Anal. Chem. 1999, 71, 1496-1499
Reanalysis of Solute Retention on Immobilized Human Serum Albumin Using Fractal Geometry Eric Peyrin* and Yves Claude Guillaume
Laboratoire de Chimie Analytique, Faculte´ de Me´ decine et Pharmacie, Place Saint-Jacques, 25030 Besanc¸ on Cedex, France
Earlier experimental data for sucrose dependence of dansyl amino acid retention on immobilized human serum albumin (Peyrin E.; et al. Anal. Chem. 1998, 70, 2812) are reexamined within a fractal framework. A mathematical development based on the fractal geometry of Mandelbrot is proposed to provide a more realistic picture of the molecular association between the ligand and the site II cavity. The fractal dimension D of the cavity surface is calculated using the theoretical approach from previous data. Results show that the surface morphology of the cavity is strongly influenced by the surface tension effects of sucrose molecules, the salting-out agent leveling the surface irregularities. In addition, dansyl amino acid retention and thermodynamic parameter variations are discussed using this fractal concept of surface fluctuations. Affinity chromatography with protein immobilized on the support is specially suited for studying drug-protein interactions. A number of previous reports have examined the mechanisms of the compound binding on various protein stationary phases. Allenmark et al.1 described the molecular interactions which were implicated in the retention behavior of different solutes on immobilized bovine serum albumin (BSA). Hermansson2 and more recently Schill et al.3 investigated the binding and stereoselectivity properties of the R1-glycoprotein (AGP) column. The association constants for warfarin, salicylic acid, and diazepam with immobilized human serum albumin (HSA) were determined by Shimamori and Nakano.4 The thermodynamic processes involved in the binding and separation of warfarin and thyroxine enantiomers on the HSA column were characterized by Loun and Hage5,6 using frontal analysis. Wainer’s group7 defined the stereochemical aspects of benzodiazepine binding to HSA using a quantitative structure-enantioselective retention relationship (QSERR). Numerical simulations of the chromatographic process were applied by Vidal-Madjar et al.8 to determine the equilibrium isotherm of phenylbutazone with HSA immobilized on dihydroxysilica. (1) Allenmark, S.; Bomgren, B.; Boren, H. J. Chromatogr. 1984, 316, 617. (2) Hermansson, J. J. Chromatogr. 1983, 269, 71. (3) Schill, I.; Wainer, I. W.; Barkan, A. J. Liq. Chromatogr. 1986, 9, 641. (4) Shimamori, Y.; Nakano, N. I. Yakugaku Zashii 1983, 163, 771. (5) Loun, B.; Hage, D. S. Anal. Chem. 1994, 66, 3814. (6) Loun, B.; Hage, D. S. J. Chromatogr. 1992, 579, 225. (7) Kaliszan, R.; Noctor, T. A. G.; Wainer, I. W. Mol. Pharmacol. 1992, 42, 512. (8) Vidal-Madjar, M.; Jaulmes, A.; Racine, M.; Sebille, B. J. Chromatogr. 1988, 458, 13.
