Evaluation of the Interaction of Propranolol with 1, 2-Dimyristoyl-sn

Langmuir 2007, 23, 1959-1964

1959

Evaluation of the Interaction of Propranolol with 1,2-Dimyristoyl-sn-glycero-3-phosphocholine (DMPC) Liposomes: The Partitioning Model Jan Cocquyt,*,† Pieter Saveyn,† Paul Van der Meeren,† and Marcel De Cuyper‡ Particle and Interfacial Technology Group, Faculty of Bioscience Engineering, Ghent UniVersity, Coupure Links 653, B-9000 Ghent, Belgium, and Interdisciplinary Research Center, Katholieke UniVersiteit LeuVen-Campus Kortrijk, Sabbelaan 53, B-8500 Kortrijk, Belgium ReceiVed July 21, 2006. In Final Form: NoVember 4, 2006 The sorption behavior of the amine containing β-receptor blocking agent propranolol (Ppn) in 1,2-dimyristoylsn-glycero-3-phosphocholine (DMPC) vesicles was investigated. Both protonated and unprotonated Ppn were measured in the continuous phase after removal of the vesicles containing sorbed Ppn by centrifugation. In contrast, by analyzing the surface charge density, deduced from electrophoretic mobility measurements, only the sorbed protonated Ppn was determined. A partitioning model was used to describe the sorption behavior. Sensitivity analysis revealed that sufficiently reliable and independent parameters were obtained. The partition coefficient of the unprotonated Ppn was about 22 times higher than that of the protonated analogue. Statistical analysis revealed a significant increase in the intrinsic partition coefficients of both Ppn analogues with an increase in the salt concentration.

1. Introduction Important categories of pharmaceuticals, such as anesthetics and β-receptor blockers, can interact both specifically1 and aspecifically2 with phospholipid bilayers. Propranolol (Ppn) (Figure 1) is a β-receptor blocker that also has a local anesthetic activity.3 Some authors have reported that the Ppn naphthalene rings interact aspecifically with the hydrocarbon core of the phosphatidylcholine bilayer.4,5 From these observations, a partitioning model in which the amount sorbed is not limited seems justified. In earlier works where models were used to describe the interaction of charged drug molecules with lipid membranes, the electrostatic interactions were often neglected, and thus the obtained interaction constants were only apparent ones.5-15 Calculations in which the electrostatic interaction component was taken into account to obtain the intrinsic interaction coefficients of both charged and uncharged species have been * To whom correspondence should be addressed. Telephone: ++32 (0)9 264 6003. Fax: ++32 (0)9 264 6242. E-mail: [email protected]. † Ghent University. ‡ Katholieke Universiteit Leuven-Campus Kortrijk. (1) Schlieper, P.; Steiner, R. Chem. Phys. Lipids 1983, 34, 81. (2) Smith, H. J. J. Mol. Cell. Cardiol. 1982, 14, 495. (3) Cao, A.; Hantz-Brachet, E.; Azize, B.; Taillandier, E.; Perret, G. Chem. Phys. Lipids 1991, 58, 225. (4) Krill, S. L.; Lau, K. Y.; Plachy, W. Z.; Rehfeld, S. J. J. Pharm. Sci. 1998, 87, 751. (5) Albertini, G.; Donati, C.; Phadke, R. S.; Ponzi Bossi, M. G.; Rustichelli, F. Chem. Phys. Lipids 1990, 55, 331. (6) Pauletti, G. M.; Wunderli-Allenspach, H. Eur. J. Pharm. Sci. 1994, 1, 273. (7) de Paula, E.; Schreier, S. Biochim. Biophys. Acta 1995, 1240, 25. (8) Garcia, D. A.; Perillo, M. A. Colloids Surf., B 1997, 9, 49. (9) Ottiger, C.; Wunderli-Allenspach, H. Eur. J. Pharm. Sci. 1997, 5, 223. (10) Kra¨mer, S. D.; Braun, A.; Jakits-Deiser, C.; Wunderli-Allespach, H. Pharm. Res. 1998, 15, 739. (11) Varga, E.; Szo¨llo¨si, J.; Antal, K.; Kovacs, P.; Szabo, J. Z. Pharmazie 1999, 54, 380. (12) Santos, N. C.; Prieto, M.; Castanho, M. A. R. B. Biochim. Biophys. Acta 2003, 1612, 123. (13) Kubo, M.; Gardner, M. F.; Hostetler, K. Y. Biochem. Pharmacol. 1986, 35, 3761. (14) Avila, C. M.; Martinez, F. Chem. Pharm. Bull. 2003, 51, 237. (15) Malheiros, S. V. P.; Pinto, L. M. A.; Gottardo, L.; Yokaichiya, D. K.; Fraceto, L. F.; Meirelles, N. C.; de Paula, E. Biophys. Chem. 2004, 110, 213.

