J. Phys. Chem. 1981, 85. 127-129
tion from the higher triplet state by a different mechanism, such as, for example, by initial charge transfer. The triplet-triplet absorption spectrum of benzophenone is w e l l - k n ~ w n . ~ ~ -It' ~consists ,~~ of two broad bands, a weak one with a maximum at 526 nm and a stronger one with a maximum at 317 nm. The long wavelength absorption has been assigned to the Tl(nir*) T,(ira*) transition, while the short wavelength band is T,(nir*) transition. The short wavedue to Tl(nir*) length transition is the one reached by the second UV laser photon. To see if excitation of Tz alone could produce photochemistry, a three-beam experiment was performed. In this experiment the benzophenone sample was excited by the light from a 200-W mercury lamp. This beam could excite the molecule to TI and it was even intense enough (102 W/cm2) to produce two-photon photochemistry by itself. If could not, however, produce a hologram because the light was incoherent and there was no second beam with which it could interfere. If the T1 Tz transition is capable of producing irreversible photochemistry then, by interfering two additional beams of coherent light of the appropriate wavelength at the point where the UV lamp light hits the sample, one should observe the growth of a hologram. The UV lamp photons excite the benzophenone to its lowest triplet state and the laser photons
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-
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(24) D. S. McClure and P. L. Hanst, J. Chem. Phys., 23, 1772 (1955).
127
excite the molecule to a higher triplet state. Experiments of this type were performed by using 442-nm HeCd, 488- and 514-nm Ar ion, and 565-600-nm R6G dye laser lines. In none of these cases could hologram growth be detected that would indicate that T1 Tz excitation could produce photochemistry. To be sure that enough UV light for the population of T1was supplied, we replaced the Hg lamp by a UV beam from an Ar ion laser (power densities up to 120 W/cm2) that by itself could not produce a hologram. No hologram formation could be observed in these experiments as well. It thus seems that the triplet AT* state is much less reactive than the second nir* triplet state. This is consistent with measurements of hydrogen abstraction rates for ketones where the lowest triplet state is mr* is nature.'J Much less is known about the photochemistry involved in the second step of hologram formation. It presumably involves the photoreaction of the LAT produced by recombination of host and ketyl radical. What is certain is that the overall reaction requires two laser photons. The product formed in this second step has a weakly structured absorption spectrum beginning on the long wavelength side around 280 nm. This absorption resembles in vibrational spacing and wavelength the absorption spectrum of benzene and may indicate the presence of a benzene-like group in the final product. Acknowledgment. The authors express their indebtedness to D. C. Alvarez for his able technical assistance.
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Mechanism of Cholesterol Gallstone Dissolution. Analysis of the Kinetics of Cholesterol Monohydrate Dissolution in Taurocholate/Lecithin Solutions by the Mazer, Benedek, and Carey Model W. I. Higuchl,' C. C. Su, J. Y. Park, M. H. Alkan,+ and E. Guiari The College of Pharmacy and Chemical Engineering DepaHment, The University of Michigan, Ann Arbor, Michigan 48109 (Received: September 17, 1980)
The recent publication by Mazer, Benedek, and Carey (MBC) of a physical model for the micellar species distribution in the taurocholate/lecithin (TC/L) systems provides a basis for a mechanistic analysis of cholesterol monohydrate (C) dissolution behavior in bile acid/L solutions. The previously published data by Kwan et al. for compressed pellet dissolution rates (G) in TC/L solutions have been analyzed by this model. In the working range reported by Kwan, the MBC model assumes a mixture of three species, i.e., the simple TC micelles (concentration Cis), the mixed micelles of L and TC (concentration C&,), and the TC monomers (concentration CLs). A kinetic rate expression for this system is thus proposed, G = ksC;, + kMCys + kICbs, where the K's are the rate constants of dissolution involving each species. Good agreement was found between Kwan's data and the above equation when only the simple TC micelle is assumed to be involved in the rate-determining step.
A recent publication by Mazer, Benedek, and Carey (MBC)'l2 describes a model for species distribution in bile acid/lecithin solutions suggested by their quasielastic light-scattering (QLS) experiments. In the case of the taurocholate/lecithin (TC/L) system, extensive QLS data were used by the authors for proposing that in the region of high bile acid-to-lecithin ratio, y,simple micelles of a 'Ankara Universitesi, Eczacilik Fakultesi, Farmasotik Teknoloji Kursusu, Tandogan/ Ankara, Turkey. 0022-365418112085-0127$01 .OO/O
relatively constant size may co-exist with mixed bile acid/lecithin micelles of a relatively constant size. This interpretation is consistent with that which may be deduced from the equilibrium dialysis experiments of Duane3 which demonstrated the presence of substantial concentrations of simple micelles in equilibrium with the mixed (1)N. A. Mazer, G. B. Benedek, and M. C. Carey, Biochemistry, 19, mi _ _ _(iwnl. ~ (2) N. A. Mazer, M. C. Carey, R. F. Kwasnick, and G. I 3 Benedek,
Biochemistry, 18, 3064 (1979). (3) W. C. Duane, Biochem. Biophys. Res. Commun., 74, 223 (1977).
