comparison with other nonelectrolytes studied so far by the same methodology. While the terms hydrophobicity and hydrophilicity are usually used as global propensities for the affinity to H2O, we use them specifically for what we learn from the induced changes in the E H1P-1P pattern. Namely, we limit ourselves in the usage of the terms hydrophobicity and hydrophilicity only within the H2Orich region where “mixing Scheme 1” is operative and the integrity of H2O is retained. The details of their physical meanings are also limited to what we have learned earlier for aqueous solutions of nonelectrolytes using the same differential approach.2-4 Hydrophobic solutes are those that enhance the hydrogen bond network of H2O in their immediate vicinities (classically known as “iceberg formation”) but concomitantly reduce the hydrogen bond probability of bulk H2O away from “icebergs”. Up to the threshold composition that depends crucially on the strength of hydrophobicity of solute, the hydrogen bond probability is high enough that the hydrogen bond network is connected throughout the entire bulk at any given instance. When the solute composition reaches the threshold value, the integrity of liquid H2O is lost and the different mixing scheme sets in pertinent to the intermediate composition region. The threshold value is limited to a very dilute concentration range; for H2O-soluble mono-ols the threshold mole fraction ranges from 0.017 to 0.07 for 2-butoxyethanol to methanol.2-4 Hydrophiles, on the other hand, form hydrogen bonds to the existing hydrogen bond network of H2O. In so doing, they act as impurity centers and rigidify the fluctuation nature of the nearby H2O network. As the concentration of hydrophilic solute increases, the influence from one impurity center on the local network becomes incompatible with that from others, and in effect, the hydrogen bonds are cleaved in between the solute molecules. When such processes cover the entire bulk, the mixing scheme pertinent for the intermediate region sets in. This cross over, or the transition of mixing scheme, is typically at about 0.1 mole fraction, though not as conspicuous as the case of hydrophobes.2-4 In the following, we limit our usage of hydrophobicity/hydrophilicity in these senses applicable only in the H2O-rich region where the integrity of liquid H2O is retained. Another issue to note here is the facts that the enthalpy and entropy effects tend to compensate each other in aqueous solutions7,8 and that some conspicuous variation in each of

Figure 2. Excess partial molar enthalpy of 1P, HE1P, in 1P-GL-H2O at 25 °C. x0GL is the initial mole fraction of GL, before the HE1P measurements.

enthalpy and entropy effects is obscured in the net free energy level. While any propensity including hydrophobcity and hydrophilicity in a general term is governed by the net free energy effect, its variation may not be conspicuous enough anymore for detection. We thus present the variations at the E . enthalpic interaction level, H1P-1P Experimental Section The D-(+)-glucose (ACS Reagent, Sigma-Aldrich), D-(+)trehalose dihydrate (99.0%, Fluka), and sucrose (reagent grade, 98%, Aldrich) were used as supplied. Stock solutions were prepared by dissolving the sample from the freshly opened bottle. They were diluted with freshly distilled H2O as required for each series of measurements. 1-Propanol (>99.5%, ACROS Organic) was used in a dry N2 atmosphere throughout the calorimetric measurements. The excess partial molar enthalpy of 1-propanol (1P), HE1P, was determined directly using a homemade titration calorimeter of a similar design to an LKB Bromma 8700.2,9 The uncertainty is estimated as (0.03 kJ mol-1. The HE1P data were used to graphically differentiate and to evaluate the 1P-1P enthalpic E . The uncertainty is estimated as (10 kJ interaction, H1P-1P -1 mol . Results and Discussion The excess partial molar enthalpy of 1P on ternary 1Psample (S)-H2O (W) is defined as,2-4

HE1P t

( ) ∂HE ∂n1P

(1) p,T,nS,nW

where ni (i ) 1P, S, or W) is the amount of 1P, S, or W, respectively. As eq 1 implies, HE1P is the response of the system in terms of HE on perturbing n1P only. Hence, it provides information about the actual enthalpic situation of 1P in the mixture. The calorimetric approximation of the above differentiation and its appropriateness was discussed at some length earlier.2,10 The results are shown in Figure 2 for 1P-glucose (GL), in Figure 3 for trehalose (TRE), and in Figure 4 for sucrose (SUC).

