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Morphology of Bile Salt Micelles as Studied by Computer Simulation Methods Lı´via B. Pa´rtay Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary
Marcello Sega Dipartimento di Fisica, UniVersita` degli Studi di Trento, 14 Via SomariVe, I-38050 PoVo (Trento), Italy, and Frankfurt Institute for AdVanced Studies, D-60438 Frankfurt, Germany
Pa´l Jedlovszky* Laboratory of Interfaces and Nanosize Systems, Institute of Chemistry, Eo¨tVo¨s Lora´ nd UniVersity, Pa´ zma´ ny Pe´ ter stny. 1/a, H-1117 Budapest, Hungary ReceiVed June 13, 2007. In Final Form: August 4, 2007 The relative arrangement of the neighboring bile ions and the shape of the hydrophobic and hydrogen-bonded primary micelles as well of the large secondary micelles formed by these ions are analyzed in detail on the basis of molecular dynamics computer simulations of 30 and 300 mM sodium cholate and sodium deoxycholate solutions. In the lower concentration considered, the systems only contain primary micelles, whereas in both of the 300 mM systems secondary micelles are also present. The simulations performed were long enough that the systems reached thermodynamic equilibrium. It is found that the neighboring cholate ions prefer alignments in which their quasi-planar tetracyclic ring systems are parallel with each other, whereas for deoxycholate an opening of the angle between these planes is observed. The shape of the micelles is characterized by the ratio of their three principal moments of inertia. The primary deoxycholate micelles are found to be rather spherical, whereas in the case of cholate somewhat flattened, disklike or oblate shaped ellipsoidal primary micelles are found, irrespective of whether these micelles are kept together by hydrogen bonds or are of hydrophobic origin. Finally, the secondary micelles are found to exhibit a large variety of shapes, ranging from flattened oblates to rodlike objects through various different irregular shapes, characterized by markedly different values of the three principal moments of inertia. The observed preferences of the relative arrangement of the neighboring ions and of the aggregate shapes as well as the differences observed in the behavior of the two bile ions studied in these respects are traced back to the molecular structure of these ions.
1. Introduction Bile salts, such as sodium cholate and sodium deoxycholate, are among the most important biological surfactants, acting as solubilizers of cholesterol, bilirubin, and various fat-soluble vitamins in the intestines of vertebrates. These molecules, biosynthetized from cholesterol in the liver, have a markedly different structure than those of conventional, widely used industrial surfactants. Namely, instead of being built up by a small, strongly polar or even charged head and a long apolar hydrocarbon tail group, these ions (e.g., the cholate ion), containing a large, rigid, and quasi-planar tetracyclic ring system, are characterized by a hydrophilic (R) and a hydrophobic (β) face. This unusual amphiphilic structure is originated in the fact that the hydrophilic (OH) and hydrophobic (CH3) groups attached to this ring system are located at different sides of it. Further, in the case of the deoxycholate ion, the polar groups are arranged along one edge of the tetracyclic ring system. Hence, this ion is characterized by a hydrophilic edge rather than a hydrophilic face. The structures of the deoxycholate and cholate ions are shown in Figure 1. The special structure of bile ions is also manifested in their unusual self-assembly behavior.1-5 Thus, the critical micellar concentration cM of bile salts is considerably lower, and the * To whom correspondence should be addressed. E-mail: pali@ chem.elte.hu.
Figure 1. Schematic (top) and spatial (bottom) structures of the deoxycholate (left) and cholate (right) ions. The notation used to mark the oxygen atoms of different positions (i.e., A-D) throughout the paper is also indicated. The vectors a and b, pointing roughly perpendicular to the quasi-planar tetracyclic ring system of these ions and along its main axis, respectively, are also shown. In the spatial view of the ions, the C atoms (as well as the CH, CH2, and CH3 united atoms) are marked by gray, the O atoms by red, and the H atoms of the OH groups by white color.
