Chiral Separation Mechanisms in Protein-Based HPLC Columns. 2

and biomedical applications of affinity chromatography: Recent trends and developments .... QCM/HCC as a platform for detecting the binding of war...
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Anal. Chem. 1996, 68, 1218-1225

Chiral Separation Mechanisms in Protein-Based HPLC Columns. 2. Kinetic Studies of (R)- and (S)-Warfarin Binding to Immobilized Human Serum Albumin Bounthon Loun and David S. Hage*

Department of Chemistry, University of Nebraska, Lincoln, Nebraska 68588

This work used plate height measurements to investigate the kinetics of (R)- and (S)-warfarin binding to an immobilized HSA column. The dissociation rate constants for (R)- and (S)-warfarin on this column increased from 0.06 to 1.9 s-1 and from 0.06 to 0.36 s-1 between 4 and 45 °C. The corresponding association rate constants increased from 2.4 × 104 to 3.2 × 105 M-1 s-1 for (R)warfarin and from 4.4 × 104 to 7.2 × 104 M-1 s-1 for (S)-warfarin over the same temperature range. From the dissociation data, it was found that an increase in temperature led to a large decrease in the plate height due to stationary phase mass transfer for both enantiomers. Further studies indicated that (R)- and (S)-warfarin had similar activation energies for their binding to HSA. For (R)-warfarin, most of this energy requirement was due to the change in enthalpy of the system, while for (S)warfarin, it was mainly due to the change in entropy. All of these results agree with an earlier model, in which (R)and (S)-warfarin were proposed to interact with regions on the interior and exterior of HSA, respectively. In addition, these results offer a number of useful insights into the mechanisms of protein-based chiral separations. The resolution and analysis of chiral compounds remains one of the greatest challenges in the field of separation science.1,2 Many methods have been developed for the separation of chiral compounds, but one particularly promising approach involves the use of immobilized proteins as chromatographic stationary phases.1-3 A number of different proteins have been used for this purpose, including R1-acid glycoprotein, serum albumin, ovomucoid, avidin, and cellulase. Together, these proteins can be used to separate a variety of cationic, anionic, and neutral molecules.1-3 There is a reasonable amount of information regarding what types of mobile phases should be used with these protein supports for chiral separations (e.g., see ref 2), but much less is known about the actual nature of these separation processes.1 This has led to a number of recent reports on the thermodynamic properties and binding mechanisms for the interactions of some chiral compounds with model proteins, such as human serum (1) Armstrong, D. W. Anal. Chem. 1987, 59, 84A. (2) Allenmark, S. Chromatographic Enantioseparation: Methods and Applications, 2nd ed.; Ellis Horwood: New York, 1991; Chapter 7. (3) Allenmark, S. In Chiral Separation by HPLC; Krustlovic, A. M., Ed.; Ellis Horwood: New York, 1989; Chapter 11.

1218 Analytical Chemistry, Vol. 68, No. 7, April 1, 1996

albumin4,5 or turkey ovomucoid.6 However, there are still few data available on the kinetics of these interactions. Such data would be particularly useful in the design of new protein-based separations, since protein supports tend to have lower efficiencies than more traditional types of chromatographic columns.3 This work will study the kinetic processes involved in proteinbased chiral separations by using the binding of (R)- and (S)warfarin to immobilized human serum albumin as a model system. Human serum albumin (HSA) is a 66 500 Da plasma protein7 that is involved in the binding and transport of a wide range of small organic and inorganic compounds.8,9 Warfarin is a common anticoagulant agent that is known to bind to HSA. This agent exists in two enantiomeric forms, (R)and (S)-warfarin. Both forms bind to the same general area on HSA10 but have different equilibrium constants for these interactions.5 This binding occurs at the warfarin-azapropazone site of HSA,10 a region which has recently been identified as being in the IIA subdomain of this protein.11 In an earlier report,5 frontal analysis was used to examine the equilibrium constants and thermodynamic processes involved in the binding of (R)- and (S)-warfarin to an immobilized HSA column. It was confirmed that (R)- and (S)-warfarin were binding to the same general region on HSA; however, it was also found that very different processes were involved in these interactions. For example, even though the total changes in free energy for the binding of (R)- and (S)-warfarin were similar at 37 °C, the contribution due to entropy was greater for the (R)-enantiomer. These results suggested that (R)-warfarin was interacting mainly with the binding site interior, while (S)-warfarin was interacting more with the site’s outer surface. This model was confirmed by examining the retention of (R)- and (S)-warfarin on the HSA column under various organic modifier conditions.5 This current study investigates the binding and dissociation kinetics of (R)- and (S)-warfarin with immobilized HSA through (4) Yang, J.; Hage, D. S. J. Chromatogr. 1993, 645, 241. (5) Loun, B.; Hage, D. S. Anal. Chem. 1994, 66, 3814. (6) Pinkerton, T. C.; Howe, W. J.; Ulrich, E. L.; Comiskey, J. P.; Haginaka, J.; Murashima, T.; Walkenhorst, W. F.; Westler, W. M.; Markley, J. L. Anal. Chem. 1995, 67, 2354. (7) Dugiaczyk, A.; Law, S. W.; Dennison, O. E. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 71. (8) Sjo ¨holm, I. In Drug-Protein Binding; Reidenberg, M. M., Erill, S., Eds.; Praeger Publishers: New York, 1986; Chapter 4. (9) Mu ¨ ller, W. E.; Fehske, K. J.; Schla¨fer, S. A. C. In Drug-Protein Binding; Reidenberg, M. M., Erill, S., Eds.; Praeger Publishers: New York, 1986; Chapter 2. (10) Sudlow, G.; Birkett, D. J.; Wade, D. N. Mol. Pharmacol. 1976, 12, 1052. (11) He, X. M.; Carter, D. C. Nature 1992, 358, 209. 0003-2700/96/0368-1218$12.00/0

