Partitioning of Charged Local Anesthetics into ... - ACS Publications

J. Phys. Chem. B 1998, 102, 3295-3304

3295

Partitioning of Charged Local Anesthetics into Model Membranes Formed by Cationic Surfactant: Effect of Hydrophobicity of Local Anesthetic Molecules Hitoshi Matsuki,*,† Shoji Kaneshina,‡ Hiroshi Kamaya,† and Issaku Ueda† Department of Anesthesia, Department of Veterans Administration Medical Center, and UniVersity of Utah School of Medicine, Salt Lake City, Utah 84148, and Department of Biological Science and Technology, Faculty of Engineering, The UniVersity of Tokushima, Minamijosanjima, Tokushima 770, Japan ReceiVed: December 4, 1997; In Final Form: February 25, 1998

The partitioning of five hydrochloride salts of local anesthetics, dibucaine (DC‚HCl), tetracaine (TC‚HCl), bupivacaine (BC‚HCl), lidocaine (LC‚HCl), and procaine (PC‚HCl), into surface-adsorbed films and micelles formed by decylammonium chloride (DeAC) was studied by the surface tension of aqueous solutions of DeAC-local anesthetic mixtures. Thermodynamic quantities of the partitioning of the anesthetics, total surface density, and compositions of the anesthetics in the surface-adsorbed film and micelle were evaluated by applying thermodynamic equations to the surface tension data. The quantities of the anesthetics partitioned into the molecular aggregates of DeAC were determined from the phase diagrams of surface adsorption and micelle formation. The phase diagrams of surface adsorption and micelle formation showed that the local anesthetic partitioned into the surface-adsorbed film and micelle of DeAC decreases in the order of DC‚HCl, TC‚HCl, BC‚HCl, LC‚HCl, and PC‚HCl. A good correlation was seen between the partitioning order and anesthetic potency of these local anesthetics. The phase diagrams of DeAC-BC‚HCl, DeAC-LC‚HCl and DeAC-PC‚HCl systems behaved peculiarly that the compositions of these systems in the adsorbed film and micelle had negative values. The results suggested that weakly hydrophobic anesthetics such as BC‚HCl, LC‚HCl, and PC‚HCl did not partition into the hydrophobic environment of the adsorbed film and micelle of DeAC. Strongly hydrophobic local anesthetics such as DC‚HCl and TC‚HCl partitioned into the aggregates of DeAC. The difference is attributable to the hydrophobicity of their molecules. By comparing the compositions of micelle with those of surface-adsorbed film at the critical micelle concentration, it was shown that the partitioning of the anesthetics was also influenced by the geometry of the aggregates into which the anesthetics were partitioned.

Introduction Reports on the interaction modes between local anesthetics and biological membrane molecules are accumulating.1-22 Because phospholipids are the main constituent of cell membranes, phospholipid vesicles have been used in most studies as a model for biological membranes. On the other hand, molecular aggregates formed by surfactant molecules, such as surface-adsorbed films and micelles, also form microscopic hydrophobic environments similar to phospholipid bilayers. The experimental values using phospholipid bilayers are usually time-consuming and difficult to get reproducible values because they must be obtained in a metastable equilibrium state. Acquisition of the experimental values of surface-adsorbed films and micelles is easier than bilayers because they attain thermodynamic equilibrium values in a short time. Therefore, the use of the aggregates of surfactant as a model membrane may be more advantageous for thermodynamic experiments. Few studies of partitioning of local anesthetics into micelles23-25 and into insoluble monolayers26 have been reported. The present study reports the partitioning of local anesthetics into surface-adsorbed films and micelles formed by cationic * On leave from the Department of Biological Science and Technology, Faculty of Engineering, The University of Tokushima, Minamijosanjima, Tokushima 770, Japan. To whom correspondence should be addressed at this address. † University of Utah. ‡ The University of Tokushima.