1496 Analytical Chemistry, Vol. 71, No. 8, April 15, 1999
In earlier reports, Peyrin et al.,9-11 using affinity chromatography, studied the interactions implied in the binding of negatively charged test molecules, i.e. the dansyl amino acids, on the HSA site II cavity. The role of both the binding crevice structural behavior and the hydrophobic effect on the retention mechanism of solutes was proven using temperature studies and differential scanning calorimetry.12 More recently, to gain more insight into the complex problem area of the mechanism of retention and chiral recognition, a study of the surface tension effect of sucrose on the solute retention factor was carried out by varying the salting-out agent concentration in the mobile phase.13 It was demonstrated that the compound retention decrease accompanying the sucrose concentration increase was governed by a restriction of the binding cavity surface area accessible to the salting-out agent due to the increased surface tension effects. On the assumption that the binding cavity is a sphere and by use of a model that takes into account the curvature dependence of surface energy, this behavior was attributed to a reduction in the curvature radius of the site II pocket.13 In this paper, an approach based on the fractal geometry of Mandelbrot was proposed to provide a more precise and more realistic understanding of the molecular processes that take place in the sucrose dependence of dansyl amino acid binding on the HSA site II cavity. This implied a fractal description of the surface of the pocket, which was consistent with the molecular roughness concept of the protein surface. A simple mathematical development was carried out to link the fractal surface dimension D to the sucrose concentration c and the solute retention factor. The fractal dimension D of the cavity surface was estimated for the different chromatographic conditions, and earlier experimental data were reexamined according to this novel theoretical approach. THEORY The concept of fractal geometry developed by Mandelbrot14 can be used to describe complex irregular or fragmented structures. It has been applied successfully in a variety of areas such as astronomy, economy, geomorphology, or biology. A (9) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. J. Chromatogr. Sci. 1998, 36, 97. (10) Peyrin, E.; Guillaume, Y. C. Chromatographia 1998, 48, 431. (11) Peyrin, E.; Guillaume, Y. C.; Morin, N.; Guinchard, C. J. Chromatogr. 1998, 808, 113. (12) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1997, 69, 4979. (13) Peyrin, E.; Guillaume, Y. C.; Morin, N.; Guinchard, C. Anal. Chem. 1998, 70, 2812. (14) Mandelbrot, B. Recherche 1978, 9, 1. 10.1021/ac981180m CCC: $18.00
© 1999 American Chemical Society Published on Web 03/04/1999
number of fractal applications to protein structures have been described in recent reports. The allosteric effects of proteins and enzymes have been investigated through fractal mechanisms by Li et al.15 This group has also presented a simple fractal analysis to characterize the thermodynamic behavior of proteins.16 Sutaria et al.17 have used fractal analysis to examine the kinetics of the binding of antigen in solution to an antibody immobilized on a biosensor. Abad-Zapareto et al.18 have demonstrated that the exponent of the Box-Cox transformation is related to both the shape and the fractal dimension of the protein. The local atomic group packing which characterizes the protein surface relief can be analyzed within a fractal framework. Specifically, the degree of irregularity, i.e. the roughness of a protein surface, is represented by the fractal dimension D. A smooth spherical surface has a dimension D equal to 2. When the surface irregularity increases, the fractal dimension varies between 2 and 3. The fractal dimension can be defined by the following equation:19
sD /s ) r D-2
(1)
where s and sD are respectively the smooth (geometric) and the irregular (apparent) spherical surfaces and r is the corresponding radius. In our previous report on the sucrose dependence of solute binding on a site II cavity, the variation of the retention factor was linked to the sucrose concentration c and the change of pocket curvature radius and can be expressed by the following equation:13
[
∂∆ ln k′ ∂ ln c
]
T
) 4ncS
P
(
1 1 Z rc rcS
)
(2)
where cS is the smallest sucrose concentration equal to 0.04 M and c represents the other concentrations. ∆ ln k′ is the change in ln k′ observed with the variation from cS to c, Z is a constant associated with the radius of the sucrose molecule, ncSP is the excess of the sucrose molecule for the surface area of the cavity implicated in the binding process at 0.04 M and rc and rcS are the curvature radius values corresponding to c and cS, respectively. As the cavity is assumed to be spherical, eq 2 can be rewritten as
[
∂∆ ln k′ ∂ ln c
]
T
(
) 8ncSP Zπ 1/2
1
sc
1/2
-
1
)
scS1/2
(3)
where sc and scS are the surface areas of the spherical cavity for c and cS, respectively. This last equation implies that the solute retention decrease with increasing c was the result of a reduction of the pocket spherical surface, which was considered to be completely smooth. Such behavior could be responsible for a strong limitation in the spatial region accessible to the ligand and thus an alteration in (15) Li, H. Q.; Chen, S. H.; Zhao, H. M. Biophys. J. 1990, 58, 1313. (16) Li, H. Q.; Chen, S. H.; Zhao, H. M. Int. J. Biol. Macromol. 1990, 12, 374. (17) Sutaria, M.; Sadana, A. Biotechnol. Prog. 1997, 13, 464. (18) Abad-Zapareto, C.; Lin, C. T. Biopolymers 1990, 29, 1745. (19) Farin, D.; Avnir, D. In Proceedings of the IUPAC Symposium on the Characterization of Porous Solids; Unger, K. K., Behrens, D., Kral, H., Eds.; Elsevier: Amsterdam, 1988.
