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Articles Evaluation of the Interaction of Propranolol with 1,2-Dimyristoyl-sn-glycero-3-phosphocholine (DMPC) Liposomes: The Langmuir Model Pieter Saveyn,*,† Jan Cocquyt,† Marcel De Cuyper,‡ and Paul Van der Meeren† Particle and Interfacial Technology Group, Faculty of Bioscience Engineering, Ghent UniVersity, Coupure Links 653, B-9000 Gent, Belgium, and Interdisciplinary Research Center, Laboratory of BioNanoColloids, Katholieke UniVersiteit LeuVen - campus Kortrijk, B-8500 Kortrijk, Belgium ReceiVed January 4, 2008. ReVised Manuscript ReceiVed March 25, 2008 The interaction of the amine containing β-receptor blocking agent propranolol (Ppn) with dimyristoylphosphatidylcholine (DMPC) vesicles was studied. Using a centrifugation assay, the protonated as well as unprotonated amount of the drug sorbed was verified, whereas the binding of the protonated Ppn was deduced from the surface charge density of the vesicles as calculated from electrophoretic mobility measurements. Assuming a 1:1 binding, a Langmuir model with only two parameters was found to be sufficient to fit all experimental data. Sensitivity analysis revealed that the estimated values of these parameters were reliable and independent from each other. These parameters were truly intrinsic, as electrostatic interactions were accounted for in the model. It was found that the pKa of Ppn shifted from 9.24, when disolved in water, downward by 1.34 units upon sorption, indicating that the intrinsic partition coefficient of the unprotonated Ppn was about 22 times higher than that of the protonated analog. In addition, a significant increase in the affinity of both Ppn analogs with increasing salt concentration was found. Theoretical analysis revealed that the Langmuir sorption model may be considered as a partitioning model with decreasing partition coefficient as the sorbed amount increases. Thus, the Langmuir model provides a better fit than a simple partition model at conditions that induce a substantial amount of propranolol sorbed, such as high pH and high propranolol concentrations.
1. Introduction During the last decades, a lot of attention has been spent on lipid-drug interactions. A first justification for this research is based on the fact that a lot of pharmaceutically active compounds are characterized by a poor water solubility. Hereby, liposomes do not only serve as convenient aqueous delivery vehicles of sparingly water soluble compounds, but they may also enable site-specific targeting and/or increased circulation (longevity), depending on the lipid composition.1 In addition, the activity as well as toxicity of a lot of drugs is affected by their interaction with biological membranes.2 These interactions have been studied intensively during the last decades, especially on model membranes, such as monolayers and liposomes. Studying local anesthetics, it has been shown that some drugs interact with membranes in a nonspecific manner.3,4 In this case, a partition coefficient is used to describe the absorption of the drug into the lipidic membrane, whose interior is considered as the hydrophobic phase. However, other drugs have a more specific interaction. Zhang et al.5 found that upon tetracaine sorption into dimyristoylphosphatidylcholine (DMPC) or dipalmitoylphosphatidylcholine (DPPC) membranes, the drug’s tertiary amine was positioned near the phosphate of the phospholipid headgroup, † ‡
Ghent University. Katholieke Universiteit Leuven - campus Kortrijk.
(1) Banerjee, R. J. Biomater. Appl. 2001, 16, 3–21. (2) dePaula, E.; Schreier, S. Braz. J. Med. Biol. Res. 1996, 29, 877–894. (3) Ohki, S.; Ohshima, H. Colloids Surf., B 1996, 5, 291–305. (4) Banerjee, S.; Bennouna, M.; Ferreira-Marques, J.; Ruysschaert, J. M.; Caspers, J. J. Colloid Interface Sci. 1999, 219, 168–177. (5) Zhang, J. Z.; Hadlock, T.; Gent, A.; Strichartz, G. R. Biophys. J. 2007, 92, 3988–4001.