surfactant, decylammonium chloride (DeAC). We chose five hydrochloride salts of local anesthetics (dibucaine (DC‚HCl), tetracaine (TC‚HCl), bupivacaine (BC‚HCl), lidocaine (LC‚ HCl), and procaine (PC‚HCl)) for this purpose. Since the hydrophobicity of the anesthetics varies among agents, it is expected that the role of hydrophobicity of anesthetic molecules on the partitioning is elucidated. The surface tension of the aqueous solutions of five DeAC-local anesthetic mixtures was measured to investigate the partitioning of the anesthetics into the molecular aggregates of DeAC. The differences in partitioning among local anesthetics into the aggregates are discussed by the phase diagrams of surface adsorption and micelle formation. We also consider the effect of geometry of molecular aggregates on the partitioning of the anesthetics. Experimental Section Materials. Five local anesthetic hydrochlorides (dibucaine: 2-butoxy-N-[2-(diethylamino)ethyl]-4-quinolinecarboxamide (DC‚ HCl), tetracaine: 2-(dimethylamino)ethyl 4-(butylamino)benzoate (TC‚HCl), bupivacaine: 1-n-butyl-2′,6′-dimethyl-2piperidinecarboxanilide (BC‚HCl), lidocaine: 2-(diethylamino)N-(2,6-dimethylphenyl)acetamide (LC‚HCl), and procaine: 2-(diethylamino)ethyl p-(amino)benzoate (PC‚HCl)) were purchased from Sigma Chemical Co. The anesthetics were recrystallized several times from ethanol except for dibucaine hydrochloride, which was recrystallized from an ethanol and

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3296 J. Phys. Chem. B, Vol. 102, No. 17, 1998

Matsuki et al. reported previously.28 The densities of aqueous solutions of the anesthetics, DeAC, and their mixtures were measured by a vibrating-tube density meter (Anton Paar DMA60/602).29 All measurements were performed at 298.15 ( 0.01 K by immersing the measurement glass cell in a thermostated water bath under atmospheric pressure. The experimental error for estimating the value of surface tension was less than 0.05 mN m-1. Results

Figure 1. Molecular structures of (A) five local anesthetics and (B) DeAC.

carbon tetrachloride mixture. Decylammonium chloride (DeAC) was synthesized and purified by the method reported previously.27 Their purities were confirmed by elemental analysis, and those of DC‚HCl, TC‚HCl, and DeAC were also checked by observing the absence of a minimum on the surface tension vs concentration curves in the vicinity of the critical micelle concentration. The molecular structures of these anesthetics and surfactant are illustrated in Figure 1. Water was distilled triply after deionization, where the second and third stages were from dilute alkaline permanganate solution. Automatic Surface Tension Measurements. The surface tension of the aqueous surfactant-anesthetic solutions was measured by an automatic system of drop volume method as

The plots of the surface tension γ of five aqueous anesthetic solutions against their molality m1 are illustrated in Figure 2A. The γ values of local anesthetics varied among agents depending on the hydrophobicity of the molecules. The degree of decreases in the γ values for DC‚HCl and TC‚HCl is large, and their γ vs m1 curves have a break point at the concentration corresponding to the critical micelle concentration (cmc).29 DC‚ HCl and TC‚HCl are hydrophobic enough to form micelles by themselves in the aqueous solution. On the other hand, the γ value of LC‚HCl decreased slightly with increasing m1 and that of PC‚HCl did not appreciably change with m1. BC‚HCl showed medium decreases in the γ values among the anesthetics, but the BC‚HCl solution at concentrations above 150 mmol kg-1 could not be measured due to lower solubility originated from the high Krafft temperature.30 These anesthetics are weakly hydrophobic and the hydrophobicity among the anesthetics decreases in the order of BC‚HCl, LC‚HCl, and PC‚HCl. Figure 2B shows the γ vs m1 curve of DeAC. The γ value of DeAC decreased steeply with increasing m1, and the curve has a distinct break point at the cmc. DeAC forms molecular aggregates that are suitable as model membranes at water/air interface (surfaceadsorbed film) and in the aqueous solution (micelle). Partitioning of five local anesthetics into surface-adsorbed films and micelles formed by DeAC was examined by measuring the surface tension of aqueous solutions of DeAC-anesthetic mixtures. The surface tension of the aqueous solutions of the mixtures was measured as a function of the total molality of DeAC and local anesthetic, m (mol kg-1 solvent), and the mole fraction of anesthetic in the total components, X2, at constant temperature and pressure. Here m and X2 are defined respectively by

Figure 2. Surface tension vs molality curves of pure components: (A) local anesthetics (1) DC‚HCl, (2) TC‚HCl, (3) BC‚HCl, (4) LC‚HCl, (5) PC‚HCl; (B) DeAC.

