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Stepwise Self-Association of Penicillin V As Deduced by Frontal Derivative Chromatography Noriaki Funasaki,* Seiji Ishikawa, and Saburo Neya Kyoto Pharmaceutical University, Misasagi, Yamashina-ku, Kyoto 607-8414, Japan Received December 14, 1999 The aggregation pattern of penicillin V (PCV) in a 0.15 M potassium chloride solution at 298.2 K is investigated by frontal derivative chromatography on Sephadex G-10 columns and is quantitatively analyzed on the basis of a stepwise aggregation model and a trimer-dodecamer model. The aggregation parameters for these models are best fitted to the observed centroid volume data. The derivative chromatogram of PCV is simulated on the basis of plate theory with the aggregation models. The height and position of the peak simulated on the basis of the stepwise aggregation model are in excellent agreement with the observed ones, whereas those simulated on the basis of the trimer-dodecamer model remarkably differ from the observed ones, particularly in dilute solutions. Thus, PCV forms dimer and self-associates stepwise.
Introduction Many drugs form aggregates in water by hydrophobic interactions. This causes significant changes in bioactivity, chemical stability, and osmotic pressure of the drugs in aqueous solutions. This topic has been reviewed in monographs1,2 and review articles.3,4 The self-association patterns of drugs are usually classified into two categories, micellar and stepwise (nonmicellar) associations. The micellization of surfactants is roughly characterized by the presence of critical micelle concentration (cmc) and a single size of micelle. According to Tanford, however, the concept of cmc is inexact but convenient and the use of this concept is probably a cause of confusion in the thermodynamic analysis of micelleforming systems.5 The micellization of a surfactant can be explained by stepwise aggregation models: the micelle is distributed from dimer to infinite size.1,4,6-8 Thus, drugs9,10 and bile salts11-13 exhibit less micellar selfassociation patterns than surfactants.1,4,14 According to Mukerjee, the simplest type of association, dimerization, must take place in all the self-associating * Author for correspondence. (1) Mukerjee, P. Physical Chemistry: Enriching Topics from Colloid and Surface Science; van Olphen, H., Mysels, K. J., Eds.; Theorex: La Jolla, CA, 1975; Chapter 9. (2) Attwood, D.; Florence, A. T. Surfactant Systems; Chapman and Hall: London, 1983; Chapter 4. (3) Florence, A. T. Adv. Colloid Interface Sci. 1968, 2, 115. (4) Funasaki, N. Adv. Colloid Interface Sci. 1993, 43, 87. Funasaki, N.; Hada, S.; Neya, S. Trends Phys. Chem. 1997, 6, 253. (5) Tanford, C. Hydrophobic Effects: Formation of Micelles and Biological Membranes; John Wiley & Sons: New York, 1973; Chapter 7. (6) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: New York, 1992; Chapter 16. (7) Nagarajan, R. Adv. Colloid Interface Sci. 1986, 26, 205. (8) Funasaki, N.; Shim, H.-S.; Hada, S.; Neya, S. J. Phys. Chem. 1992, 96, 1998 and references therein. (9) Funasaki, N.; Hada, S.; Neya, S. Chem. Pharm. Bull. 1994, 42, 779. (10) Funasaki, N.; Uemura, Y.; Hada, S.; Neya, S. Langmuir 1996, 12, 2214. (11) Funasaki, N.; Hada, S.; Neya, S. J. Phys. Chem. B 1999, 103, 169. (12) Funasaki, N.; Ueshiba, R.; Hada, S.; Neya, S. J. Phys. Chem. 1994, 98, 11541 and references therein. (13) Funasaki, N. In Bile Acid/Salt Surfactant Systems; Hinze, W. L., Ed.; Organized Assemblies in Chemical Analysis; Jai Press: Greenwich, CT, 2000; Vol. 2, Chapter 2. (14) Funasaki, N.; Hada, S.; Neya, S. Bull. Chem. Soc. Jpn. 1992, 65, 314.