© 1996 American Chemical Society

the use of plate height measurements. In this approach, van Deemter-type plots will be used to estimate the various plate height contributions for (R)- and (S)-warfarin on an immobilized HSA support. The values obtained for the plate height due to stationary phase mass transfer data will then be used to determine the dissociation rate constants for the interactions of (R)- and (S)warfarin with HSA. By using these results along with the known equilibrium constants for this system,5 the association rate constants for warfarin/HSA binding can also be obtained. Information on the activation energies and changes in enthalpy or entropy that occur during formation of the warfarin/HSA activated complex can be determined by performing these studies at several different temperatures. The resulting data should provide a more detailed understanding of how these compounds bind to HSA and of the processes that give rise to band-broadening for chiral molecules and other solutes on immobilized protein columns. THEORY Plate height measurements were used in this work to examine the band-broadening processes on an immobilized HSA column and to measure the kinetics of warfarin/HSA interactions. Previous studies have used affinity columns and plate height measurements to study the binding of concanavalin A with various sugars.12,13 However, little work has been done using this technique with other types of biomolecules. The basis for this method involves a detailed examination of the various bandbroadening processes that occur on the column of interest. As with other chromatographic systems, the total plate height (Htot) measured for a solute injected onto an immobilized protein column can be written as the sum of the contributing terms:

Htot ) Hm + HL + Hsm + Hs + Hec

(1)

In eq 1, the factors on the right-hand side represent the plate height contributions due to mobile phase mass transfer (Hm), longitudinal diffusion (HL), stagnant mobile phase mass transfer (Hsm), stationary phase mass transfer (Hs), and extracolumn bandbroadening (Hec).14 Of all the terms in eq 1, the one that is most directly related to the kinetics of solute-ligand binding is the plate height contribution due to stationary phase mass transfer (Hs). For a column that contains a stationary phase with a fixed number of ligand sites (e.g., an immobilized protein support), the following expression can be used to relate Hs to the reaction rate between an injected solute and the immobilized ligand:14

Hs )

2uk′ kd(1 + k′)2

is small versus the amount of immobilized ligand in the column (i.e., linear elution conditions are present).14 To estimate the value of Hs from measurements of the total plate height (Htot), it is necessary to first correct Htot for other sources of band-broadening. Extracolumn band-broadening (Hec) can be determined by measuring the plate height for the solute as it is injected onto the chromatographic system when all components except the column are present. The plate height contribution due to longitudinal diffusion (HL) in HPLC is usually much smaller than the other plate height terms and is often considered negligible.13,14 A number of different expressions have been derived to describe the plate height term for mobile phase mass transfer (Hm).15-19 However, with all of these equations, it can generally be assumed that Hm is independent of flow rate or has only a small flow rate dependence under the typical operating conditions used in HPLC. This last assumption is useful since it allows Hm to be estimated from the intercepts of plots made for (Htot - Hec) versus u on HPLC columns.13,14 The plate height contribution due to stagnant mobile phase mass transfer (Hsm) is the only item in eq 1 that shows a dependence on linear velocity that is similar to that seen for Hs. The value of Hsm for a porous, spherical support can be described by the following equation:13,14

Hsm )

2uVp[1 + (Vmk′/Vp)]2

(3)

k-1Vm(1 + k′)2

In eq 3, Vp is the volume of mobile phase within the pores of the support (i.e., the volume of stagnant mobile phase), Vm is the total volume of mobile phase in the column (i.e., the column void volume), and k-1 is a combination of geometrical and physical factors (e.g., particle size and diffusion coefficients) that describe the mass transfer of solute from the inside to the outside of the porous support.20 One way of estimating Hsm can be seen by combining eqs 1-3. The result is the following expression that describes the relationship between the individual plate height terms Hm, Hsm, or Hs and the total plate height after correction for extracolumn band-broadening (Htot - Hec):

(Htot - Hec) ) Hm +

2uVp[1 + (Vmk′/Vp)]2 k-1Vm(1 + k′)2

+

2uk′ kd(1 + k′)2 (4)

(2)

In eq 2, u is the linear velocity of mobile phase in the column, k′ is the capacity factor of the solute, and kd is the apparent rate constant for the dissociation of solute from the immobilized ligand. In this relationship, it is assumed either that solute-ligand binding occurs at a single type of site in the column or that the net rate of these interactions can be described by a single set of rate constants. It is also assumed that the amount of injected solute (12) Muller, A. J.; Carr, P. W. J. Chromatogr. 1984, 284, 33. (13) Anderson, D. J.; Walters, R. R. J. Chromatogr. 1986, 376, 69. (14) Walters, R. R. In Analytical Affinity Chromatography; Chaiken, I. M., Ed.; CRC Press: Boca Raton, FL, 1987; Chapter 3.

Equation 4 indicates that a plot of (Htot - Hec) versus linear velocity (u) should give a straight line with an intercept of Hm and a slope that is equal to a combination of factors given in the last two terms on the right (i.e., Hsm and Hs). For a nonretained solute (i.e., k′ ) 0), eq 4 reduces to the form shown below: (15) Van Deemter, J. J.; Zuiderweg, F. J.; Klinkenberg, A. Chem. Eng. Sci. 1956, 5, 271. (16) Giddings, J. C. Anal. Chem. 1963, 35, 1338. (17) Huber, J. F. K. J. Chromatogr. Sci. 1969, 7, 85. (18) Horvath, C.; Lin, H.-J. J. Chromatogr. 1976, 126, 401. (19) Kennedy, G. J.; Knox, J. H. J. Chromatogr. Sci. 1972, 10, 549. (20) Hage, D. S.; Walters, R. R.; Hethcote, H. W. Anal. Chem. 1986, 58, 274.

