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Base Properties of β-Blockers and Benzodiazepines in Sodium Dodecyl Sulfate Micelles. A Spectrophotometric and Potentiometric Study
Acid/Base Properties of β-Blockers and Benzodiazepines in Sodium Dodecyl Sulfate Micelles. A Spectrophotometric and Potentiometric Study BALTAZAR
DE
CASTRO†, PAULA GAMEIRO†, CARLA GUIMARA˜ ES‡, JOSEÄ L. F. C. LIMA‡,
AND
SALETTE REIS*,‡
Contribution from the CEQUP/Departamento de Quı´mica, Faculdade de Cieˆncias, and CEQUP/Departamento de Quı´mica-Fı´sica, Faculdade de Farma´cia, Universidade do Porto, 4050, Porto, Portugal Received June 4, 1997.
Accepted forpublication November 7, 1997.
Abstract 0 The effect of sodium dodecyl sulfate (SDS) micelles on the acid−base properties of two family of pharmaceutical drugs (βblockers and benzodiazepines) at 25 °C and I ) 0.1 M NaCl have been studied. The characterization of the several solution equilibria for the system drug/SDS micelle solution was performed by potentiometry and spectrophotometry, below and above the critical micelle concentration (cmc). Two widely used models have been applied to quantify the effect of micelles on the pKa of the drugs, and the results obtained point to different interactions of each family of drugs with the micelles.
Introduction Aqueous micelle solutions are structurally “simple” and are often used as models for the more complex and metastable biological membranes, as their interphases are structurally similar.1 Tensioactive agents, both naturally occurring and administered, also play an important role in the pharmocokinetic properties of drugs and in their formulation. Their uptake is controlled by naturally occurring micelles in the intestinal tract (e.g. bile acids) and also by those intentionally incorporated in pharmaceutical formulations.2-4 Information regarding micellar effects on the pKa values of a wide variety of acids and bases is of interest in connection with the increasing use of aqueous micellar systems as solvents in analytical chemistry5 as well as in other areas, such as micellar catalysis.5-10 In this work we report the effect of SDS micellar solutions on the acid-base properties of substance with pharmacological interest,11,12 namely two β-blockers (atenolol and nadolol) and two benzodiazepines (midazolam and nitrazepam). Two models were used to quantify the micellar effects of equilibrium constants (Berezin8 and the PIE13 models). Their difference lies mainly in an assumption used by the PIE model that the counterions of SDS (Na+) exchange with other cationic species in solution. Application of both models has been extremely helpful in choosing the model that best describes the effect of micelles on the pKa of the drugs used and have allowed the determination of their binding constants to SDS.
Experimental Section Reagents and SolutionssAll compounds were used as received: atenolol and nadolol, from Sigma; sodium dodecyl sulfate (SDS), from Aldrich; nitrazepam and midazolam, a gift from Hoffman-La Roche; and HCl (Titrisol) and all other chemical, from † ‡
Departamento de Quı´mica. Departamento de Quı´mica-Fı´sica.
356 / Journal of Pharmaceutical Sciences Vol. 87, No. 3, March 1998
Merck (grade pro analysi). Solutions were prepared with double deionized water (conductivity less than 0.1 µS cm-1). Potentiometric and Spectrophotometric Measurementss All potentiometric measurements were carried out with a Crison 2002 pH meter and 2031 buret controlled by a personal computer which was also used for data manipulation. The electrode assembly was made up of an Orion 900029/4 AgCl/Ag reference electrode and a Russel SWL glass electrode. System calibration was performed by the Gran method14 in terms of hydrogen ion concentration, using strong acid-strong base titration {HCl (0.001 M)/NaOH(≈0.02 M)} with solutions whose ionic strength was adjusted to 0.1 M with NaCl. Titrations were always carried out under a nitrogen atmosphere at 25 °C in a double-walled glass cell. All absorption spectra were recorded with a Hitachi U-2000 dual-beam spectrophotometer using quartz cells with 1 cm path length that were thermostated at 25 °C. Potentiometric Determination of Acidity Constantss Acidity constants for atenolol and nadolol were obtained by titrating 20.00 mL of acidified solutions (1 mM HCl) of the β-blocker (0.8 mM), either in pure water or in aqueous solutions of SDS (0.5, 1, 2, 2.5, 3, 4, 7, 10, 20 mM), with NaOH (≈20 mM). All titrations were performed at 25 °C under nitrogen, and for all solutions the ionic strength was adjusted to 0.1 M with NaCl. For midazolam, the potentiometric determination of the acidity constants was performed using conditions similar to those described above, but the midazolam concentration was 0.7 mM and that of SDS 1, 2, 2.5, 3, 4, 7, 10, 20 mM. System calibration was always performed before and after each determination by titrating HCl with NaOH, both for aqueous and micellar media; in the latter experiments the concentration of SDS was that of the titrated solution. The characteristics of the glass electrode were similar below and above the critical micelle concentration, except that the response time was longer at high concentrations of SDS. Calculations were performed with data obtained from at least six independent titrations, each with more than 30 points, and the experimental titration data were analyzed using the computer program Superquad.15 The errors reported in this work were calculated by the method of Albert and Serjeant,16 in which the errors are calculated as the maximum difference between the logarithm of the average of the antilogarithms of the calculated pKa values and their individual values. Spectrophotometric Determination of Acidity Constantss Acidity constants of the β-blockers and the benzodiazepines were obtained from UV data of solutions (aqueous and micellar media) of nitrazepam (2.6 × 10-5 to 5 × 10-5 M), atenolol, and nadolol (5 × 10-5 to 1 × 10-4 M), for which the ionic strength was adjusted to 0.1 M with NaCl. The SDS concentrations used were the same as the potentiometric studies, viz. 0.5, 1, 2, 2.5, 3, 4, 7, 10, and 20 mM. For all solutes, no changes in the wavelength of the maximum absorption were detected upon addition of SDS at these concentrations. Aliquots of strong base or strong acid were added to 20 mL of the stock solution to adjust-log [H+] to the desired value; -log [H+] measurements and system calibration were performed by potentiometry as described previously. The calculations were performed with the program SQUAD 8517 by using data from at least two independent experiments, each with more than six solutions, and in the range from 200 to 350 nm, at 2 nm intervals.