whereas its ester bond was located in the region of the lipids’ ester bonds. This positioning was observed for both the neutral and protonated form. This way of interaction is likely to result in a maximum possible number of drug molecules adsorbed per unit area of membrane6 and therefore may be described by the Langmuir sorption model. In this work, the Langmuir model was used to describe the sorption behavior of propranolol (Ppn, Figure 1) in DMPC liposomes. Furthermore, the results were compared to the earlier elaborated partitioning model7 in terms of its ability to fit simultaneously both electrophoretic mobility data, reflecting only the protonated Ppn sorbed, and data obtained from a phase separation assay, reflecting the sum of both protonated and unprotonated Ppn sorbed. Besides the sorption affinity, the Langmuir model provides also the acid dissociation constant of Ppn in the bilayer, revealing the affinity of the DMPC membrane for either Ppn form. Therefore, this study contributes not only to the quantification but also to the understanding of liposomal incorporation, which can be an important variable in quantitative structure-activity relationship (QSAR) studies,8–11 as it is correlated with many pharmacokinetic and pharmacodynamic processes.12 (6) Barghouthi, S. A.; Puri, R. K.; Eftink, M. R. Biophys. Chem. 1993, 46, 1–11. (7) Cocquyt, J.; Saveyn, P.; Van der Meeren, P.; De Cuyper, M. Langmuir 2007, 23, 1959–1964. (8) Betageri, G. V.; Rogers, J. A. Pharm. Res. 1989, 6, 399–403. (9) Choi, Y. W.; Rogers, J. A. Pharm. Res. 1990, 7, 508–512. (10) Rogers, J. A.; Choi, Y. W. Pharm. Res. 1993, 10, 913–917. (11) Beigi, F.; Gottschalk, I.; Hagglund, C. L.; Haneskog, L.; Brekkan, E.; Zhang, Y. X.; Osterberg, T.; Lundahl, P. Int. J. Pharm. 1998, 164, 129–137.
10.1021/la800025y CCC: $40.75 2008 American Chemical Society Published on Web 05/10/2008
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Figure 1. Molecular structure of the unprotonated (left) and protonated (right) form of propranolol.
2. Materials and Methods 2.1. Materials. R/S-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 8.0 buffers, and acetic acid for the pH 4.0 buffer were all from Merck (Darmstadt, Germany). All buffers were at a concentration of 5 mM and were brought to the desired pH with 1 N KOH. They contained either no KCl, 5 mM KCl, or 75 mM KCl. All chemicals used were proanalysis grade. 2.2. Preparation of Liposomes. After addition of the buffer to the DMPC powder, this dispersion was stirred on a magnetic stirrer for 3 h at 37 °C; this is where the DMPC bilayers are in the liquidcrystalline state.13 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 DMPC liposomes was measured by electrophoretic light scattering (ELS) using a Zetasizer IIc apparatus (Malvern, Worcestershire, U.K.). The temperature was maintained at 37 °C, and the electric field strength was maintained 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. The calculation of the electrophoretic mobility is described in detail in ref 7. 2.4. Determination of the Amount Sorbed. Determination of the amount of Ppn sorbed in the DMPC liposomes was described in detail before.7 In practice, the total DMPC concentration, [DMPC]tot, was 2.9 mM, corresponding to 2.0 g/L. The concentration of sorbed Ppn, [Ppn]bilayer, expressed in mol/mol DMPC, was derived from the difference between the total propranolol, [Ppn]tot, and DMPC, [DMPC]tot, concentrations and the residual propranolol, [Ppn]sup (derived from UV-spectrophotometry), and DMPC, [DMPC]sup, concentrations (derived from phosphate analysis) in the supernatant obtained after centrifugation for 1 h at 4000g at 37 °C:
[Ppn]bilayer ) ([Ppn]tot - [Ppn]sup) ⁄ ([DMPC]tot - [DMPC]sup) (1) The sorption experiments were performed at pH 7.0 in 5 mM TES buffer containing 0, 5, or 75 mM of KCl. 2.5. Data Fitting. The sorption data and the electrophoretic mobility data were fitted simultaneously. The sum of squared differences between measured and calculated electrophoretic mobilities (expressed in µ m · cm/s/V) or sorbed concentrations (in mol/ mol DMPC) was first normalized for the variance of the data series and then minimized using the Nelder-Mead simplex method.14 The normalized sum of squared differences (NSSD) for each of the (12) Testa, B.; Crivori, P.; Reist, M.; Carrupt, P. A. Perspect. Drug DiscoVery Des. 2000, 19, 179–211. (13) Cao, A.; Hantzbrachet, E.; Azize, B.; Taillandier, E.; Perret, G. Chem. Phys. Lipids 1991, 58, 225–232. (14) Lagarias, J. C.; Reeds, J. A.; Wright, M. H.; Wright, P. E. SIAM J. Optim. 1998, 9, 112–147.