systems being considered. The formation of higher multimers may often overshadow it and may lead to difficulties involved in even detecting it.1 Frontal derivative chromatography is an excellent method for detecting it and determining the dimerization constant, because the frontal derivative chromatogram of the dimerizing system exhibits a characteristic pattern.4,9,11,14 The frontal derivative chromatogram of the dimerizing system has a single peak, which shifts to the smaller elution side with increasing concentration. On the other hand, those of higher polymerizing systems exhibit bimodality.4,9,11,13,14 This characteristic pattern of dimerization can be used to detect dimer even in the presence of other multimers.11,12 In general, dimerization does not causes any inflection, corresponding to a cmc, in concentration dependence of physical properties. This often leads us to the misinterpretation that dimer is absent in micellar systems. In 1994 we showed by frontal gel filtration chromatography (GFC) that penicillin V (PCV) self-associates stepwise in a 150 mmol dm-3 (mM) potassium chloride solution at 298.2 K.9 In particular, we determined the dimerization constant of PCV on the basis of GFC data, such as the centroid volume and the position and height of the trailing peak.9 The validity of these methods has been demonstrated for chlorpromazine hydrochloride and methylene blue by comparison with UV spectrophotometry.14-16 Very recently, however, it was reported that PCV forms only two species, trimer and dodecamer,17 in remarkable contrast with our model. In the present work we provide further chromatographic evidence for our stepwise aggregation model of PCV to resolve the above disagreement on the aggregation pattern of PCV. Experimental Section Materials. A specimen of PCV (potassium phenoxymethylpenicillinate) was received from Sigma. Sephadex G-10 (Pharmacia) columns were treated as suggested by the manufacturer. The double-distilled water was degassed just before each GFC experiment. (15) Funasaki, N.; Hada, S.; Neya, S. Bull. Chem. Soc. Jpn. 1994, 67, 65. (16) Funasaki, N.; Hada, S. Paiement, J. J. Phys. Chem. 1991, 95, 4131. (17) Varela, L. M.; Rega, C.; Suarez-Filloy, M. J.; Ruso, J. M.; Prieto, G.; Attwood, D.; Sarmiento, F.; Mosquera, V. Langmuir 1999, 15, 6285.
10.1021/la991639n CCC: $19.00 © 2000 American Chemical Society Published on Web 05/20/2000
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Methods. All GFC experiments were carried out in a 150 mM potassium chloride solution under a flow rate of ca. 0.36 cm3 min-1. Two columns, B and C, were used for PCV. The columns were jacketed in order to maintain them at a constant temperature of 298.2 ( 0.2 K. A large volume of sample was applied so that the plateau region appeared on the elution curve. The concentration of PCV in eluate was monitored continuously with a differential refractometer. These data were saved in a computer for further analysis. The chromatographic data were subjected to the treatments of smoothing and baseline corrections. The GFC experiments were carried out at a number of concentrations; the numbers n of data points are 9 on column B and 7 for column C. For cases of two concentrations of C0 ) 0.2002 and 0.2600 M on column C, 2.00 cm3 of eluate was taken in a test tube with a fraction collector, because the refractometer did not respond to such high concentrations. The derivative chromatogram was approximated by the difference chromatogram. Simulations of chromatograms were carried out by a plate theory (discontinuous flow model).15 The number of the plate (N) and the void volume (V0) of the column are the same as those already reported (N ) 30 for column B and N ) 12 for column C).9 The reason for the small number of the plate on column C is that the concentration in eluate was determined at an interval of 2 cm3, a rather large volume, on the column. Further details on experiments and simulations were reported elsewhere.4,14,15
Figure 1. (a) Frontal chromatogram of PCV at C0 ) 0.2002 M and S ) 42.50 cm3 and (b) its derivative with definitions of chromatographic parameters.