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Figure 3. Excess partial molar enthalpy of 1P, HE1P, in 1P-TRE0 H2O at 25 °C. xTRE is the initial mole fraction of TRE, before the HE1P measurements.

HE1P,

Figure 4. Excess partial molar enthalpy of 1P, in 1P-SUCH2O at 25 °C. x0SUC is the initial mole fraction of SUC, before the HE1P measurements.

From these data, what we define as the solute(1P)-soluteE ,2-4 (1P) enthalpic interaction, H1P-1P E H1P-1P tN

( ) ∂HE1P ∂n1P

p,T,nS,nW

) (1 - x1P)

( ) ∂HE1P ∂x1P

(2)

p,T,nS,nW

is evaluated.2-5 x1P is the mole fraction of 1P, and N is the total E , the first identity of eq 2, amount. The definition of H1P-1P suggests how the actual enthalpic situation of 1P (HE1P) changes E on an infinitesimal addition of 1P. Thus, H1P-1P signifies the 1P-1P interaction in terms of enthalpy. The second equality E . of eq 2 provides the means to approximately evaluate H1P-1P We draw a smooth curve through all of the data points of HE1P versus x1P by aid of a flexible ruler. We read the data off the smooth curve drawn and approximate the derivative with δHE1P/δx1P. As we discussed at some length, δx1P ) 0.008 provides an acceptable approximation.2,11 It is, however,

E Figure 5. 1P-1P enthalpic interaction, H1P-1P , in 1P-GL-H2O at 25 °C. x0GL is the initial mole fraction of GL.

E Figure 6. 1P-1P enthalpic interaction, H1P-1P , in 1P-TRE-H2O at 0 25 °C. xTRE is the initial mole fraction of TRE.

inevitable that the uncertainty increases drastically to (10 kJ mol-1, from the original data point determined within (0.03 kJ mol-1. This disadvantage is well-compensated for by the gain of qualitative information as it will become evident below. There is a computer graphic technique, B-spline, in order to take derivatives from a data set. Its limitation, to our specific purpose that we deal with data points, with an inflection point is E discussed elsewhere.2,12 The resulting H1P-1P data are plotted in Figure 5 for 1P-GL-H2O, in Figure 6 for TRE, and in Figure E pattern 7 for SUC. As is evident from Figures 5-7, the H1P-1P retains the peak shape, which assures that the mole fractions of the sample saccharides are low enough that the ternary system is still in the “mixing Scheme 1” regime and the integrity of liquid H2O is retained, from the start (x1P ) 0) to point X. For convenience, we define the peak point X as the intersect of the two straight lines extended from the both sides of the peak. We monitor the changes of the locus of point X induced by the presence of the sample saccharide. The changes show a typical behavior of an amphiphile, C in Figure 1. As discussed above, the rate of decrease of the x1P locus represents the strength of

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Koga et al. TABLE 1: Relative Hydrophobicity/Hydrophilicity Indices

E Figure 7. 1P-1P enthalpic interaction, H1P-1P , in 1P-SUC-H2O at 25 °C. x0SUC is the initial mole fraction of SUC.

Figure 8. Dependence of the x1P locus of point X on x0SAC (SAC ) GL or FR). The slopes provide the hydrophobicity measures for monosaccharides. E the inherent hydrophobicity and that for the H1P-1P value, the hydrophilicity of the sample. Figure 8 shows the x1P locus for the monosaccharide samples against the initial mole fraction 0 (SAC ) GL or FR). For fructose (FR), of the saccharide, xSAC we use the earlier data.6 The figure indicates that FR is a stronger hydrophobe than GL, which is understandable since FR has an extra -CH2 group compared with GL. The strength of hydrophobicity may be represented by the slopes in Figure 8, which are listed in Table 1. With an inevitably large error of the order of 10%, the negative slope is about 1.8:1 for FR versus GL, which is almost proportional to the number of -CH2 groups. We pointed out earlier that for poly-ols and poly(ethylene glycols), the hydrophobicity scales almost with the number of carbon atoms in the alkyl chain.13 However, a recent acoustical attenuation and complex dielectric spectroscopy indicated that one molar aqueous fructose solution (about 0.018 mole fraction) reaches the tautomeric equilibrium in 20 min, and at equilibrium, about 28% take the fructofuranose form that contains an extra -CH2 group, while 72% are in fructopyranose.14 In the presence