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85,
128 20
J rn
No. 2, 1981
Letters
TABLE I: Initial Dissolution Rates ( G ) of Cholesterol Monohydrate in Sodium TaurocholateILecithin Solutions Containing 0.01 M Phosphate Buffer at pH 7.4=
1
1 8
0.00
t
I /
I I I
l o 6 G in mM NaTC/mM L, mg cm-2 s-' 10'[Na+]~,M 174132 116132 87/32 46.4112.823.216.4 27.4 148 40 16 12 3.6 87 22b 20 6.5 42.4 193 These G values are the data interpolated at constant total sodium ion concentration. Extrapolated data.
I
0.08
0.16
0.24
0.32
0.48
0.40
TOTAL SODIUEI C O N C . [NatIT.
0.56
0.64
M
Flgure 1. Determination of G values at constant total sodium ion concentration by interpolating the G values reported by Kwan et al., at [Na+IT = 0.274 and 0.424 M, respectively. The NaTC concent a t i s (mM)/lecithin concentrations (mM) are (0) 174/32; (0)116132; ( 0 ) 87/32; (X) 46.4/12.8; (A)23.216.4.
micelles in this y region. Although the model is a first approximation, it provides a basis, for the first time, for treating and analyzing data on cholesterol monohydrate dissolution rates in terms of the micellar species involved in the interface-controlled kinetic^.^^^ The MBC model specifies basically three kinds of species in the coexistence region for the TC/L system namely, a simple micelle, a mixed micelle, and monomeric bile salt. We hereby propose the following rate expression for cholesterol monohydrate dissolution kinetics in this y region: where G is the cholesterol monoh drate compressed disk 2 C& are the bile acid dissolution rate per unit area, CBS, concentrations for the simple micelle and the mixed micelle, respectively, Cbs is the intermicellar bile acid concentration, and ks, k M , kI are interfacial rate constants for each species. The relationship of bile acid concentrations involving all species is where C& is the total bile acid concentration. According to the MBC model, the bile acid concentration in the mixed micelle is assumed to be proportional to the lecithin concentration, C,"
C&
= KCP
(2)
where K is a constant. Substituting eq 2 into eq 1,we get
G = ks[@s - (KCP + Cbs)l + h K C P + ~ I C B S(3) Since the dissolution rates of cholesterol in taurocholate or in TC/L solutions are known to be micelle controlled, the k&S term is considered to be negligible. We may now consider the experimental cholesterol monohydrate dissolution rate data of Kwan et ala4for (4) K. H. Kwan, W. I. Higuchi, A. M. Molokhia, and A. F. Hofmann, J. Pharrn. Sci., 66, 1094 (1977). (5) S. L. Gupta, N. F. H. Ho, J. Y . Park,W. I. Higuchi, and K. H. Kwan, manuscript in preparation.
LOG G EXPERlMENTAl
Flgure 2. Comparison of G values calculated from nonlinear curvefitting program vs. Gvalues reported by Kwan at (a) added [NaCI] = 0.1 M; (b) added [NaCi] = 0.25 M; (c) interpolated (Na'], = 0.274 M; and (d) interpolated [Na+IT= 0.424 M. Dotted line represents the theoretical curve and the sold line represents the least-squares straight line. Also presented in (c), the G values calculated vs. G values obtained with NaTC solutions containing no lecithin (A)by interpolating to [Na'], = 0.274 M.