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(Htot - Hec) ) Hm +

2uVp k-1Vm

(5)

This new expression predicts that a plot of (Htot - Hec) versus u for a nonretained solute will give a linear relationship with a slope of (2Vp/k-1Vm). By using this slope and independent estimates of Vm and Vp, the value of k-1 for the given solute and support can be obtained. These data can then be used along with eq 3 to estimate the value of Hsm when the solute is injected onto the same support but in the presence of an immobilized ligand. The values of Hm and Hsm that are determined from eqs 3-5 can be used to correct the term (Htot - Hec) for any bandbroadening contributions that are not related to solute-ligand interactions. The portion of (Htot - Hec) that remains should then be equal to the value of Hs for the solute. To obtain rate constant information from this term, Hs needs to be determined at several linear velocities. The results are then used to make a plot of Hs versus [uk′/(1 + k′)2]. According to eq 2, the result should be a linear relationship with a slope of (2/kd) and an intercept of zero. This provides the value of kd for the solute-ligand interactions. If the association equilibrium constant (Ka) for solute-ligand binding is also known, then it is possible to calculate the corresponding apparent association rate constant (ka) by using the relationship Ka ) (ka/kd). Many of the parameters that make up the plate height terms in eqs 2-5 are temperature dependent (e.g., kd, k′, and k-1). This means that each of these plate height terms must be determined under the same temperature conditions in order to obtain accurate estimates of kd and ka. By using this approach to determine kd and ka over a range of temperatures, information can also be obtained on the energetics of solute-ligand binding. For example, according to the activated complex theory, the second-order association rate constant for solute-ligand binding (ka) can be related to the absolute temperature (T) through the following equation:21

ln(ka/T) ) ln(κR/Nh) - (∆Hq/RT) + (∆Sq/R)

(6)

In eq 6, R is the ideal gas law constant, N is Avogadro’s number, h is Planck’s constant, and κ is the transmission coefficient for the reaction (usually taken as being equal to 1). The term ∆Hq is the change in enthalpy during the formation of the activated complex from the initial reactants, and ∆Sq is the associated change in entropy for this process. Equation 6 predicts that a plot of ln(ka/T) versus 1/T will yield a linear relationship with a slope of -∆Hq/R and an intercept of [ln(κR/Nh) + (∆Sq/R)]. The values of ∆Hq and ∆Sq can be determined from the slope and intercept by using the known values of the other factors that appear in these terms. From the resulting parameters, the change in free energy on going from the initial reactants to the activated complex (∆Gq) can also be calculated, as shown below.21

∆Gq ) ∆Hq - T∆Sq

(7)

A relationship similar to that in eq 6 can be derived for the dissociation rate constant (kd). For instance, the temperature (21) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms; McGraw-Hill: New York, 1981; Chapter 6.

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Analytical Chemistry, Vol. 68, No. 7, April 1, 1996

dependence of the association equilibrium constant for an analyte that has single site binding with an immobilized ligand is given by5

ln(Ka) ) -∆H/RT + ∆S/R

(8)

where ∆H is the net change in energy due to enthalpy on going from the reactants to the final product and ∆S is the net change in entropy for the reaction. Since Ka ) (ka/kd), eqs 6 and 8 can be rearranged and combined to give the following expression for kd:

ln(kd/T) ) ln(κR/Nh) - ({∆Hq - ∆H}/RT) + ({∆Sq - ∆S}/R) (9)

This equation is of the same form as that seen for ka in eq 6, but with the use of the energy terms {∆Hq - ∆H} and {∆Sq - ∆S} instead of ∆Hq and ∆Sq. These new terms simply represent the changes in enthalpy and entropy, respectively, that occur when going from the final product back to the activated complex during analyte-ligand dissociation. EXPERIMENTAL SECTION Reagents. The HSA (Cohn fraction V, 99% globulin-free) and 3,3′,5-L-triiodothyronine (L-T3) were from Sigma (St. Louis, MO). The (R)-(+)- and (S)-(-)-warfarin were provided by DuPont Pharmaceuticals (Wilmington, DE). The Nucleosil Si-1000 (7 µm particle diameter, 1000 Å pore size) was obtained from Alltech (Deerfield, IL). Reagents for the bicinchoninic acid (BCA) protein assay were from Pierce (Rockford, IL). All other chemicals and biochemicals used in this work were of the purest grades available. All solutions were prepared with water obtained from a NANOpure water system (Barnstead, Dubuque, IA). Apparatus. The chromatographic system consisted of one CM3000 isocratic pump and one SM3100 UV/visible variable wavelength absorbance detector from Milton Roy (Riviera Beach, FL). Samples were injected by using a Rheodyne 7010 injection valve (Cotati, CA) equipped with a Phase Sep event marker (Phase Separations, Queensferry, U.K.) and a 20 µL sample loop. Data were collected with a Milton Roy Chromlink interface and LCAdvantage software. Chromatograms were processed by programs written in Microsoft QuickBASIC (Redmond, WA) using double-precision logic. The columns and mobile phases were maintained at a constant temperature by an Isotemp 9100 circulating water bath (Fisher Scientific, Pittsburgh, PA). The columns were packed with an Alltech HPLC column slurry packer. Methods. The immobilized HSA support used in this work was prepared as described previously.5 In this method, the HSA was attached to diol-bonded Nucleosil Si-1000 silica by the Schiff base method.22 The diol coverage of the Nucleosil prior to activation was 20 ( 3 µmol (1 SD of the mean) per gram of silica, as determined in duplicate by an iodometric titration. After immobilization, the HSA support was washed several times with 2 N sodium chloride and 0.067 M potassium phosphate buffer (pH 7.4). It was then stored at 4 °C in the pH 7.4 phosphate buffer until further use. The protein content of this support, as (22) Larsson, P.-O. Methods Enzymol. 1984, 104, 212.