Partitioning of Anesthetics into Surfactant Aggregates

J. Phys. Chem. B, Vol. 102, No. 17, 1998 3297

Figure 3. Surface tension vs total molality curves at constant composition: (A) DeAC-DC‚HCl system (1) X2 ) 0, (2) 0.190, (3) 0.350, (4) 0.500, (5) 0.640, (6) 0.735, (7) 0.828, (8) 0.916, (9) 1; (B) DeAC-TC‚HCl system (1) X2 ) 0, (2) 0.288, (3) 0.500, (4) 0.613, (5) 0.702, (6) 0.782, (7) 0.862, (8) 0.932, (9) 1; (C) DeAC-BC‚HCl system (1) X2 ) 0, (2) 0.180, (3) 0.348, (4) 0.500, (5) 0.624, (6) 0.750, (7) 0.860, (8) 0.940, (9) 1; (D) DeAC-LC‚HCl system (1) X2 ) 0, (2) 0.280, (3) 0.500, (4) 0.660, (5) 0.800, (6) 0.900, (7) 0.940, (8) 0.980, (9) 1; (E) DeAC-PC‚HCl system; (1) X2 ) 0, (2) 0.300, (3) 0.500, (4) 0.670, (5) 0.800, (6) 0.880, (7) 0.910, (8) 0.950, (9) 1.

m ) m1 + m2

(1)

X2 ) m2/m

(2)

where m1 and m2 represent the molalities of DeAC and local anesthetic, respectively. Experimental results for five DeAClocal anesthetic mixtures are demonstrated in the form of γ vs m curves at constant X2 in Figure 3. The γ values of all mixtures decreased with increasing m. The shape of the γ vs m curves of the DeAC-DC‚HCl and DeAC-TC‚HCl systems changed with X2 from DeAC (X2 ) 0) to anesthetics (X2 ) 1) and the γ

vs m curves of both systems had a break point at concentrations corresponding to the cmc in the whole composition range. In the DeAC-DC‚HCl system, the composition dependence of γ reversed the order at 15.76 mmol kg-1 because the γ vs m curve of pure DeAC intersects that of pure DC‚HCl at the concentration. The break point corresponding to the cmc was also observed on the γ vs m curve in the composition range from pure DeAC (X2 ) 0) to X2 ) 0.940 for the DeAC-LC‚HCl system, and 0.910 for the DeAC-PC‚HCl system. For the DeAC-BC‚HCl system, we were able to determine the cmc values up to X2 ) 0.860 although BC‚HCl is insoluble at high


Matsuki et al.

Figure 4. Total molality vs composition curves at constant surface tension: (A) DeAC-DC‚HCl system, (B) DeAC-TC‚HCl system, (C) DeACBC‚HCl system, (D) DeAC-LC‚HCl system, (E) DeAC-PC‚HCl system; (1) γ ) 65 mN m-1, (2) 60, (3) 55, (4) 50, (5) 45, (6) 40, (7) 35, (8) C vs X2.

concentration near pure BC‚HCl. The composition dependences of m at constant γ for five systems were obtained by reading the m values at a given γ value from Figure 3. The m vs X2 curves of five systems at constant γ are shown in Figure 4. The m values of the systems except for DeAC-DC‚HCl system increased with increasing X2. The slopes of the curve are steeper at lower γ region. The m values of the DeAC-BC‚HCl, DeAC-LC‚HCl, and DeAC-PC‚HCl systems increased greatly at higher X2 region. The m values of the DeAC-DC‚HCl system decreased slightly with increasing X2 at a high γ while those increased with X2 at a low γ as expected from Figure 3A. From the break point of the γ vs m curve in Figure 3, the values of the total molality at the cmc C and the surface tension at the cmc γC for five systems were determined. Figures 5 and 6 depict the C vs X2 curves and the γC vs X2 curves of five systems, respectively. The C values of all systems increased with increasing X2. The C vs X2 curves of the DeAC-BC‚ HCl, DeAC-LC‚HCl, and DeAC-PC‚HCl systems increased steeply at higher X2 region. On the other hand, the behavior of γC vs X2 curves differed among systems. The γC values of the DeAC-DC‚HCl, DeAC-TC‚HCl, and DeAC-BC‚HCl systems increased with increasing X2. That of the DeAC-PC‚ HCl system decreased with increasing X2. The γC values of DeAC-LC‚HCl system decreased in the low X2 region and increased in the high X2 region: the γC vs X2 curve had a shallow minimum near X2 ) 0.800.

Figure 5. Critical micelle concentration vs composition curves: (1) DeAC-DC‚HCl system, (2) DeAC-TC‚HCl system, (3) DeAC-BC‚ HCl system, (4) DeAC-LC‚HCl system, (5) DeAC-PC‚HCl system.