micelles that are formed just above the cM are characterized by much smaller aggregation numbers than in the case of simple surfactants. Thus, for instance, the critical micellar concentration value of both the cholate and deoxycholate ions is below
10.1021/la701749u CCC: $37.00 © 2007 American Chemical Society Published on Web 10/18/2007
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10 mM,6 whereas the mean aggregation number of their micelles is only about 2-5 in solutions of 10-50 mM concentrations.1 In accordance with these data, we have recently estimated the cM of sodium cholate and sodium deoxycholate to be about 2.7 and 4.1 mM, respectively, and the mean aggregation number of cholate and deoxycholate in a 30 mM aqueous solution to be about 4.5 and 4.1, respectively, by means of computer simulation methods.5 Another unusual feature of the self-assembly behavior of the bile salts is that the mean size of their aggregates shows a strong concentration dependence. For instance, in solutions above 100 mM concentration, the mean aggregation number of both the cholate and deoxycholate ions is about 20.1 The concentration dependence of the mean aggregate size was also observed by computer simulation; the mean size of the cholate and deoxycholate aggregates was found to increase to about 20 and 7, respectively, when the concentration of the system was increased to 300 mM.5 Explanation of this unusual aggregation behavior of the bile salts has been attempted several times by assuming various different aggregation mechanisms.7-13 The first of these schemes was the primary-secondary micelle model of Small.7 According to this model, the first step of aggregation, occurring just above the critical micellar concentration, is the formation of small, primary micelles in the usual way; that is, the bile ions turn to each other by their hydrophobic β side and water is expelled from the interior of the aggregate. However, at high enough concentrations, hydrogen bonds are formed between the hydrophilic R faces of the bile ions belonging to different primary micelles, leading to the formation of large, secondary micelles. Recently, we have performed molecular dynamics computer simulations of aqueous solutions of sodium cholate and sodium deoxycholate in three different concentrations, that is, 30, 90, and 300 mM.5 The simulations were long enough to reach thermodynamic equilibrium between aggregates of various sizes and monomeric bile ions. Our results have not only confirmed the main idea that is behind the assumption of Small, but also revealed that the details of the aggregation scheme are rather sensitive to the details of the molecular structure of the surfactant and thus can be varied from system to system. Namely, while the aggregation behavior of the deoxycholate ions was found to follow the prediction of Small, in the case of the cholate ions, the faces of which are more hydrophilic than those of deoxycholate ions (as they contain one more OH group), hydrogen-bonded primary aggregates also occur in addition to the usual, hydrophobically bound primary micelles. In other words, both of the main elements that are involved in forming the structure of the secondary micelles are already present at low concentrations. In (1) Fontell, K. The Micellar Structure of Bile Salt Solutions. In Surface Chemistry; Ekwall, P., Groth, K., Runnstro¨m-Reio, V., Eds.; Munksgaard: Copenhagen, 1965; pp 252-267. (2) Hinze, W. L.; Hu, W.; Quina, F. H.; Mohammadzai, I. U. Bile Acid/Salt Surfactant Systems: General Properties and Survey of Analytical Applications. In Organized Assemblies in Chemical Analysis; Hinze, W. L., Ed.; JAI Press: Stamford, CT, 2000; Vol. 2, pp 1-70. (3) Furusawa, T.; Matuura, R. Hyomen 1967, 5, 749. (4) Cabral, D. J.; Small, D. M. In Handbook of Physiology; Schultz, S. G., Forte, J. G., Rauner B. B., Eds.; Waverly Press: New York, 1989; Vol. 3, pp 621-662. (5) Pa´rtay, L. B.; Sega, M.; Jedlovszky, P. J. Phys. Chem. B 2007, 111, 9886. (6) Reis, S.; Guimara˜es Moutinho, C.; Matos, C.; de Castro, B.; Gameiro, P.; Lima, J. L. F. C. Anal. Biochem. 2004, 334, 117 and references therein. (7) Small, D. M. In The Bile Acids; Nair, P. P., Kritchevsky, D., Eds.; Plenum Press: New York, 1971; Vol. 1, Chapter 8. (8) Li, G.; McGown, L. B. J. Phys. Chem. 1994, 98, 13711. (9) Oakenfull, D. G.; Fisher, L. R. J. Phys. Chem. 1977, 81, 1838. (10) Zana, R. J. Phys. Chem 1978, 82, 2440. (11) Oakenfull, D. G.; Fisher, L. R. J. Phys. Chem. 1978, 82, 2443. (12) Oakenfull, D. G.; Fisher, L. R. J. Phys. Chem. 1980, 84, 936. (13) Ventaketusan, P.; Cheng, Y.; Kahne, D. J. Am. Chem. Soc. 1994, 116, 6955.