material (marka)

hydrophobicityb

hydrophilicityc

ref

H2O (A) 1-propanol(B) glucose (P) fructose (Q) sucrose (R) trehalose (Y) 2-propanol (C) tert-butanol (D) methanol (E) ethyleneglycol (F) glycerol (G) 1,2-propanediol ((H) 1,3-propanediol (J) tetramethylurea (K) acetone (L) urea (M) trimethylammine oxide(T) poly(EG)(MW200) (V) poly(EG)(MW600) (W)

0 -1 -0.20 -0.37 -0.7 -0.71 -0.80 -1.44 -0.21 -0.15 -0.15 -0.59 -0.35 -0.63 -0.58 0 -0.35 -0.57 -2.19

0 0 -1260 -1260 -2100 -2100 -170 940 -900 -980 -1270 -930 -1270 -3400 -1450 -2020 -330 -3830 -8870

this work 6 this work this work 16 11 17 17 9 18 18 19 19 20 21 14 14

Marks shown in Figure 11. b Slope of the x0S dependence of the x1P E locus of point X in the H1P-1P pattern. c Slope of the x0S dependence of E value at point X. x0S is the initial mole fraction of the the H1P-1P sample nonelectrolyte in 1P-sample-H2O. a

Figure 9. x0SAC dependence of the x1P locus of point X for disaccharides, where SAC ) trehalose (TRE) or sucrose (SUC). The slopes provide the hydrophobicity measures for disaccharides. Up to the break points, both TRE and SUC show the same hydrophobicity, but above the thresholds, the hydrophobicity decreases to 1/5 for SUC and 1/3.5 for TRE.

of ethanol, this ratio increases in favor of fructofuranose, but even in pure ethanol, it increases to 57%. If so, the above ratio would be 1.3:1 to 1.5:1, more likely to be closer to the former for a dilute enough ethanol-H2O that retain the integrity of H2O. The discrepancy from our finding remains an open question regarding the tautomeric equilibrium. For aqueous solution of GL, on the other hand, almost 100% is known to remain in the glucopyranose form and have one -CH2 in aqueous solution.15 Figure 9 shows the same plots for the disaccharide samples. Unlike monosaccharides, both TRE and SUC seem to show breaks in slope beyond the estimated uncertainty below 0.01 mole fraction of disaccharide, while more data points are required to substantiate such an observation. If true, however, this hints that both disaccharides undergo tautomeric changes

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TABLE 2: Composition Dependent Hydrophobicity of Disaccharides disaccharides

hydrophobicitya below

thresholdb

hydrophobicitya above

sucrose trehalose

-0.70 (R)c -0.71 (Y)c

0.007 0.009

-0.14 (R′)c -0.20 (Y′)c

a

Slope of the x0S dependence of the x1P locus of point X in the pattern. b Mole fraction of disaccharide. c Refer to Figure 11.

E H1P-1P

E Figure 10. Dependence of H1P-1P value at point X on the initial mole fraction of the sample saccharides, x0SAC (SAC ) FR, GL, TRE, or SUC). The slopes provide the hydrophilicity measures for each saccharide.

