Anal. Chem. 1998, 70, 2812-2818
Sucrose Dependence of Solute Retention on Human Serum Albumin Stationary Phase: Hydrophobic Effect and Surface Tension Considerations Eric Peyrin,† Yves Claude Guillaume,*,† Nadia Morin,‡ and Christiane Guinchard†
Laboratoire de Chimie Analytique and Laboratoire de Chimie Physique et Minerale, Faculte de Medecine et Pharmacie, Place Saint Jacques, 25030 Besancon Cedex, France
In a chromatographic system using human serum albumin (HSA) as a stationary phase, D,L dansyl amino acids as solutes, and sucrose as a mobile-phase modifier, a study on the surface tension effect of sugar on compound retention was carried out by varying the salting-out agent concentration c and the column temperature T. The thermodynamic parameters for solute transfer from the mobile to the stationary phase were determined from linear van’t Hoff plots. An enthalpy-entropy compensation study revealed that the type of interaction between solute and HSA was independent of the molecular structure of the dansyl amino acids and the mobile-phase composition. An analysis of the experimental variations in the retention factor and the enantioselectivity values with c was performed using a theoretical model. It was shown that the decrease in solute retention accompanying the sucrose concentration increase was principally governed by a structural rearrangement of the binding cavity due to the increased surface tension effects. The cavity apolar residues were assumed to fold out of contact with the medium in order to reduce the surface area accessible to sucrose molecules, thus implying a restriction of the curvature radius of the cavity. Such behavior caused a decrease in the hydrophobic interaction for ligand binding on HSA explaining the observed thermodynamic parameter trends over the sucrose concentration range. Human serum albumin (HSA) is an acidic, water-soluble protein, which acts as a transport protein in vivo. It has been used to develop chiral stationary phases in high-performance liquid chromatography. A number of recent reports have examined the thermodynamic properties and binding mechanisms involved in the interactions of some model compounds with HSA. Soltes and Sebille1 have investigated the stereoselectivity of the reversible binding interactions between the D- and L-tryptophan enantiomers and fragments of HSA by applying three novel high-performance liquid chromatographic arrangements. The thermodynamic and kinetic processes involved in the binding and separation of (R)†
Laboratoire de Chimie Analytique. Laboratoire de Chimie Physique et Minerale. (1) Soltes, L.; Sebille, B. Chirality 1997, 9, 373. ‡
2812 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
and (S)-warfarin on a HSA column were characterized using frontal analysis technique of Loun and Hage.2 Tittelbach and Gilpin3 studied the influence of subtle changes in the protein structure on the specific binding and chromatographic selectivity for differently substituted L-tryptophans. As well, earlier studies have investigated the role of various mobile-phase parameters on the compound-HSA binding. Binding and its influence on the support’s chromatographic performance have been examined in relation to the ionic strength and the addition of small amounts of organic solvents.4-6 Lloyd et al.7 compared the retention factors of benzoin enantiomers measured in liquid chromatography and capillary electrophoresis using differing concentrations of methanol, ethanol, propanol, and acetonitrile in mobile phase. The effects of changing the pH of the mobile phase and the column temperature on the kinetics of D- and L-tryptophan binding with HSA were determined to optimize chiral separation.8 In