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this respect, the role of the hydrophobic and hydrogen-bonded primary aggregates is symmetric. The structure of the secondary aggregates can equally be described in terms of hydrophobic primary micelles that are attached together by hydrogen bonds, and in terms of hydrogen-bonded aggregates that are attached together via the formation of micelles by their hydrophobic faces.5 An anticipated consequence of the unusual aggregation of the bile ions is that the shape of their aggregates is probably markedly different from that of conventional micelles (i.e., spherical, rodlike, or bilayer). In particular, one can expect a rather irregular shape for the large secondary aggregates. Although the expected unusual morphology of the bile salt micelles should ultimately originate from their unusual molecular structure (and hence, it can be different even for different bile salts), to our knowledge, no systematic study of the morphology of bile salt micelles has been reported yet. In this paper, we present a detailed analysis of the shape of primary and secondary micelles of both cholate and deoxycholate ions on the basis of the results of our recent molecular dynamics simulations.5 Since the effect of the molecular structure is manifested in the determination of the shape of the micelles through the relative arrangement of the neighboring ions in the aggregate, we also focus our interest on the relative orientation of the neighboring ions and discuss the differences observed between the aggregates of cholate and deoxycholate. The paper is organized as follows. In section 2, details of the calculations performed are given. The relative orientation of the neighboring ions and the shape of the micelles are discussed in detail in sections 3 and 4, respectively. Finally, in section 5, the results are summarized and the conclusions of this study are drawn.
2. Details of the Calculations 2.1. Molecular Dynamics Simulations. The computer simulations performed are described in our previous paper,5 and therefore, only a brief summary of their details is given here. The aqueous solutions of sodium cholate and sodium deoxycholate were simulated at three different concentrations, that is, 30, 90, and 300 mM. Since secondary aggregates were never found in the 30 mM solutions but occurred in the 300 mM solutions of both salts,5 here we limit our analyses to these two concentrations, showing all the important features of the bile salt micelles. The simulations were performed in the isothermal-isobaric (N,p,T) ensemble at the temperature of 298 K and pressure of 1 bar. The 30 and 300 mM systems consisted of 10 ion pairs and 18 000 water molecules, and 124 ion pairs and 20 000 water molecules, respectively. Cubic simulation box and standard periodic boundary conditions were applied. The tetracyclic ring system of the bile ions was described by the potential model of Ho¨ltje et al., developed originally for cholesterol.14 This potential model is based on the GROMOS87 force field.15,16 The potential parameters of the ligands attached to this tetracyclic ring system as well as of the Na+ counterions were also taken from the GROMOS87 force field. The CH, CH2, and CH3 groups were treated as united atoms. Finally, water molecules were described by the rigid, three-site SPC/E potential model.17 The simulations were performed by using the GROMACS program package.18 The temperature and pressure of the system (14) Ho¨ltje, M.; Forster, T.; Brandt, B.; Engels, T.; von Rybinski, W.; Ho¨ltje, H. D. Biochim. Biophys. Acta 2001, 1511, 156. (15) Hermans, J.; Berendsen, H. J. C.; van Gunsteren, W. F.; Postma, J. P. M. Biopolymers 1984, 23, 1513. (16) van Gunsteren, W.; Berendsen, H. J. C. Groningen Molecular Simulation (GROMOS) Library Manual; Biomos: Groningen, 1987. (17) Berendsen, H. J. C.; Grigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 91, 6269. (18) Lindahl, E.; Hess, B.; van der Spoel, D. J. Mol. Model. 2001, 7, 306.