Discussion Since DeAC and local anesthetics are hydrochloride salts of tertiary amine, decylammonium, and local anesthetic cations


J. Phys. Chem. B, Vol. 102, No. 17, 1998 3299 surface density of DeAC and local anesthetic, ΓH, and the mole fraction of local anesthetic in the surface-adsorbed film, XH2 , can be obtained from the thermodynamic analysis of surface tension data at concentrations below the cmc. Here ΓH and XH2 are defined respectively by

ΓH ) ΓH1 + ΓH2

(7)

XH2 ) ΓH2 /ΓH

(8)

where ΓH1 and ΓH2 refer to the surface densities of DeAC and local anesthetic. They are defined with reference to the two dividing planes making the excess numbers of moles of water and air zero.33 The ΓH values were evaluated from the slope of the γ vs m curves at concentrations below the cmc shown in Figure 3 through the following equation:34,35

ΓH ) -(m/2RT)(∂γ/∂m)T,p,X2

(9)

where A‚H+ and A represent their protonated (charged) and free base (uncharged) forms, respectively. The first step of the dissociation is complete. In the second step, they partially dissociate into the uncharged form and proton. The acid dissociation constant Ka of a local anesthetic cation is expressed as

The evaluated ΓH values of five systems are shown in the form of ΓH vs m plots in Figure 7. The ΓH values of all systems increased with increasing m and approached the values of saturated adsorption near the cmc when the mixture has a cmc. The regular variation of ΓH of the mixture with X2 was observed for all systems although the ΓH values of pure local anesthetics considerably changed among them. It is noted that the ΓH values of pure DeAC, DC‚HCl, TC‚HCl, and BC‚HCl changed discontinuously in the low concentration region. These correspond to the phase transition in the surface-adsorbed films,36 but we do not focus our attention on this phenomenon in this study. Another surface quantity, XH2 was calculated to quantify their partitioning into the surface-adsorbed film of DeAC. The XH2 values were obtained at constant surface tension by applying the equation34,35

Ka ) [A][H+]/[A‚H+]

XH2 ) X2 - (2X1X2/m)(∂m/∂X2)T,p,γ

Figure 6. Surface tension at the cmc vs composition curves: (1) DeAC-DC‚HCl system, (2) DeAC-TC‚HCl system, (3) DeAC-BC‚ HCl system, (4) DeAC-LC‚HCl system, (5) DeAC-PC‚HCl system.

are weak electrolytes. They dissociate in the aqueous solution by the following two steps:

A‚HCl S A‚H+ + Cl-

(3)

A‚H+ S A + H+

(4)

(5)

where the square brackets denote concentration. The ratio of charged and uncharged molecules in the aqueous solution is determined by the Henderson-Hasselbalch equation

pH ) pKa + log[A]/[A‚H+]

(6)

We measured the pH values of the aqueous solutions of pure DeAC, anesthetics, and their mixtures. The pH values were between 5.0 and 5.5 in the experimental concentration range. DeAC and local anesthetics have relatively high pKa values at 298.15 K: DeAC 11.64,31 local anesthetics (DC‚HCl 8.73, TC‚ HCl 8.46, BC‚HCl 8.17, LC‚HCl 7.92, and PC‚HCl 9.05).32 Because of the high pKa values, the influence of partial dissociation of these cations in the aqueous solution is negligible from eq 6. We assumed that DeAC and the local anesthetics are essentially uni-univalent electrolytes in the present study. The partitioning of local anesthetics into model membranes of DeAC is now considered by investigating the miscibilities of DeAC and local anesthetics in molecular aggregates formed by DeAC. In the following section, the miscibilities of DeAC and local anesthetics are discussed in two cases, the miscibilities in the surface-adsorbed film of DeAC and that in the micelle of DeAC. Partitioning of Local Anesthetics into the Surface-Adsorbed Film of DeAC. Two useful surface quantities, the total

(10)

to the m vs X2 curves given in Figure 4. The calculated m vs XH2 curves (broken line) and the m vs X2 curves (continuous line) construct the phase diagrams of surface adsorption. The phase diagrams for five systems are shown in Figure 8. The XH2 value was positive in the whole composition range and smaller than the X2 value in the low surface tension range of the DeAC-DC‚HCl system and over the entire surface tension range of the DeAC-TC‚HCl system. This means that the adsorbed film is richer in DeAC than the aqueous solution. In the high surface tension range of the DeAC-DC‚HCl system, XH2 also had a positive value but slightly larger value than X2: the adsorbed film is enriched in DC‚HCl in the range. The behavior of the DeAC-DC‚HCl system may be attributable to the fact that the surface activities of DeAC and DC‚HCl at high γ values and at low γ values reverse as seen in Figure 3A. The relation XH2 < X2 also held for the DeAC-BC‚HCl, DeACLC‚HCl, and DeAC-PC‚HCl systems; however, the m vs XH2 curves of these systems behaved peculiarly. All XH2 values of the DeAC-PC‚HCl system showed negative signs and the absolute values increased with an increase of X2. The XH2 values of the DeAC-BC‚HCl and DeAC-LC‚HCl systems were negative in the low composition range. Then they steeply approached the X2 values with increasing X2 and the sign of XH2 changed from negative to positive in the high composition


Matsuki et al.