S0022-3549(97)00219-0 CCC: $15.00 Published on Web 02/12/1998
© 1998, American Chemical Society and American Pharmaceutical Association
Theoretical Treatment of Acidity in Micellar Media It is well-known that organized assemblies modify the equilibria and acid-base properties of chemical processes,5,6,8 and a number of mathematical models were developed over the last years to quantify micellar effects on equilibrium constants of different substances.1,7-9,13,18-24 These models can provide a quantitative interpretation of changes in the apparent acid-base equilibrium of the drugs, studied in the present work, in SDS media. For the dissociation of protonated substrate
HB+ h H+ + B
(1)
the value of the dissociation constant in the presence of surfactants (pKapp)
Kapp )
Ka ) [B]f[H+]f/[HB+]f
B f h Bb
Km B ) [B]b/[B]fCD
+ m + + HB+ f + Yb h Yf + HBb KHB+/Y) [HB ]b[Y]f/[HB ]f[Y]b + H+ f + Yb h Hb + Yf
KH+/Y ) [H+]b[Y]f/[H+]f[Y]b
+ Bb + H + b h HBb
Ka,b ) [HB+]bCD/[B]b[H+]b
From these equilibria and with the assumptions of the PIE model it is possible to derive the following equation for Kapp
Kapp ) [H+]f ) Ka
([B]f + [B]b)
+
[H ]f
([HB+]f + [HB+]b)
(2)
is the value of intermicellar pH () -log [H+]f) when:13
[B]f + [B]b ) [HB+]f + [HB+]b
(3)
In these and following expressions, HB+ represents protonated species, B the neutral species, H+ the proton, and Y+ the counterion of the anionic surfactant (the subscript f denotes the species in water and b denotes the species bounded to the micelles). Berezin and co-workers proposed that from the dissociation of protonated substrate different species partioned between the micellar and aqueous pseudophases and thus expressed the apparent acidity constant, Kapp, as8
Kapp ) [H+]f ) Ka
+ HB+ f h Hf + B f
(1 + Km B CD) m (1 + KHB +CD)
(4)
where CD is the micellized detergent concentration (equal to the difference between the total detergent concentration, CT, and the critical micellar concentration, cmc, i.e., CD ) m m CT - cmc), KHB + and KB are the binding constants with micelles for the protonated and neutral forms of the substrate, and Ka is the dissociation constant of HB+ in water. In the PIE model,13 the ionization of a micellar-bond substance is described by an intrinsic acidity constant, Km a , whose value reflects the medium properties of the micelle, and the micelles are assumed to act as a separate phase uniformly distributed throughout the solution (pseudophase assumption). The medium properties of the micelles are assumed to be independent of solution composition. Recently, the above treatment was extended to the variation of Kapp over a wide range of surfactant concentration and in the presence of added salts.23 The micelle surface is assumed to act as an ion-exchanger, e.g. the distribution of proton and alkaline metal ions in solution of anionic micelles is described by an ion-exchange constant. For mathematical simplicity, the fraction of bound counterion, R, is assumed to be constant and independent of surfactant concentration, counterion concentration, and counterion type. Within the framework of the PIE model, the equilibrium of β-blockers and benzodiazepines in anionic micellar media is be described by the set of equilibria that characterized their dissociation and the partition of the protonated and neutral species between the micelles and the solution and that are depicted in the following scheme.
(1 + Km B CD) m (1 + KHB +/Y(Yb/Yf))
(5)
where Yb ) (1 - R)CD - W and Yf ) RCD + cmc + W + [BY]T, with W ) [H+]b + [HB+]b. On applying both models we have used the optimum value of R ) 0.75 for the ionization degree of the anionic micelles,1,13 and a value of 1.4 mM for the cmc of SDS in 0.1 M NaCl.25 The fit of the experimental results to the two models where performed with the non linear subroutine of Delta Graph Pro 3.5.