Figure 2. Combinations of affinity parameters of protonated Ppn (a+) and unprotonated Ppn (a0) yielding the same minimal NSSD (4.1) and ∆pKa (-1.30) according to the Langmuir model where the affinity parameters were assumed independent of salt concentration. The full line corresponds to the bisector.
three sorption data series was weighted twice as much in the fit compared to each of the nine ELS data series.
3. Theory In the same way as in the partitioning model,7 the vesicle interface region was subdivided 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 nonbound concentrations of the protonated and the unprotonated form of Ppn in the bulk solution are calculated using the Henderson-Hasselbalch equation:
log([Ppn+]free ⁄ [Ppn0]free) ) pKa(w) - pH
(2)
where pKa(w), the negative logarithm of the acid dissociation constant of Ppn in water, is 9.24 at 37 °C.15 The concentration of unprotonated Ppn in the aqueous phase close to the interface, [Ppn0]aq.int, equals the nonbound concentration in the bulk continuous phase, [Ppn0]free, whereas the concentration of protonated Ppn in the aqueous part of the interphase region, [Ppn+]aq.int, is related to the nonbound concentration of protonated Ppn in the bulk continuous phase, [Ppn+]free, by a Boltzmann distribution:
[Ppn+]aq.int ) [Ppn+]free exp(-Fψint ⁄ RT)
(3)
where R is the universal gas constant (8.31 J/(K mol)), T is the kelvin temperature, F is Faraday’s constant (96 485 C), and ψint is the electrostatic potential at the bilayer interface. In the Langmuir model, the bilayer concentrations of protonated and unprotonated Ppn, [Ppn+]bilayer and [Ppn0]bilayer, respectively, are related to the concentrations at the aqueous part of the interface, [Ppn+]aq.int and [Ppn0]aq.int, respectively, by max [Ppn+]bilayer ) [Ppn+]bilayer a+[Ppn+]aq.int ⁄ (1 + a+[Ppn+]aq.int) (4) max [Ppn0]bilayer ) [Ppn0]bilayer a0[Ppn0]aq.int ⁄ (1 + a0[Ppn0]aq.int) (5)
where a+ and a0 represent the sorption affinity parameters for (15) Pauletti, G. M.; Wunderliallenspach, H. Eur. J. Pharm. Sci. 1994, 1, 273–282.