Figure 1. Molecular structure of propranolol.

made only rarely.16-19 The aim of the present work is to obtain intrinsic water-lipid membrane partition coefficients by exploring a wide range of experimental conditions, such as different pH values and salt concentrations. Hereby, the reliability of the estimated partition coefficients was increased by splicing, i.e., fitting simultaneously measured electrophoretic mobilities (reflecting only the protonated sorbed Ppn) as well as the aqueous phase depletion data (measuring both the protonated and the unprotonated Ppn sorbed) to the same partition-based sorption model. Sensitivity analysis revealed that this combined knowledge was required to obtain independent estimations of the model parameters. 2. Materials and Methods 2.1. Materials. D/L-Propranolol hydrochloride was obtained from Acros Organics (Geel, Belgium). 1,2-Dimyristoyl-sn-glycero-3phosphocholine (DMPC) was used as received from Avanti PolarLipids (Birmingham, AL). Hydrazinium chloride and sodium molybdate used for the phosphate analysis, N-tris(hydroxymethyl)methyl-2-amino-ethane sulfonic acid (TES) for the pH 7.0 and pH 8.0 buffers, and acetic acid for the pH 4.0 buffer were all from Merck (Darmstadt, Germany). All buffers were 5 mM, were brought to the right pH with 1 N KOH, and contained either no KCl, 5 mM KCl, or 75 mM KCl. All chemicals used were pro-analysis grade. 2.2. Preparation of Liposomes. After addition of the buffer to the DMPC powder, the dispersion was stirred on a magnetic stirrer (16) Bennouna, M.; Ferreira-Marques, J.; Banerjee, S.; Caspers, J.; Ruysschaert, J. M. Langmuir 1997, 13, 6533. (17) Matos, C.; de Castro, B.; Gameiro, P.; Lima, J. L. F. C.; Reis, S. Langmuir 2004, 20, 369. (18) Escher, B. I.; Schwarzenbach, R. P.; Westall, J. C. EnViron. Sci. Technol. 2000, 34, 3954. (19) Banerjee, S.; Caspers, J.; Bennouna, M.; Sautereau, A. M.; Tocanne, J. F.; Ruysschaert, J. M. Langmuir 1995, 11, 1134.

10.1021/la062139e CCC: $37.00 © 2007 American Chemical Society Published on Web 12/30/2006