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were kept constant employing the weak coupling algorithms of Berendsen.19 The bond lengths of the water molecules and bile anions were kept fixed using the SETTLE20 and LINCS21 algorithms, respectively. Lennard-Jones interactions were truncated to zero beyond the cutoff distance of 9.0 Å. The longrange part of the electrostatic interactions was accounted for using the Ewald summation method in the Smooth Particle Mesh Ewald implementation.22 The integration time step of 2 fs was used in the simulations. The systems were equilibrated by performing 20-50 ns long simulations. During this time, even the slowest varying quantities, such as the mean size of the various aggregates, reached their equilibrium values. In the production phase of the simulations, 20 ns long trajectories were generated. This time was found to be at least 1 order of magnitude longer than the characteristic lifetime of the monomers as well as that of the connected state of two bile ions (irrespective of whether this connection is based on hydrogen bonds or is of hydrophobic origin).5 For the analyses, 1000 sample configurations per system, separated by 20 ps long trajectories each, were saved in the production phase of the simulations. 2.2. Connectivity Criteria and Cluster Definition. To unambiguously identify the clusters of the bile ions, the connectivity between two such ions has to be defined. Based on the behavior of their various pair correlation functions in our previous paper, we have defined two different types of connectivities between two bile ions.5 According to these definitions, two ions are hydrogen-bonded (H-bonded) to each other if the distance between any of their O atoms is less than 3.35 Å and, at the same time, at least one H atom that is bonded to one of these two O atoms is closer to the other O atom than 2.45 Å. Further, two ions are hydrophobically bound (P-bonded) to each other if a methyl group directly attached to the tetracyclic ring system of one of the molecules is closer than 5.5 Å to a similar methyl group of the other molecule. In addition to these two definitions, a third, general connectivity criterion, based on the behavior of the center-of-mass-center-of-mass pair correlation function, has also been established. According to this criterion, two bile ions are connected (C-bonded) to each other if the distance between their centers-of-mass is less than 10.75 Å. We have also demonstrated that the vast majority of the ion pairs that are either H- or P-bonded to each other satisfy also the criterion of being C-bonded and, conversely, that the C-bonded pairs are usually either H- or P-bonded to each other.5 Based on these connectivity criteria, we define three different types of aggregates. Thus, a hydrogen-bonded cluster (CH cluster) is the assembly of bile ions that are kept together by C and H bonds (i.e., from any ion belonging to the cluster, one can reach any other ion of the cluster via bile ion pairs that are both Cand H-bonded to each other). Similarly, hydrophobic (CP) clusters are defined as assemblies of bile ions that are kept together by C and P bonds. Finally, general (CPH) clusters are assemblies of bile ions that are kept together by C and either H or P bonds (i.e., neighbors are linked together both by a C bond and by either a H or a P bond). Obviously, secondary micelles can only be detected using this third, general cluster definition, whereas the first two, specific cluster definitions can capture the two different types (i.e., hydrogen-bonded or hydrophobic) of primary micelles as well as the primary micellar elements of the large secondary aggregates. (19) Berendsen, H. J. C.; Postma, J. P. M.; DiNola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684. (20) Miyamoto, S.; Kollman, P. A. J. Comput. Chem. 1992, 13, 952. (21) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. J. Comput. Chem. 1997, 18, 1463. (22) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. J. Chem. Phys. 1995, 103, 8577.
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Figure 2. Cosine distribution of the angle R, formed by the vectors a of two neighboring cholate (left) and deoxycholate (right) ions that are H-bonded (full lines) and P-bonded (dotted lines) to each other in the 30 mM (top) and 300 mM (bottom) systems simulated. The schematic arrangements of the neighboring ions corresponding to the different peaks are also indicated (the arrows point to the hydrophobic face of the ions, along the C-Me bonds).