Results and Discussion Frontal Chromatogram of PCV. A large volume of a dilute PCV solution was applied on the Sephadex G-10 column, so that the plateau region appeared on the chromatogram (Figure 1a). This chromatogram is termed the frontal chromatogram. Because the concentration C of PCV in the plateau is the same C0 as that applied, this chromatogram affords us quantitative information on the self-association of PCV. We may assume that the equivalent sharp boundary for the leading or trailing edge of the solute zone begins or terminates in the plateau region (centroid) of the elution profile and satisfies the relationships4,18,19
V′c ) Vc )
∫0C V dC/C0 0
leading boundary
∫0C V dC/C0 - S 0
trailing boundary
(1) (2)
Here S denotes the applied volume of the sample. For these determinations the volume coordinate, V, is assigned a zero value when the leading boundary of the applied sample enters the column bed. According to this approximation (called asymptotic theory), the elution curve for a nonassociable solute is expected to fall within a rectangle of height C0 and width S.4,15-18 Because the centroid volumes, Vc′ and Vc, at the leading and trailing boundaries were equal to each other within experimental errors, we took the average of them as Vc. Frontal derivative chromatograms (Figure 1b) reflect aggregation patterns.4,13 As we have shown,4,14,15 we can determine the monomer concentration C1 from
C1 ) (Vc - Vm)C/(V1 - Vm)
Figure 2. (a) Observed derivative chromatograms of PCV of C0 ) 0.04177 M at the leading (closed circles) and trailing (open circles) boundaries on column B and (b) simulated on the basis of the stepwise aggregation model (solid lines) and the trimerdodecamer model (dashed lines) with N ) 30 and V0 ) 4.0 cm3.
(3)
Here V1 and Vm denote the centroid volumes of the monomer and aggregates of PCV, respectively: V1 ) 24.00 cm3 and Vm ) 7.03 cm3 on column B and V1 ) 21.84 cm3 and Vm ) 6.35 cm3 on column C. From eq 3 the monomer concentration of PCV was determined as a function of the (18) Ackers, G. K.; Thompson, T. E. Proc. Natl. Acad. Sci. U.S.A. 1965, 53, 342. (19) Ackers, G. K Adv. Protein Chem. 1970, 24, 343.
total PCV concentration. According to multiple equilibrium theory for self-association,1,4 the micellar weight average aggregation number nw is calculated from
nw ) d(log(C - C1))/d(log C1)
(4)
Our data showed that PCV forms a dimer at low concentrations and larger multimers at higher concentrations (data reported).9 Figure 2a shows the observed derivative chromatograms of C0 ) 0.041 77 mM at the leading and trailing boundaries on column B. The volume coordinate for the trailing boundary is shown as V - S: the volume coordinate is assigned a zero value when the trailing boundary of the applied sample leaves the column bed. The shape of the derivative chromatogram at the trailing boundary reflects the aggregation pattern. The peak heights at low concentrations are plotted against the PCV concentrations of applied solutions in Figure 3. The peak at the leading boundary is higher than that at the trailing boundary. This result indicates that PCV self-associates even at very low concentrations.4,9 The peak height at the trailing boundary is almost proportional to the applied concentration below 0.05 M. This behavior is characteristic of dimerization. Thus, trimer and higher aggregates of PCV are negligible at these low concentrations.4,9
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According to this model, the total PCV concentration can be written as ∞
C ) C1 + 2K2C12 +
Figure 3. Peak heights at the leading (closed circles) and trailing (open circles) boundaries plotted against the applied concentration of PCV: O and b, observed; solid lines, simulated on the basis of the stepwise aggregation; dashed lines, simulated on the basis of the trimer-dodecamer model with N ) 30 and V0 ) 4.0 cm3.