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for 3 h at 37 °C, i.e., where the DMPC bilayers are in the liquidcrystalline state.3 The resulting dispersion is expected to contain mainly multilamellar liposomes. Equal volumes of the phospholipid dispersion and of a Ppn solution were then mixed and incubated for 12 h at 37 °C. 2.3. Electrophoretic Mobility Measurements. The electrophoretic mobility of the DMPC liposomes was measured by electrophoretic light scattering using a Zetasizer IIc apparatus (Malvern, Worcestershire, U.K.). The temperature was maintained at 37 °C, and the electric field strength at 1400 V/m (direct current). The average of at least three consecutive measurements, each lasting 30 s, was taken. The DMPC concentration was 0.2 g/L. Measurements were done at different Ppn concentrations at pH 4.0, 7.0, and 8.0 in buffers containing 0, 5, or 75 mM KCl. 2.4. Determination of the Amount Sorbed. The free Ppn remaining in solution after the incubation period was separated from the liposomes by centrifugation for at least 1 h at 4000g at 37 °C. In addition to nonsorbed Ppn, the supernatant contained Ppn sorbed to a small fraction of liposomes that were not sedimented by centrifugation. The supernatant was diluted with the corresponding buffer to a concentration suitable for UV spectroscopy. The light absorbance at 260, 275, 289, 302, 317, 335, and 350 nm was measured on a UVIKON 933 double beam UV-vis spectrophotometer (bandwith set at 2 nm) and fitted to the corresponding data of a standard Ppn solution in the same buffer at the same wavelengths, allowing a background absorbance, which decreased exponentially with increasing wavelength, to be introduced as a correction for the light scattered by the liposomes present in the supernatant: the equation P1 × (absorbance of the standard Ppn solution) + P2 × exp(-P3 × wavelength) was fitted to the obtained spectrum with P1, P2, and P3 as adjustable parameters. The sum of the squared differences between the fitted equation and the experimentally determined absorbance of the supernatant was minimized by adjusting P1, P2, and P3. The product of P1 and the concentration of the standard solution gives the Ppn concentration in the supernatant, [Ppn]sup, expressed as mol/m3. The fitted Ppn absorbance at the maximum of the main peak was always more than 5 times higher than the fitted background absorbance at this wavelength. The total DMPC concentration, [DMPC]tot, was 2.9 mol/m3, corresponding to 2.0 g/L. The residual supernatant DMPC concentration, [DMPC]sup, expressed as mol/m3, was determined through phosphate analysis according to Vaskovsky.20 The concentration of sorbed Ppn, [Ppn]bilayer, expressed in moles per mole of DMPC, can be found using a mass balance both in the sedimented fraction [Ppn]bilayer ) ([Ppn]tot - [Ppn]sup)/([DMPC]tot - [DMPC]sup)

(1)

and in the supernatant [Ppn]bilayer ) ([Ppn]sup - [Ppn]free)/([DMPC]sup)

(2)

series and then minimized using the Nelder-Mead simplex method.21 The normalized sum of squared differences (NSSD) for each of the three sorption data series was weighted twice as much in the fit compared to each of the nine ELS data series.

3. Theory In elaborating the partition theory, the interface region is divided into two parts: the aqueous part close to the bilayer and the bilayer itself. The sorption of Ppn is governed by two equilibria: a first one between the bulk aqueous phase and the aqueous part of the interface region and a second one between the aqueous part of the interface region and the bilayer. The concentration of unprotonated Ppn in the aqueous part of the interface region, [Ppn0]aq,int, equals the nonbound concentration in the bulk aqueous phase, [Ppn0]free, whereas the concentration of protonated Ppn in the aqueous part of the interface region, [Ppn+]aq,int, is related to the nonbound concentration of protonated Ppn in the bulk aqueous phase, [Ppn+]free, by a Boltzmann distribution:

[Ppn+]aq,int ) [Ppn+]free exp(-Fψint/RT)

(4)

where R is the universal gas constant (8.31 J/(K mol)), T is the kelvin temperature, F is Faraday’s constant (96485 C), and ψint is the electrostatic potential at the bilayer interface. The nonbound concentrations of the protonated and the unprotonated forms of Ppn in the bulk aqueous phase are calculated using the Henderson-Hasselbalch equation:

log([Ppn+]free/[Ppn0]free) ) pKa(w) - pH

(5)

where pKa(w), the negative logarithm of the acid dissociation constant of Ppn in water, is 9.24 at 37 °C.6 The bilayer concentrations of protonated Ppn and unprotonated Ppn, [Ppn+]bilayer and [Ppn0]bilayer, respectively, both expressed in moles per mole of DMPC, are related to the respective Ppn concentrations in the aqueous part of the interface region:

[Ppn+]bilayer ) Kp[Ppn+]aq,int

(6)