a previous work, Peyrin et al.9 studied the retention mechanism of a series of dansyl amino acids on a HSA column over a wide range of mobile-phase pH and column temperatures. A change in the retention mechanism was observed at pH ) 7.0 and 7.5 for all dansyl amino acids.9 It was demonstrated by differential scanning calorimetry (DSC) that this was due to a phase transition in the protein stationary phase which balanced between a disordered and ordered solidlike state.9 A model that associated both the apolar side chain organization and the surface tension of the curved solvent-accessible surface of the binding cavity was developed to explain the particular retention mechanism observed at these pH values.9 In an effort to extend the investigation of the dansyl amino acids-HSA interactions, the influence of a surface tension modifier, such as sucrose, on the binding cavity properties was examined in this work. The van’t Hoff plots for D,L-dansylnorvaline and D,L-dansyltryptophan were determined over a wide range of mobile-phase sucrose concentrations (0.04-0.87 M). To understand the dependence of retention factors and thermodynamic parameters on the sucrose concentra(2) Loun, B.; Hage, D. S. Anal. Chem. 1994, 66, 3814. (3) Tittelbach, V.; Gilpin, R. K. Anal. Chem. 1995, 67, 44. (4) Aubel, M. T.; Rogers, L. B. J. Chromatogr. 1987, 392, 415. (5) Andersson, S.; Allenmark, S. J. Liq. Chromatogr. 1989, 12, 345. (6) Allenmark, S.; Andersson, S.; Bojarski, J. J. Chromatogr. 1988, 436, 479. (7) Lloyd, D. K.; Ahmed, A.; Pastore, F. Electrophoresis 1997, 18, 958. (8) Yang, J.; Hage, D. S. J. Chromatogr. 1997, 766, 15. (9) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 4979. S0003-2700(98)00039-0 CCC: $15.00
© 1998 American Chemical Society Published on Web 06/11/1998
tion, a model that takes into account both the preferential hydration layers of solutes and protein and the curvature of the binding cavity was developed. THEORY Sudlow et al.10 have characterized two specific binding sites on HSA which are designated site I (or the warfarin site) and site II (or the benzodiazepine site). Recently, the three-dimensional structure of HSA was determined crystallographically.11 Binding sites are located respectively in hydrophobic cavities in subdomains IIA and IIIA, which exhibit similar chemistry. It has been shown that L-dansylnorvaline and L-dansyltryptophan had a single binding region on HSA that is known to be located at site II.12 In a previous study,13 it was demonstrated that the D enantiomers of these dansyl amino acids interacted on the HSA with a stronger affinity in the same location than the L enantiomers. The ligand-protein interaction consisted of two steps.13-15 The guest molecule approaches the cavity by mutual penetration of the hydration layers14 (this step is driven by the hydrophobic effect). In the second step, which is responsible for chiral recognition,13 the solute binds to the cavity through a variety of specific short-range interactions15 (hydrogen-bonding, electrostatic, van der Waals, and steric interactions). As well, the Gibbs free energy ∆G° of dansyl amino acids and transfer from the mobile to the stationary phases can be broken down as follows:
∆G° ) ∆G°H + ∆G°S
In a chromatographic system, if the addition of a component such as sucrose disturbs the surface tension of the mobile phase, then its concentration in the surface layer of HSA stationary phase or solute must differ from its concentration inside the mobile phase. The excess amount of this component found per unit area of surface is given by the Gibbs adsorption isotherm:
1 ∂σ n )S RT ∂ ln c
(
)
(2)
T