3. Relative Orientation of the Neighboring Ions in the Clusters The shape of the clusters of the bile ions is strongly determined by the relative orientation of the neighboring ions. Therefore, any meaningful analysis of the cluster morphology should start with the investigation of the relative arrangement of the connected bile ion pairs. Here, we present the analysis of the relative orientation of both the plane and the main axis of the neighboring ions. For this purpose, we have defined two vectors on the rigid tetracyclic ring system of the bile ions. Vector a points along the C-CH3 bond from the C atom that joins the first and second six-membered rings toward the methyl group, whereas vector b points from the other C atom shared by the first two hexameric rings to the C atom at which the pentanoate group is attached to the five-membered ring of the ion. The definition of vectors a and b is illustrated in Figure 1. In this way, the relative orientation of the planes and axes of the ring systems of the neighboring ions can be characterized through the angles formed by their vectors a and by their vectors b (denoted here as R and β), respectively. The cosine distributions of the angles R and β are shown in Figures 2 and 3, respectively, separately for those neighboring ion pairs that are H-bonded and those that are P-bonded to each other in all the four systems studied. As is seen from Figure 2, the P(cos R) distributions of both the H-bonded and P-bonded cholate pairs show a sharp peak at -1, that is, at the R value of 180°. A similar peak is given by the P-bonded deoxycholate pairs, whereas this peak is lacking at the P(cos R) distribution
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Figure 3. Cosine distribution of the angle β, formed by the vectors b of two neighboring cholate (left) and deoxycholate (right) ions that are H-bonded (full lines) and P-bonded (dotted lines) to each other in the 30 mM (top) and 300 mM (bottom) systems simulated.
of the H-bonded deoxycholate pairs. This peak, denoted as I, is given by neighbors that form a dimer, sticking together either by their hydrophilic or hydrophobic faces. Examples for such cholate ion pairs are given in Figures 4a and 5a, respectively, as taken out from instantaneous equilibrium configurations. Since the hydrophilic part of the deoxycholate ion is an edge rather than a face, the hydrogen-bonded deoxycholate pairs are sticked together at these edges, allowing the opening of the angle between the planes of the two ring systems. Thus, the dominant peak of P(cos R) for the H-bonded deoxycholate pairs, denoted here as II, is rather broad and is located between -0.6 and -0.3 (i.e., at about 110°-130°). Such deoxycholate pairs are shown in Figure 4b and 4c. Finally, the distributions of the P-bonded pairs show a small peak at about -0.3, denoted as III, which can be attributed to the neighboring ions that belong to hydrophobic aggregates of somewhat larger size (i.e., trimers, tetramers, etc.). Such a cholate trimer is depicted in Figure 5b. The schematic arrangement of the neighboring ion pairs corresponding to peaks I, II, and III are also illustrated in Figure 3. The P(cos β) distributions of the P-bonded pairs usually show a peak at about -1 (denoted as IV) and a smaller one at cos β ) 1. These peaks correspond to the antiparallel (see, e.g., the dimer in Figure 5a) and parallel alignments of the neighboring ring axes, respectively, and are again characteristic of the strongly sticked dimers. The dominance of the antiparallel alignment over the parallel one is probably of steric origin; namely that the bulky methyl groups can be somewhat farther apart from each other in the former arrangement. In some cases, a small peak, denoted as V, appears close to the cos β value of 0, indicating the slight preference of the neighboring ring axes for the perpendicular alignment in these cases. This preference is probably a feature of the larger hydrophobic aggregates. This preference is illustrated in Figure 6, showing a hydrophobically bound deoxycholate tetramer, taken out from a larger CPH cluster, from two different views. The P(cos β) distribution of the H-bonded pairs shows a more complicated picture, due to the large variety of the possible hydrogen-bonding patterns that can be formed by two neighboring anions between their O atoms of different positions. The four possible positions of the O atoms in the cholate ion are denoted here by A, B, C, and D. In the deoxycholate ion, the O atoms can only occupy the positions A, B, and C. This notation of the
Figure 4. Typical arrangements of the neighboring H-bonded bile ions, taken out from instantaneous equilibrium configurations of the systems simulated. (a) Cholate pair, linked together by four hydrogen bonds, giving rise to peak I of the P(cos R) distribution and peak VII of the P(cos β) distribution. (b and c) Deoxycholate pairs linked together by two (b) and one (c) hydrogen bonds, with an opened angle between their planes that gives rise to peak II of the P(cos R) distribution. (d) A H-bonded cholate trimer, kept together by five hydrogen bonds. (e) Antiparallel oriented deoxycholate pair, kept together by three hydrogen bonds (including two OA-OC-type ones), giving rise to peak VI of the P(cos β) distribution. (f) Parallel oriented deoxycholate pair, kept together by two hydrogen bonds, giving rise to peak VII of the P(cos β) distribution. Color-coding is the same as that in Figure 1.