[Ppn0]bilayer ) Kn[Ppn0]aq,int

(7)

where Kp and Kn represent the intrinsic partition coefficients, expressed in cubic meters per mole of DMPC. The experimental data are fitted by the partitioning model through the adjustment of both Kp and Kn. From both partition coefficients, the shift in the negative logarithm of the Ppn acid dissociation constant from the pKa(w) in water to the pKa(bilayer) in the bilayer may be derived:

where [Ppn]free and [Ppn]tot, both expressed in moles per cubic meter, are the nonbound and the total Ppn concentrations, respectively. Merging both equations allows the calculation of [Ppn]free:

∆pKa ) pKa(bilayer) - pKa(w) ) log{[Ppn+]bilayer[Ppn0]aq,int/

[Ppn]free ) ([Ppn]sup[DMPC]tot - [DMPC]sup[Ppn]tot)/ ([DMPC]tot - [DMPC]sup) (3)

Calculation of the Electrophoretic Mobility. From the total and the protonated Ppn concentrations in the bilayer, [Ppn]bilayer and [Ppn+]bilayer, both expressed as moles per mole of DMPC and calculated using the partitioning model, the theoretical interfacial surface charge density, σint, expressed in coulombs per square meter, was calculated:

The concentration of sorbed Ppn, [Ppn]bilayer, can be calculated using either eq 1 or eq 2. The sorption experiments were performed at pH 7.0 in 5 mM TES buffers containing 0, 5, or 75 mM KCl. 2.5. Data Fitting. The sorption data and the electrophoretic mobility data were fitted simultaneously. The sum of the squared differences between the measured and calculated electrophoretic mobilities (in µm‚cm/(s V)) or sorbed concentrations (in moles per mole of DMPC) was first normalized for the variance of the data (20) Vaskovsky, V. E.; Kostetsky, E. Y.; Vasendin, I. M. J. Chromatogr. 1975, 114, 129.

[Ppn0]bilayer[Ppn+]aq,int} ) log(Kp/Kn) (8)

σint ) σ0 + F[Ppn+]bilayer/{Na(paDMPC + [Ppn]bilayerpaPpn)} (9) where Na is Avogadro’s number (6.022 × 1023 mol-1). The (21) Lagarias, J. C.; Reeds, J. A.; Wright, M. H.; Wright, P. E. SIAM J. Control Optim. 1998, 9, 112.

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projected surface areas of DMPC, paDMPC, and Ppn, paPpn, are 60 and 30 Å2, respectively.22,23 The surface charge density in the absence of Ppn (σ0) was derived directly from the electrophoretic mobility experiments. The electrostatic potential at the bilayer interface ψint, expressed in volts, was calculated from σint, according to the GouyChapman equation:

sinh(Fψint/2RT) ) σint/(8RT[salt]0w)1/2

(10)

where 0 is the permittivity in vacuum (8.854 × 10-12 F/m) and w is the dielectric constant of water. The salt concentration [salt] is the sum of the concentration of dissociated buffer species, the KCl concentration, and the concentration of protonated Ppn in the bulk, all expressed as moles per cubic meter. The zeta-potential ζ, i.e., the potential at a distance (z) of 2 Å from the bilayer surface,24 was calculated using the GouyChapman theory:

ζ ) (2RT/F) ln{(1 + Γ0 exp(-κz))/(1 - Γ0 exp(-κz))} (11) with

Γ0 ) (exp(FΨint/RT) - 1)/(exp(Fψint/RT) + 1) The Debye screening length is given by

κ -1 ) (0wRT/F2[salt])1/2 From ζ, the electrophoretic mobility uef was calculated according to the Dukhin equation:

3 3ηF u ) ζ˜ 20wRT ef 2 2 3 ζ˜ {A + 8 sinh (ζ˜ /4)} + {4 ln(cosh(ζ˜ /4))}{4 sinh(ζ˜ /2) - B} 2 2{κr + 4 sinh2(ζ˜ /4)(2 + 3mp ) - 12mp ln(cosh(ζ˜ /4))} δ δ (12)

where ζ˜ ) (Fζ)/(RT) is the reduced zeta potential; m A ) 3(mm ˜ - 2mpδ + 2Mpδ); B ) 3(mpδζ˜ + 2mm δζ δ - 2Mδ ); p m p m p m p/m mδ ) m + m ; mδ ) m - m ; m ) (2RT0w)/(3ηλp/m); m ˜ /2) - mp exp(-ζ˜ /2); and Mpδ ) mp exp(ζ˜ /2) + mm Mm δ m exp(ζ exp(-ζ˜ /2). For the present calculations, the liposome radius, r, was taken to be 500 nm. The parameters mp and mm are dimensionless and characterize the contribution of the electro-osmotic flow to the surface ion fluxes. The limiting ion mobilities of K+ and Cl-, λp and λm, are 0.0070 and 0.0073 m2 Ω-1 mol-1, respectively. The two partition coefficients were adjusted to obtain an optimum fit between the electrophoretic mobility calculated from the Dukhin equation (eq 12) and the experimentally determined electrophoretic mobility data, as well as between the calculated Ppn sorption from eqs 6 and 7 and the experimentally determined sorption data from eq 1 or 2.

4. Results The symbols in Figure 2 represent the experimentally determined amount of Ppn sorbed in DMPC vesicles at pH 7 in the absence of KCl (circles) or in the presence of 5 mM KCl (22) Egorova, E. M. Electrophoresis 1994, 15, 1125. (23) Surewicz, W. K.; Leyko, W. Biochim. Biophys. Acta 1981, 643, 387. (24) Eisenberg, M.; Gresalfi, T.; Riccio, T.; McLaughlin, S. Biochemistry 1979, 18, 5213.

Figure 2. Amount of Ppn sorbed in a 2 g/L DMPC liposomal dispersion at pH 7 in buffers containing no KCl (circles), 5 mM KCl (squares), and 75 mM KCl (triangles). Empty symbols correspond to data that were included in the fit, whereas filled symbols were not included in the fit. The lines represent the partitioning model fit. The equilibration time was 12 h except for the data points indicated in gray, for which it was 24 h.

(squares) or 75 mM KCl (triangles) after 12 h of incubation at 37 °C, where the vesicles are in a liquid-crystalline state.3 (At 4 °C, i.e., in the gel state, the amounts sorbed were slightly less than half of those found in the liquid-crystalline state over the entire concentration range. In addition, the size of the DMPC vesicle as such was found to have a relatively small influence on the sorption behavior of Ppn. Vesicles obtained after five freeze-thaw-extrusion cycles were shown to have an average diameter of 109 nm using dynamic light scattering and had Ppn partitioning constants that were about 12% lower than those found for multilamellar DMPC liposomes in the same experimental circumstances. This difference may be due to the higher bilayer curvature.) The symbols in gray show the corresponding amount of Ppn sorbed after an incubation time of 24 h. Since the data points found after 12 and 24 h are located on the same curve, it can be safely stated that equilibrium was reached within the first 12 h. Also, Pauletti and Wunderli-Allenspach found that the partition equilibrium of Ppn in phosphatidylcholine liposomes was reached within 20 min at pH 7.3 and at 37 °C.6 The main source of error in determining the amount of Ppn sorbed is the uncertainty in the Ppn concentration assessment. The standard error of a Ppn concentration assessment was determined independently from 10 absorbance measurements and was found to be about 4%. As the amount sorbed is determined from the difference of [Ppn]tot and [Ppn]free, its relative standard deviation was calculated according to the following:

SD(%) ) 100((0.04[Ppn]tot)2 + (0.04[Ppn]free)2)1/2/ ([Ppn]tot - [Ppn]free) (13) The data points for which this error was larger than 10% were not included in the fit and are shown in Figure 2 as filled symbols. Figure 3 shows the result of electrophoretic mobility measurements performed on DMPC vesicles at different Ppn concentrations at pH 4.0 (Figure 3a), pH 7.0 (Figure 3b), or pH 8.0 (Figure 3c). At pH 4.0, almost all of the Ppn in the aqueous phase was in the protonated cationic form, whereas, at higher pH values, an increasing fraction of the unprotonated neutral form was present. As more Ppn was sorbed, the liposome surface potential increased, leading to the repulsion of positively charged species, such as