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protonated and unprotonated Ppn, respectively, both expressed max max in m3/mol, and [Ppn+]bilayer and [Ppn0]bilayer are the maximum bilayer concentrations of the protonated and unprotonated form of Ppn, respectively, both expressed in mol/mol DMPC. The shift in the negative logarithm of the Ppn acid dissociation constant, occurring by transfer of Ppn from water [pKa(w)] to the bilayer medium [pKa(bilayer)], can then be derived by
∆pKa ) pKa(bilayer) - pKa(w) ) log
[Ppn+]bilayer[Ppn0]aq.int [Ppn0]bilayer[Ppn+]aq.int max [Ppn+]bilayer
) log max [Ppn0]bilayer
) log
a+[Ppn+]aq.int 1 + a+[Ppn+]aq.int a0[Ppn0]aq.int 1 + a [Ppn ]aq.int 0
0
[Ppn0]aq.int
Table 1. pKa-Shift (∆pKa), Sorption Affinity Parameter (a) at Different KCl Concentrations, Normalized Sum of Squared Differences (NSSD) Obtained from the Data Fit, and Degrees of Freedom (DF) Left to Fit Using the Langmuir Model, As Compared to the Partitioning Model7 full modela reduced model Aa reduced model Bb ∆pKa a (0 mM KCl) a (5 mM KCl) a (75 mM KCl) NSSD DF NSSDPartitioning7 DFPartitioning7
-1.34 12.6 14.7 17.4 3.2 173 4.1 171
-1.30 13.8 4.1 175 4.7 175
0 1.29 1.47 1.62 14.2 174 13.9 174
a In the full model, a (expressed as m3/mol) was assumed to depend on the salt concentration, whereas in the reduced model A a is assumed to be independent of the salt concentration. b In the reduced model B, ∆pKa was assumed to be zero.
[Ppn+]aq.int
max a+(1 + a0[Ppn0]aq.int) [Ppn+]bilayer max max - [Ppn+]bilayer ([Ppntot]bilayer )a0(1 + a+[Ppn+]aq.int)
(6)
According to eq 6, ∆pKa can be expressed as a function of four
tot max tot max parameters: a+, a0, [Ppn+]max bilayer, and [Ppn ]bilayer (with [Ppn ]bilayer max + 0 max ) [Ppn ]bilayer + [Ppn ]bilayer ). In order to limit the amount of freely adjustable parameters from four to three, the sum of max max [Ppn+]bilayer and [Ppn0]bilayer was restricted to one binding site per molecule of DMPC. When the data were fitted by the Langmuir model using three adjustable parameters, this is, ∆pKa, a+, and a0, the latter were found to be completely interdependent. This phenomenon is illustrated by Figure 2 for the case where the affinity parameters were assumed to be independent of salt concentration. Figure 2 reveals that many combinations of both affinity parameters give rise to the same minimized NSSD (normalized sum of squared differences) and ∆pKa values of 4.1 and -1.30, respectively. Under our experimental circumstances, only low Ppn concentrations were used to avoid structural reorganizations such as micellization16 which might change the sorption characteristics dramatically. Therefore, the interdependence shown in Figure 2 can be explained from the fact that the general Langmuir sorption model reduces to [Ppn]bilayer ) a[Ppn]max bilayer[Ppn]aq.int as [Ppn]aq.int f 0 (and hence [Ppn]bilayer f 0). Hence, at the low sorbed amounts needed to prevent structural reorganizations, the sorption affinity is not solely determined by the affinity parameter a but rather the product of the affinity parameters and the sorption maximum max a[Ppn]max bilayer, allowing both the affinity parameter a and [Ppn]bilayer to be freely adjustable with different combinations leading to the same affinity. Considering two sorbing species of different sorption affinity, variations in their affinity parameter, as shown in Figure 2, may be compensated by opposite changes in their sorption maximum. Thus, one degree of freedom has to be skipped, which has been realized by setting the affinity parameters a+ and a0 equal to each other but allowing the affinities to be max different via a different [Ppn]bilayer for each species which according to eq 6 is determined by ∆pKa. By taking a+ ) a0, eq 6 can be rewritten for the case of low sorbed amounts into
max ∆pKa ) log([Ppn+]bilayer (1 + a[Ppn0]aq.int) ⁄ max [Ppn0]bilayer (1 + a[Ppn+]aq.int)) (7)
(16) Schutze, W.; Muller-Goymann, C. C. Pharm. Res. 1998, 15, 538–543.