Figure 5. Typical arrangements of the neighboring P-bonded bile ions, taken out from instantaneous equilibrium configurations of the systems simulated. (a) Cholate pair, with parallel aligned planes and antiparallel axes, giving rise to peak I of the P(cos R) distribution and peak IV of the P(cos β) distribution. (b) Cholate trimer, giving rise to peak III of the P(cos R) distribution. Color-coding is the same as that in Figure 1.
different oxygen positions in the two ions is illustrated in Figure 1. In our previous paper,5 we showed that the most frequently occurring hydrogen bonds between two cholate ions involve
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Figure 6. (a) Top view and (b) side view of the tetrameric hydrophobic core of a larger secondary deoxycholate micelle, taken out from an instantaneous equilibrium configuration of the 300 mM system. (The full aggregate to which this hydrophobic core belongs to is shown in Figure 11a.) Two ions, aligned parallel with each other (encircled by solid lines), are laying above the other two (encircled by dashed lines), which are aligned parallel with each other and perpendicular to the two ions above them. Any pair of a top and a bottom ion gives rise to peak V of the P(cos β) distribution. Color-coding is the same as that in Figure 1.
either two D-type oxygen atoms, two B-type oxygen atoms, or a B- and a D-type oxygen atom (see, e.g., the cholate dimer shown in Figure 4a and the cholate trimer shown in Figure 4d). Besides these three types, OA-OA and OA-OC hydrogen bonds are also formed rather frequently. The fact that the deoxycholate ion differs from cholate in the lacking of the OH group in position D, the one that plays a central role in the hydrogen-bonding pattern between two cholate ions, indicates that the typical hydrogen-bonding structure of two deoxycholate ions must be rather different from that of two cholate ions. In fact, the dominant type of hydrogen bonds between two deoxycholate ions was clearly found to be between an A-type and a C-type oxygen. An example for a deoxycholate dimer forming two hydrogen bonds of this type with each other is given in Figure 4e. In addition, OB-OC, OB-OB, and OA-OB hydrogen bonds were also found to occur relatively frequently (see, e.g., Figure 4b, e, and f).5 These differences between the hydrogen-bonding patterns of two cholate ions and two deoxycholate ions are reflected in the P(cos β) distribution of the hydrogen-bonded neighbors (Figure 3). In general, these distributions are characterized by two peaks, with one between -1 and -0.5 and another one between 0.5 and 1. These peaks are marked as VI and VII, respectively. In the case of cholate, these peaks describe the relative orientations in which the B- and D-type oxygen atoms of the neighboring ions approach each other closely. Thus, in the antiparallel-like orientation VI, the two ions can form a hydrogen bond between their B-type atoms and another one between their D-type oxygen atoms, whereas the parallel-like orientation VII can be stabilized by two OB-OD hydrogen bonds (Figure 4a). On the other hand, in the case of deoxycholate, the antiparallel-like peak VI reflects the contribution of the ion pairs that are connected by one or two OA-OC hydrogen bonds and an OB-OB hydrogen bond (see, e.g., Figure 4e), whereas peak VII corresponds to the neighbors
Figure 7. Morphology maps (i.e., bivariate distribution of the I1/I2 and I2/I3 ratios of the three principal moments of inertia) of the CH clusters of the bile ions in the different systems studied. (left) All CH clusters are taken into account. (right) Only the clusters that are built up by at least three ions are taken into account in the 300 mM systems. Darker shades of gray indicate higher probabilities.
forming a B-B-type and, in some cases, also an A-A-type hydrogen bond with each other (Figure 4f).
4. Cluster Shape Analysis To characterize the general shape of the various different bile salt micelles, we have determined their three principal moments of inertia (i.e., the three eigenvalues of the inertia moment tensor), I1, I2, and I3, using the convention that
I1 e I2 e I3.