Figure 7. Total surface density vs total molality curves at constant composition: (A) DeAC-DC‚HCl system (1) X2 ) 0, (2) 0.190, (3) 0.350, (4) 0.500, (5) 0.640, (6) 0.735, (7) 0.828, (8) 0.916, (9) 1; (B) DeAC-TC‚HCl system (1) X2 ) 0, (2) 0.288, (3) 0.500, (4) 0.613, (5) 0.702, (6) 0.782, (7) 0.862, (8) 0.932, (9) 1; (C) DeAC-BC‚HCl system (1) X2 ) 0, (2) 0.180, (3) 0.348, (4) 0.500, (5) 0.624, (6) 0.750, (7) 0.860, (8) 0.940, (9) 1; (D) DeAC-LC‚HCl system (1) X2 ) 0, (2) 0.280, (3) 0.500, (4) 0.660, (5) 0.800, (6) 0.900, (7) 0.940, (8) 0.980, (9) 1; (E) DeAC-PC‚HCl system; (1) X2 ) 0, (2) 0.300, (3) 0.500, (4) 0.670, (5) 0.800, (6) 0.880, (7) 0.910, (8) 0.950, (9) 1; (b) total surface density at the cmc ΓH,C.

range. Noting the definition of XH2 given in eq 8, these findings are closely related to the magnitude and sign of the ΓH1 and ΓH2 values of five systems as clarified in the following section. The phase diagrams of surface adsorption at 50 mN m-1 for five systems are compared in Figure 9. The diagram for the DeAC-DC‚HCl system had a thin cigar shape, while that of the DeAC-TC‚HCl system had a swollen cigar shape. Further, the diagrams remarkably swelled in order of the DeAC-BC‚ HCl, DeAC-LC‚HCl, and DeAC-PC‚HCl systems although these diagrams did not close in shape. This observation

indicates that the difference in composition between X2 and XH2 increases in the order of the DeAC-DC‚HCl, DeAC-TC‚ HCl, DeAC-BC‚HCl, DeAC-LC‚HCl, and DeAC-PC‚HCl systems. The partitioning of local anesthetics into the surface-adsorbed film of DeAC was further analyzed by the respective surface densities of DeAC, ΓH1 , and local anesthetic, ΓH2 , of five systems. From the m vs X2 curves in Figure 4 and ΓH vs m curves in Figure 7, the ΓH vs X2 curves at constant γ were obtained. The values of ΓH1 and ΓH2 can be evaluated by combining the ΓH vs X2 curve at constant γ with the m vs



Figure 8. Total molality vs composition curves at constant surface tension: (A) DeAC-DC‚HCl system, (B) DeAC-TC‚HCl system, (C) DeACBC‚HCl system, (D) DeAC-LC‚HCl system, (E) DeAC-PC‚HCl system; (1) γ ) 60 mN m-1 except for the DeAC-LC‚HCl system (γ ) 65 mN m-1), (2) 55, (3) 50, (4) 45, (b) cmc, (s) m vs X2, (- - -) m vs XH2 .

Figure 9. Total molality vs composition curves at γ ) 50 mN m-1: (1) DeAC-DC‚HCl system, (2) DeAC-TC‚HCl system, (3) DeACBC‚HCl system, (4) DeAC-LC‚HCl system, (5) DeAC-PC‚HCl system; (s) m vs X2, (---) m vs XH2 .