Figure 3. Amount of Ppn sorbed in a 2 g/L DMPC liposomal dispersion at pH 7 in buffer 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 solid lines represent the Langmuir model fit, whereas the dashed lines represent the partitioning model fit.7
The Langmuir model differs from the partitioning model7 by the condition that, in the former, a maximum amount of Ppn can sorb per lipid molecule, whereas, theoretically, an unlimited amount can sorb a the partitioning model that assumes a concentration dependent partition coefficient. Taking into account the low [Ppn0]aq.int in our experimental circumstances, it follows that the denominator 1 + a+[Ppn+]aq.int in eq 4 represents the major difference between the Langmuir model and the partitioning model (eqs 8 and 9).7
[Ppn+]bilayer ) Kp[Ppn+]aq.int
(8)
[Ppn0]bilayer ) Kn[Ppn0]aq.int
(9)
It follows from eq 7 that changes in this denominator are max max balanced by changes in the ratio [Ppn+]bilayer /[Ppn0]bilayer at fixed ∆pKa.
4. Results In the “full model” approach, the sorption affinity parameter a of the Langmuir model was assumed to be dependent on the salt concentration. The resulting parameter estimations are summarized in Table 1. The solid lines in Figures 3 and 4 represent the least squared differences fit obtained with this “full Langmuir
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Figure 4. 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) with 0 mM KCl (O), 5 mM KCl (0), or 75 mM KCl (∆) added to the buffer. The solid lines represent the Langmuir model fit, whereas the dashed lines represent the partitioning model fit.7
model” for the sorption data at pH 7 and the electrophoretic mobility data at pH 4, 7, and 8. 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
SD(%) ) 100 ×
√(0.04[Ppn]tot)2 + (0.04[Ppn]free)2 [Ppn]tot - [Ppn]free
(10)
The data points for which this error was larger than 10% were not included in the fit and are shown in Figure 3 as filled symbols. To enable comparison, the best fit according to the previously described partitioning model7 was included as well (dashed line). Comparing the Langmuir to the partitioning approach (both containing two freely adjustable parameters), highly similar fits were obtained at pH 4 and 7. However, at pH 8, a significantly better fit was obtained from the Langmuir model, especially at the highest Ppn concentration. In fact, these conditions correspond to the highest [Ppn0] concentrations and hence the highest sorbed amounts. In the Langmuir “reduced model A” fit, the sorption affinity was assumed to be independent of salt concentration. From the NSSD obtained after fitting the reduced model and the NSSD obtained after fitting the full model, the critical F* value was calculated to be 28 using the equation:
F* )
(NSSDreduced - NSSDfull)DFfull NSSDfull(DFreduced - DFfull)
(11)
where DFfull and DFreduced are the number of degrees of freedom of the full model and the reduced model, respectively. This value is higher than the 99.9th percentile of an F2,173 distribution, which is 7. Thus, the observed differences in intrinsic sorption affinities at different salt concentrations were significant. The same difference in NSSD was observed when the full model is compared to the full partitioning model (NSSDPartitioning, Table 1), and, in the latter case, the DF were even lower, from which it is clear that the Langmuir model fits significantly better. In order to check whether the pKa-shift was significantly different from 0, a fit where the pKa-shift was fixed to zero (Table 1, reduced model B) was compared to the fit where the pKa-shift was freely adjustable (Table 1, full model). Based on the normalized sum of squared differences between the fit and the experimental values of the reduced model and the full model, NSSDreducedB and NSSDfull, respectively, the critical value F* was calculated to be 620 using eq 11. From the comparison of F/ to the 99.9th percentile of an F1,173 distribution, which is only 11, it is obvious that the pKa is significantly lower in the bilayer than in the water. In order to check the interdependence of the parameters derived from the full model, a sensitivity analysis was performed under all the experimental conditions used in this work. Sensitivity was defined as pδA/δp where the response A was either the electrophoretic mobility or the sorbed Ppn concentration. The sensitivity analysis aims to calculate to what extent the elec-
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Figure 5. Sensitivity of the amount of Ppn sorbed at pH 7 (a) and of the electrophoretic mobility at pH 8 (b) without any KCl (circles), with 5 mM KCl (squares), or with 75 mM KCl (triangles) in the buffer, to a change in the Ppn pKa-shift (filled symbols) or in the Ppn affinity parameter (empty symbols) according to the Langmuir model.
