A Standard Structure for Bile Acids and Derivatives

Francisco Meijide 1,*, Santiago de Frutos 1, Victor H. Soto 2, Aida Jover 1, Julio A. Seijas 3 ID , María Pilar Vázquez-Tato 3, Francisco Fraga 4 ID and José Vázquez Tato 1 1 Departamento de Química Física, Facultad de Ciencias, Universidad de Santiago de Compostela, Avda. Alfonso X El Sabio s/n, 27002 Lugo, Spain; santiagodefrutos@hotmail.com (S.d.F.); aida.jover@usc.es (A.J.); jose.vazquez@usc.es (J.V.T.) 2 Escuela de Química, Centro de Investigación en Electroquímica y Energía Química (CELEQ), Universidad de Costa Rica, 11501-2060 San José, Costa Rica; vsototellinie@gmail.com 3 Departamento de Química Orgánica, Facultad de Ciencias, Universidad de Santiago de Compostela, Avda. Alfonso X El Sabio s/n, 27002 Lugo, Spain; julioa.seijas@usc.es (J.A.S.); pilar.vazquez.tato@usc.es (M.P.V.-T.) 4 Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Santiago de Compostela, Avda. Alfonso X El Sabio s/n, 27002 Lugo, Spain; francisco.fraga@usc.es * Correspondence: francisco.meijide@usc.es

The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturallyoccurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (tbuthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers.
The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturallyoccurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (tbuthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers.
The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturallyoccurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (tbuthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers.
The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturallyoccurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (tbuthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers.
The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturallyoccurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (tbuthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers.
The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic- Modifications of the functional groups lead to a great number of BS derivatives, some naturally-occurring. For example, typical modifications of the terminal carboxylic acid group are ester (BE) and amide derivatives, while keto and amine groups are common modifications of the hydroxy groups. A variety of groups of different natures have also been linked to the steroid nucleus at the hydroxy group locations, mainly through ester and amide bonds. Compounds obtained by substitution at C3 have been particularly useful. Examples are derivatives with hydrophobic and bulky substituents (t-buthylphenyl, naphthyl, adamantyl), saccharides (mannose), and amino acids (tryptophan). In aqueous solution they behave as surfactants, the aggregates showing a wide range of structures. The subject has been reviewed recently [18]. On the other hand, the head-tail structure of BS allows the synthesis of head-to-head [19], head-to-tail [20], and tail-to-tail [21] dimers. The ratio of number of steroid groups to number of charged groups (equal to 1 in natural BS) can be easily modified for monomers, dimers, and oligomers. Consequently, the hydrophobic-hydrophilic balance of the compound is either increased or reduced, thus modifying its self-aggregation in aqueous solution. Several papers dealing with the physicochemical properties and applications in fields such as supramolecular chemistry, biomedicine, and pharmaceutics have been reported [18,[22][23][24][25][26][27][28].
The characterization of the crystal structures of BS and BA by X-ray analysis has been a topic of interest [29,30]. This knowledge can be very useful for the proposition of the structure of BS aggregates in aqueous solution, a strategy firstly and largely employed by Giglio and coworkers [31], and of the supramolecular structures of BS derivatives [32]. Miyata et al. [33][34][35][36] have carried out studies on BA crystals in a large variety of solvents and guests, also systematically modified the steroid structure. It can be concluded from these studies that the solid state structure depends on subtle differences in donor-acceptor relationships among the hydrogen bonding groups of guest and steroid molecules. The solution of the crystal structures of the four 3,12-dihydroxy epimers of DCA was used to successfully predict the hydrogen bond network of the 3-oxo-12α-hydroxy derivative [8]. On the other hand, the ability to form hydrogen bonds by CA plus the characteristics of head-to-head dimers have been used for designing a crystal, in which a single water molecule is encapsulated between two cholic residues in an ice-like structure [17]. Miyata et al. have also studied the supramolecular chirality in crystals generated from chiral [37][38][39][40] and achiral [41,42] molecules, and rationalized a hierarchical organization in BA crystals like that in proteins [3,43,44].
Nowadays interesting and promising applications have emerged, mainly related to the ability of BA to form inclusion compounds in the solid state. For example, the crystallization may be used for the resolution of racemates [13,[45][46][47][48][49][50] and for the delayed release of drugs [32].
Although BS have been the object of numerous studies by different techniques concerning to their surfactant behavior in solution, the number of publications related to their crystal structures is limited, and much lower than those corresponding to BA and BE. Some structures of the derivatives outlined before in the solid state have also been reported, including some dimers. In the case of head-to-head dimers, an internal coordinate system consisting of five angles (three torsion and two common) has been proposed [51] to describe the relative orientation in the space of the two bile acid residues.
When analyzing the structure of steroid derivatives, most of the studies have mainly focused the attention on the flexibility of the side chain and on the hydrogen bond network, while the structure of the steroid nucleus is barely mentioned, with the exception of the D-ring conformation. Only some recent papers have introduced the analysis of the angle formed by horizontal and vertical planes [10] and the angle between C3-C10-C13 carbon atoms [51]. The comparison of structural data from published crystal structures of bile acid derivatives will provide information on the constancy (or lack thereof) of the geometrical parameters of the steroid nucleus. It will also allow for obtaining the average geometrical parameters of the steroid nucleus. Thus, average distances and bond angles of the cyclopentanoperhydrophenanthrene skeleton and the lateral chain can be obtained. This average structure can be useful as a standard reference for further comparative studies. For example, it will allow for the analysis of the resulting geometry when important chemical modifications are introduced to the structure.
In this paper, we analyze the crystal structures of two BEs derived from CA: a dimer with the two steroid units linked by a urea bridge (30, Table 2), and a monomer with an amino isophthalic residue attached to the C3 position of the steroid nucleus (24, Table 1). The geometric characteristics of these two BEs, together with those corresponding to 28 other structures (mainly from CA and DCA solved by our research group, Tables 1 and 2), are used to construct the standard steroid. Table 2. Chemical structure and partial numbering of the dimers analyzed in this paper (30/AcOEt and 30/DMSO make reference to the recrystallization solvent included as a guest in the crystal structure).