determined in duplicate by a BCA protein assay,23 was 204 ( 1 (1 SD) nmol of HSA per gram of silica.5 The immobilized HSA support and the diol-bonded silica that was used to make this support were each downward slurry-packed at 3500 psi into two separate 4.5 cm × 4.1 mm i.d. columns of a previously published design.24 Both columns were enclosed in water jackets for temperature control. All studies, except those examining the temperature dependence of (R)- and (S)-warfarin binding with HSA, were performed at 37 ( 0.1 °C. All mobile phases and packing solvents in this work were prepared with 0.067 M potassium phosphate buffer (pH 7.4). Prior to use, all mobile phases were passed through a 0.45 µm cellulose acetate filter and degassed under vacuum for 10 min. Elution of the (R)- and (S)warfarin was detected by monitoring the absorbance of the mobile phase at 310 nm. Band-broadening studies were performed by making injections of (R)- or (S)-warfarin onto the immobilized HSA column at flow rates ranging from 0.09 to 0.35 mL/min. At least three replicate injections were made under each set of conditions. The mobile phase used in this study was 0.067 M phosphate buffer (pH 7.4) containing 0-13 µM L-T3 as a competing agent. The L-T3 solutions were prepared as described previously25 and were used to control the capacity factors for (R)- and (S)-warfarin during the bandbroadening studies. All experiments with the HSA column used a mobile phase concentration of L-T3 that produced a capacity factor for (R)- or (S)-warfarin that was approximately equal to 1, since these retention conditions give the highest and most easily measured values for Hs.14 The warfarin samples were made at a concentration of 5-9 µM in the desired mobile phase. Consistent results for the retention times and variances were obtained throughout this range of concentrations, indicating that linear elution conditions were present during these studies. The retention times and variances of the (R)- and (S)-warfarin peaks were calculated by using the modified B/A tenth-height method.26 These values were then used to determine the total plate height for each peak. The column void volume (Vm) and plate height for a nonretained solute were determined by injecting (R)-warfarin onto the diol-bonded silica column. The column pore volume (Vp) was determined from the measured value of Vm and information on the relative pore volume and packing density of the Nucleosil Si-1000 support, as provided by the manufacturer. Corrections for the extracolumn elution time and band-broadening were made by injecting (R)- or (S)-warfarin onto the system when no column was present. The linear velocity of the mobile phase was determined under each set of conditions by dividing the length of the diol-bonded silica column by its elution time for (R)or (S)-warfarin, after correcting for the time due to solute travel through the extracolumn system components. The experiments described in this work were performed on the same HSA column over the course of 9 months and ∼500 sample injections. Frontal analysis studies showed that there was a 44% decrease in the column binding capacity for (S)-warfarin during this period of time. However, the association equilibrium constants measured for (R)- and (S)-warfarin varied by less than 5% during the same time period.5 This observation is important (23) Smith, P. K.; Krohn, R. I.; Hermanson, G. T.; Mallia, A. K.; Gartner, F. H.; Provenzano, M. D.; Fujimoto, E. K.; Goeke, N. M.; Olson, B. J.; Klenk, D. C. Anal. Biochem. 1985, 150, 76. (24) Walters, R. R. Anal. Chem. 1983, 55, 591. (25) Loun, B.; Hage, D. S. J. Chromatogr. B 1995, 665, 303. (26) Anderson, D.; Walters, R. R. J. Chromatogr. Sci. 1984, 22, 353.

Figure 1. Total plate height (Htot) versus linear velocity (u) for injections of (R)-warfarin onto an immobilized HSA column at temperatures of 4 (×), 15 (4), 25 (]), 37 (+), and 45 °C (9). The average capacity factors for (R)-warfarin in these plots were 1.2, 1.0, 0.7, 0.9, and 0.9, respectively. All other conditions are given in the text.

since this current study was concerned more with the nature of the interactions at the HSA binding sites rather than the actual amount of sites that were present. Furthermore, the effective number of HSA sites that were available for (R)/(S)-warfarin binding could be adjusted in each study by varying the amount of L-T3 that was added to the mobile phase as a competing agent. This, plus the relatively small amounts of (R)- and (S)-warfarin that were injected, helps to explain why no noticeable nonlinear elution effects were noted, even during the final stages of work with the HSA column. RESULTS AND DISCUSSION Evaluation of Plate Height Parameters. The first step of this study involved determining the total plate heights for (R)and (S)-warfarin on the HSA column at various linear velocities or flow rates. Figure 1 shows a typical series of van Deemtertype plots that were obtained for (R)-warfarin over temperatures ranging from 4 to 45 °C. Under the flow rate conditions that were used in this work, the graphs in Figure 1 gave a linear relationship between Htot and the linear velocity, as predicted by the model used in eq 4. The correlation coefficients for the plots in Figure 1 ranged from 0.9203 to 0.9818 over the six to nine data points in each graph. Similar results were observed with (S)-warfarin, with correlation coefficients of 0.9268 to 0.9785 being obtained for six or seven points measured over the same range of temperatures and flow rates. Estimates of the plate height contribution due to extracolumn band-broadening (Hec) indicated that this term represented only about 1% of the total plate height that was measured for (R)- and (S)-warfarin in the presence of the HSA column. Although this was an insignificant contribution to Htot, the values measured for Hec were still used in all later work to calculate a total plate height term that was corrected for extracolumn processes (Htot - Hec). The linear behavior seen in Figure 1 supports a model in which the plate height contribution due to longitudinal diffusion (HL) is negligible. This was confirmed by estimating HL according to equations given in the literature.27 Based on a tortuosity factor of 1.0 and an approximate diffusion coefficient of 10-5 cm2/s at (27) Poole, C. F.; Poole, S. K. Chromatography Today; Elsevier: New York, 1991.