Figure 6. Parameter combinations corresponding to the minimized normalized sum of squared differences between the experimental data and the full Langmuir model (shown as +) and with the normalized sum of these squared differences being 0.1% higher than the minimum (line).
trophoretic mobility and the sorbed Ppn concentration are affected by a change in the value of each of the two adjustable parameters p obtained from the fit. In addition, the estimated values of these parameters are only reliable when a change of their values gives a different sensitivity profile in the calculated response range, as this means that the parameters are not interdependent and, hence, the set of values obtained from the fit is unique. The parameter p is either the pKa-shift or the sorption affinity parameter. In all the experimental conditions tested, the impact of a change in the pKa-shift was larger than that of the same relative change in the sorption affinity parameter except for the sorbed amount at the lowest KCl concentration (Figure 5). At pH 4 and 7, the plots of the sensitivities of the electrophoretic mobility to a change in the pKa-shift or to a change in the sorption affinity parameter had the same shape over the entire Ppn concentration range (results not shown), indicating that there was not enough information available in these two data sets to derive both the pKa-shift and the sorption affinity parameter separately. Also, at pH 8, the plots of the sensitivities of the electrophoretic mobility had the same shape below 0.1 mM added Ppn for all three salt concentrations (Figure 5b). This was not the case above 0.1 mM added Ppn where the sensitivity to a change in the Ppn affinity decreased with the concentration of added Ppn (Figure 5b). The plots of the sensitivities of the amount sorbed at pH 7 had different shapes (Figure 5a) over the entire concentration range. It can be concluded that mainly the sorption experiment at pH 7 and the electrophoretic mobility experiment at pH 8 provided sufficient information to derive both the sorption affinity and the pKa-shift from the same fit. In order to further clarify the relationship between the parameters in the full model, combinations of pKa-shift and sorption affinity with the NSSD minimized and with the NSSD 0.1% higher than the minimum are shown in Figure 6. In Figure
max max Figure 7. [Ppn+]bilayer /[Ppn0]bilayer ratio of the maximum bilayer concentrations according to the full Langmuir model at pH 7.0 without KCl (O), with 5 mM KCl (0), or with 75 mM KCl (∆).
6, it can be seen that a relatively small variation of the pKa-shift makes the NSSD 0.1% higher. On the other hand, the differences between the affinities at the three different salt concentrations seem to be relatively small compared to the variation in affinity constant required to increase the NSSD with 0.1%. Thus, Figure 6 confirms the conclusions obtained using the F-tests: the pKashift is very significantly different from zero, whereas the differences between the affinities at different salt concentrations are less significant.
5. Discussion From eqs 4 and 8, it is clear that the expression 1 + a+[Ppn+]aq.int constitutes the difference between the Langmuir and the partitioning model. It has also been stated in the Theory section that, in the Langmuir model, changes in this expression are max max balanced by the ratio [Ppn+]bilayer /[Ppn0]bilayer . Figure 7 shows a plot of this ratio according to the Langmuir model at pH 7 at the different salt concentrations used in this study. At pH 4, nearly the same figure was obtained, while, at pH 8, a highly similar behavior was found, except that the increase in the ratio 0 max [Ppn+]max bilayer/[Ppn ]bilayer was less pronounced (results not shown). By adjusting the latter ratio, the concentration of both protonated and unprotonated Ppn in the bilayer is regulated according to the pKa(bilayer) value, reflecting the preference of the bilayer for either form. As the amount of added Ppn approaches zero, it can be max max derived from eq 7 that log([Ppn+]bilayer /[Ppn0]bilayer ) is equal to the pKa-shift which, according to Figure 7, is log(0.046),
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respectively. These small variations had only a minor effect on the quality of the fit, as observed from the comparison of the Langmuir and the partitioning fit in Figure 4a and b. At pH 8, on the other hand, the partition coefficients in the Langmuir model varied by about a factor of 2 and yielded a visually observable better fit in Figure 4c. With an increase in the pH (Figure 8) or the salt concentration (results not shown), the amount of sorbed Ppn increased and, therefore, the decrease in calculated Langmuir partition coefficients was more pronounced upon adding Ppn, resulting in a better overall fit.