Synthesis
To synthesize compound 24, 0.77 mL (4.55 mmol) of DEPC were added to a dispersion of 2 g (4.75 mmol) of methyl 3β-aminocholate (the synthesis of this reactive has been well-established [53]), in 15 mL of dimethylformamide under an argon atmosphere. Once the solid was dissolved, 2.32 g (5.5 mmol) of 5-t-butoxycarbonylaminoisophthalic acid was added, and the mixture was stirred for 10 min (the protection of the amino group of the amino isophthalic acid with di-tert-butyl dicarbonate (BOC) is also a well-known synthetic process [54]. After cooling at 0 °C, 1 mL (7 mmol) of triethylamine was added dropwise. The reaction mixture was maintained at this temperature for 45 min, and then at room temperature for 6 hours. DMF was evaporated under reduced pressure; the reaction crude dissolved in 200 mL of ethyl acetate and was washed with 3 × 75 mL of water. The organic phase was dried with sodium sulphate, concentrated, and purified by column chromatography with 20:1 ethyl acetate:methanol. Finally, BOC was removed, dissolving 2 g of the product obtained in the last step in 50 mL of methanol and bubbling HCl gas for 30 min. After evaporation of the solvent, 100 mL of water was added, and the solution was neutralized with 1 M NaOH until neutral pH in an ice bath. The solid corresponding to compound 24 was filtered, washed with abundant water, and dried in a vacuum oven. Its characterization was done by X-ray diffraction.
The synthesis of the dimer listed as compound 30 has been reported previously [51].

X-ray Diffraction Analysis
Colorless prismatic crystals of compound 24 were obtained from methanol, and crystals of compound 30 in ethyl acetate/methanol. X-ray diffraction data for both compounds were collected on a Bruker Smart-CCD-1000 at the temperature of 100 K. Molecular graphics were made with Mercury software. CIF files are available as electronic supporting material. CCDC 1812924 and 1812925 contain the supplementary crystallographic data for compounds 24 and 30, respectively, and can be obtained free of charge from The Cambridge Crystallographic Data Center.

Results and Discussion
α-OH β-NH

Synthesis
To synthesize compound 24, 0.77 mL (4.55 mmol) of DEPC were added to a dispersion of 2 g (4.75 mmol) of methyl 3β-aminocholate (the synthesis of this reactive has been well-established [53]), in 15 mL of dimethylformamide under an argon atmosphere. Once the solid was dissolved, 2.32 g (5.5 mmol) of 5-t-butoxycarbonylaminoisophthalic acid was added, and the mixture was stirred for 10 min (the protection of the amino group of the amino isophthalic acid with di-tert-butyl dicarbonate (BOC) is also a well-known synthetic process [54]. After cooling at 0 °C, 1 mL (7 mmol) of triethylamine was added dropwise. The reaction mixture was maintained at this temperature for 45 min, and then at room temperature for 6 hours. DMF was evaporated under reduced pressure; the reaction crude dissolved in 200 mL of ethyl acetate and was washed with 3 × 75 mL of water. The organic phase was dried with sodium sulphate, concentrated, and purified by column chromatography with 20:1 ethyl acetate:methanol. Finally, BOC was removed, dissolving 2 g of the product obtained in the last step in 50 mL of methanol and bubbling HCl gas for 30 min. After evaporation of the solvent, 100 mL of water was added, and the solution was neutralized with 1 M NaOH until neutral pH in an ice bath. The solid corresponding to compound 24 was filtered, washed with abundant water, and dried in a vacuum oven. Its characterization was done by X-ray diffraction.
The synthesis of the dimer listed as compound 30 has been reported previously [51].