where σ is the surface tension of the mobile phase and c and n are respectively the concentration of sucrose in the mobile phase and the excess of sucrose molecules for the accessible to solvent surface area S for the part of the cavity implied in the binding process (SP) or solute (SSol). The energies of solute or cavitymedium solvation are neglected when it is assumed that the solute or cavity-solvent interfaces are chemically inert. If the surface tension is the predominant factor that will change the free energy for the binding cavity (∂G°PH) and solute (∂G°SolH) at any given temperature and sucrose concentration, then it is possible to estimate the surface of contact SP and SSol between the solvent and binding cavity and solute, respectively, as follows:
(∂G°PH)T,C ) SP(∂σ)T,C
(3)
(∂G°SolH)T,C ) SSol(∂σ)T,C
(4)
(1)
where ∆G°H and ∆G°S are the components of the Gibbs free energy of transfer due to respectively the hydrophobic and specific interactions. It has been known for many years that polyhydric alcohols and sugars stabilize proteins against heat denaturation.16,17 It is argued that this stabilization is due to the effects of these molecules on hydrophobic interactions. Bach et al.18 have shown that sugars, such as sucrose, strengthened the pairwise hydrophobic interaction between hydrophobic groups. The hydrophobic effect is dominated by three factors: (i) the cavitation energy, (ii) the energy of solute-medium solvation interaction, and (iii) the loss of solvent entropy in the first hydration shell due to a change in the water structure.14 Timasheff et al.19 reported that the stabilization of proteins in an aqueous sucrose medium is related to the increase in the free energy of enlarging the surface of the solvent cavities which contain the bulky solute molecule, i.e., the cavitation energy (i). This study indicated that the solvent composition in the surface layer of protein is related to the effect of sucrose on the surface tension of the solvent19 and that the sucrose molecules are preferentially excluded from the protein domain.19 (10) Sudlow, G.; Birkett, D. J.; Wade, D. N. Mol. Pharmacol. 1975, 11, 824. (11) He, X. M.; Carter, D. C. Nature 1992, 358, 209. (12) Sudlow, G.; Birkett, D. J.; Wade, D. N. Mol. Pharmacol. 1976, 12, 1052. (13) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. J. Chromatogr. Sci. 1998, 36, 97. (14) Leckband, D. E.; Israelachvili, J. N.; Schmitt, F. J.; Knoll, W. Science 1992, 255, 1419. (15) Ross, P. D.; Subramanian, S. Biochemistry 1981, 20, 3096. (16) Frigon, R. P.; Lee, J. C. Arch. Biochem. Biophys. 1972, 153, 587. (17) Gerlsma, S. Y. J. Biol. Chem. 1968, 243, 957. (18) Bach, J. F.; Oakenfull, D.; Smith, M. B. Biochemistry 1979, 18, 5191. (19) Timasheff, S. N.; Lee, J. C.; Pittz, E. P.; Tweedy, N. J. Colloid Interface Sci. 1976, 55, 658.
and
Thus, for St ) SP + SSol, (∂G°H) is equal to
(∂G°H)T,C ) St(∂σ)T,C
(5)
(∂G°H)T,C ) (∂G°PH)T,C + (∂G°SolH)T,C
(6)
where
When the solute is transferring from a mobile to a stationary phase, the variation of St, i.e., ∆St, is determined by the following equations:
(
)
∂(∆G°H) ∂σ
T,C
) ∆St
(7)
with
(∂∆G°H)T,C ) (∂∆G°PH)T,C + (∂∆G°SolH)T,C
(8)
Using eq 2, the ∆nt value representing the variation of nt (corresponding to St) is linked to the surface change ∆St by
∆nt 1 ∂σ )RT ∂ ln c ∆St
(
)
T
(9)
For a planar and constant surface of the binding cavity, a Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
2813
of the cavity wall residues to move to accommodate the guest molecule.22 Also, the surface cavity accessible to mixed solvent cannot be considered to be constant over the sucrose concentration range studied. Thus, Eq 12 can be rewritten as follows:
( Figure 1. Schematic drawing of the HSA-solute association process (see Eq 11 in the text).