Results and Discussion Acidity Constants in the Presence of Micellar MediasThe data concerning the acidity constants of nadolol, atenolol, midazolam, and nitrazepam, both in aqueous solution and in micellar media, are included in Table 1. For all compounds, the acidity constants obtained in bulk aqueous solutions by both experimental methods are practically identical and are also very similar to those reported in the literature.11,26-31 A few comments must be made regarding the data in Table 1. First, the spectrophotometric determination of the pKa of midazolam, despite earlier claims that changes in the protonated and nonprotonated bands are too small to be of significance,28 yielded values similar to those obtained potentiometrically, albeit with a larger error. The low solubility of nitrazepam precluded the potentiometric determination of its acidity constant. Nitrazepam has two acid equilibria in the pH range studied,
H2B+ h H+ + HB h B- + H+
(6)
and each equilibrium was treated independently, because their pKa values are separated by more than 7 log units;16 furthermore as the second dissociation yields negatively charged species, it is excluded from the foregoing discussion and will be treated separately. An analysis of Table 1 shows that the apparent acidity of our compounds are independent of SDS concentration up to the cmc but start to decrease above this value. This behavior has been observed for many indicators, for which at least one form is cationic, that interact with anionic micelles5,19,32 and, in general, stronger interactions with micelles cause larger shifts in the pKa values.5 For the compounds studied, we observe a pKa shift of ≈0.5 log units for the β-blockers and of ≈1 for the benzodiazepines; as strong interactions of cationic species with anionic micelles drive equilibrium described by eq 1 to the left, thus increasing the value of pKapp, these results suggest that the interactions with protonated benzodiazepines are stronger than that with β-blockers. Figure 1 shows the potentiometric titration curves for midazolam and for nadolol, and the shift in pKa values, as Journal of Pharmaceutical Sciences / 357 Vol. 87, No. 3, March 1998
Table 1sAcidity Constants (pKapp) of Atenolol, Nadolol, Midazolam, and Nitrazepam, in Aqueous Solution and in SDS, Obtained by Potentiometry or Spectrophotometry at 25 °C and I ) 0.1 M in NaCl atenolol
nadolol
midazolam
nitrazepam spectrophotometry
[SDS]/M
potentiometry
spectrophotometry
potentiometry
spectrophotometry
potentiometry
0 5.0 × 10-4 1.0 × 10-3 2.0 × 10-3 2.5 × 10-3 3.0 × 10-3 4.0 × 10-3 7.0 × 10-3 1.0 × 10-2 2.0 × 10-2
9.32 ± 0.05 9.32 ± 0.02 9.32 ± 0.02 9.34 ± 0.05 9.39 ± 0.01 9.43 ± 0.04 9.51 ± 0.02 9.63 ± 0.05 9.70 ± 0.06 9.70 ± 0.05
9.29 ± 0.03 9.30 ± 0.03 9.30 ± 0.03 9.33 ± 0.02 9.37 ± 0.01 9.44 ± 0.02 9.54 ± 0.01 9.63 ± 0.01 9.70 ± 0.03 9.71 ± 0.03
9.51 ± 0.02 9.51 ± 0.05 9.51 ± 0.04 9.52 ± 0.03 9.60 ± 0.02 9.75 ± 0.03 9.82 ± 0.07 9.93 ± 0.04 9.99 ± 0.08 9.99 ± 0.03
9.52 ± 0.02 9.52 ± 0.01 9.52 ± 0.02 9.53 ± 0.01 9.59 ± 0.01 9.76 ± 0.04 9.84 ± 0.01 9.96 ± 0.01 10.02 ± 0.05 10.02 ± 0.05
5.91 ± 0.01
2.98 ± 0.01
10.55 ± 0.03
5.91 ± 0.01 6.65 ± 0.04 6.73 ± 0.03 6.80 ± 0.02 6.89 ± 0.02 6.97 ± 0.07 7.02 ± 0.02 7.08 ± 0.01
2.99 ± 0.01 3.32 ± 0.01 3.45 ± 0.01 3.54 ± 0.01 3.61 ± 0.01 3.67 ± 0.01 3.81 ± 0.03 3.82 ± 0.03
10.55 ± 0.04 10.66 ± 0.03 10.77 ± 0.03 10.85 ± 0.01 10.93 ± 0.03 11.11 ± 0.05 11.21 ± 0.05 11.51 ± 0.03
Figure 1sPotenciometric titration curves of nadolol (open symbols) and of midazolam (filled symbols) in aqueous solution (circles) and in micellar media of 0.01 M of sodium dodecyl sulfate (triangles), with NaOH (≈20 mM).
indicated by the equivalent points, is larger for the benzodiazepine. Recalling the results reported for potentiometric titrations of amino acids and peptides in micellar media,5 our data support stronger interactions of the benzodiazepine with SDS micelles. Application of Theoretical ModelssWe applied the Berezin model to our data. Equation 4 was rewritten as
(
)
Kapp Ka Kapp m ) KHB - Km + B CD Ka
1-
(7)
and for the benzodiazepines, plots from eq 7 yields straight m 4 lines, with slopes (KHB +) of 1.1 × 10 for midazolam and of 3 2.8 × 10 for the first dissociation of nitrazepam (Ka1). The 2 corresponding intercepts (Km B ) were 7.8 × 10 and 3.5 × 102 and the goodness of fit was R2 ) 0.96 and 0.98, respectively. Application of eq 7 to the β-blockers yields a parabola, which means that this simple model does not adequately describe their changes in acid-base properties in micellar media. As it is clear from our data, the linearized form of eq 7 is a useful screening test to determine if this model can be used to describe the effect of micelles on acid-base 358 / Journal of Pharmaceutical Sciences Vol. 87, No. 3, March 1998
Figure 2sExperimental data for the dependence of Kapp on surfactant concentration (CD) for atenolol (b) and nadolol (O) and best fit by the Berezin model (− −) and by the PIE model (s).
properties, but as it gives a high weight to the low concentrations points, we have fitted eq 4 directly to our data, and the results are presented in Table 2. We also applied the PIE model to our data and obtained good fits for both the benzodiazepines and the β-blockers. In accordance with the results outlined above, as the data for benzodiazepines are fitted to an equation with more parameters, a better fit is always to be expected; however, as the calculated amount of Na+ exchanged with the other cationic species in solution is negative, the applicability of this model is precluded on chemical grounds. In fact, as + Na+ exchanges with H+ f and HBf , the concentration of exchanged Na+, W, must be equal to the concentration of bound H+ and HB+, W ) [H+]b + [HB+]b, and this quantity was found to be negative when the PIE model is applied to benzodiazepines, an impossible result as both bound concentrations must be non-negative. As shown above, the data for the β-blockers could not be described by the simple Berezin model in its linear form, although a nonlinear fit to eq 4 was obtained. A much better fit, however, is obtained with the PIE model, thus implying the existence of ionic exchange of the protonated form of these compounds with Na+ bound to the surfactant surface (Figure 2). The second hydrolysis of nitrazepam, as referred above, poses a different problem as we are dealing with deproto-
Table 2sBinding Constants to Micelles of Protonated and Nonprotonated Forms of the β-Blockers and Benzodiazepines, with and without Ionic Exchange of the Counterions of SDS with Other Cationic Species in Solution without exchange
with exchange
drug
KmB
m KHB +
R2
KmB
m KHB +/Y
Wa
R2
atenolol nadolol midazolam
72 80 800
294 442 11200
0.960 0.892 0.966
134 271 226
200 464 1760
9 × 10-5 11 × 10-5 −15 × 10-5
0.992 0.981 0.997
without exchange drug
KmHB
KHm2B+
nitrazepamb
365
2830
without exchange R2
KBm-
KmHB
0.987
31
616
with exchange R2
KmHB
KHm2B+/Y
Wa
R2
0.992
312
1090
−2 × 10-7
0.986
a W ) [H+]b + [HB+]b; see the text. b For nitrazepam, the first set under “without exchange” refers to the first dissociation constant and the second set to the second dissociation constant.