X-ray Diffraction Analysis
Colorless prismatic crystals of compound 24 were obtained from methanol, and crystals of compound 30 in ethyl acetate/methanol. X-ray diffraction data for both compounds were collected on a Bruker Smart-CCD-1000 at the temperature of 100 K. Molecular graphics were made with Mercury software. CIF files are available as electronic supporting material. CCDC 1812924 and 1812925 contain the supplementary crystallographic data for compounds 24 and 30, respectively, and can be obtained free of charge from The Cambridge Crystallographic Data Center.

Synthesis
To synthesize compound 24, 0.77 mL (4.55 mmol) of DEPC were added to a dispersion of 2 g (4.75 mmol) of methyl 3β-aminocholate (the synthesis of this reactive has been well-established [53]), in 15 mL of dimethylformamide under an argon atmosphere. Once the solid was dissolved, 2.32 g (5.5 mmol) of 5-t-butoxycarbonylaminoisophthalic acid was added, and the mixture was stirred for 10 min (the protection of the amino group of the amino isophthalic acid with di-tert-butyl dicarbonate (BOC) is also a well-known synthetic process [54]. After cooling at 0 °C, 1 mL (7 mmol) of triethylamine was added dropwise. The reaction mixture was maintained at this temperature for 45 min, and then at room temperature for 6 hours. DMF was evaporated under reduced pressure; the reaction crude dissolved in 200 mL of ethyl acetate and was washed with 3 × 75 mL of water. The organic phase was dried with sodium sulphate, concentrated, and purified by column chromatography with 20:1 ethyl acetate:methanol. Finally, BOC was removed, dissolving 2 g of the product obtained in the last step in 50 mL of methanol and bubbling HCl gas for 30 min. After evaporation of the solvent, 100 mL of water was added, and the solution was neutralized with 1 M NaOH until neutral pH in an ice bath. The solid corresponding to compound 24 was filtered, washed with abundant water, and dried in a vacuum oven. Its characterization was done by X-ray diffraction.
The synthesis of the dimer listed as compound 30 has been reported previously [51].

X-ray Diffraction Analysis
Colorless prismatic crystals of compound 24 were obtained from methanol, and crystals of compound 30 in ethyl acetate/methanol. X-ray diffraction data for both compounds were collected on a Bruker Smart-CCD-1000 at the temperature of 100 K. Molecular graphics were made with Mercury software. CIF files are available as electronic supporting material. CCDC 1812924 and 1812925 contain the supplementary crystallographic data for compounds 24 and 30, respectively, and can be obtained free of charge from The Cambridge Crystallographic Data Center.

Synthesis
To synthesize compound 24, 0.77 mL (4.55 mmol) of DEPC were added to a dispersion of 2 g (4.75 mmol) of methyl 3β-aminocholate (the synthesis of this reactive has been well-established [53]), in 15 mL of dimethylformamide under an argon atmosphere. Once the solid was dissolved, 2.32 g (5.5 mmol) of 5-t-butoxycarbonylaminoisophthalic acid was added, and the mixture was stirred for 10 min (the protection of the amino group of the amino isophthalic acid with di-tert-butyl dicarbonate (BOC) is also a well-known synthetic process [54]. After cooling at 0 °C, 1 mL (7 mmol) of triethylamine was added dropwise. The reaction mixture was maintained at this temperature for 45 min, and then at room temperature for 6 hours. DMF was evaporated under reduced pressure; the reaction crude dissolved in 200 mL of ethyl acetate and was washed with 3 × 75 mL of water. The organic phase was dried with sodium sulphate, concentrated, and purified by column chromatography with 20:1 ethyl acetate:methanol. Finally, BOC was removed, dissolving 2 g of the product obtained in the last step in 50 mL of methanol and bubbling HCl gas for 30 min. After evaporation of the solvent, 100 mL of water was added, and the solution was neutralized with 1 M NaOH until neutral pH in an ice bath. The solid corresponding to compound 24 was filtered, washed with abundant water, and dried in a vacuum oven. Its characterization was done by X-ray diffraction.
The synthesis of the dimer listed as compound 30 has been reported previously [51].