the enantioselective properties of the site II cavity. Nevertheless, no significative differences within the experimental error were observed between the enantioselectivity values when the sucrose concentration varied from cS to c.13 A more realistic model must consider the packing density of amino acid residues defining the surface structure and thus its fractal dimension. In this case, the change in surface area accessible to the sucrose molecule was treated as a modification in the texture of the spherical surface. Therefore, in assimilating the radius r constant over the sucrose concentration range, we obtain the following equation using eq 1:
sc ) s(scS /s)(Dc-2)/(DcS-2)
(4)
where Dc and DcS are the fractal dimensions of the surfaces sc and scS, respectively. By combining eqs 3 and 4, we obtain
[
∂∆ ln k′ ∂ ln c
]
[
) 8ncSPZπ 1/2
T
1 (Dc-2)/(DcS-2) 1/2
1/2
s
[(scS/s)
-
]
1
]
scS1/2
(5)
Considering P as the slope of the ∆ ln k′ vs ln c plot, the rearrangement of eq 5 gives Dc as a function of the solute retention behavior:
[ [
ln
Dc ) 2 (2 - DcS)
[
P s 8ncSPZ π
1/2
()
+
ln(scS/s)
()] s scS
1/2
]] +1
(6)
Equation 6 links the fractal dimension of the surface with the variation of solute retention in relation to sucrose concentration, i.e. P, at constant T. This provides a mathematical treatment of the surface morphology dependence of the binding process of dansyl amino acid on the site II cavity. RESULTS AND DISCUSSION Estimation of the Fractal Dimension of the Cavity Surface. The calculation of the Dc value from the slope P using eq 6 required a knowledge of various physical parameters. The fractal dimension of the surface of a protein has been investigated in a number of studies. Typically, the value for the surface fractal dimension is 2.2.20 At the lowest sucrose concentration cS, the surface of the binding cavity was expected to be maximally irregular, as in the native state of the protein.13 Thus, DcS was fixed at a value equal to 2.2. The radius curvature r and the corresponding smooth spherical surface of the binding cavity were determined from our preceding study21 and were found equal to 8.5 and 908 Å2, respectively. Incorporating s, r, and DcS values into eq 1, we obtained an scS value equal to 1393 Å2. Z was found equal to 4.0 Å from the van der Waals volume of sucrose.22 ncSP values were calculated from the retention data for the sucrose concentration domain 0-0.04 M corresponding to a retention factor increase with increasing c. Values of -8.3 and -10 were (20) Fushman, D. J. Biomol. Struct. Dyn. 1990, 7, 1333. (21) Peyrin, E.; Guillaume, Y. C.; Guinchard, C. Anal. Chem. 1998, 70, 4235. (22) Back, J. F.; Oakenfull, D.; Smith, M. B. Biochemistry 1979, 18, 5191.
Analytical Chemistry, Vol. 71, No. 8, April 15, 1999
1497
Table 1. Physical Parameter Values Used in Eqs 1 and 6 DcS r a
2.2 8.5 Å
s scS
908 Å2 1393 Å2
Z ncSP
4.0 Å -8.3,a -10.0b
For dansyl norvaline. b For dansyl tryptophan.
Table 2. Fractal Dimension Values Da Calculated from Eq 6 for Different Sucrose Concentrations c (M) at Various Column Temperatures T D c (M)
T ) 283 K
T ) 293 K
T ) 303 K
0.09 0.22 0.44 0.66 0.87
2.170 (0.003) 2.090 (0.002) 2.030 (0.002) 2.000 (0.003) 1.970 (0.001)
2.180 (0.004) 2.100 (0.002) 2.040 (0.003) 2.010 (0.002) 1.980 (0.002)
2.180 (0.003) 2.110 (0.003) 2.060 (0.001) 2.030 (0.003) 2.010 (0.002)
a
Figure 2. Plots of ln k′ vs D at T ) 278 (0), 283 (]), 288 (b), 293 (×), 298 ([), 303 (O), and 308K (+) for L-dansyltryptophan.