at these compositions in the presence of 1P. Table 2 lists the threshold value and the slopes, that is, hydrophobicity, for both composition regions. We note, however, in Figures 6 and 7 that E is intact below and above the the peak pattern in H1P-1P threshold, indicating that the integrity of H2O is retained. Hence, we may safely suggest that the breaks in the slopes in Figure 11 are due to tautomeric changes reducing the hydrophobicity E by 3.5- to 5-fold. Figure 10 plots the H1P-1P values at point X 0 . against the initial mole fraction of sample saccharides, xSAC Within the uncertainty limit, the distinction among the members in the mono- and disaccharides is not apparent. The slopes are approximately in the ratio of 1:2 for mono- to disaccharides. This is consistent with our earlier findings for poly-ols13 that the hydrophilicity scales with the number of oxygen. What is striking, however, is that there is no sign of a break in slope in Figure 10 at the thresholds for disaccharides observed in Figure 9. The tautomeric changes suggested above must, if indeed true, bring about changes in the hydrophobicity by 3.5- to 5-fold without affecting hydrophilicity. Earlier, we used the same 1Pprobing methodology to study the effect of an ionic liquid, 1-butyl-3-methylimidazolium ([bmim]+) chloride ([bmim]Cl).16 We found that the similar plots of the changes in the locus of E pattern on addition of [bmim]Cl show a point X of H1P-1P break at the same threshold value for both hydrophobicity and hydrophilicity plots. The threshold value of the mole fraction was found to correspond to that at which the mode of ion paring makes a subtle change, from complete dissociation to H2Omediated ion paring.17 We now compare the hydrophobicity/hydrophilicity scale we devised above for saccharides with those for general nonelectrolytes to which we have applied the same 1P-probing

Figure 11. Relative hydrophobicity/hydrophilicity map for nonelectrolytes including the four saccharides studied in this work. The abscissa shows the slope of the x0S dependence of the x1P locus of point X and E value of point X. The obvious plots for H2O the ordinate of the H1P-1P (A) and the probing 1P (B). The saccharides studied here are plotted as P, GL; Q, FR; R, SUC; and Y, TRE. The rest of nonelectrolytes are listed together with references. C: 2-propanol.18 D: tert-butanol.13 E: methanol.19 F: ethyleneglycol.19 G: glycerol.11 H: 1,2-propanediol.20 J: 1,3-propanediol.20 K: tetramethylurea.21 L: acetone.21 M: urea.22 T: trimethylammoniumoxide.23 V: polyethyleneglycol (MW 200).16 W: polyethyleneglycol (MW 600).16 R′ and Y′ are SUC and TRE respectively above the break; see Table 2 and the text.

methodology. The results are listed in Table 1. Figure 11 is the map of hyrophobicity and hydrophilicity using the slope data shown in Table 1. The abscissa is the slope of the x1P locus versus x0S, where x0S is the initial mole fraction of the sample, E value at point X while the ordinate is the slope of the H1P-1P 0 versus xS. Thus, H2O is placed at the origin (0, 0) as A, and the probing 1P is at B (-1, 0). More hydrophobic tert-butanol is plotted as D, while less hydrophobic methanol is placed at E. A typical hydrophilic species, urea, is shown as M on the ordinate with zero hydrophobicity. Thus, more hydrophobic species are mapped toward the west slight north of the origin, and the hydrophiles are toward the south. Amphiphiles are mapped toward the southwest, and the distance from the origin on the map would distinguish amphiphiles by the strength of respectively hydrophobicity and hydrophilicity. The saccharides studied here are apparently moderate hydrophiles, plotted as GL (P), FR (Q), TRE(Y), and SUC (R) in Figure 11. The latter two are identical. Typical “osmolytes”,1 trimethylammine oxide (T) and glycerol (G), are plotted together with 1P (B) and urea (M). Also shown in Figure 11 is the hydrophobicity for TRE and SUC above the threshold composition listed in Table 2. Thus, the so-called “osmolytes” that we have studied by the 1P-probing methodology so far turned out to be moderate amphiphiles. The closeness of these points to the origin, H2O, may have some bearing on the function of the “osmolytes” in the H2O-stressed situation. How the mechanisms work are yet to be elucidated. Although the probing 1P has the ratio of the hydrophobic and hydrophilic surfaces similar to those of most biopolymers,24-26 there must be hydrophobic or hydrophilic specific effects that dictate the behavior of biopolymers in aqueous solutions. Thus, the series of similar studies are awaited using another more hydrophilic nonelectrolyte, glycerol, for example as the probe.