Analytical Chemistry, Vol. 68, No. 7, April 1, 1996

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25 °C,27 it was determined that even the highest value for HL would have made up only 2% of Htot for both (R)- and (S)-warfarin at the lowest linear velocity that was sampled in this study (i.e., 0.005 cm/s). Similar results would be expected for the other temperatures that were used in this work. The plate contribution due to mobile phase mass transfer (Hm) was determined from the intercepts of plots like those in Figure 1. For this particular HSA column, Hm made up a significant portion of the total measured plate height. As shown in Figure 1, the intercepts (or Hm values) for plots of Htot versus u were found to increase as the temperature decreased. This was expected since several equations for Hm have proposed that this term has an inverse relationship with the analyte’s diffusion coefficient.16-18 A small change in Hm with k′ was also noted when comparing the total plate heights measured on the HSA column for (R)- or (S)-warfarin versus sodium nitrate (a nonretained solute). Such a relationship between Hm and analyte retention has been proposed in earlier work.28,29 However, these variations in Hm with k′ and temperature were not a problem in this study, since plots like those in Figure 1 made it possible to estimate Hm separately under each set of experimental conditions. The band-broadening contribution due to stagnant mobile phase mass transfer (Hsm) was determined by injecting (R)warfarin onto a diol-bonded silica column, a support that has little or no interactions with this solute. Under the same conditions as used in Figure 1, plots of Htot versus u were linear, with correlation coefficients ranging from 0.8113 to 0.9805 (mean, 0.8765) for data obtained over six flow rates. Based on these data, k-1 was found to vary from 0.5 to 1.6 s-1, with this parameter showing a steady increase when going from 4 to 45 °C. The same k-1 values were assumed to be present for (S)-warfarin, since the two warfarin enantiomers should have had identical mass transfer properties within the mobile phase. By using these results, Hsm for (R)- or (S)-warfarin on the HSA column was estimated under each set of experimental conditions. The calculated values for Hsm varied between 0.005 and 0.035 cm, depending on the linear velocity, temperature, and capacity factors that were present in each study (see eq 3). The last step in the plate height studies was to examine the portion of Htot that was left after correcting for Hec, Hm, and Hsm. According to eq 4, the remainder should represent Hs (i.e., the plate contribution due to stationary phase mass transfer). To test this, plots were made of the remaining plate height values versus the term [uk′/(1 + k′)2]. Some typical examples of these plots are shown in Figure 2. All such graphs for both (R)- and (S)warfarin gave linear behavior with intercepts that were statistically equal to zero (i.e., zero was within (2 SD of each intercept). The correlation coefficients of these plots were between 0.8665 and 0.9887 over five to seven data points for (R)-warfarin and between 0.8849 and 0.9881 over six or seven data points for (S)-warfarin. All of this information indicated that there was good agreement between these plots and the results that were predicted for Hs on the basis of eq 2. Kinetics of HSA Binding to (R)- and (S)-Warfarin. According to eq 2, information on the rate constants for warfarin/ HSA dissociation (kd) could be obtained from the slopes of plots like those in Figure 2. Table 1 summarizes the dissociation rate (28) Karger, B. L.; Snyder, L. R.; Horvath, C. An Introduction to Separation Science; John Wiley & Sons: New York, 1973; Chapter 5. (29) Knox, J. H. J. Chromatogr. Sci. 1977, 15, 352.

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Figure 2. Plots of Hs versus [uk′/(1 + k′)2] for (R)-warfarin on an immobilized HSA column at temperatures of 4 (9), 15 (+), 25 ()), 37 (4) and 45 °C (×). The parameters for the best-fit lines are summarized in the text. Table 1. Equilibrium and Rate Constants for the Binding of (R)- and (S)-Warfarin to Immobilized HSAa temp (°C)

Ka (M-1 × 105)

ka (M-1 s-1 × 104)

4 15 25 37 45

4.0 ((0.2) 3.3 ((0.2) 2.6 ((0.1) 2.1 ((0.2) 1.7 ((0.1)

(R)-Warfarin 2.4 ((0.4) 3.3 ((0.4) 10 ((1) 12 ((2) 32 ((10)

0.06 ((0.01) 0.10 ((0.01) 0.40 ((0.03) 0.56 ((0.08) 1.9 ((0.6)

4 25 37 45

7.3 ((1.0) 3.4 ((0.1) 2.6 ((0.4) 2.0 ((0.1)

(S)-Warfarin 4.4 ((0.9) 4.8 ((0.4) 6.2 ((1.2) 7.2 ((1.1)

0.06 ((0.01) 0.14 ((0.01) 0.24 ((0.03) 0.36 ((0.05)

kd (s-1)

a The numbers in parentheses represent (1 SD. The dissociation rate constants (kd) were determined by band-broadening measurements performed at pH 7.4 in 0.067 M potassium phosphate buffer. The association equilibrium constants (Ka) were obtained from ref 5. The association rate constants (ka) were calculated from the other values in the table by using the relationship Ka ) (ka/kd).