Values in parentheses are standard deviations.
Figure 1. Plot of ∆D/∆T (0.01 D unit/°C) vs c (M).
obtained for dansylnorvaline and dansyltryptophan, respectively. All values are summarized in Table 1. Using data from a previous paper,13 the fractal dimensions were determined from the ∆ ln k′ vs ln c plots of dansylnorvaline and dansyltryptophan at all column temperatures. Identical results were obtained from the experimental data for these solutes. Table 2 contains a list of D values for sucrose concentrations 0.09, 0.22, 0.44, 0.66, and 0.87 M at T equal to 283, 293, and 303 K. The fact that no difference in D value was observed from dansylnorvaline and dansyltryptophan data treatments confirmed that solute retention was controlled by a chemical modification in the texture of the surface with increasing c. Further evidence for this feature was provided by a study on the temperature dependence of the surface fractal dimension. The variation of D when column temperature changed, i.e. ∆D/∆T, was calculated at sucrose concentrations equal to 0.09, 0.22, 0.44, 0.66, and 0.87 M. The plot of ∆D/∆T against c was drawn (Figure 1). The correlation coefficient for the linear fit was equal to 0.988. The typical standard deviations of the slope and intercept were respectively 0.005 and 0.01. For the low c values, the change in fractal dimension due to the temperature dependence was considered negligible (∆D/∆T ) 3 × 10-4 and 6 × 1498 Analytical Chemistry, Vol. 71, No. 8, April 15, 1999
10-4 D unit/°C for c ) 0.09 and 0.22 M, respectively). Similar results were found by Dewey,23 who showed that the fractal surface of native lysosyme was relatively independent of temperature in the range 4-41 °C. With an increasing sucrose concentration, a weak but significative increase in D was observed corresponding to a variation of D in relation to temperature equal to 1.3 × 10-3 and 1.6 × 10-3 D unit/°C for c ) 0.66 and 0.87 M, respectively. For high c values, the exclusion of sucrose molecules from the cavity surface area was facilitated by the increase in thermal energy. This produced a weaker salting-out effect on the binding pocket surface, which can be reorganized more easily with a less smooth morphology. On the basis of this explanation, it would appear obvious that the sucrose molecules altered the rough nature of the protein surface by increasing the surface tension of the mobile phase. This was consistent with a study reported by Kendrick et al.,24 who observed that the sucrose molecules restrict the conformational fluctuations of recombinant interleukin 1 receptor antagonist and thus induce a less irregular native state of the protein. Surface Fractal Dimension Dependence of Solute Binding. Our earlier chromatographic data on the dependence of the logarithmic retention factor and thermodynamic parameters for dansyl amino acids on the sucrose concentration13 were reassessed in accordance with the fractal model relating the rough morphology of the cavity surface. The ln k′ values were plotted against D at column temperatures of 278, 283, 288, 293, 298, 303, and 308 K. In the same way, ∆H° and ∆S°* (corresponding to ∆S°/R + ln φ,11,12 where R is the gas constant and φ is the phase ratio) values were plotted against fractal dimension average values. Figures 2-4 represent the respective variations of ln k′, ∆H°, and ∆S°* with increasing D for L-dansyltryptophan. These variations were the same for each solute enantiomer. The plots of ln k′ were expressed by a second-order polynomial equation. The correlation coefficients of the fits were over 0.994. The plots of ∆H° and ∆S°* vs D can be described by two straight lines corresponding to the two sucrose concentration domains 0.04-0.22 and 0.44-0.87 M, (23) Dewey, T. G. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 12101. (24) Kendrick, B. S.; Chang, B. S.; Arakawa, T.; Peterson, B.; Randolph, T. W.; Manning, M. C.; Carpenter, J. F. Proc. Natl. Acad. Sci. U.S.A. 1997, 94, 11917.