X-ray Diffraction Analysis
Colorless prismatic crystals of compound 24 were obtained from methanol, and crystals of compound 30 in ethyl acetate/methanol. X-ray diffraction data for both compounds were collected on a Bruker Smart-CCD-1000 at the temperature of 100 K. Molecular graphics were made with Mercury software. CIF files are available as electronic supporting material. CCDC 1812924 and 1812925 contain the supplementary crystallographic data for compounds 24 and 30, respectively, and can be obtained free of charge from The Cambridge Crystallographic Data Center.

Synthesis
To synthesize compound 24, 0.77 mL (4.55 mmol) of DEPC were added to a dispersion of 2 g (4.75 mmol) of methyl 3β-aminocholate (the synthesis of this reactive has been well-established [53]), in 15 mL of dimethylformamide under an argon atmosphere. Once the solid was dissolved, 2.32 g (5.5 mmol) of 5-t-butoxycarbonylaminoisophthalic acid was added, and the mixture was stirred for 10 min (the protection of the amino group of the amino isophthalic acid with di-tert-butyl dicarbonate (BOC) is also a well-known synthetic process [54]. After cooling at 0 • C, 1 mL (7 mmol) of triethylamine was added dropwise. The reaction mixture was maintained at this temperature for 45 min, and then at room temperature for 6 h. DMF was evaporated under reduced pressure; the reaction crude dissolved in 200 mL of ethyl acetate and was washed with 3 × 75 mL of water. The organic phase was dried with sodium sulphate, concentrated, and purified by column chromatography with 20:1 ethyl acetate:methanol. Finally, BOC was removed, dissolving 2 g of the product obtained in the last step in 50 mL of methanol and bubbling HCl gas for 30 min. After evaporation of the solvent, 100 mL of water was added, and the solution was neutralized with 1 M NaOH until neutral pH in an ice bath. The solid corresponding to compound 24 was filtered, washed with abundant water, and dried in a vacuum oven. Its characterization was done by X-ray diffraction.
The synthesis of the dimer listed as compound 30 has been reported previously [51].

X-ray Diffraction Analysis
Colorless prismatic crystals of compound 24 were obtained from methanol, and crystals of compound 30 in ethyl acetate/methanol. X-ray diffraction data for both compounds were collected on a Bruker Smart-CCD-1000 at the temperature of 100 K. Molecular graphics were made with Mercury software. CIF files are available as electronic supporting material. CCDC 1812924 and 1812925 contain the supplementary crystallographic data for compounds 24 and 30, respectively, and can be obtained free of charge from The Cambridge Crystallographic Data Center.