nation of neutral into negatively charged species, thus implying the application of the PIE model to be inadequate. Application of the electrostatic model of Berezin to Ka2 of nitrazepam yieldel fits that were not as good (R2 ) 0.94), and the values of the binding constants were Km HB ≈ 5 × 102 and KBm- ≈ 10. If KBm- is assumed to be zero, eq 7 simplifies to Ka/Kapp ) 1 + Km HB CD and this equation 2 yields Km HB ≈ 4 × 10 , in reasonable agreement with the values calculated from the Ka1 data. Table 2 includes the binding constants of protonated and nonprotonated forms of the drugs studied to micelles. It is evident that the binding constants for neutral species are always smaller than those of positively charged (protonated) species and that the binding of negatively charged nitrazepam is 1-2 orders of magnitude smaller than binding of neutral species and 2-3 orders of magnitude smaller than that of positively charged species. The neutral forms of β-blockers bind more weakly than the corresponding forms of benzodiazepines. These observations correlate with the known higher hydrophobic properties of benzodiazepines and provide support for stronger hydrophobic interactions of the nonprotonated form of these molecules with the lipophilic side chains of SDS. No such clear-cut analysis can be made for the binding constants of the protonated (positively charged) forms of the drugs studied, as they are obtained using different chemical models for binding. However, as the binding of benzodiazepines to micelles is always stronger than for β-blockers, and as no physically realistic model can invoke ionic exchange in the binding of benzodiazepines, we can expect the interaction of these two classes of drugs with the micelle to be different.
References and Notes 1. He, Z.; O’Connor, P. J.; Romsted, L. S.; Zanette, D. J. Phys. Chem. 1989, 93, 4219-4226. 2. Nook, T.; Doelker, E.; Buri, P. Pharm. Acta Helv. 1987, 62, 274-281. 3. Gibaldi, M.; Stuart, F. J. Pharm. Sci. 1970, 59, 579-589. 4. Yamaguchi, T.; Ikeda, C.; Sekine, Y. Chem. Pharm. Bull. 1986, 34, 3362-3369. 5. Khaledi, M. G.; Rodgers, A. H. Anal. Chim. Acta 1990, 239, 121-128.
6. Gerakis, A. M.; Koupparis, M. A.; Efstathiou; C. E. J. Pharm. Biomed. Anal. 1993, 11, 33-41. 7. Funasaki, N. J. Phys. Chem. 1979, 83, 1998-2003. 8. Pramauro, E.; Pelizzetti, E. Anal. Chim. Acta 1981, 126, 253-257. 9. Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russian Chem. Rev. 1973, 42, 787-802. 10. Sudho¨lter, E. J. R.; Langkruis, G. B.; Engberts, B. F. N. J. Royal Netherlands Chem. Soc. 1980, 99, 73-82. 11. Barbosa, J.; Sanz-Nebot, V.; Torrero, M. E. J. Pharm. Biomed. Anal. 1990, 8, 675-679. 12. Olsen, R. W.; Venter, J. C. (Eds) Benzodiazepine/Gaba Receptors and Chloride Channels, Alan R. Liss: New York, 1986. 13. Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 18441850. 14. Gran, G. Analyst 1952, 77, 661-671. 15. Gans, P.; Sabatini, A.; Vacca, A. J. Chem. Soc. Dalton Trans. 1985, 1195-1200. 16. Albert. A.; Serjent, E. P. The Determination of Ionization Constants; 2nd ed., Chapman Hall: London, 1971. 17. Leggett, D. J.; MacBryde, W. A. E. Anal. Chem. 1975, 47, 1065-1070. 18. Romsted, L. S.; Zanette, D. J. Phys. Chem. 1988, 92, 46904698. 19. Pal, T.; Jana, N. R. Langmuir 1996, 12, 3114-3121. 20. Bunton, C. A.; Ohmenzetter, K.; Sepulveda, L. J. Phys. Chem. 1977, 81, 2000-2004. 21. Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755-1761. 22. Romsted, L. S. J. Phys. Chem. 1985, 89, 5107-5113. 23. Romsted, L. S. J. Phys. Chem. 1985, 89, 5113-5118. 24. Cordes, E. H. Pure Appl. Chem. 1978, 50, 617-625. 25. Jones, M. N.; Chapman, Micelles, Monolayers and Biomenbranes, Wiley-Liss: New York, 1995; p 68. 26. Grosvenor, M. P.; Lo¨froth, J. E. Pharm. Res. 1995, 12, 682686. 27. Barrett, J.; Smyth, W. F.; Davidson, I. E. J. Pharm. Pharmacol. 1973, 25, 387-393. 28. Pfendt, B.; Janjı´c, T. J.; Popovı´c, G. V. Analyst 1995, 120, 2145-2151. 29. Han, W. W.; Yakatan, G. J.; Maness, D. D. J. Pharm. Sci. 1977, 66, 795-798. 30. Andersin, R. J. Pharm. Biomed. Anal. 1991, 9, 451-455. 31. Orive, M. M.; Gallo, B.; Alonso, R. M.; Vicente, F.; Vire´, J. C.; Patriarche, G. J. Mikrochim. Acta 1989, 1, 181-190. 32. Rychlovsky, P.; Nemcova´, I. Talanta 1988, 35, 211-214.
Acknowledgments Partial finantial support was provided by the JNICT (Lisboa). C.G. thanks PRAXIS XXI for a fellowship.