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Cocquyt et al. Table 1. Partition Coefficients (Kn and Kp), pKa Shift (∆pKa), Normalized Sum of Squared Differences (NSSDs) Obtained from the Data Fit, and Degrees of Freedom (DFs) Left To Fit Using the Partitioning Model Where [KCl] is the KCl Concentration (in mM)a full model [KCl]

Kp

Kn

∆pKa

reduced model A Kp

Kn

∆pKa

0 0.529 11.5 -1.336 0.594 13.1 -1.343 5 0.586 14.0 -1.380 0.594 13.1 -1.343 75 0.634 16.3 -1.411 0.594 13.1 -1.343 NSSD 4.1 4.7 DF 171 175

reduced model B Kp

Kn

0.635 0.722 0.762 13.9 174

∆pKa 0 0 0

a In the full model, both Kn and Kp (expressed as m3/mol of DMPC) are assumed to depend on the salt concentration, whereas in the reduced model A, they are assumed to be independent of the salt concentration. In the reduced model B, the same partition coefficient was used for both Kp and Kn.

Figure 3. Effect of Ppn on the electrophoretic mobility of a 0.2 g/L DMPC liposomal dispersion at pH 4 (a), pH 7 (b), and pH 8 (c) without any KCl (O), with 5 mM KCl (0), or with 75 mM KCl (4) added to the buffer. The lines represent the partitioning model fit.

protonated Ppn and protons. The latter led to an increased pH in the aqueous part of the interface region, leading to an increased fraction of unprotonated Ppn. At each pH, the vesicle dispersions were prepared without any KCl or with 5 or 75 mM KCl. Using the Dukhin theory (eq 12), it was found that, in the Ppn concentration range studied for each of the three different salt concentrations, the electrophoretic mobility was almost linearly dependent on the amount of positively charged Ppn sorbed. Thus, the electrophoretic mobility leveled off with increasing Ppn concentration (Figure 3), not because of the limitations of the Dukhin theory at high surface charge densities25 but rather because of the increasing repulsion (25) Egorova, E. M.; Dukhin, A. S.; Svetlova, I. E. Biochim. Biophys. Acta 1992, 1104, 102.

of the nonsorbed protonated Ppn by the surface, which becomes more positively charged due to Ppn sorption. Salt reduces this repulsion, leading to more Ppn sorption (Figure 2). Although more Ppn was sorbed (Figure 2), lower electrophoretic mobilities were measured in 75 mM KCl (Figure 3). This may be ascribed to the increased electrostatic screening. Furthermore, at pH 8 the electrophoretic mobility increased less with increasing Ppn concentration (Figure 3c), which follows logically from the fact that more Ppn was in the unprotonated and thus uncharged form as the pH increased. Table 1 shows the parameters obtained by fitting the partitioning model. The pKa shift was calculated from the partition coefficients using eq 8. To check the interdependence of the parameters derived from the full model, a sensitivity analysis was performed under all of the experimental conditions used in this work (Figure 4). Sensitivity was defined as p δA/δp where the response A was either the electrophoretic mobility or the sorbed Ppn concentration and p was one of the partition coefficients. The sensitivity analysis aims to calculate to what extent the electrophoretic mobility and the sorbed Ppn concentration are affected by a change in the value of each of the partition coefficients obtained from the fit. In addition, the estimated values of the partition coefficients are only reliable when a change of their values gives a different sensitivity profile in the calculated response range, as this means that the partition coefficients are not interdependent and, hence, the set of values obtained from the fit is quite unique. Comparing the behavior of the sensitivities to a change in the two partition coefficients versus the added Ppn concentration in all experimental conditions, it was clear that the shape of the two curves differed markedly for both the sorption data (Figure 4a) and the electrophoretic mobility data (Figure 4b). The sensitivity of the amount sorbed at pH 7 to a change in the partition coefficient of the unprotonated Ppn and to a change in the partition coefficient of the protonated Ppn were of the same order of magnitude (Figure 4a). At pH 4 and at pH 7, the effect of a change in the partition coefficient of unprotonated Ppn on the electrophoretic mobility was negligible compared to the effect of a change in the partition coefficient of protonated Ppn (results not shown). At pH 8, however, the electrophoretic mobility became more sensitive to a change in the partition coefficient of the unprotonated Ppn (Figure 4b). Thus, it can be concluded that the electrophoretic mobility data could be used to estimate the partition coefficient of the positively charged compound. Only the combination of these data with the shape and the magnitude of the sorption curves results in reliable partition coefficients for both compounds. Fitting either the electrophoretic mobility data or the sorption