Dimer
The crystal structure of compound 30 from DMSO/methanol has been obtained and published [52] (we will refer to it as 30/DMSO). In this paper, we instead describe the crystal obtained from ethyl acetate/methanol (30/AcOEt). Table 3 shows a summary of the crystal data and experimental details. The dimer crystallized in the P2 1 2 1 2 1 space group, and its packing showed a bilayer structure, with alternating hydrophobic and hydrophilic layers. The horizontal planes [10] of the two cholic residues were almost parallel (0.92 • being the angle between them), meaning that their α-faces are oriented to the same direction, transmitting the bifacial character of each steroid residue to the dimer. Within the layers, dimers are located in a face-to-face orientation, with β-interdigitation between C18 and C19 methyl groups (Figure 1a), contributing to the stabilization of the bilayer by hydrophobic forces (a similar situation appears in 30/DMSO, Figure 1b).  Additional stabilization arises from the hydrogen bonding network, involving the nitrogen and oxygen atoms of the urea bridge (all O7H and O12H groups), and one of the two carboxylic terminal groups of the dimer. The hydrogen bonding pattern in the constituent monomer, with the free carboxylic group (without hydrogen bonds), is the same as in 30/DMSO. The lateral chains adopt a tttt conformation in both cases. In the other monomer, the hydrogen bond pattern is the same as in 30/DMSO, except for an additional bond between O7H and water ( Figure 2). This difference could explain why this monomer in 30/AcOEt adopts a ttgitg conformation while in 30/DMSO it also adopts a tttt one. The angle between horizontal planes is higher in 30/DMSO (4.9°), and the angles between vertical planes are 1.2 and 8.7° in 30/DMSO and 30/AcOEt, respectively.  Additional stabilization arises from the hydrogen bonding network, involving the nitrogen and oxygen atoms of the urea bridge (all O7H and O12H groups), and one of the two carboxylic terminal groups of the dimer. The hydrogen bonding pattern in the constituent monomer, with the free carboxylic group (without hydrogen bonds), is the same as in 30/DMSO. The lateral chains adopt a tttt conformation in both cases. In the other monomer, the hydrogen bond pattern is the same as in 30/DMSO, except for an additional bond between O7H and water ( Figure 2). This difference could explain why this monomer in 30/AcOEt adopts a ttgi tg conformation while in 30/DMSO it also adopts a tttt one. The angle between horizontal planes is higher in 30/DMSO (4.9 • ), and the angles between vertical planes are 1.2 • and 8.7 • in 30/DMSO and 30/AcOEt, respectively. Additional stabilization arises from the hydrogen bonding network, involving the nitrogen and oxygen atoms of the urea bridge (all O7H and O12H groups), and one of the two carboxylic terminal groups of the dimer. The hydrogen bonding pattern in the constituent monomer, with the free carboxylic group (without hydrogen bonds), is the same as in 30/DMSO. The lateral chains adopt a tttt conformation in both cases. In the other monomer, the hydrogen bond pattern is the same as in 30/DMSO, except for an additional bond between O7H and water ( Figure 2). This difference could explain why this monomer in 30/AcOEt adopts a ttgitg conformation while in 30/DMSO it also adopts a tttt one. The angle between horizontal planes is higher in 30/DMSO (4.9°), and the angles between vertical planes are 1.2 and 8.7° in 30/DMSO and 30/AcOEt, respectively.  Although many analogies have been found between 30/DMSO and 30/AcOEt, the main difference between the two crystal structures concerns the constitution of the bilayers. Although the bilayers in both structures have similar widths (11.36 Å in 30/DMSO and 10.98 Å in 30/AcOEt), they are linear in 30/DMSO and corrugated in 30/AcOEt (Figure 1). The result is that the crystals belong to different space groups, being monoclinic I2 for 30/DMSO. This agrees with the well-known fact that the solvent can modify the final crystal structure of bile acids and derivatives [14,55,56]. Table 4 shows details of the crystal structures for these and other different BE dimers. As a brief summary of the conclusions deduced by comparison of the results we can mention: 1) Four of the five dimers crystallize in the monoclinic crystal system, three of them in the P21 and the other in the I2. In this case, corresponding to 30/DMSO, apart from the screw axis typical of the P21 crystals, the crystal structure also presents a centring vector [1/2,1/2,1/2] and a 2-fold rotation axis with direction [0,1,0] at 0,y,0. The crystal corresponding to the remaining dimer, 30/AcOEt, is orthorhombic P212121.
2) The tet conformation is the most common one. 3) All these dimers have the tendency to be arranged with the lateral chains fully or nearly fully extended. 4) With the exception of 28, in the crystal structures of the other three dimers where the molecules are arranged in bilayers, these are β interdigitated. The bilayers are corrugated in 30/AcOEt and 28 and linear in 30/DMSO and 27. The thicknesses of the corrugated bilayers are slightly smaller than the thicknesses of the linear bilayers (Table 4).

Monomer
A summary of the crystal data and experimental details corresponding to this diester derivative of CA (with a 5-amino-isophthalic group attached to the 3β position of the steroid nucleus, through an amide bond in compound 24) is listed in Table 3. This dimer crystallizes in the monoclinic P21 space group with one guest water molecule, having the asymmetric unit formed by two different molecules of the steroid. The main difference between these two molecules concerns the conformation of the D ring, since the phase angle of pseudorotation values [57] are indicatives of half chair and close to β-envelope conformations. However, the conformations of the lateral chains are very similar, both being tgtt. Figure 4 presents the view of packing in the crystal along the b axis, and shows a bilayer organization of α interdigitated molecules, with a width of 13.54 Å. This bilayer is stabilized by  (Figure 1). The result is that the crystals belong to different space groups, being monoclinic I2 for 30/DMSO. This agrees with the well-known fact that the solvent can modify the final crystal structure of bile acids and derivatives [14,55,56]. Table 4 shows details of the crystal structures for these and other different BE dimers. As a brief summary of the conclusions deduced by comparison of the results we can mention: (1) Four of the five dimers crystallize in the monoclinic crystal system, three of them in the P2 1 and the other in the I2. In this case, corresponding to 30/DMSO, apart from the screw axis typical of the P2 1 crystals, the crystal structure also presents a centring vector [1/2,1/2,1/2] and a 2-fold rotation axis with direction [0,1,0] at 0,y,0. The crystal corresponding to the remaining dimer, 30/AcOEt, is orthorhombic P2 1 (Table 4).