JS970219K
Journal of Pharmaceutical Sciences / 359 Vol. 87, No. 3, March 1998
DE
CASTRO†, PAULA GAMEIRO†, CARLA GUIMARA˜ ES‡, JOSEÄ L. F. C. LIMA‡,
AND
SALETTE REIS*,‡
Contribution from the CEQUP/Departamento de Quı´mica, Faculdade de Cieˆncias, and CEQUP/Departamento de Quı´mica-Fı´sica, Faculdade de Farma´cia, Universidade do Porto, 4050, Porto, Portugal Received June 4, 1997.
Accepted forpublication November 7, 1997.
Abstract 0 The effect of sodium dodecyl sulfate (SDS) micelles on the acid−base properties of two family of pharmaceutical drugs (βblockers and benzodiazepines) at 25 °C and I ) 0.1 M NaCl have been studied. The characterization of the several solution equilibria for the system drug/SDS micelle solution was performed by potentiometry and spectrophotometry, below and above the critical micelle concentration (cmc). Two widely used models have been applied to quantify the effect of micelles on the pKa of the drugs, and the results obtained point to different interactions of each family of drugs with the micelles.
Introduction Aqueous micelle solutions are structurally “simple” and are often used as models for the more complex and metastable biological membranes, as their interphases are structurally similar.1 Tensioactive agents, both naturally occurring and administered, also play an important role in the pharmocokinetic properties of drugs and in their formulation. Their uptake is controlled by naturally occurring micelles in the intestinal tract (e.g. bile acids) and also by those intentionally incorporated in pharmaceutical formulations.2-4 Information regarding micellar effects on the pKa values of a wide variety of acids and bases is of interest in connection with the increasing use of aqueous micellar systems as solvents in analytical chemistry5 as well as in other areas, such as micellar catalysis.5-10 In this work we report the effect of SDS micellar solutions on the acid-base properties of substance with pharmacological interest,11,12 namely two β-blockers (atenolol and nadolol) and two benzodiazepines (midazolam and nitrazepam). Two models were used to quantify the micellar effects of equilibrium constants (Berezin8 and the PIE13 models). Their difference lies mainly in an assumption used by the PIE model that the counterions of SDS (Na+) exchange with other cationic species in solution. Application of both models has been extremely helpful in choosing the model that best describes the effect of micelles on the pKa of the drugs used and have allowed the determination of their binding constants to SDS.
Experimental Section Reagents and SolutionssAll compounds were used as received: atenolol and nadolol, from Sigma; sodium dodecyl sulfate (SDS), from Aldrich; nitrazepam and midazolam, a gift from Hoffman-La Roche; and HCl (Titrisol) and all other chemical, from † ‡
Departamento de Quı´mica. Departamento de Quı´mica-Fı´sica.
356 / Journal of Pharmaceutical Sciences Vol. 87, No. 3, March 1998
Merck (grade pro analysi). Solutions were prepared with double deionized water (conductivity less than 0.1 µS cm-1). Potentiometric and Spectrophotometric Measurementss All potentiometric measurements were carried out with a Crison 2002 pH meter and 2031 buret controlled by a personal computer which was also used for data manipulation. The electrode assembly was made up of an Orion 900029/4 AgCl/Ag reference electrode and a Russel SWL glass electrode. System calibration was performed by the Gran method14 in terms of hydrogen ion concentration, using strong acid-strong base titration {HCl (0.001 M)/NaOH(≈0.02 M)} with solutions whose ionic strength was adjusted to 0.1 M with NaCl. Titrations were always carried out under a nitrogen atmosphere at 25 °C in a double-walled glass cell. All absorption spectra were recorded with a Hitachi U-2000 dual-beam spectrophotometer using quartz cells with 1 cm path length that were thermostated at 25 °C. Potentiometric Determination of Acidity Constantss Acidity constants for atenolol and nadolol were obtained by titrating 20.00 mL of acidified solutions (1 mM HCl) of the β-blocker (0.8 mM), either in pure water or in aqueous solutions of SDS (0.5, 1, 2, 2.5, 3, 4, 7, 10, 20 mM), with NaOH (≈20 mM). All titrations were performed at 25 °C under nitrogen, and for all solutions the ionic strength was adjusted to 0.1 M with NaCl. For midazolam, the potentiometric determination of the acidity constants was performed using conditions similar to those described above, but the midazolam concentration was 0.7 mM and that of SDS 1, 2, 2.5, 3, 4, 7, 10, 20 mM. System calibration was always performed before and after each determination by titrating HCl with NaOH, both for aqueous and micellar media; in the latter experiments the concentration of SDS was that of the titrated solution. The characteristics of the glass electrode were similar below and above the critical micelle concentration, except that the response time was longer at high concentrations of SDS. Calculations were performed with data obtained from at least six independent titrations, each with more than 30 points, and the experimental titration data were analyzed using the computer program Superquad.15 The errors reported in this work were calculated by the method of Albert and Serjeant,16 in which the errors are calculated as the maximum difference between the logarithm of the average of the antilogarithms of the calculated pKa values and their individual values. Spectrophotometric Determination of Acidity Constantss Acidity constants of the β-blockers and the benzodiazepines were obtained from UV data of solutions (aqueous and micellar media) of nitrazepam (2.6 × 10-5 to 5 × 10-5 M), atenolol, and nadolol (5 × 10-5 to 1 × 10-4 M), for which the ionic strength was adjusted to 0.1 M with NaCl. The SDS concentrations used were the same as the potentiometric studies, viz. 0.5, 1, 2, 2.5, 3, 4, 7, 10, and 20 mM. For all solutes, no changes in the wavelength of the maximum absorption were detected upon addition of SDS at these concentrations. Aliquots of strong base or strong acid were added to 20 mL of the stock solution to adjust-log [H+] to the desired value; -log [H+] measurements and system calibration were performed by potentiometry as described previously. The calculations were performed with the program SQUAD 8517 by using data from at least two independent experiments, each with more than six solutions, and in the range from 200 to 350 nm, at 2 nm intervals.