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ones for the neutral form. Nevertheless, when paPpn was either halved or doubled, none of the obtained partition constants differed by more than 5%. When the estimated vesicle size was either halved to 250 nm or doubled to 1000 nm, none of the parameters obtained from the fit changed by more than 2%. Thus, it is clear that even drastic changes in the assumed value of either paPpn or the particle size did not significantly influence the conclusions drawn from the parameters obtained.

5. Discussion The full lines in Figures 2 and 3 represent the least-squared differences fit using the full partitioning model, which assumed the intrinsic partition coefficients to be dependent on the electrolyte concentration. To check the latter hypothesis, the experimental data were also fitted to a reduced model A; the latter contained only two electrolyte-insensitive adjustable parameters, i.e., the partition coefficients of neutral and protonated Ppn. Using the NSSDs and the degrees of freedom (DFs) of the full model fit and the reduced model A fit (Table 1), a critical F* value of 7.0 was obtained using the following equation:

F* ) {(NSSDreduced - NSSDfull)DFfull}/ {NSSDfull(DFreduced - DFfull)} (14)

Figure 4. Sensitivity of the amount of Ppn sorbed at pH 7 (a) and of the electrophoretic mobility at pH 8.0 (b) without any KCl (circles), with 5 mM KCl (squares), or with 75 mM KCl (triangles) in the buffer to a change in the partition coefficient of protonated Ppn (empty symbols) or unprotonated Ppn (filled symbols) according to the partitioning model.

Figure 5. Parameter combinations corresponding to the minimized weighted sum of squared differences between the experimental data and the full partitioning model (+) and to the weighted sum of these squared differences being 0.1% higher than the minimum (oval).

data separately did not result in sufficiently independent partition coefficients. These could only be obtained by using both data series in the fit. Figure 5 shows combinations of the two partition coefficients with the NSSD minimized as well as with the NSSD being 0.1% higher than the minimum. As the three curves are well separated, this result confirms that the obtained partition coefficients were significantly dependent on the salt concentration. As a second part of the sensitivity analysis, the effects of variation of the values of the input-parameters, such as the estimated projected surface area of a sorbed Ppn molecule in the bilayer, paPpn, and the liposome size on the output-parameters obtained from the fit was investigated. Whereas paPpn mainly influences the surface charge density, the particle size has an effect on the electrophoretic mobility calculated according to the Dukhin equation (eq 12). A higher paPpn leads to slightly higher partitioning coefficients for the positively charged form and lower

This is higher than 4.6, the 99.9th percentile of an F4,171 distribution, indicating that the differences between the partition coefficients at different salt concentrations were significant. Using the same equation, a critical F* value of 140 was obtained from the NSSD of the reduced model B fit, which contained only three adjustable parameters, i.e., a partition coefficient of Ppn for each of the three salt concentrations studied. These coefficients were assumed to be independent of the Ppn state of ionization. As this critical F* value is much higher than 5.4, the 99.9th percentile of an F3,171 distribution, the partition coefficient of the neutral form is significantly higher than that of the positively charged form. This is in line with the results of Matos et al.,17 who found that the partition coefficient of the neutral form of indomethacin and acemetacin in egg phosphatidylcholine liposomes was an order of magnitude higher than that of the charged form. From eq 8, it follows that the pKa of Ppn is shifted significantly upon sorption in the bilayer. This pKa shift can be interpreted in terms of the energy transfer of H3O+ ions from the aqueous environment to the membrane and is related to the difference between the free energy for deprotonation in the membrane, ∆ Gobilayer, and that in an aqueous environment, ∆Gow, by