∑3 iC1i exp(ai - bi2/3 - ci4/3)
(8)
The term a corresponds to the driving force of micellization due to the transfer of the hydrophobic group from water to the micelle. The term b expresses the reduction of hydrophobic surface area caused by spherical micelle formation. The term c denotes the electrostatic repulsion between the hydrophilic groups at the micellar surface. The terms b and c stop further micellar growth.4,5,8 These stepwise aggregation constants were determined by minimizing the sum, SS, of the squares of the differences in Vc between theory and experiment: n
SS )
∑1 (Vc,calcd - Vc,obsd)2
(9)
Here n stands for the number of data points; n ) 9 for column B and n ) 7 for column C. A combination of eqs 3 and 8 with V1 ) 24.00 and Vm ) 7.03 cm3 on column B and V1 ) 21.84 and Vm ) 6.35 cm3 on column C yields a calculated centroid volume, Vc,calcd, for a given concentration. The best fit parameters were determined to be K2 ) 4.38 M-1, a ) 78.2, b ) 75.8, and c ) 19.3.9,20,21 Differently from the stepwise aggregation model written in eq 8, Valera et al. proposed that PCV forms trimers and dodecamers alone.17 According to their model, the total concentration of PCV is written as
C ) C1 + 3K3C13 + 12K12C112 Figure 4. Plots according to eq 5: O, observed; solid line, simulated on the basis of the stepwise aggregation model; dashed line, simulated on the basis of the trimer-dodecamer model with N ) 30 and V0 ) 4.0 cm3.
The peak volume decreases with increasing concentration (data not shown). According to asymptotic theory, the volume, Vp, of the trailing peak for the dimerization system approximately obeys the following equation: 4,9,14,15,18
{(V1po - V2p∞)/(Vp - V2p∞)}2 ) 1 + 9.6K2Cmax (5) Here Cmax denotes the concentration at the peak volume, Vp, at the trailing boundary (Figure 1) and K2 stands for the dimerization constant. The V1po value may be estimated from extrapolation of the Vp values to zero concentration, and the V2p∞ value may be set as the Vp value of blue dextran; V1po ) 23.50 cm3 and V2p∞ ) 6.35 cm3 for column B. As Figure 4 shows, eq 5 holds true at dilute concentrations. The dimerization constant of PCV evaluated from the slope of the linear portion in Figure 4 is 4.7 M-1 and is close to 4.38 M-1, obtained from the centroid volume data.9 Two Self-Association Models of PCV. We have proposed a stepwise aggregation model for PCV:
Ki iA1 ) Ai i ) 2, 3, 4, ...
(6)
Ki ) [Ai]/C1i
(7)
(10)
Using our observed Vc data, we determined the best fit trimerization and dodecamerization constants of K3 ) 71.93 M-2 and K12 ) 19.53 × 109 M-11, respectively. Simulations of Derivative Chromatograms. The derivative chromatogram at the trailing boundary reflects the aggregation pattern. The derivative chromatogram of the dimerizing system at the trailing boundary uniquely has a single peak, whereas those of the other multimerizations exhibit bimodality.4,11,13-15 This characteristic feature of dimerization can be used for detecting dimer in the presence of other multimers. Furthermore, we simulated the derivative chromatograms at C0 ) 0.041 77 M on the basis of the two aggregation models for PCV. As Figure 2b shows, our stepwise model (solid lines) is clearly better fit to the observed chromatogram (Figure 2a) at C0 ) 0.041 77 M than the trimer-dodecamer model (dashed lines). In particular, the peak positions of the derivative chromatogram simulated on the basis of the trimer-dodecamer model are distant from the observed ones. This disagree(20) We estimated the coefficients, a, b, and c for octa- and heptaethylene glycol decyl ethers (in mole fraction units),8 sodium taurodeoxycholate,12 chlorpromazine hydrochloride,16 and propantheline bromide (in millimolar units).10 The magnitude of coefficient a, is related to the cmc, and (b/c)3/2 is close to the micellar aggregation number.8 Because PCV has a small cmc value and forms small micelles, the coefficient a is large and the ratio b/c is small. Although we recently determined the structure of the dimer of propantheline bromide by nuclear magnetic resonance, its dimerization constant was not easily estimated from this structure.21 Thus, it is not easy to quantify these coefficients in terms of micellar structures of PCV, because those structures and the relation between micellar structures and aggregation constants are unknown. (21) Hada, S.; Ishikawa, S.; Neya, S.; Funasaki, N. J. Phys. Chem. B 1999, 103, 2579.