(
)
T
) -∆ntRT
(
)
∂∆G°H ∂ ln c
T
) 2nPRT
) 2∆nPRT
(13)
T
) 2(ncP - ncsP)RT
(14)
(10)
(11)
A schematic drawing of the HSA-solute association process representing this approximation is shown in Figure 1. Combining Eqs 10 and 11, the following is obtained:
(
)
∂[∆(∆G°H)] ∂ ln c
A similar equation was developed by Wymann to analyze the thermal unfolding data of proteins.20 The ∆nt values are predicted to correlate with the accessible to solvent surface area or hydrophobic character of the solute. Thus, two dansyl amino acids with different molecular structures are assumed to exhibit nonsimilar variations of ∆G°H with ln c at T constant. Considering nSol as the n value for the solute molecule and nP as the n value for the surface of the binding cavity implied in the interaction process, it was assumed that, in a first approximation, ∆nt was equal to
∆nt ∼ (nSol - nP) - (nSol + nP) ∼ - 2 nP
T
If [∆(∆G°H)] and ∆nP are the variations of (∆G°H) and nP when the sucrose concentration varied from the smallest concentration cs (ncsP) to other concentrations c (ncP), then Eq 13 can be rewritten as
combination of eqs 7 and 9 gives
∂(∆G°H) ∂ ln c
)
∂[∆(∆G°H)] ∂ ln c
However, in Eq 14, no allowance has been made for the curvature of the binding cavity surface. Assuming that this surface has a curvature radius r, the surface tension σ(r) is linked to the surface tension of a planar surface σ(∞) by9,23
(
σ(r) ) σ(∞) 1 -
2Z r
)
(15)
where Z is the radius of a sucrose molecule coming tangentially to the cavity surface. Consequently, a derivation of Eq 15 gives
( ) [ ]( ∂σ(r) ∂ ln c
∂σ(∞) ) T ∂ ln c
T
)
2Z 1+ σ(∞) r
[
(
Z r ∂ ln c
∂ 1-2
)
]
T
(16)
Using Eq 2 for the cavity planar surface SP (σ ) σ(∞)), the combination with Eq 16 yields
(12)
( ) [ ∂σ(r) ∂ ln c
[ ( )]
1 ∂ r 2Z 1- σ(∞)2Z r ∂ ln c
]( )
-nPRT ) T SP
(17)
As the sucrose is preferentially excluded from the binding cavity domain,19 nP is predicted to be a negative value corresponding to negative adsorption of sucrose molecules to protein. Therefore, from Eq 12, ∆G°H is expected to decrease with c increasing by enhancement of the hydrophobic interaction between the solute and stationary phase. However, as the presence of sucrose in the aqueous mobile phase increases the surface tension of the medium,19 the apolar groups of the binding cavity were expected then to reduce the area of solvent-protein contact by increasing their nonpolar attractions. The cavity hydrophobic groups prefer to migrate toward the protein interior out of contact with the solvent in order to relieve this energetically unfavorable situation. Such a migration is mechanically reasonable on the basis of the existence of relative flexible parts in the rigid solidlike structure of the binding cavity core.21 The interaction between the protein and small molecules requires a certain deformability
As the binding cavity is assumed to be spherical, SP is equal to λ4πr2, where λ represents the part of spherical surface accessible to solvent; thus
(20) Wyman, J. Adv. Protein Chem. 1964, 19, 223. (21) Ericksson, A. E.; Baase, W. A.; Zhang, X. J.; Heinz, D. W.; Blaber, M.; Baldwin, E. P.; Matthews, B. W. Science 1992, 255, 178.
(22) Matsumura, M.; Yahanda, S.; Yasumura, S.; Yutani, K.; Aiba, S. Eur. J. Biochem. 1988, 171, 715. (23) Choi, D. S.; Jhon, M. S.; Eyring, H. J. Chem. Phys. 1970, 53, 2608.