13948 J. Phys. Chem. B, Vol. 111, No. 50, 2007 Acknowledgment. We thank Dr. Subramanian Iyer and Mr. Foon Yip for help extended towards this project. Financial supports by the Danish Research Council (Grants 21-04-0087 and 272-06-0505), and the Ministry of Education, Culture, Sports, Science and Technology, Japan are gratefully acknowledged. Supporting Information Available: Table SUP of the excess partial molar enthalpy of 1P, HE1P, in 1P-saccharidesH2O at 25 °C, including the preliminary HE1P data for 1PTMAO (trimethylammine oxide)-H2O at 25 °C. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Somero, G. N. In Water and Life; Somero, G. N., Osmond, C. B., Bolis, C. L., Eds.; Springer-Verlag: Berlin, 1992; Chapter 1, pp 3-18. (2) Koga, Y. Solution thermodynamics and Its Application to Aqueous Solutions:A Differential Approach; Elesevier: Amsterdam, 2007. (3) Koga, Y. J. Phys. Chem. 1996, 100, 5172. (4) Koga, Y. Netsusokutei (J. Jpn. Soc. Calor. Therm. Anal.), 2003, 30, 54. Available in a pdf form on request to the author at [email protected]. (5) Koga, Y. Netsusokutei (J. Jpn. Soc. Calor. Therm. Anal.), 2007, 34, 3. Available in a pdf form on request to the author at [email protected]. (6) To, E. C. H.; Westh, P.; Koga, Y. Fluid Phase Equilib. 2000, 73, 151. (7) Lumry, R.; Rajender, S. Biopolymers 1990, 9, 1125. (8) Lumry, R. Biophys. Chem. 2003, 105, 545. (9) Koga, Y. Can. J. Chem. 1988, 66, 1187. (10) Koga, Y. In ComprehensiVe Handbook of Calorimetry and thermal Analysis; Sorai, M., Ed.; John Wiley & Sons: Chichester, 2004; 3.1.3, p 195.

Koga et al. (11) Parsons, M. T.; Westh, P.; Davies, J. V.; Trandum, Ch.; To, E. C. H.; Chiang, W. M.; Yee, E. G. M.; Koga, Y. J. Solution Chem. 2001, 30, 1007. (12) Koga, Y.; Katayanagi, H.; Davies, J. V.; Kato, H.; Nishikawa, K.; Westh, P. Bull. Chem. Soc. Jpn. 2006, 79, 1347. (13) Miki, K.; Westh, P.; Koga, Y. J. Phys. Chem. B 2005, 109, 19536. (14) Behrends, R.; Kaatze, U. ChemPhysChem 2005, 6, 1133. (15) Lehmann, J. Carbohydrates: Structure and Biology; Thieme: Stuttgart, 1998; p 32, translated by Hains, A. H. (16) Miki, K.; Westh, P.; Nishikawa, K.; Koga, Y. J. Phys. Chem. B 2005, 109, 9014. (17) Katayanagi, H.; Shimozaki, H.; Nishikawa, K.; Miki, K.; Westh, P.; Koga, Y. J. Phys. Chem. B 2004, 108, 19451. (18) Hu, J.; Chiang, W. M.-D.; Westh, P.; Chen, D. H. C.; Haynes, C. A.; Koga, Y. Bull. Chem. Soc. Jpn. 2001, 74, 809. (19) Koga, Y. J. Solution Chem. 2003, 32, 803. (20) Parsons, M. T.; Koga, Y. J. Phys. Chem. B 2002, 106, 7090. (21) Chen, D. H. C.; Liu, A. P. C.; Koga, Y. Fluid Phase Equilib. 2001, 189, 31. (22) To, E. C. H.; Hu, J.; Haynes, C. A.; Koga, Y. J. Phys. Chem. B 1998, 102, 10958. (23) The preliminary results of HE1P in 1P-TMAO-H2O are given in Table SUP (Supporting Information). The data were subjected to the same analysis as the present work, and the relative hydrophobicity/hydrophilicity index was evaluated. A fuller account will be forthcoming. (24) Hermann, R. B. J. Phys. Chem. 1972, 76, 2754. (25) Makhataze, G. I.; Privalov, P. L. AdV. Protein Chem. 1995, 47, 307. (26) Amidon, G. L.; Yalkowsky, S. H.; Leung, S. J. Pharm. Sci. 1974, 63, 1858.