Figure 3. Plot of ∆H° vs D for L-dansyltryptophan.
Figure 4. Plot of ∆S°* vs D for L-dansyltryptophan. Table 3. Fractal Dimension Contributions to Enthalpy Term Changes D∆H°/DD ((kJ/mol)/D unit) and Entropic Term Changes D∆S°*/DD for Dansyltryptophan and Dansylnorvaline at the Two Sucrose Concentration Domainsa dansyltryptophan
dansylnorvaline
c (M)
∂∆H°/∂D
∂∆S°*/∂D
∂∆H°/∂D
∂∆S°*/∂D
0.04-0.22 0.44-0.87
-6.0 -25.0
-7.1 -15.0
-13.6 -23.3
-8.6 -21.6
a
See Figures 3 and 4.
respectively. From the slopes of two linear fits (r2 > 0.956), the fractal dimension contributions to the enthalpic and entropic energy changes were determined for dansylnorvaline and dansyltryptophan. Table 3 shows these values for each sucrose concentration domain. On the basis of the retention and thermodynamic variations, a simple descriptive picture of dansyl amino acid binding on the HSA site II cavity was exposed via the fractal concept of the surface topology: (i) At a low sucrose concentration from 0.04 to 0.22 M, the irregular surface was weakly affected by the salting-out properties
of the sucrose molecule. For example, Dc)0.09M ≈ 2.18 and Dc)0.22M ≈ 2.10 corresponding to a significative degree of disorder at the spherical surface. The solute was always able to form stabilizing contacts with the cavity surface by allowing a great number of interactions with exposed residue molecular irregularities. Thus, the retention factor decrease between Dc)0.04M and Dc)0.22M (Figure 2) was accompanied by a relatively reduced variation of ∆H° and ∆S°* in relation to D for the corresponding sucrose concentration domain (Table 3). (ii) As the sucrose concentration increased between 0.44 and 0.87 M, the surface tension effect of sucrose resulted in a smooth morphology of the surface structure (Dc)0.66M ≈ 2.01 and Dc)0.87M ≈ 1.98). The stronger decreased affinity of the solute for the smooth binding region between Dc)0.44M and Dc)0.87M (Figure 2) can be explained by a smoothing of the surface heterogeneity. Therefore, the enthalpy and entropy changes in solute transfer from the mobile to the stationary phase varied more intensively with D in this sucrose concentration range (Table 3). This behavior, i.e. a greater affinity of ligand for an irregular surface than for a smooth surface, has been suggested by some authors over the past few years. The hydrophobic effect implied in biomolecular association is related using the scaled particle theory to the molecular surface (atom packing level) rather than the classical accessible surface.25 In addition, increasing surface roughness is associated with higher surface energies in systems with packing densities similar to those observed for amino acid residues in proteins.26 Finally, the probability of particles sticking to a single crystal surface is higher for atomically rough planes than for smooth planes.27 CONCLUSION In this paper, the concept of roughness of a protein surface was applied to the sucrose dependence of dansyl amino acidsite II cavity interactions. The degree of irregularity of the cavity surface was characterized by the fractal dimension, which was calculated from earlier experimental data using a simple mathematical approach. It was shown that the surface tension effect of the sucrose molecules smoothed the surface heterogeneity. This was responsible for a decrease in solute binding at the cavity surface when the sucrose concentration was increased by a reduction of stabilizing contacts between the dansyl amino acid and the exposed residues of the cavity surface. This behavior was confirmed by a thermodynamic behavior reanalysis using the fractal model. Received for review October 29, 1998, Accepted January 12, 1999. AC981180M (25) Jackson, R. M.; Sternberg, M. J. Protein Eng. 1994, 7, 371 (26) Rees, D. C.; Wolfe, G. M. Protein Sci. 1993, 2, 1882. (27) Somorjai, G. Chemistry in Two Dimensions: Surfaces; Cornell University Press: Ithaca, NY, 1981.
Analytical Chemistry, Vol. 71, No. 8, April 15, 1999
1499