2814 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
T
The change in free energy for the binding cavity (∂G°HP) at any given temperature T is obtained by a combination of Eqs 3 and 17:
[(
(∂G°HP)T ) SP
)(
)
-nPRT 2Z 1(∂ ln c)T r SP
( ( )) ]
(2Zσ(∞)) ∂
1 r
(18)
T
(∂G°HP)T )
∆ ln k′ )
2Z -n RT 1 (∂ ln c)T + 8λZπσ(∞)(∂r)T (19) r
(
P
)
( )
(
) -nPRT 1 -
T
)
2Z ) -nrPRT r
(
2Z r
)
(21)
Thus, Eq 10 can be rewritten as follows:
(
)
∂(∆G°H) ∂ ln c
T
(
) 2nrPRT ) 2nPRT 1 -
[
)
2Z r
(22)
]
∂[∆(∆G°H)] ∂ ln c
(20)
where nrP is the nP value for the curvature of radius r. By substituting the nP value by the nrP value in Eq 11 and considering SSol as constant over the sucrose concentration range, this leads to
∆nt ) -2nrP ) -2nP 1 -
(27)
where ∆ ln k′ is the change in ln k′ observed with the variation from cs to c. Consequently,
For a r constant, the following equation is obtained:
∂G°HP ∂ ln c
-∆(∆G°H) RT
T
) -RT
(
)
∂(∆ ln k′) ∂ ln c
T
(28)
Using Eqs 24 and 28, the following is obtained:
[
]
∂(∆ ln k′) ∂ ln c
(
) 4ncsPZ T
)
1 1 rc rcs
(29)
This equation links the variation of the ∆ ln k′ with the sucrose concentration and both the preferential hydration layer of the binding cavity and the change of curvature radius from rcs to rc. As well, for a pair of D,L enantiomers, the separation factor R between D and L dansyl amino acids is given by the following equation:
R ) k′D/k′L
(30)
and thus Eq 14 gives
(
)
∂∆(∆G°H) ∂ ln c
) T
(
2ncsPRT
)
(
)
2Z 2Z 1- 2ncsPRT 1 rc rcs
(23)
where k′D and k′L are the capacity factors of D and L enantiomers. When the sucrose concentration varies from cS to c, the variation of ln R at Τ constant is represented by
(∆ ln R)T ) (∆ ln k′D)T - (∆ ln k′L)T
when rcs and rc are the r values corresponding to cs and c, respectively. The rearrangement of Eq 23 gives the following:
(
)
∂(∆(∆G°H)) ∂ ln c
T
)
-4ncsPZRT
(
)
1 1 rc rcs
(24)
Therefore, the variation of the accessible to solvent cavity surface and thus nP over the sucrose concentration range implied in Eq 14 can be linked to a change in curvature radius r. It is known that the retention factor for a solute is related to the change in free energy incurred during the transfer of solute between the mobile and the stationary phase. This relationship is represented by the equation
ln k′ )
-∆G° + ln φ RT
(25)
where φ represents the phase ratio (volume of the stationary phase divided by the volume of the mobile phase). Substitution of Eq 1 into Eq 25 leads to
ln k′ )
-(∆G°H + ∆G°S) + ln φ RT
(26)
When the sucrose concentration varies from cS to c, ∆G°S is considered to be constant and the variation of the retention factor is only dependent on the variation of ∆G°H. Thus, in rewriting Eq 26, the following is obtained:
(31)
As D and L enantiomers of each solute have the same accessible to solvent surface area, ∆(∆G°H) values for the two compounds are identical. Using Eq 27, the following equality is obtained:
(∆ ln k′D)T ) (∆ ln k′L)T
(32)
(∆ ln R)T ) 0
(33)
(R)T ) constant
(34)
Thus,
and
Equations 32-34 reflect the fact that the sucrose molecules act exclusively on the hydrophobic step of the HSA-solute interaction without effecting enantioselectivity. EXPERIMENTAL SECTION Apparatus. The HPLC system consisted of a Merck Hitachi pump L7100 (Nogent-sur-Marne, France), an Interchim Rheodyne injection value model 7125 (Montluc¸ on, France) fitted with a 20µL sample loop, and a Meck L 4500 diode array detector. An HSA protein chiral Shandon column (150 mm × 4.6 mm) was used with controlled temperature in an Interchim Crococil oven TM 701. After each use, the column was stored at 4 °C until Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
2815