composition curves given in Figure 8. The resulting ΓH1 vs X2 and ΓH2 vs X2 curves of five systems at γ ) 50 mN m-1 are shown together with the ΓH vs X2 curve in Figure 10. Both ΓH1 and ΓH2 values of the DeAC-DC‚HCl and the DeAC-TC‚ HCl systems were positive, and the ΓH1 values decreased with

increasing X2 while ΓH2 values increased with X2. The ΓH values of these systems were larger than the ΓH1 and ΓH2 values in the whole composition range. In contrast, the behavior of the ΓH1 vs X2 and the ΓH2 vs X2 curves of the DeAC-BC‚HCl, the DeAC-LC‚HCl, and the DeAC-PC‚HCl systems is quite different from the former systems although the ΓH values of all systems decreased with increasing X2. The ΓH2 values of the DeAC-BC‚HCl and the DeAC-LC‚HCl systems changed the sign from negative to positive with increasing X2. Furthermore, it is noteworthy that the ΓH2 values of the DeAC-PC‚HCl system were negative over the whole composition range measured. When the XH2 values of these systems were smaller than zero, the ΓH1 values were larger than the ΓH values because of the negative ΓH2 values from eq 8. Therefore, the peculiar behavior of the m vs XH2 curves of these systems seen in Figure 8C-E is attributable to the negative adsorption of BC‚HCl, LC‚HCl, and PC‚HCl at the water/air interface, respectively.37 The BC‚HCl, LC‚HCl, and PC‚HCl molecules adsorb positively in the absence of DeAC molecules as given in Figure 7C-E. In the presence of DeAC molecules, the BC‚ HCl and LC‚HCl molecules adsorb negatively except at the considerably high composition region and PC‚HCl molecules do so in the whole composition region measured. The findings imply that they are excluded from the surface-adsorbed film of DeAC. The BC‚HCl and the LC‚HCl molecules are hardly partitioned into the adsorbed film, and the PC‚HCl molecules are not partitioned at all. The results of the latter three systems


Matsuki et al.

Figure 10. Surface density vs composition curves at γ ) 50 mN m-1: (A) DeAC-DC‚HCl system, (B) DeAC-TC‚HCl system, (C) DeACBC‚HCl system, (D) DeAC-LC‚HCl system, (E) DeAC-PC‚HCl system; (1) ΓH, (2) ΓH1 , (3) ΓH2 .

form a striking contrast with the positive partitioning of DC‚ HCl and TC‚HCl into the adsorbed film of DeAC at all compositions. Looking at the magnitude of the ΓH2 values of five systems, they increased in the order of PC‚HCl, LC‚HCl, BC‚HCl, TC‚HCl, and DC‚HCl. The difference in partitioning among five local anesthetics arises from the difference in hydrophobicity among local anesthetic molecules. DC‚HCl and TC‚HCl have a larger hydrophobic group of aromatic ring than do the other local anesthetics, so that they can be partitioned into the adsorbed film of DeAC easier than others. The hydrophobicity of BC‚HCl, LC‚HCl, and PC‚HCl is lower compared with DC‚HCl and TC‚HCl, and they are squeezed out from the surface-adsorbed film of DeAC due to their low hydrophobicity. Complete exclusion of PC‚HCl from the adsorbed film of DeAC seems to be caused by the strong hydrophilicity of the amino group of the aromatic ring in the molecule in addition to that of ionic polar head group. Partitioning of Local Anesthetics into the Micelle of DeAC. DeAC forms micelles in the aqueous solution. We examined the mode of five local anesthetics partitioning into the micelle of DeAC at the cmc. Two useful micelle quantities similar to the surface-adsorbed film are the total aggregation number of DeAC and local anesthetic, NM, and the mole fraction of local anesthetic in the micelle, XM 2: M NM ) NM 1 + N2

(11)

M M XM 2 ) N2 /N

(12)

M respectively. Here NM 1 and N2 are the aggregation numbers of DeAC and local anesthetic in one micelle particle. They are defined by the surface excess quantity using the spherical dividing surface, which makes the excess number of moles of water zero in a way similar to that for the surface density.38 Although unlike the ΓH1 and ΓH2 values, the respective NM 1 and M NM 2 values cannot be evaluated thermodynamically, the X2 values can be obtained by the following relation:34,35

XM 2 ) X2 - (2X1X2/C)(∂C/∂X2)T,p

(13)

The composition dependence of cmc in Figure 5 and eq 13 enable us to calculate the numerical values of XM 2 of the five systems. The phase diagrams of micelle formation for the five systems were constructed from the values of X2 and XM 2 and are shown in Figure 11. It is clear that the phase diagrams of micelle formation for five systems bear a marked resemblance in shape to those of surface adsorption at γ ) 50 mN m-1 given in Figure 9. The relation X2 > XM 2 held for five systems over the whole range of composition. The composition difference between X2 and XM 2 increased in the same order as observed in the phase diagrams of surface adsorption. The results indicate that although the micelle of five systems exists in greater quantities in DeAC than in aqueous solution, the relative ease



Figure 12. Surface tension at the cmc vs composition curves: (1) DeAC-DC‚HCl system, (2) DeAC-TC‚HCl system, (3) DeAC-BC‚ HCl system, (4) DeAC-LC‚HCl system (5) DeAC-PC‚HCl system; H,C C (s) γC vs XM 2 , (- - -) γ vs X2 .