∆Gobilayer - ∆Gow ) 2.303RT(pKa(bilayer) - pKa(w)) (15) As the pKa shift in this work is an intrinsic one, the electrostatic contribution to this energy difference is already accounted for and, hence, does not need to be included. The dominating energy contribution is the Born energy, which is due to the difference in the dielectric constant between the bulk water and the membrane:26,27

EBorn ) (e02Na/8π0rp)((1/bilayer) - (1/w))

(16)

where e0 is the proton charge (1.602 × 10-19 C) and bilayer is the dielectric constant at the sorption site in the bilayer. The (26) Israelachvili, J. Intermolecular and Surface Forces; St. Edmundsbury Press Limited: Suffolk, 1992; pp 37-38. (27) Zouni, A.; Clarke, R. J.; Holzwarth, J. F. J. Phys. Chem. 1994, 98, 1732.

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radius of the H3O+ ion, rp, is 0.17 nm.28,29 By combining eqs 15 and 16, it can be calculated from the pKa shift that bilayer is ∼30. Using neutron diffraction, it was found that the amine side chain of Ppn is positioned near the phosphate of the phospholipid headgroup.30 In addition, the infrared bands corresponding to the symmetric and asymmetric stretching modes of the DMPC phosphate headgroups are affected considerably by sorption of Ppn.3 By low-frequency impedance measurements31 and polarity probe experiments,32 the dielectric constant near the phosphate and ester groups in phosphatidylcholine bilayers was determined to be ∼30. In addition, the pKa shift determined indirectly in our work agrees well with the pKa shift of the amine group of hexadecyl-linked imidazolidine radicals in DMPC bilayers measured using electron spin resonance spectroscopy33 and with (28) Cevc, G.; Marsh, D. Phospholipid Bilayers; Wiley: New York, 1987; pp 182-184. (29) Horvath, A. L. Handbook of Aqueous Electrolyte Solutions; Ellis Horwood: Chichester, 1985. (30) Herbette, L.; Katz, A. M.; Sturtevant, J. M. Mol. Pharmacol. 1983, 24, 259. (31) Ashcroft, R. G.; Coster, H. G. L.; Smith, J. R. Biochim. Biophys. Acta 1981, 643, 191. (32) Bellemare, F.; Fragata, M. J. Colloid Interface Sci. 1985, 107, 553. (33) Khramtsov, V. V.; Marsh, D.; Weiner, L.; Reznikov, V. A. Biochim. Biophys. Acta 1992, 1104, 317.

Cocquyt et al.

the reported pKa shifts determined using nuclear magnetic resonance methods on a series of other amine-containing drugs embedded in phosphatidylcholine vesicles.34,35

6. Conclusions A sensitivity analysis showed that reliable intrinsic partition coefficients of Ppn in dimyristoyl phosphatidylcholine liposomes could be obtained from a partitioning model by splicing electrokinetic and sorption data, which were obtained in a range of different pH and salt concentrations. Statistical analysis revealed that these coefficients increased significantly with salt concentration. The intrinsic pKa was found to be 1.3 to 1.4 units lower in the liposome bilayer than in the bulk aqueous phase. The change in standard free energy for deprotonation corresponding to this shift was attributed to a shift in the dielectric constant from 74 in the aqueous phase to 30 in the bilayer. Acknowledgment. This work was sponsored by Strategisch Basis Onderzoek (SBO) Project No. IWT/30238 to M.D.C. LA062139E (34) Kitamura, K.; Takegami, S.; Kobayashi, T.; Makihara, K.; Kotani, C.; Kitade, T.; Moriguchi, M.; Inoue, Y.; Hashimoto, T.; Takeuchi, M. Biochim. Biophys. Acta 2004, 1661, 61. (35) Watts, A.; Poile, T. W. Biochim. Biophys. Acta 1986, 861, 368.