constants that were obtained for (R)- and (S)-warfarin at temperatures between 4 and 45 °C. The kd values for (R)-warfarin varied from 0.06 to 1.9 s-1 over this temperature range, and the values for (S)-warfarin varied from 0.06 to 0.36 s-1. The precision of all dissociation rate constants that were measured in this work was between (7 and (32% (1 RSD). As mentioned earlier, a previous study used frontal analysis to measure the association equilibrium constants (Ka) for (R)- and (S)-warfarin on the same type of HSA column as used in this work.5 The results are summarized in Table 1. Based on these equilibrium constants and the corresponding kd values, the association rate constants (ka) for the binding of (R)- and (S)warfarin to the immobilized HSA could be determined. Table 1 also contains a summary of these values. The ka values that were determined for (R)-warfarin ranged from 2.4 × 104 to 3.2 × 105 M-1 s-1 between 4 to 45 °C. The ka values for (S)-warfarin ranged from 4.4 × 104 to 7.2 × 104 M-1 s-1 under the same conditions. The precision of these association rate constants was estimated to be between (8 and (32% (1 RSD). The rate constants obtained on the immobilized HSA column are comparable to those reported under equivalent conditions for HSA or bovine serum albumin (BSA) in the presence of solutes that have equilibrium constants for protein binding that are similar to those for (R)- and (S)-warfarin (e.g., the interactions of

Table 2. Parameters for the Temperature Dependence of (R)- and (S)-Warfarin Binding Kinetics with Immobilized HSAa compound

∆Hq (kcal/mol)

∆Sq (cal/mol K)

(R)-warfarin 10.5 ((1.8) -0.9 ((0.1) (S)-warfarin 1.9 ((0.4) -31 ((3)

-T∆Sq at 37 °C ∆Gq at 37 °C (kcal/mol) (kcal/mol) 0.3 ((0.1) 9.6 ((0.7)

10.8 ((1.8) 11.5 ((0.8)

a The numbers in parentheses represent (1 SD. All values were determined with data obtained at pH 7.4 in 0.067 M potassium phosphate buffer. The numbers given for ∆Sq were calculated by using one as the value for κ in eq 6.

Figure 3. Change in ln(ka/T) versus 1/T for (R)-warfarin (9) and (S)-warfarin (0) on an immobilized HSA column, as plotted according to eq 6. The best-fit line for (R)-warfarin is y ) -5300((900)x + 23((3), where the numbers in parentheses represent (1 SD. The best-fit line for (S)-warfarin is y ) -900((200)x + 8.3((0.7). The correlation coefficients for these plots are -0.9583 and -0.9564, respectively.

L-triiodothyronine with BSA, bilirubin with its primary site on BSA, and salicylazosulfapyridine with its various binding sites on HSA).30-32 The kd values in Table 1 are somewhat lower than estimates made for soluble HSA with an equimolar or excess amount of racemic warfarin;33-36 however, the relatively large amounts of solute used in the earlier reports make their results suspect, since such conditions may cause warfarin to bind to a large number of low-affinity, and probably nonspecific, regions on HSA.33 A general inspection of Table 1 shows that both the association and dissociation rate constants increased with temperature but that Ka had a net decrease with temperature. This was caused by the larger increase in kd versus ka. At all of the temperatures that were examined in this work, the association equilibrium constants were largest for the (S)-enantiomer. However, the way in which this larger equilibrium constant was produced varied with temperature. For example, even though the kd values for (R)- and (S)-warfarin were similar at low temperatures (4 °C), the difference in ka values led to a greater binding strength for (S)warfarin under these conditions. At higher temperatures (3745 °C), it was the larger dissociation rate constant for (R)-warfarin that led to the weaker binding of this compound to HSA. The temperature dependence of the kinetics of warfarin/HSA binding was examined in more detail by plotting the rate constant data in Table 1 according to eqs 6 and 9. The results obtained for plots of ln(ka/T) versus 1/T are shown in Figure 3. The graphs for both (R)- and (S)-warfarin were linear over the entire temperature range studied. The best-fit parameters for these graphs are given in the legend of Figure 3. Plots prepared for

(30) Whittem, T.; Ferguson, D. C. Endocrinology 1990, 127, 2190. (31) Jansen, J. A. Acta Pharmacol. Toxicol. 1977, 41, 401. (32) Reed, R. G. J. Biol. Chem. 1971, 252, 7483. (33) Rietbrock, N.; Lassmann, A. Naunyn-Schmiedeberg’s Arch. Pharmacol. 1980, 313, 269. (34) Maes, V.; Engelborghs, Y.; Hoebeke, J.; Maras, Y.; Vercruysse, A. Mol. Pharmacol. 1982, 21, 100. (35) Kremer, J. M. H.; Bakker, G.; Wilting, J. Biochim. Biophys. Acta 1982, 708, 239. (36) Rietbrock, N.; Menke, G.; Reuter, G.; Lassmann, A.; Schmeidl, R. J. Clin. Chem. Clin. Biochem. 1985, 23, 719.