examination by eq 3. These data correspond to the high y region, 2.7 C y C a,and therefore to the coexistence region for the TC/L system. The experimental conditions were also such that the rates were essentially interface controlled rather than diffusion/convection ~ontrolled.~ It was decided to treat and analyze the experimental G values with and without a correction for the total sodium ion concentration differences in the systems. This procedure of comparing data at constant total counterion was developed from previous experience with cholesterol mowhere nohydrate dissolution in sodium chenodeo~ycholate~ rate constants were found to be relatively constant when the rates were compared at constant total sodium ion. Figure 1shows the experimental G values of Kwan et al. plotted against [Na+IT. A smooth curve has been drawn for each of the systems. The G values interpolated a t [ N ~ + ]= T 0.274 M and [ N ~ + ]=T 0.424 M as indicated by the bar lines have been employed as a part of the present analysis by using the MBC model. The interpolated G values are tabulated in Table I. By means of a nonlinear least-squares best-fitting program, the G, ks, k M ,K , and Cbs values were determined and these are given in Table 11. It was found that the Cbs values determined are in good a reement with that degi = 6 mM) and the K duced by the MBC model (i.e., CBs values also fall in the range of the values reported by the MBC model. Figure 2, a and b, shows the G values de-
The Journal of Physical Chemistry, Vol. 85, No. 2, 1981
Letters
120
TABLE 11: Parameters and G Values Obtained from Nonlinear Curve-Fitting Program for Cholesterol Monohydrate Dissolution in Sodium Taurocholate/Lecithin Solutions
l o 6 G in mM NaTC/mM L, mg cm-’s“ fitting condition [NaCl] added = 0 . 1 Ma [NaCl] added = 0.25 Ma [ N ~ + ]=T0.274 Mb [ N ~ + ]=T 0 . 4 2 4 Mb
106k,, cm s-’ 101OkM, cm s”
0.9 1.5 1.1 1.9
2.5 2.5 10.0 10.0
K
Css,’mM
174132
116132
87/32
2.2 2.2 2.1 2.2
6.5 6.1 6.7 5.8
87 142 113 187
35 57 48 77
9 14 15 21
a Uncorrected G values from Kwan’s data were used in the fitting program. employed in nonlinear curve-fitting program.
46.4112.8 23.216.4
11 17 15 24
4.1 3.5 6.5
Interpolated G values from Figure 1 were
termined from the experimental G values not corrected for total sodium ion (Le., added NaCl of 0.10 and 0.25 M, respectively). Figure 2, c and d, shows the G values determined by using the corrected G values. A better fit observed in Figure 2, c and d, indicates the necessity of having the comparison based on constant total sodium ion concentration. Figure 2c also includes recently obtained experimental data for sodium taurocholate without any added lecithin by using the same methodology as Kwan et al.4 The experimental G values for the pure sodium taurocholate cases show systematic negative deviations which can be shown to be, in part, due to a small contribution from diffusion/convection resistance which is of the order of 10% of the total transport resistance in the case of pure TC, but less important in the cases of the mixed TC/L system^.^^' I t is seen from Table I1 that kM is generally several orders of magnitude smaller than ks. This is interpreted to mean that the simple micelles are the principal species responsible for the interfacial transport of cholesterol in the coexistence region in the TC/L system and that the mixed micelles are relatively ineffective compared to the simple micelles. This finding is very interesting as it is known that the mixed micelles solubilize more cholesterol a t equilibrium than the simple micelles.* As is often the case, however, equilibrium factors do not necessarily determine the kinetics. The explanation for ks >> kMmust reside in the free energy of activation for the simple micelle case being significantly lower than that for the mixed micelle case. A more detailed understanding would require more information on the nature of molecular events at the
interface including the approach and the configuration of the micelles and the state of the surface cholesterol molecule during a “collision”. Duane’s equilibrium dialysis experiments on the TC/L system were limited to low TC concentrations (540mM). These experiments, however, are consistent with the deductions of Mazer et al. and the present results. The K values that may be estimated from Duane’s data are in the range of 2.2-2.8 a t the higher concentrations. In many bile acid systems, including the TC/L system, the monomer concentrations would be expected to vary much more than those for conventional detergent micelle systems because the micelle aggregation numbers are relatively low.”” Consequently, the application of the conce ts of the critical micelle concentration (cmc) and the CBS may be questioned. Also, because the monomer activity may vary in the coexistence region, K should vary or possess a tendency to vary; in general, K would be expected to increase somewhat with increasing bile acid concentration at constant lecithin levels. Nevertheless, the good self-consistency of the dissolution rate data analysis by simple micelle-mixed micelle coexistence theory over a wide range of rates (-40-fold) is very encouraging as this approach provides a unique opportunity for investigating mechanisms associated with this important biological problem.
(6)S. Prakongpan, W.I. Higuchi, K. H. Kwan, and A. M. Molokhia, J . Pharm. Sci.. 65. 685 (1976). (7)W.I. Higuchi, S. Prakongpan, V. Surpuriya, and F. Young, Science, 178,633 (1972). (8) M. C. Carey and D. N. Small, J. Clin. Invest., 61, 998 (1978).
(9)Y. Chang and J. R. Cardinal, J. Phorm. Sci., 67, 174 (1978). (10)P.Mukerjee and J. R. Cardinal, J . Pharm. Sci., 65, 883 (1976). (11)D. M. Small in “The Bile Acids, Chemistry, Physiology, and Metabolism”, P. P. Nair and D. Kritchevsky, Ed., Vol. 1 1971,Chapter 8,p 249.
P
Acknowledgment. Part of the work was supported by NIH Grant AM16694. Discussions with Dr. J. L. Fox and M. L. Lamson of The University of Michigan are appreciated.