(1)
The ratio of two pairs of these three values (e.g., I1/I2 and I2/I3) can then be used to describe the shape of the given aggregate. Thus, for instance, for spherical micelles I1 ≈ I2 ≈ I3 and hence I1/I2 ≈ 1 and I2/I3 ≈ 1, for disklike aggregates I1 ≈ I2 , I3 and thus I1/I2 ≈ 1 and I2/I3 ≈ 0, whereas for rodlike clusters I1 , I2 ≈ I3 and thus I1/I2 ≈ 0 and I2/I3 ≈ 1. The statistics of the morphology of the various bile salt clusters can be described by the P(I1/I2, I2/I3) bivariate distribution of these two ratios of the principal moments of inertia. The P(I1/I2, I2/I3) morphology maps are shown in Figures 7-9 as obtained for the CH, CP, and CPH clusters, respectively, in the different systems investigated. The hydrogen-bonded (CH) aggregates (see Figure 7) give rise to various cluster shapes ranging between the {I1/I2 ≈ 1; I2/I3 ≈ 0.4} and {I1/I2 ≈ 0.8; I2/I3 ≈ 1} points of the morphology map. However, the majority of the CH clusters are just dimers,5 for which such a morphology analysis is of little relevance.
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Figure 10. Example of a spherical hydrophobically bound (CP) deoxycholate cluster containing an extra, self-solubilized deoxycholate ion in its hydrophobic interior, taken out from an instantaneous equilibrium configuration of the 300 mM deoxycholate system. The self-solubilized central ion is encircled by a dashed line for clarity. Color-coding is the same as that in Figure 1.
Figure 8. Morphology maps of the CP clusters of the bile ions in the different systems studied. (left) All CP clusters are taken into account. (right) Only the clusters that are built up by at least four ions are taken into account. Darker shades of gray indicate higher probabilities.
Figure 9. Morphology maps of the CPH clusters of the cholate (top) and deoxycholate (bottom) ions in the 300 mM systems studied. Only the clusters that are built up by at least five ions are taken into account. Darker shades of gray indicate higher probabilities.
Therefore, we have also calculated the P(I1/I2, I2/I3) distributions for the CH clusters that contain at least three bile ions in the 300 mM systems. (In the 30 mM systems, such clusters occur with very low probabilities,5 and hence, no statistically relevant analysis
of them can be performed.) The morphology maps of the large CH aggregates, contrary to the ones that take dimers also into account, show characteristic peaks at certain points (Figure 7). Thus, in the case of cholate, the maximum appears at I1/I2 ≈ 1 and I2/I3 ≈ 0.5, corresponding to an oblate ellipsoidal (or disklike) shape, that is, when the largest principal moment of inertia is about twice of the other two (see, e.g., the cluster on Figure 4d). On the other hand, the larger hydrogen-bonded deoxycholate aggregates are of rather spherical shape, as the peak of the corresponding P(I1/I2, I2/I3) distribution appears close to the {I1/ I2 ) 1; I2/I3 ) 1} corner of the map. The morphology maps of the CP clusters are shown in Figure 8 as obtained in the different systems studied. To eliminate again the effect of the small aggregates, we have repeated the analysis for clusters containing at least four bile ions. (We have also calculated the morphology maps of the CP clusters built up by at least three ions, but they were never found to be considerably different from those obtained for all the CP clusters, and therefore, these maps are omitted from Figure 8.) Not surprisingly, the maps including the contribution of even the dimers look rather similar to those obtained for all the CH clusters (including dimers). This similarity prevails when only larger aggregates are taken into account: deoxycholate ions form nearly spherical aggregates, whereas cholate ions form oblate or disk shaped hydrophobic aggregates. The observed differences in the typical shape of the cholate and deoxycholate aggregates ultimately originate in the fact that the cholate ion has a hydrophobic and a hydrophilic face, whereas deoxycholate ions are characterized by a hydrophilic edge only. In larger hydrogen-bonded aggregates, the deoxycholate ions turn toward each other, whereas in hydrophobic aggregates they turn away from each other by this hydrophilic edge, which allows a much more spherical arrangement of the ions than what can be reached through the face-to-face-like arrangement of the cholate ions. An example for such a large spherical hydrophobic deoxycholate micelle is shown in Figure 10. As can be seen, all the participating ions, with the exception of the central one, turn outward by their hydrophilic edge. This arrangement of the ions, however, results in a large hole in the middle of the aggregate, which is filled here by another deoxycholate ion (i.e., the central
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different irregular shapes for which I1 < I2 < I3. Examples for disklike, rodlike, and irregular shaped secondary micelles are shown in Figure 11. This wide variety of shapes of the existing secondary micelles can be explained by the fact that such micelles are formed due to the interplay of two different interactions. Namely, spherical or slightly aspherical oblate shaped primary hydrophobic micelles are linked together by forming hydrogen bonds with each other through the outward-oriented hydrophilic part of the constituting ions, resulting in various, often branching assemblies of these spherical or ellipsoidal objects.