Monomer
A summary of the crystal data and experimental details corresponding to this diester derivative of CA (with a 5-amino-isophthalic group attached to the 3β position of the steroid nucleus, through an amide bond in compound 24) is listed in Table 3. This dimer crystallizes in the monoclinic P2 1 space group with one guest water molecule, having the asymmetric unit formed by two different molecules of the steroid. The main difference between these two molecules concerns the conformation of the D ring, since the phase angle of pseudorotation values [57] are indicatives of half chair and close to β-envelope conformations. However, the conformations of the lateral chains are very similar, both being tgtt. Figure 4 presents the view of packing in the crystal along the b axis, and shows a bilayer organization of α interdigitated molecules, with a width of 13.54 Å. This bilayer is stabilized by hydrogen bonds between molecules of the same geometry (identical color in Figure 4), as well as by a π-π stacking between the aromatic rings of two molecules with different geometry (different color in Figure 4). The aromatic planes are almost parallel (with an angle of 1.97 • ), the benzyl rings being slightly displaced. The distance between their centroids is 3.349 Å ( Figure 5) and the distance of the centroid-aromatic plane is 3.193 Å. These values are similar to those published for other aromatic compounds [58], including graphite [59]. On the other hand, the limit to the π-π interaction is the summation of the van der Waals radii between the involved atoms. Alvarez [60] has suggested that an accurate van der Waals radius for the carbon atom is equal to 1.77 Å. Therefore, the maximum distance for a π-π interaction would be 3.54 Å, a value which agrees well with the one given above. hydrogen bonds between molecules of the same geometry (identical color in Figure 4), as well as by a π-π stacking between the aromatic rings of two molecules with different geometry (different color in Figure 4). The aromatic planes are almost parallel (with an angle of 1.97°), the benzyl rings being slightly displaced. The distance between their centroids is 3.349 Å ( Figure 5) and the distance of the centroid-aromatic plane is 3.193 Å. These values are similar to those published for other aromatic compounds [58], including graphite [59]. On the other hand, the limit to the π-π interaction is the summation of the van der Waals radii between the involved atoms. Alvarez [60] has suggested that an accurate van der Waals radius for the carbon atom is equal to 1.77 Å. Therefore, the maximum distance for a π-π interaction would be 3.54 Å, a value which agrees well with the one given above.  It is remarkable that only molecules with different symmetry are linked through hydrogen bonds, the pattern being the same for both molecules. The interaction implies the amide C=O, O7H and O12H groups. This last group acts as an acceptor from water hosted at the hydrophilic part of the bilayer. Neither the ester at the lateral chain, nor the amine group in the aromatic substituent participates in the hydrogen bonding network in the crystal.

Standard Steroid
We have analyzed the structures of the steroid moiety of all the compounds listed in Tables 1  and 2, paying attention to the bond distances and bond angles between carbon atoms. Some compounds were recrystallized from several solvents (resulting in their inclusion as guests), while others crystallized with two different molecules in the asymmetric unit. The total number of data is 48. Table 5 shows the values of the mean distances between bonded carbon atoms in the steroid skeleton, including the 18 and 19 methyl groups and the atoms of the lateral chain. The shortest and largest lengths are 1.502 ± 0.020 Å and 1.558 ± 0.010 Å, corresponding to C23-C24 and C9-C10 bonds, respectively. As expected, the differences in the distances among the different compounds analyzed are small, particularly in the more condensed B and C rings. Figure 6a analyzes those results according to the standard deviations in the bond lengths, which are less than 0.01 Å (those in green), between 0.01 and 0.015 Å (those in black), and greater than 0.015 Å (those in red). In a similar way, hydrogen bonds between molecules of the same geometry (identical color in Figure 4), as well as by a π-π stacking between the aromatic rings of two molecules with different geometry (different color in Figure 4). The aromatic planes are almost parallel (with an angle of 1.97°), the benzyl rings being slightly displaced. The distance between their centroids is 3.349 Å ( Figure 5) and the distance of the centroid-aromatic plane is 3.193 Å. These values are similar to those published for other aromatic compounds [58], including graphite [59]. On the other hand, the limit to the π-π interaction is the summation of the van der Waals radii between the involved atoms. Alvarez [60] has suggested that an accurate van der Waals radius for the carbon atom is equal to 1.77 Å. Therefore, the maximum distance for a π-π interaction would be 3.54 Å, a value which agrees well with the one given above.  It is remarkable that only molecules with different symmetry are linked through hydrogen bonds, the pattern being the same for both molecules. The interaction implies the amide C=O, O7H and O12H groups. This last group acts as an acceptor from water hosted at the hydrophilic part of the bilayer. Neither the ester at the lateral chain, nor the amine group in the aromatic substituent participates in the hydrogen bonding network in the crystal.