further use. Throughout the study, the column pressure was maintained constant. Solvents and Samples. HPLC grade acetonitrile (Merck) was used without further purification. Sodium hydrogen phosphate, sodium dihydrogen phosphate, and sucrose were supplied by Prolabo (Paris, France). Water was obtained from an Elgastat option water purification system (Odil, Talant, France) fitted with a reverse-osmosis cartridge. D,L-dansylnorvaline and D,L-dansyltryptophan were obtained from Sigma Aldrich (Saint Quentin, France) and were made fresh daily at a concentration of 20 mg/L in acetonitrile. Sodium nitrate was used as a dead time marker (Merck). The mobile phase consisted of a 0.05 M sodium phosphate buffer-acetonitrile (87-13 v/v) at pH ) 8.0 with sucrose concentrations varying from 0.04 to 0.87 M. A 20-µL sample of each solute or a mixture of these were injected and the retention times were measured. Temperature Studies. Compound retention factors were determined over the temperature range 5-35 °C. The chromatographic system was allowed to equilibrate at each temperature for at least 1 h prior to each experiment. To study this equilibration, the compound retention time of the D-dansylnorvaline was measured every hour for 5 h and again after 23 and 24 h. The maximum relative difference of the retention time of this compound was always 0.6%, making the chromatographic system sufficiently equilibrated for use after 1 h. All solutes were injected three times at each temperature and sucrose concentration. Once the measurements were completed at the maximum temperature, the column was immediately cooled to ambient conditions to minimize the possibility of any unfolding of the immobilized HSA. RESULTS AND DISCUSSION Van’t Hoff Plots. The free energy ∆G° from eq 25 can be broken down into enthalpic and entropic terms to give the van’t Hoff equation:24
-∆H° + ∆S°* RT
(35)
∆S°* ) ∆S°/R + ln φ
(36)
ln k′ )
If the solute binds to a fixed number of specific sites with a constant enthalpy of association, then a plot of ln k′ vs 1/T should be linear with a slope of -∆H°/R and an intercept of ∆S°*. The retention factor of each of the D,L dansyl amino acids was calculated for a wide variation range of sucrose concentration c (0.04-0.87 M) at all column temperatures. From these retention factors, the plots of ln k′ in relation to 1/T were determined for different sucrose concentrations. The van’t Hoff plots were all linear for L and D dansyl amino acids. The correlation coefficients for the linear fits were in excess of 0.973. The typical standard deviations of slope and intercept were respectively 0.009 and 0.06. Figure 2 shows the van’t Hoff plots for L dansyl tryptophan at all sucrose concentration values. These linear behaviors were thermodynamically what was expected when there was no change in the retention mechanism in relation to temperature. Tables 1 and 2 contain a complete list of ∆H° and ∆S°* values for all solutes and at all sucrose concentrations. (24) Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 183.
2816 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
Figure 2. Van’t Hoff plots for L-dansyltryptophan at all sucrose concentrations c (M). Table 1. Thermodynamic Parameter ∆H˚ (kJ/mol)a at Different Sucrose Concentrations c (M) for the D,L Dansyl Amino Acid Transfer from the Mobile to the HSA Stationary Phase dansyltryptophan
dansylnorvaline
c
D
L
D
L
0.04 0.09 0.22 0.44 0.65 0.87
-19.1 (0.1) -18.9 (0.1) -18.4 (0.05) -17.9 (0.09) -17.0 (0.08) -16.3 (0.1)
-16.6 (0.09) -16.5 (0.09) -16.0 (0.07) -15.4 (0.04) -14.7 (0.1) -13.9 (0.05)
-15.3 (0.08) -14.3 (0.06) -13.7 (0.1) -12.9 (0.2) -12.1 (0.1) -11.5 (0.04)
-13.3 (0.09) -12.2 (0.05) -11.3 (0.06) -10.5 (0.09) -10.0 (0.05) -9.3 (0.1)
a
Values in parentheses are standard deviations.
Table 2. Thermodynamic Parameter ∆S°* a at Different Sucrose Concentrations c (M) for the D,L Dansyl Amino Acid Transfer from the Mobile to the HSA Stationary Phase dansyltryptophan
dansylnorvaline
c
D
L
D
L
0.04 0.09 0.22 0.44 0.65 0.87
-6.7 (0.2) -6.5 (0.09) -6.0 (0.07) -5.6 (0.09) -5.2 (0.09) -4.7 (0.06)
-6.0 (0.05) -5.9 (0.05) -5.3 (0.07) -4.8 (0.08) -4.5 (0.1) -3.9 (0.1)
-5.6 (0.1) -5.6 (0.09) -4.8 (0.1) -4.5 (0.1) -3.9 (0.08) -3.2 (0.04)
-4.4 (0.1) -4.2 (0.06) -3.5 (0.07) -3.0 (0.05) -2.7 (0.08) -2.0 (0.1)
a
Values in parentheses are standard deviations.