S0022-3549(97)00219-0 CCC: $15.00 Published on Web 02/12/1998
© 1998, American Chemical Society and American Pharmaceutical Association
Theoretical Treatment of Acidity in Micellar Media It is well-known that organized assemblies modify the equilibria and acid-base properties of chemical processes,5,6,8 and a number of mathematical models were developed over the last years to quantify micellar effects on equilibrium constants of different substances.1,7-9,13,18-24 These models can provide a quantitative interpretation of changes in the apparent acid-base equilibrium of the drugs, studied in the present work, in SDS media. For the dissociation of protonated substrate
HB+ h H+ + B
(1)
the value of the dissociation constant in the presence of surfactants (pKapp)
Kapp )
Ka ) [B]f[H+]f/[HB+]f
B f h Bb
Km B ) [B]b/[B]fCD
+ m + + HB+ f + Yb h Yf + HBb KHB+/Y) [HB ]b[Y]f/[HB ]f[Y]b + H+ f + Yb h Hb + Yf
KH+/Y ) [H+]b[Y]f/[H+]f[Y]b
+ Bb + H + b h HBb
Ka,b ) [HB+]bCD/[B]b[H+]b
From these equilibria and with the assumptions of the PIE model it is possible to derive the following equation for Kapp
Kapp ) [H+]f ) Ka
([B]f + [B]b)
+
[H ]f
([HB+]f + [HB+]b)
(2)
is the value of intermicellar pH () -log [H+]f) when:13
[B]f + [B]b ) [HB+]f + [HB+]b
(3)
In these and following expressions, HB+ represents protonated species, B the neutral species, H+ the proton, and Y+ the counterion of the anionic surfactant (the subscript f denotes the species in water and b denotes the species bounded to the micelles). Berezin and co-workers proposed that from the dissociation of protonated substrate different species partioned between the micellar and aqueous pseudophases and thus expressed the apparent acidity constant, Kapp, as8
Kapp ) [H+]f ) Ka
+ HB+ f h Hf + B f
(1 + Km B CD) m (1 + KHB +CD)
(4)
where CD is the micellized detergent concentration (equal to the difference between the total detergent concentration, CT, and the critical micellar concentration, cmc, i.e., CD ) m m CT - cmc), KHB + and KB are the binding constants with micelles for the protonated and neutral forms of the substrate, and Ka is the dissociation constant of HB+ in water. In the PIE model,13 the ionization of a micellar-bond substance is described by an intrinsic acidity constant, Km a , whose value reflects the medium properties of the micelle, and the micelles are assumed to act as a separate phase uniformly distributed throughout the solution (pseudophase assumption). The medium properties of the micelles are assumed to be independent of solution composition. Recently, the above treatment was extended to the variation of Kapp over a wide range of surfactant concentration and in the presence of added salts.23 The micelle surface is assumed to act as an ion-exchanger, e.g. the distribution of proton and alkaline metal ions in solution of anionic micelles is described by an ion-exchange constant. For mathematical simplicity, the fraction of bound counterion, R, is assumed to be constant and independent of surfactant concentration, counterion concentration, and counterion type. Within the framework of the PIE model, the equilibrium of β-blockers and benzodiazepines in anionic micellar media is be described by the set of equilibria that characterized their dissociation and the partition of the protonated and neutral species between the micelles and the solution and that are depicted in the following scheme.
(1 + Km B CD) m (1 + KHB +/Y(Yb/Yf))
(5)
where Yb ) (1 - R)CD - W and Yf ) RCD + cmc + W + [BY]T, with W ) [H+]b + [HB+]b. On applying both models we have used the optimum value of R ) 0.75 for the ionization degree of the anionic micelles,1,13 and a value of 1.4 mM for the cmc of SDS in 0.1 M NaCl.25 The fit of the experimental results to the two models where performed with the non linear subroutine of Delta Graph Pro 3.5.
Results and Discussion Acidity Constants in the Presence of Micellar MediasThe data concerning the acidity constants of nadolol, atenolol, midazolam, and nitrazepam, both in aqueous solution and in micellar media, are included in Table 1. For all compounds, the acidity constants obtained in bulk aqueous solutions by both experimental methods are practically identical and are also very similar to those reported in the literature.11,26-31 A few comments must be made regarding the data in Table 1. First, the spectrophotometric determination of the pKa of midazolam, despite earlier claims that changes in the protonated and nonprotonated bands are too small to be of significance,28 yielded values similar to those obtained potentiometrically, albeit with a larger error. The low solubility of nitrazepam precluded the potentiometric determination of its acidity constant. Nitrazepam has two acid equilibria in the pH range studied,
H2B+ h H+ + HB h B- + H+
(6)
and each equilibrium was treated independently, because their pKa values are separated by more than 7 log units;16 furthermore as the second dissociation yields negatively charged species, it is excluded from the foregoing discussion and will be treated separately. An analysis of Table 1 shows that the apparent acidity of our compounds are independent of SDS concentration up to the cmc but start to decrease above this value. This behavior has been observed for many indicators, for which at least one form is cationic, that interact with anionic micelles5,19,32 and, in general, stronger interactions with micelles cause larger shifts in the pKa values.5 For the compounds studied, we observe a pKa shift of ≈0.5 log units for the β-blockers and of ≈1 for the benzodiazepines; as strong interactions of cationic species with anionic micelles drive equilibrium described by eq 1 to the left, thus increasing the value of pKapp, these results suggest that the interactions with protonated benzodiazepines are stronger than that with β-blockers. Figure 1 shows the potentiometric titration curves for midazolam and for nadolol, and the shift in pKa values, as Journal of Pharmaceutical Sciences / 357 Vol. 87, No. 3, March 1998