Figure 11. Critical micelle concentration vs composition curves: (1) DeAC-DC‚HCl system, (2) DeAC-TC‚HCl system, (3) DeAC-BC‚ HCl system, (4) DeAC-LC‚HCl system, (5) DeAC-PC‚HCl system; (s) C vs X2, (- - -) C vs XM 2.

with which local anesthetic partitioned into the micelle of DeAC also decreases in the order of DC‚HCl, TC‚HCl, BC‚HCl, LC‚ HCl, and PC‚HCl. Further, the negative values of XM 2 were found for DeAC-BC‚HCl, DeAC-LC‚HCl, and DeAC-PC‚ HCl systems. This suggests that strongly hydrophobic local anesthetics such as DC‚HCl and TC‚HCl can be partitioned into the hydrophobic environment of the micelle of DeAC while weakly hydrophobic anesthetics as BC‚HCl, LC‚HCl, and PC‚ HCl cannot. We next consider the effect of hydrophobicity of local anesthetic molecules on partitioning and the negative partitioning of the anesthetics. The partitioning ability of charged local anesthetics into hydrophobic environments such as model membranes was estimated by several physical quantities: partition coefficient of the anesthetics between octanol and buffer solution,39,40 that between lipid matrices and buffer solution,41 differences in the partition coefficients between solid-gel and liquid-crystalline membranes of phospholipid,13 adsorbability of them onto the activated carbon surface,42 selectivity coefficients in the local anesthetic cation-selective electrodes,43,44 etc. The observed partitioning order of local anesthetics into molecular aggregates of DeAC, DC‚HCl > TC‚HCl > BC‚HCl > LC‚HCl > PC‚ HCl was consistent with the magnitude of these quantities. Moreover, comparing the present results with anesthetic potency,40,45,46 a good correlation between the partitioning of local anesthetics into the hydrophobic environment and anesthetic potency of these local anesthetics was seen. The magnitude of the partitioning ability of local anesthetics into the hydrophobic environment is in accord with the potency of the anesthetic action, the more hydrophobic the local anesthetic molecules become, the stronger they have the anesthetic effects. BC‚HCl, LC‚HCl, and PC‚HCl molecules were not partitioned into the molecular aggregates of DeAC except for the high X2 region of BC‚HCl and LC‚HCl. However, local anesthetic molecules must be transferred into the hydrophobic environment of biological membranes from the solution and expand the membranes before local anesthetic action occurs.47 The clinical potencies are in the order of BC‚HCl, LC‚HCl, PC‚HCl. The present results of the negative partitioning of these anesthetics appear to contradict the above mechanism of local anesthesia. However, the present study is limited to the charged

form (cationic form). Local anesthetic cations partially dissociate into charged and uncharged (free base form) forms in the solution as given in eq 4, and this process is pH-dependent from eq 6. Since the physiological pH value in vivo has a value of ca. 7.4, the uncharged form in vivo considerably increases as compared with that in this study. The partitioning of uncharged anesthetics into the membrane in vivo is no longer negligible. The uncharged form seems to be easily partitioned into the membrane compared with the charged one because of the disappearance of repulsive electrostatic interaction between the cationic polar head group. Finally, the difference between the partitioning of the local anesthetics into the surface-adsorbed film and into the micelle was analyzed. The partitioning of anesthetics into the micelle can be compared with that into the adsorbed film at the cmc since the micelle coexists with the adsorbed films at the cmc. The relation between the mole fraction of local anesthetic in M the surface-adsorbed film at the cmc, XH,C 2 , and X2 is ex34,35 pressed by the form H,C XH,C ) XM )(∂γC/∂X2)T,p 2 2 - (X1X2/RTΓ