ln(kd/T) versus 1/T produced similar linear behavior, with correlation coefficients of -0.9723 (N ) 5) and -0.9959 (N ) 4) being obtained for (R)- and (S)-warfarin. The best-fit slopes for these plots were -6900 ( 900 and -3500 ( 200, respectively, with best-fit intercepts of 16.4 ( 0.4 and 4.2 ( 0.1. The linearity of all these plots indicated that there was good agreement between the experimental data and the equations that were used in this work to describe warfarin/HSA binding. From the slopes and intercepts of the plots in Figure 3, it was possible to determine the values of the change in enthalpy (∆Hq) and entropy (∆Sq) on going from the initial reactants to the activated complex between (R)- or (S)-warfarin and HSA. The values that were obtained are summarized in Table 2. By using these results along with eq 7, it was also possible to determine the total change in free energy on going from the reactants to the activated complex (∆Gq). Table 2 includes the values that were calculated for ∆Gq at a temperature of 37 °C. Note in Table 2 that the ∆Gq values at 37 °C are similar for (R)- and (S)-warfarin (i.e., 10.8 versus 11.5 kcal/mol), but the relative contributions of enthalpy and entropy to ∆Gq differ dramatically for these two enantiomers. For (R)-warfarin, most of the energy needed for activation was from the change in free energy due to enthalpy, where the large positive value for ∆Hq indicates that more bond breaking than formation occurred on going from the free solute and protein to the solute-protein activated complex. For (S)-warfarin, most of the energy needed for activation resulted from the free energy change due to entropy (-T∆Sq). In this case, the positive value observed for -T∆Sq indicates that the activated complex for (S)-warfarin with HSA had a higher degree of order than the initial reactants. One interesting observation is that the dominant energy terms in Table 2 for the formation of the activated complex are just the opposite of those terms that are most important in determining the net change in free energy (∆G) that is gained on going from free (R)- or (S)warfarin to the final warfarin/HSA complex. With (R)-warfarin, it has been found at 37 °C that ∆G is determined mainly by the net increase in entropy of the system (-T∆S), while for (S)warfarin the net change in enthalpy (∆H) is what drives the binding process.5 Mechanism of Warfarin/HSA Binding. Previous thermodynamic studies with the warfarin/HSA system have suggested a model in which (S)-warfarin interacts mainly with the exterior of HSA, while (R)-warfarin interacts more with the interior of the HSA binding pocket.5 The kinetic data obtained in this study fit this model and can be used to further define the steps that are involved in these binding processes. For example, Table 2 indicates that the initial stages of (R)-warfarin/HSA binding involve a significant amount of bond breaking, such as might occur during Analytical Chemistry, Vol. 68, No. 7, April 1, 1996

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Figure 4. Energy diagrams for the binding of (R)-warfarin (s) and (S)-warfarin (‚‚‚) to immobilized HSA at 37 °C (a) and 4 °C (b). The terms W + HSA, [W-HSA], and W-HSA represent the initial reactants, the activated complex, and the final warfarin/HSA complex, respectively.

the weakening of hydrogen bonds or dipole-dipole interactions between water molecules and (R)-warfarin or HSA. Once these interactions have been weakened, the water can then be released from the solute and/or protein, thus allowing (R)-warfarin to go into the HSA binding pocket. If a sufficient amount of solvent is released during this process, the result would be a net increase in entropy, as was observed in the earlier thermodynamic studies.5 For (S)-warfarin, the data in Table 2 show that a higher degree of order was seen for the activated complex than for the initial reactants, such as might occur during the adsorption of (S)warfarin to the surface of HSA. Following this initial adsorption, various interactions between (S)-warfarin and HSA could take place to stabilize this complex (e.g., hydrogen bonds, ionic interactions, or dipole interactions). If enough interactions are formed, the result would be a net gain in enthalpy, as is seen during (S)-warfarin/HSA binding.5 Warfarin/HSA binding was further studied by examining the changes in free energy that occur at various stages of this reaction (see Figure 4). In this diagram, it was assumed that there was the same initial energy level for HSA and either (R)- or (S)-warfarin in solution. The energy difference between this initial state and each activated complex (∆Gq) was then calculated by using the data in Table 2. The difference in energy between the reactants and products (∆G) was determined by using data from ref 5. The reaction profiles for (R)- and (S)-warfarin at both 4 and 37 °C are provided in Figure 4. At 37 °C, (S)-warfarin has a higher energy barrier than (R)-warfarin for both association and dissociation with HSA. This helps explain why (S)-warfarin has smaller association and dissociation rate constants than (R)-warfarin at this temperature (see Table 1). At 4 °C, (R)-warfarin has the largest activation barrier for association, but an energy barrier for dissociation that is approximately equal to that for (S)-warfarin. This explains why ka is smaller for (R)-warfarin than for (S)-warfarin at 4 °C, while the value of kd is essentially the same for the two enantiomers at this temperature. Note in Figure 4 that the activation energies for association and dissociation are slightly larger at 37 °C than at 4 °C for both (R)- and (S)-warfarin, even though Table 1 indicates that the values of ka and kd were higher under these conditions. This reflects 1224 Analytical Chemistry, Vol. 68, No. 7, April 1, 1996

Figure 5. Change in the plate height contribution due to stationary phase mass transfer (Hs) as a function of temperature for (R)- and (S)-warfarin on an HSA column. These results were calculated by using eq 2 along with the best-fit parameters that were obtained by applying eq 9 to the kd values in Table 1.