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centration: ∞
C ) C1 +
∑2 iKiC1i
(12)
For a simple self-associating system containing monomer, dimer, and trimer alone, the total concentration can be written as
C ) C1 + 2K2C12 + 3K3C13 Figure 5. Simulated derivative chromatograms of PCV at C0 ) 0.2002 M and S ) 42.50 cm3 on column C with N ) 17 and V0 ) 4.0 cm3: solid line, the stepwise aggregation model; dashed line, the trimer-dodecamer model.
ment is mainly ascribed to the neglect of dimer in the trimer-dodecamer model. As Figure 3 shows, the peak heights simulated on the basis of the stepwise aggregation model (solid lines) are in an excellent agreement with the observed ones, but those simulated on the basis of the trimer-dodecamer model (dashed lines) are not so. This plot is useful to show dimerization. Figure 4 shows that the peak volume data simulated on the basis of the stepwise aggregation model (solid line) are in an excellent agreement with the observed ones, but those simulated on the basis of the trimerdodecamer model (dashed line) are far from the observed ones. This plot is also useful to show dimerization. Furthermore, as Figure 5 shows, the derivative chromatogram of PCV at C0 ) 0.2002 M simulated on the basis of the stepwise aggregation model (solid line) is slightly closer to the observed one (Figure 1b) than that simulated on the basis of the trimer-dodecamer model (dashed line). Because in this concentrated solution the dimer is not a major aggregate, the difference between the two models is not so remarkable as that in dilute solutions. Thus, our stepwise model is better than the trimerdodecamer model. Dimerization and Cmc. Experimentally, the cmc is defined as a concentration at which solution properties of a surfactant abruptly change,1 though Tanford criticized the concept of cmc.5 Though a few theoretical definitions of cmc have been proposed, we have recently shown that the cmc is best defined as the total concentration at which the third derivative of the monomer concentration with respect to the total concentration is null:4,12
d3C1/dC3 ) 0
(11)
This theoretical definition of cmc is in excellent agreement with the observed values for surfactants, bile salts, and drugs.4,12 Any theoretical model of self-association gives the total concentration as a function of monomer con-
(13)
Application of eq 11 to eq 13 yields the condition for the presence of the cmc:
K3 g 4K22/9
(14)
This system contains a substantial amount of dimer below the cmc. Unless eq 14 is satisfied, there is no cmc. The analysis of this simple system demonstrates that the system containing aggregates larger than trimer can have the cmc, when aggregation constants satisfy appropriate conditions, and that there is no cmc for the system containing dimer alone, regardless of the magnitude of the dimerization constant, because K2 must be a negative value as deduced from eq 14. The system forming dimer and aggregates larger than trimer contains a substantial amount of dimer at the cmc. A good example for such a system is chlorpromazine hydrochloride: the monomer concentration is lower than the cmc in solutions even above the cmc.16 The cmc is an approximate, though convenient, concept even for surfactants. Because the micellization of surfactants occurs in a highly cooperative manner, the presence of dimers is often overlooked. As the selfassociation of a system takes place less cooperatively, the cmc becomes a more inaccurate concept. Once the presence of cmc is presumed for such a self-associating system, the micellar aggregation numbers observed by many methods would be greater than 3 and the presence of dimer would be neglected. There is a controversy about the presence of dimers of bile salts as well as drugs and surfactants. Very recently, we have shown that sodium taurocholate and taurodeoxycholate form homodimers by frontal derivative chromatography.11 In conclusion, our stepwise aggregation model for the self-association of PCV is better than the trimerdodecamer model. Acknowledgment. Thanks are due to Ms. Kayo Nomura for her calculations. This work is supported by grants-in-aid from the Ministry of Education, Science, Culture, and Sports of Japan (No. 11672153 and Frontier Research Program). LA991639N