Table 1sAcidity Constants (pKapp) of Atenolol, Nadolol, Midazolam, and Nitrazepam, in Aqueous Solution and in SDS, Obtained by Potentiometry or Spectrophotometry at 25 °C and I ) 0.1 M in NaCl atenolol
nadolol
midazolam
nitrazepam spectrophotometry
[SDS]/M
potentiometry
spectrophotometry
potentiometry
spectrophotometry
potentiometry
0 5.0 × 10-4 1.0 × 10-3 2.0 × 10-3 2.5 × 10-3 3.0 × 10-3 4.0 × 10-3 7.0 × 10-3 1.0 × 10-2 2.0 × 10-2
9.32 ± 0.05 9.32 ± 0.02 9.32 ± 0.02 9.34 ± 0.05 9.39 ± 0.01 9.43 ± 0.04 9.51 ± 0.02 9.63 ± 0.05 9.70 ± 0.06 9.70 ± 0.05
9.29 ± 0.03 9.30 ± 0.03 9.30 ± 0.03 9.33 ± 0.02 9.37 ± 0.01 9.44 ± 0.02 9.54 ± 0.01 9.63 ± 0.01 9.70 ± 0.03 9.71 ± 0.03
9.51 ± 0.02 9.51 ± 0.05 9.51 ± 0.04 9.52 ± 0.03 9.60 ± 0.02 9.75 ± 0.03 9.82 ± 0.07 9.93 ± 0.04 9.99 ± 0.08 9.99 ± 0.03
9.52 ± 0.02 9.52 ± 0.01 9.52 ± 0.02 9.53 ± 0.01 9.59 ± 0.01 9.76 ± 0.04 9.84 ± 0.01 9.96 ± 0.01 10.02 ± 0.05 10.02 ± 0.05
5.91 ± 0.01
2.98 ± 0.01
10.55 ± 0.03
5.91 ± 0.01 6.65 ± 0.04 6.73 ± 0.03 6.80 ± 0.02 6.89 ± 0.02 6.97 ± 0.07 7.02 ± 0.02 7.08 ± 0.01
2.99 ± 0.01 3.32 ± 0.01 3.45 ± 0.01 3.54 ± 0.01 3.61 ± 0.01 3.67 ± 0.01 3.81 ± 0.03 3.82 ± 0.03
10.55 ± 0.04 10.66 ± 0.03 10.77 ± 0.03 10.85 ± 0.01 10.93 ± 0.03 11.11 ± 0.05 11.21 ± 0.05 11.51 ± 0.03
Figure 1sPotenciometric titration curves of nadolol (open symbols) and of midazolam (filled symbols) in aqueous solution (circles) and in micellar media of 0.01 M of sodium dodecyl sulfate (triangles), with NaOH (≈20 mM).
indicated by the equivalent points, is larger for the benzodiazepine. Recalling the results reported for potentiometric titrations of amino acids and peptides in micellar media,5 our data support stronger interactions of the benzodiazepine with SDS micelles. Application of Theoretical ModelssWe applied the Berezin model to our data. Equation 4 was rewritten as
(
)
Kapp Ka Kapp m ) KHB - Km + B CD Ka
1-
(7)
and for the benzodiazepines, plots from eq 7 yields straight m 4 lines, with slopes (KHB +) of 1.1 × 10 for midazolam and of 3 2.8 × 10 for the first dissociation of nitrazepam (Ka1). The 2 corresponding intercepts (Km B ) were 7.8 × 10 and 3.5 × 102 and the goodness of fit was R2 ) 0.96 and 0.98, respectively. Application of eq 7 to the β-blockers yields a parabola, which means that this simple model does not adequately describe their changes in acid-base properties in micellar media. As it is clear from our data, the linearized form of eq 7 is a useful screening test to determine if this model can be used to describe the effect of micelles on acid-base 358 / Journal of Pharmaceutical Sciences Vol. 87, No. 3, March 1998
Figure 2sExperimental data for the dependence of Kapp on surfactant concentration (CD) for atenolol (b) and nadolol (O) and best fit by the Berezin model (− −) and by the PIE model (s).
properties, but as it gives a high weight to the low concentrations points, we have fitted eq 4 directly to our data, and the results are presented in Table 2. We also applied the PIE model to our data and obtained good fits for both the benzodiazepines and the β-blockers. In accordance with the results outlined above, as the data for benzodiazepines are fitted to an equation with more parameters, a better fit is always to be expected; however, as the calculated amount of Na+ exchanged with the other cationic species in solution is negative, the applicability of this model is precluded on chemical grounds. In fact, as + Na+ exchanges with H+ f and HBf , the concentration of exchanged Na+, W, must be equal to the concentration of bound H+ and HB+, W ) [H+]b + [HB+]b, and this quantity was found to be negative when the PIE model is applied to benzodiazepines, an impossible result as both bound concentrations must be non-negative. As shown above, the data for the β-blockers could not be described by the simple Berezin model in its linear form, although a nonlinear fit to eq 4 was obtained. A much better fit, however, is obtained with the PIE model, thus implying the existence of ionic exchange of the protonated form of these compounds with Na+ bound to the surfactant surface (Figure 2). The second hydrolysis of nitrazepam, as referred above, poses a different problem as we are dealing with deproto-
Table 2sBinding Constants to Micelles of Protonated and Nonprotonated Forms of the β-Blockers and Benzodiazepines, with and without Ionic Exchange of the Counterions of SDS with Other Cationic Species in Solution without exchange
with exchange
drug
KmB
m KHB +
R2
KmB
m KHB +/Y
Wa
R2
atenolol nadolol midazolam
72 80 800
294 442 11200
0.960 0.892 0.966
134 271 226
200 464 1760
9 × 10-5 11 × 10-5 −15 × 10-5
0.992 0.981 0.997
without exchange drug
KmHB
KHm2B+
nitrazepamb
365
2830
without exchange R2
KBm-
KmHB
0.987
31
616
with exchange R2
KmHB
KHm2B+/Y
Wa
R2
0.992
312
1090
−2 × 10-7
0.986
a W ) [H+]b + [HB+]b; see the text. b For nitrazepam, the first set under “without exchange” refers to the first dissociation constant and the second set to the second dissociation constant.