Standard Steroid
We have analyzed the structures of the steroid moiety of all the compounds listed in Tables 1  and 2, paying attention to the bond distances and bond angles between carbon atoms. Some compounds were recrystallized from several solvents (resulting in their inclusion as guests), while others crystallized with two different molecules in the asymmetric unit. The total number of data is 48. Table 5 shows the values of the mean distances between bonded carbon atoms in the steroid skeleton, including the 18 and 19 methyl groups and the atoms of the lateral chain. The shortest and largest lengths are 1.502 ± 0.020 Å and 1.558 ± 0.010 Å, corresponding to C23-C24 and C9-C10 bonds, respectively. As expected, the differences in the distances among the different compounds analyzed are small, particularly in the more condensed B and C rings. Figure 6a analyzes those results according to the standard deviations in the bond lengths, which are less than 0.01 Å (those in green), between 0.01 and 0.015 Å (those in black), and greater than 0.015 Å (those in red). In a similar way, Figure 5. View of the crystal packing of compound 24 along a direction in which the π-π interaction is clearly seen. The red points correspond to the centroids of the involved aromatic rings.
It is remarkable that only molecules with different symmetry are linked through hydrogen bonds, the pattern being the same for both molecules. The interaction implies the amide C=O, O7H and O12H groups. This last group acts as an acceptor from water hosted at the hydrophilic part of the bilayer. Neither the ester at the lateral chain, nor the amine group in the aromatic substituent participates in the hydrogen bonding network in the crystal.

Standard Steroid
We have analyzed the structures of the steroid moiety of all the compounds listed in Tables 1 and 2, paying attention to the bond distances and bond angles between carbon atoms. Some compounds were recrystallized from several solvents (resulting in their inclusion as guests), while others crystallized with two different molecules in the asymmetric unit. The total number of data is 48. Table 5 shows the values of the mean distances between bonded carbon atoms in the steroid skeleton, including the 18 and 19 methyl groups and the atoms of the lateral chain. The shortest and largest lengths are 1.502 ± 0.020 Å and 1.558 ± 0.010 Å, corresponding to C23-C24 and C9-C10 bonds, respectively. As expected, the differences in the distances among the different compounds analyzed are small, particularly in the more condensed B and C rings. Figure 6a analyzes those results according to the standard deviations in the bond lengths, which are less than 0.01 Å (those in green), between 0.01 and 0.015 Å (those in black), and greater than 0.015 Å (those in red). In a similar way, we have determined the mean values of all the angles between consecutive carbon atoms in the steroid nucleus and the lateral chain, the results being recompiled in Table 6 (the angle C2-C3-C4 was not considered for 11 because of the sp 2 hybridization of the central atom). The highest value corresponds to the C13-C17-C20 angle (119.4 • ), and the lowest to C17-C13-C14 (100.2 • ) inside the cyclopentane ring. The angle C17-C20-C22 (in the flexible lateral chain) shows the highest standard deviation, and surprisingly, the angle C9-C10-C19 presents the highest constancy of values for the compounds analyzed. The results were also analyzed according to their standard deviations in Figure 6b ( we have determined the mean values of all the angles between consecutive carbon atoms in the steroid nucleus and the lateral chain, the results being recompiled in Table 6 (the angle C2-C3-C4 was not considered for 11 because of the sp 2 hybridization of the central atom). The highest value corresponds to the C13-C17-C20 angle (119.4°), and the lowest to C17-C13-C14 (100.2°) inside the cyclopentane ring. The angle C17-C20-C22 (in the flexible lateral chain) shows the highest standard deviation, and surprisingly, the angle C9-C10-C19 presents the highest constancy of values for the compounds analyzed. The results were also analyzed according to their standard deviations in Figure  6b (color code: ≤0.75° green, 0.75-1.50° black, and >1.50° red).     [62]. Since the asymmetric unit in the crystal of cholesterol has eight molecules, mean values of bond distances and bond angles were calculated for comparison purposes. In progesterone, apart from the length corresponding to the C4-C5 double bond, the other lengths presenting differences with the standard steroid (greater than 0.015 Å) are those corresponding to the C4-C5 bond's neighbors (C3-C4 and C5-C10), as well as the C2-C3, C5-C6 and C9-C10 bonds. Excluding the bond angles in which C2, C3, and C4 atoms (participating in double bonds) are involved, the remaining values do not differ greatly from those of the standard steroid. In fact, the differences between them are similar to those observed between the compounds used to define the standard steroid.
In cholesterol, only the C23-C24 bond length is greater than 0.015 Å in comparison to this length in the standard steroid. On the other hand, the differences between the bond angles are very small, the greatest being 2.2° in the C22-C23-C24 bond angle.
Although significant changes are not to be expected, we have also calculated the angles between the horizontal and vertical planes for the steroid molecules in the 48 structures resulting in the crystal packings. The results are shown in Table 7, and the main conclusion is the confirmation of the validity of these two planes for comparisons and discussions. The average angle value for the standard steroid is 88.2 ± 0.5°. Therefore, the standard steroid defined here behaves very well in the discussed aspects. Table 7. Values of the angles between the horizontal and vertical planes, and conformations of the lateral chain in the steroids analyzed in this paper (a and b refer either to the two molecules in the asymmetric unit, or to the two monomers in a dimer).