Enthalpy-Entropy Compensation Study. Investigation of the enthalpy-entropy compensation temperature is an extra thermodynamic approach to the analysis of physicochemical data.25 Mathematically, enthalpy-entropy compensation can be expressed by the formula:
∆H° ) β∆S° + ∆G°β
(37)
where ∆G°β is the Gibbs free energy of a physicochemical interaction at a compensation temperature β. ∆H° and ∆S° are (25) Sander, L. C.; Field, L. R. Anal. Chem. 1980, 42, 2009.
Figure 3. Plots of ln k′T against -∆H° (kJ/mol) for the sucrose concentrations equal to 0.44 (A) and 0.87 M (B).
respectively the corresponding standard enthalpy and entropy. According to Eq 37, when enthalpy-entropy compensation is observed with a group of compounds in a particular chemical interaction, all of the compounds have the same free energy (∆G°β) at temperature β. If, therefore, enthalpy-entropy compensation is observed for dansyl amino acids, all will have the same net retention at the compensation temperature β, although their temperature dependencies may differ. Rewriting Eq 37 using Eq 35 gives
ln k′T ) ln k′β -
∆H° 1 1 R T β
(
)
(38)
where
ln k′β ) -
∆G°β + ln φ Rβ
(39)
Equation 38 shows that, if a plot of ln k′T against -∆H° is linear, then the solutes are retained by an essentially identical interaction mechanism. A plot of ln k′T (T ) 293 K) calculated for each of the D,L dansyl amino acids against -∆H° for the different values of the sucrose concentration was drawn. The correlation coefficients for the linear fits were at least equal to 0.962. Figure 3 shows ln k′T values plotted as a function of -∆H° for the sucrose concentrations equal to 0.44 and 0.87 M.The high degree of correlation can be considered to be adequate to verify enthalpy-entropy compensation.26 This is in agreement with a previous study9 in which the type of interaction was found to be the same for various dansyl amino acids using a similar chromatographic system. Enthalpyentropy compensation was also used to test the retention mechanism of dansyl amino acids when the sucrose concentration in the mobile phase changed. For a set of compounds where there is the enthalpy-entropy compensation, the slope of ln k′ vs -∆H° will be the same for the same type of reaction.27 The relative difference in the slope values obtained for all sucrose concentrations was inferior to 5%, thus indicating that the type of interaction for the solutes was the same whatever the mobile-phase composition. (26) Cole, L. A.; Dorsey, J. G. Anal. Chem. 1992, 64, 1317. (27) Tomasella, F. P.; Fett, J.; Cline Love, L. J. Anal. Chem. 1991, 63, 474.
Figure 4. Plots of ∆ ln k′ against ln c for D,L-dansyltryptophan at a column temperature of 288 K.