nation of neutral into negatively charged species, thus implying the application of the PIE model to be inadequate. Application of the electrostatic model of Berezin to Ka2 of nitrazepam yieldel fits that were not as good (R2 ) 0.94), and the values of the binding constants were Km HB ≈ 5 × 102 and KBm- ≈ 10. If KBm- is assumed to be zero, eq 7 simplifies to Ka/Kapp ) 1 + Km HB CD and this equation 2 yields Km HB ≈ 4 × 10 , in reasonable agreement with the values calculated from the Ka1 data. Table 2 includes the binding constants of protonated and nonprotonated forms of the drugs studied to micelles. It is evident that the binding constants for neutral species are always smaller than those of positively charged (protonated) species and that the binding of negatively charged nitrazepam is 1-2 orders of magnitude smaller than binding of neutral species and 2-3 orders of magnitude smaller than that of positively charged species. The neutral forms of β-blockers bind more weakly than the corresponding forms of benzodiazepines. These observations correlate with the known higher hydrophobic properties of benzodiazepines and provide support for stronger hydrophobic interactions of the nonprotonated form of these molecules with the lipophilic side chains of SDS. No such clear-cut analysis can be made for the binding constants of the protonated (positively charged) forms of the drugs studied, as they are obtained using different chemical models for binding. However, as the binding of benzodiazepines to micelles is always stronger than for β-blockers, and as no physically realistic model can invoke ionic exchange in the binding of benzodiazepines, we can expect the interaction of these two classes of drugs with the micelle to be different.
References and Notes 1. He, Z.; O’Connor, P. J.; Romsted, L. S.; Zanette, D. J. Phys. Chem. 1989, 93, 4219-4226. 2. Nook, T.; Doelker, E.; Buri, P. Pharm. Acta Helv. 1987, 62, 274-281. 3. Gibaldi, M.; Stuart, F. J. Pharm. Sci. 1970, 59, 579-589. 4. Yamaguchi, T.; Ikeda, C.; Sekine, Y. Chem. Pharm. Bull. 1986, 34, 3362-3369. 5. Khaledi, M. G.; Rodgers, A. H. Anal. Chim. Acta 1990, 239, 121-128.
6. Gerakis, A. M.; Koupparis, M. A.; Efstathiou; C. E. J. Pharm. Biomed. Anal. 1993, 11, 33-41. 7. Funasaki, N. J. Phys. Chem. 1979, 83, 1998-2003. 8. Pramauro, E.; Pelizzetti, E. Anal. Chim. Acta 1981, 126, 253-257. 9. Berezin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russian Chem. Rev. 1973, 42, 787-802. 10. Sudho¨lter, E. J. R.; Langkruis, G. B.; Engberts, B. F. N. J. Royal Netherlands Chem. Soc. 1980, 99, 73-82. 11. Barbosa, J.; Sanz-Nebot, V.; Torrero, M. E. J. Pharm. Biomed. Anal. 1990, 8, 675-679. 12. Olsen, R. W.; Venter, J. C. (Eds) Benzodiazepine/Gaba Receptors and Chloride Channels, Alan R. Liss: New York, 1986. 13. Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 18441850. 14. Gran, G. Analyst 1952, 77, 661-671. 15. Gans, P.; Sabatini, A.; Vacca, A. J. Chem. Soc. Dalton Trans. 1985, 1195-1200. 16. Albert. A.; Serjent, E. P. The Determination of Ionization Constants; 2nd ed., Chapman Hall: London, 1971. 17. Leggett, D. J.; MacBryde, W. A. E. Anal. Chem. 1975, 47, 1065-1070. 18. Romsted, L. S.; Zanette, D. J. Phys. Chem. 1988, 92, 46904698. 19. Pal, T.; Jana, N. R. Langmuir 1996, 12, 3114-3121. 20. Bunton, C. A.; Ohmenzetter, K.; Sepulveda, L. J. Phys. Chem. 1977, 81, 2000-2004. 21. Fernandez, M. S.; Fromherz, P. J. Phys. Chem. 1977, 81, 1755-1761. 22. Romsted, L. S. J. Phys. Chem. 1985, 89, 5107-5113. 23. Romsted, L. S. J. Phys. Chem. 1985, 89, 5113-5118. 24. Cordes, E. H. Pure Appl. Chem. 1978, 50, 617-625. 25. Jones, M. N.; Chapman, Micelles, Monolayers and Biomenbranes, Wiley-Liss: New York, 1995; p 68. 26. Grosvenor, M. P.; Lo¨froth, J. E. Pharm. Res. 1995, 12, 682686. 27. Barrett, J.; Smyth, W. F.; Davidson, I. E. J. Pharm. Pharmacol. 1973, 25, 387-393. 28. Pfendt, B.; Janjı´c, T. J.; Popovı´c, G. V. Analyst 1995, 120, 2145-2151. 29. Han, W. W.; Yakatan, G. J.; Maness, D. D. J. Pharm. Sci. 1977, 66, 795-798. 30. Andersin, R. J. Pharm. Biomed. Anal. 1991, 9, 451-455. 31. Orive, M. M.; Gallo, B.; Alonso, R. M.; Vicente, F.; Vire´, J. C.; Patriarche, G. J. Mikrochim. Acta 1989, 1, 181-190. 32. Rychlovsky, P.; Nemcova´, I. Talanta 1988, 35, 211-214.
Acknowledgments Partial finantial support was provided by the JNICT (Lisboa). C.G. thanks PRAXIS XXI for a fellowship.
JS970219K
Journal of Pharmaceutical Sciences / 359 Vol. 87, No. 3, March 1998