5. Summary and Conclusions
Figure 11. Examples of (a) disklike, (b) rodlike, and (c) irregular shaped secondary micelles, taken out from instantaneous equilibrium configurations of the 300 mM systems simulated. Color-coding is the same as that in Figure 1.
one). This ability of the deoxycholate ions for self-solubilization can be of great importance in their major biological function of being the detergent of various fat-soluble nutrient molecules and vitamins, since the solubilization of these target solubilizates can simply occur by replacing the central bile ion occupying the hole readily present in the middle of the aggregate. The morphology of the secondary micelles can be characterized through the P(I1/I2, I2/I3) distribution of the CPH clusters (i.e., the aggregates that contain both H-bonded and P-bonded pairs). Again, small clusters (i.e., that are not true secondary micelles) have been excluded from the analysis: in calculating the morphology maps, only pentamers and larger CPH aggregates have been taken into account. Since such aggregates occur in the 30 mM systems with vanishingly small probabilities,5 these maps have only been calculated in the 300 mM systems. The obtained P(I1/I2, I2/I3) distributions, shown in Figure 9, indicate that the secondary micelles show a large variety of shapes, ranging from strongly aspherical, flattened oblates, when the two small principal moments of inertia are only 20-25% of the largest one, to slightly elongated prolates, when I1 ≈ 0.75I2 and I2 ≈ I3, through various
In this paper, we have analyzed the shape of various different (i.e., hydrogen-bonded or hydrophobic) primary micelles and large secondary micelles of cholate and deoxycholate ions. It is found that the unusual arrangement of the hydrophobic and hydrophilic groups leads to unusual micellar shapes. This effect is particularly evident in the case of the cholate ions, characterized by a hydrophobic and a hydrophilic face of a quasi-planar ring system. This molecular structure leads to flat, disklike or oblate shaped aggregates, for which the largest principal moment of inertia is about double that of the other two. The deoxycholate ions tend to form more spherical primary aggregates, irrespective of whether these aggregates are kept together by hydrogen bonds or hydrophobic interactions. The reason for this aggregate shape originates in the fact that the tetracyclic quasi-planar ring system of the deoxycholate ion is characterized by a hydrophilic edge rather than a hydrophilic face. Thus, face-to-face-type arrangements of the deoxycholate ions are far less dominant than those of the cholate ions; the deoxycholate micelles are organized according to the arrangement of the hydrophilic edges of the ions, which can result in quasi-spherical aggregate shapes. These aggregates are dominantly of hydrophobic origin.5 This type of arrangement of several deoxycholate ions can lead to the occurrence of micelles having a large hole in their middle, which can be filled by incorporating an extra deoxycholate ion. This self-solubilization ability of the deoxycholate ions can be of great importance in their primary biological role, since such aggregates keep the space where fat-soluble target solubilizate molecules can be readily incorporated by simply exchanging with the self-solubilized deoxycholate ion. Finally, the large secondary micelles exhibit a large variety of shapes, including rather irregular shapes, as well. This behavior can be understood by considering the fact that they are kept together by the simultaneous action of two markedly different interactions. Thus, these secondary aggregates can be regarded as assemblies of small, spherical or slightly aspherical oblate shaped elemental objects (primary micelles) that are linked together, forming complex objects (secondary micelles) of various shapes. Acknowledgment. This work has been supported by the Hungarian-Italian bilateral collaboration program between MTA and CNR and partly by the Hungarian OTKA Foundation under Project No. T049673. P.J. is an Eo¨tvo¨s fellow of the Hungarian State, which is gratefully acknowledged. P.J. also acknowledges support from the Hungarian Academy of Sciences through Bolyai Ja´nos fellowship. The simulations have partly been performed using the HPC facility of the Physics Department of the University of Trento. LA701749U