Dependence of the Selectivity and Retention Factor on Sucrose Concentration. From the retention factors, the ∆ ln k′ values for each solute and the R values (Eq 30) for the two enantiomer pairs were calculated at different sucrose concentrations and column temperatures. At T constant, when the concentration varied from cS to c, no significative differences within the experimental error were observed between ∆ ln k′D and ∆ ln k′L values (Eq 32) and the associated enantioselectivity values were found to be constant (Eq 34). These observations provide strong corroborating evidence that the sucrose molecules act only on the hydrophobic part (and not on the specific chiral part) of the interaction HSA-solute. As well, the plots of ∆ ln k′ in relation to ln c were determined for all solutes at each temperature. These plots exhibited a second-order polynomial function of ln c in all cases. The correlation coefficients of the fits were in excess of 0.991. Accordingly, with the experimental equality found above (∆ ln k′D ) ∆ ln k′L), identical curves were obtained for the two enantiomers of each dansyl amino acid at different column temperatures. Figure 4 represents the decreasing variations at a temperature equal to 288 K for the ∆ ln k′ of D,L-dansyltryptophan with increasing ln c. Since Eqs 32 and 34 were verified, the negative slope of the curve observed in Figure 4 was attributed exclusively to a decrease in the hydrophobic interaction between the solute and cavity when the sucrose concentration increased. As ncsP has a constant negative value for a solute, this negative slope implied that rc became lower than rcs as c increased (Eq 29). This is consistent with the proposed theory, i.e., a retention behavior implying a reduction of curvature radius of the binding cavity when the sucrose concentration varied from 0.04 (cs) to 0.87 M by antipathy (or mutual repulsion) between its apolar residues and mixed solvent. The sucrose contribution in increasing the cavitation energy term, which would have to enhance the interaction HSA-solute, was largely counterbalanced by the associated restriction of both the surface accessible to solvent and the curvature radius for the binding cavity. This revealed the importance of the binding cavity curvature state for the hydrophobic interaction between dansyl amino acids and stationary phase as can be inferred in the previous study9 of the pH dependence on the retention for the same compounds. Theoretical Application to Thermodynamic Parameter Variations with a Sucrose Concentration. For all the dansyl Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
2817
molecules from the cavity and solute was reduced by the interpenetration of solvation layers of the two components. Thus, this phenomenon contributed significantly to the classical negative sign of both the ∆H° and the ∆S°* values observed in reversedphase liquid chromatography.28 When the sucrose concentration increased from cs to c, according to the theory, the strong effect of the sugar on the surface tension reduced the curvature radius of the cavity by folding its hydrophobic residues out of contact with the mobile phase. The energetic gain associated with the solute “hydrophobic” transfer in the protein stationary phase decreased in relation to the decrease in the apolar contact of the cavity with the solvent. Thus, the ∆H° values became progressively less negative and were accompanied by the conventional increasing variation of ∆S°* values attributed to a weaker immobilization process.
Figure 5. Plots of ∆H° (kJ/mol) (a) and ∆S°* (b) against sucrose concentration c (M) for L-dansyltryptophan.
amino acids, ∆H° and ∆S°* values were plotted against the sucrose concentration values and showed the same variations. Panels a and b of Figure 5 represent these two plots, respectively, for L-dansyltryptophan. When c increased, both ∆H° and ∆S°* increased, becoming less negative. Such thermodynamic behavior can be explained by our theory as follows: At the lowest sucrose concentration cs, the curvature radius and the accessible to solvent surface area of the the binding cavity were expected to be maximal, as in the native state of a protein. The sugar molecules acted on the solute binding on HSA essentially by an increase in the hydrophobic effect. Thus, when the solute was transferred from the mobile to the stationary phase, the amount of work required for the exclusion of the sucrose
2818 Analytical Chemistry, Vol. 70, No. 14, July 15, 1998
CONCLUSION In this paper, a theoretical model was proposed to investigate the retention behavior of D,L dansyl amino acids on the HSA stationary phase using sucrose as mobile-phase modifier. From this model, the effect of sugar on the surface tension of a medium was implied in the hydrophobic step of ligand binding on HSA through (i) a positive action by classical enhancement of the mutual penetration of the two species solvation layers and (ii) a reverse contribution due to the restriction of the contact surface area of the cavity with the mobile phase. The results obtained from the treatment of the experimental values of both the retention factor and the enantioselectivity indicated that a decrease in the hydrophobic effect, due to a diminishing curvature radius of the cavity, must be considered in order to describe the retention behavior. The thermodynamic parameter trends with a sucrose concentration for solute transfer from the mobile to the stationary phase supported the fact that the nonspecific interaction was controlled primarily by contribution ii, i.e., the structural behavior of the binding cavity. ACKNOWLEDGMENT We thank Mireille Thomassin for her technical assistance. Received for review January 16, 1998. Accepted April 22, 1998. AC980039A (28) Alvarez-Zepeda, A.; Barman, B. N.; Martire, D. E. Anal. Chem. 1992, 64, 1978.