the fact that, at the higher temperature, a greater fraction of the warfarin, HSA, and/or final complex would have had sufficient internal energy to reach the activated complex through association or dissociation. Effect of Temperature on Stationary Phase Mass Transfer and HSA Column Efficiency. Based on the results presented earlier, it was found that there were three main terms that contributed to the total plate height of the HSA column. These terms were Hm, Hs, and Hsm. It was also found that all of these terms were temperature dependent. The size of the plate height contributions due to Hsm and Hm at various temperatures were evaluated and discussed previously. The plate height contributions due to Hs as a function of temperatures are given in Figure 5. These results show the Hs values that would be expected for (R)- and (S)-warfarin under identical retention and elution conditions (i.e., k′ ) 1.0 and u ) 0.015 cm/s). The values of k′ and u that were chosen for making this graph are representative of the average experimental conditions used in this study. It can be seen that there was a marked temperature dependence in Hs for (R)and (S)-warfarin under the conditions used in this work. Both enantiomers had a decrease in Hs with increasing temperature, with the largest change occurring between 0 and 20 °C. Since these results represent constant linear velocity and retention conditions, this decrease in Hs reflects the corresponding increase in kd with temperature that was observed for (R)- and (S)-warfarin in Table 1. Figure 5 shows that the Hs values for (R)- and (S)-warfarin were different at most of the temperatures examined in this work. This follows the results in Table 1, which show that (R)- and (S)warfarin had similar kd values only when working near 4 °C. This is significant, since it means that even compounds that bind to the same site on an immobilized protein can have different dissociation kinetics and, thus, different degrees of band-broadening associated with these interactions. Although Figure 5 gives the results for Hs that would be expected at a particular set of k′ and u values, this graph also illustrates the trends that would be expected under other retention and linear velocity conditions. It is possible to estimate Hs for (R)- and (S)-warfarin under other conditions by simply using eq 2 to multiply the results in Figure 5 by the appropriate ratios of the new and old linear velocities or capacity factors.

A comparison of the values in Figure 5 with the total plate heights in Figure 1 indicates that Hs accounted for most of the observed change in Htot with linear velocity for the HSA column. But it should be noted that the relative importance of Hs will be different at other degrees of analyte retention. For example, when (R)- and (S)-warfarin were injected onto the same HSA column in the absence of any competing agent (i.e., the L-T3 mobile phase additive), the k′ values that were measured ranged from 13.9 to 16.4 at 4 °C and from 6.9 to 7.4 at 45 °C. According to eq 2, this corresponds to about a 10-20-fold decrease in Hs versus the values given in Figure 5 at k′ ) 1. Under such strong retention conditions, both Hsm and Hs become important in determining the overall increase in Htot with linear velocity. As mentioned earlier, most of the band-broadening measured for the HSA column in this study appeared to come from Hm. Fortunately, this plate height term can be reduced by using a narrower diameter support.16-19 A decrease in support size will also reduce the expected plate height contribution due to Hsm.13,14 The stationary phase mass transfer term (Hs) is unique in this regard since it is independent of particle size (see eq 2). Thus, as more efficient chromatographic supports are developed, this particular term should become of increasing interest and concern in describing the band-broadening of protein-based chiral separations. CONCLUSIONS This study examined the kinetics of (R)- and (S)-warfarin binding to an immobilized HSA column through the use of plate height measurements. Plots of the total plate height versus linear velocity on the HSA column gave linear behavior for both enantiomers over the temperature range of 4-45 °C. By evaluating the various terms that contributed to the total plate height, it was possible to obtain the plate height contribution due to stationary phase mass transfer (Hs) for each compound. This term, in turn, provided a means of determining the dissociation rate constants for (R)- and (S)-warfarin on the immobilized HSA column. The dissociation rate constants (kd) for both (R)- and (S)warfarin were found to increase with temperature, with values going from 0.06 to 1.9 s-1 and from 0.06 to 0.36 s-1, respectively, between 4 and 45 °C. One consequence of this increase in kd (37) Allenmark, S.; Bomgren, B.; Bore´n, H. J. Chromatogr. 1982, 237, 473. (38) Domenici, E.; Bertucci, C.; Salvadori, P.; Fe´lix, G.; Cahagne, I.; Motellier, S.; Wainer, I. W. Chromatographia 1990, 29, 170.

was a corresponding decrease in Hs with increasing temperature, particularly when working at temperatures between 0 and 20 °C. This means that any band-broadening due to the direct interactions of these compounds with the immobilized HSA can be minimized by working above this temperature range. The fact that different kd values were observed for (R)- and (S)-warfarin at most temperatures is also significant since it indicates that these enantiomers typically had different values for Hs. Qualitative differences in the band-broadening of enantiomers have been observed previously on albumin columns,4,37,38 but this is the first known case in which a kinetic source for these differences has actually been demonstrated. Through the use of the kd values and previous equilibrium constant measurements, the association rate constants (ka) for (R)and (S)-warfarin were determined. On going from 4 to 45 °C, ka was estimated to increase from 2.4 × 104 to 3.2 × 105 M-1 s-1 for (R)-warfarin and from 4.4 × 104 to 7.2 × 104 M-1 s-1 for (S)-warfarin. By examining the temperature dependence of these values, it was possible to study the changes in enthalpy, entropy, and total free energy that occurred during the formation of the activated complex between (R)- or (S)-warfarin and the immobilized HSA. These enantiomers had similar activation energies at 37 °C. However, for (R)-warfarin, most of this energy was due to the change in enthalpy of the system, while for (S)-warfarin, it was mainly due to the change in entropy. Energy profiles constructed from these data showed good agreement with both the relative association and dissociation rates that were observed for (R)- and (S)-warfarin. The data presented in this work give a fairly detailed picture of the kinetic processes that occur during the interactions of (R)- and (S)-warfarin with immobilized HSA. These kinetic results, and corresponding thermodynamic data, help to provide clues regarding the chromatographic behavior of chiral compounds in the presence of immobilized HSA or other protein-based supports. ACKNOWLEDGMENT This work was supported by the National Institutes of Health under Grant No. GM44931. Received for review August 14, 1995. Accepted January 17, 1996.X AC950827P X

Abstract published in Advance ACS Abstracts, February 15, 1996.

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