6. Conclusions Figure 8. Partition coefficients calculated from the Langmuir model for protonated Ppn (Kp,Langmuir) (empty symbols) and for unprotonated Ppn (Kn,Langmuir) (filled symbols) in the presence of 5 mM KCl at pH 4.0 (squares), pH 7.0 (triangles), or pH 8.0 (circles). For comparison, the partition coefficients of both protonated and unprotonated Ppn obtained from the partitioning model7 are shown as a solid and a dashed line, respectively.
corresponding to a ∆pKa of -1.34, which was indeed also found from the Langmuir fit (Table 1). A pKa-shift of -1.34 corresponds to a 22 times higher affinity of unprotonated compared to protonated Ppn and is in line with the results of Miyazaki et al.17 This shift was earlier attributed to a difference in the dielectric constant between the bulk water (74) and the membrane (∼30).7 max From eqs 4 and 5, it follows that the factors [Ppn+]bilayer a+/ max + + 0 0 0 0 (1 + a [Ppn ]aq.int) and [Ppn ]bilayera /(1 + a [Ppn ]aq.int) in the Langmuir model may be regarded as analogous to the partition coefficients in the partitioning model. They were therefore called Kp,Langmuir and Kn,Langmuir. In Figure 8, these factors are calculated from the Langmuir fit and compared to the partition coefficients from the partitioning model for the case where 5 mM KCl was added. Limiting the amount of Ppn sorbed to a maximum of one Ppn molecule per lipid molecule in the Langmuir model caused a decrease in the calculated partition coefficients with Ppn concentration, whereas the partition coefficients obtained from the partitioning model used were constant. At pH 4 and 7, this decrease in partition coefficient was limited to 7 and 16%,
The Langmuir model has been extended to include sorption limitation at high concentrations without having to introduce an additional degree of freedom. From the estimated parameters, a concentration dependent partitioning coefficient was derived. Especially at conditions that favor sorption, this model fitted the data better than the partitioning model. In fact, it can be regarded as a partitioning model where both partitioning constants decrease as sorption is increasing. Since the electrostatic interactions were taken into account, all parameters obtained from the fits were intrinsic. The sorption affinity of Ppn increased with salt concentration, and the pKa was 1.34 units lower in the membrane than in the bulk, due to the difference in the dielectric constant between the aqueous phase and the bilayer. Knowledge of the ionization state of membrane-embedded drugs may be of importance in the design of drug delivery formulations. Intracellular organelles, indeed, maintain their own characteristic pH value, ranging from pH 4.5 in lysosomes to about 8.0 in mitochondria.18 Thus, by selecting appropriate anionic, zwitterionic, and/or cationic lipid types, it should be possible to generate liposomes in such a way that they can provide the desired drug/liposome partition between different cell compartments. Acknowledgment. This work was sponsored by the special research foundation (BOF Ghent University No. 01D05805) to P.S. LA800025Y
(17) Miyazaki, J.; Hideg, K.; Marsh, D. Biochim. Biophys. Acta 1992, 1103, 62–68.
(18) Asokan, A.; Cho, M. J. J. Pharm. Sci. 2002, 91, 903–913.