(14)

where superscript C designates the thermodynamic quantity at values are evaluated from the XM the cmc. The XH,C 2 2 values in Figure 11, the ΓH,C values in Figure 7, and the composition dependence of γC in Figure 6 by use of eq 14. The values of C and XM XH,C 2 2 , which are compared in the forms of the γ vs H,C M C X2 and γ vs X2 plots, are shown for five systems in Figure 12. The XM 2 values of the DeAC-DC‚HCl and DeAC-TC‚ value and HCl systems were considerably larger than the XH,C 2 their phase diagrams resemble each other in shape. It was shown that the surfactant with the larger polar head and shorter hydrophobic chain is more abundant in the micelle component than in the adsorbed film in the binary mixtures of surfactant.48 In fact, the phase diagrams observed for mixtures of cationic surfactants having polar head groups of different sizes are similar to those obtained for both systems.49,50 Therefore, local anesthetics with larger polar head groups may geometrically favor interaction with globular structure compared with that with planar structure. Similarly, large difference between XM 2 and XH,C values was observed for the DeAC-BC‚HCl system 2 although both values are negative except for the XM 2 values in the high X2 region. BC‚HCl molecules seem to have most rigid molecular structure among the anesthetics as seen from Figure 1. They are nearly excluded from the molecular aggregate of DeAC, but the rigid structure of BC‚HCl seems to make them more apt to squeeze out from surface-adsorbed film than from and XM micelles. On the other hand, both XH,C 2 2 of the DeAC-

3304 J. Phys. Chem. B, Vol. 102, No. 17, 1998 PC‚HCl system had negative values and the former was larger (smaller negative value) than the latter. The PC‚HCl molecules are excluded from the micelle more than from the adsorbed film. The similar behavior was reported by Yamanaka et al.51 in the dodecylammonium chloride (DAC) and sodium chloride (NaCl) system. They clarified that NaCl molecules are not partitioned into surface-adsorbed films and micelles formed by DAC at all. They are excluded from the micelle as compared with the adsorbed film. Therefore, the effect of PC‚HCl on the partitioning into the adsorbed film and micelle is almost equivalent to that of uni-univalent inorganic salt. In the case of the DeACLC‚HCl system, both values were also negative, but the complicated behavior was found because the γC vs X2 curve of the system has a minimum as given in Figure 6. The XH,C 2 values were larger than the XM 2 value at low compositions H,C value at high while the XM 2 values were larger than the X2 compositions. LC‚HCl molecules have the effect on the molecular aggregates of DeAC like an inorganic salt when the X2 value is small. With increasing X2, the molecular structure of LC‚HCl seems to influence their partitioning into the aggregates of DeAC when the corresponding XM 2 value begins to go up to the positive direction. The partitioning of local anesthetics into molecular aggregates of DeAC depends on the hydrophobicity of the anesthetic molecules. Because local anesthetics exist in two forms at physiological pH and the pKa of the molecules determines the local anesthetic potency, the results of the anesthetics with weak hydrophobicity indirectly suggest that the uncharged form of the anesthetics plays an important part in the molecular mechanism of anesthesia. The partitioning of the anesthetics is also influenced by the geometry of the aggregates into which the anesthetics are partitioned. Acknowledgment. This study was supported in part by DVA Medical Research Funds. References and Notes (1) Papahadjopoulos, D.; Jacobson, K.; Poste, G.; Shepherd, G. Biochim. Biophys. Acta 1975, 394, 504. (2) Ueda, I.; Tashiro, C.; Arakawa, K. Anesthesiology 1977, 46, 327. (3) Ueda, I.; Chiou, J. S.; Krishna, P. R.; Kamaya, H. Biochim. Biophys. Acta 1994, 1190, 421. (4) Kamaya, H.; Ueda, I.; Moore, P. S.; Eyring, H. Biochim. Biophys. Acta 1979, 550, 131. (5) Lin, H. C.; Ueda, I.; Lin, S. H.; Shieh, D. D.; Kamaya, H.; Eyring, H. Biochim. Biophys. Acta 1980, 598, 51. (6) Davio, S. R.; Low, P. S. Biochim. Biophys. Acta 1981, 644, 157. (7) Fernandez, M. S. Biochim. Biophys. Acta 1981, 646, 27. (8) Schlieper, P.; Steiner, R. Chem. Phys. Lipid 1983, 34, 81. (9) Ohki, S. Biochim. Biophys. Acta 1984, 777, 56. (10) Eftink, M. R.; Puri, R. K.; Ghahramani, M. D. Biochim. Biophys. Acta 1985, 813, 137. (11) Frezzatti, W. A., Jr.; Toselli, W. R.; Schreier, S. Biochim. Biophys. Acta 1986, 860, 531. (12) Kaminoh, Y.; Tashiro, C.; Kamaya, H.; Ueda, I. Biochim. Biophys. Acta 1988, 946, 215. (13) Kaminoh, Y.; Kamaya, H.; Ueda, I. Biochim. Biophys. Acta 1989, 987, 63.

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Partitioning of Charged Local Anesthetics into ... - ACS Publications

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