Compound
Angle  In progesterone, apart from the length corresponding to the C4-C5 double bond, the other lengths presenting differences with the standard steroid (greater than 0.015 Å) are those corresponding to the C4-C5 bond's neighbors (C3-C4 and C5-C10), as well as the C2-C3, C5-C6 and C9-C10 bonds. Excluding the bond angles in which C2, C3, and C4 atoms (participating in double bonds) are involved, the remaining values do not differ greatly from those of the standard steroid. In fact, the differences between them are similar to those observed between the compounds used to define the standard steroid.
In cholesterol, only the C23-C24 bond length is greater than 0.015 Å in comparison to this length in the standard steroid. On the other hand, the differences between the bond angles are very small, the greatest being 2.2 • in the C22-C23-C24 bond angle.
Although significant changes are not to be expected, we have also calculated the angles between the horizontal and vertical planes for the steroid molecules in the 48 structures resulting in the crystal packings. The results are shown in Table 7, and the main conclusion is the confirmation of the validity of these two planes for comparisons and discussions. The average angle value for the standard steroid is 88.2 ± 0.5 • . Therefore, the standard steroid defined here behaves very well in the discussed aspects. Table 7. Values of the angles between the horizontal and vertical planes, and conformations of the lateral chain in the steroids analyzed in this paper (a and b refer either to the two molecules in the asymmetric unit, or to the two monomers in a dimer).

Compound
Angle The analysis of the conformation of the lateral chain can be made through the positions of its atoms with respect to the horizontal and vertical planes (for example), or through the torsion angles from C17 to C23. However, the geometric requirements needed for the establishment of hydrogen bonds a priori indicate that the result can be very variable (see above). Therefore, for discussing the lateral chains, the second option is more appropriate. Results are recompiled in Table 7. With the exceptions of derivatives, compounds 4 and 5 (for which it is gauche), the other 46 crystal structures have trans conformations in the C13-C17-C20-C22 torsion angle. This predominant conformation is a consequence of the torsion angle C13-C17-C20-C21, which, being in the narrow range −53/−60 • , corresponds to a minimum in the energy profile for cholanic acids and related compounds [63]. This minimum is also associated with values of about 60 and −170 • for C17-C20-C22-C23 (the second torsion angle), corresponding to gauche and trans conformations, respectively. Of the found conformations, 75% are trans, and the remaining are gauche. The mentioned minimum has also values around 50 (gauche), 165 (trans), and −95 • (intermediate between gauche and trans, i tg ) for C20-C22-C23-C24. For this third torsion angle, the trans conformation appears in 71% of the crystal structures, while 29% are gauche. Finally, the conformations found for the torsion angle C22-C23-C24-O24a are the following: trans 55.5%, i tg 19%, gauche 17%, and cis 8.5%. Therefore, the variability in the conformations is greater when we move to the end of the lateral change (although trans conformations are the most common ones). This fact is a consequence of the fact that the atoms of the carboxylic group adopt positions controlled by the formation of hydrogen bonds (favored by the flexibility of the lateral chain in cholanic acids), and such a conformation is not characteristic of a specific BA and their derivatives. Indeed, the cis conformation appears in two epimers of DCA (compounds 4 and 6), the azide derivative of CA compound 23, and one of the molecules of the dimer compound 29 (the one in which its lateral chain does not participate in hydrogen bonding).
Finally, we have recompiled some information about the hydrogen bonding network in the crystal structures of monomers. We have considered the compounds with hydroxy, oxo, or amide groups at the C3 position, and hydroxy groups at the C7 or C12 positions, i.e., all the compounds of Table 3 excluding the amine (compounds 12, 21 and 22), azide (compound 23) and ester (compound 26) derivatives. The participation of water as a guest was also considered, but not other solvents. Table 8 shows the mean distances of the donor-H/acceptor systems determined from the analysis of the structures, where the donor/acceptor behavior is not specified. In the Table, values without standard deviations were found in only one crystal. It may be noticed that O3H can form hydrogen bonds with any of the hydrophylic groups present in the steroids, with the exception of the amide group (when present) and itself. This last observation also applies to O12H, but not to O7H. In only one structure, compound 8, the carboxylic groups directly formed a hydrogen bond. All the values are within accepted ones for hydrogen bonds.
In cholesterol, which only has one hydroxy group at C3, only a O3/O3 hydrogen bond is possible. The average bond length for that bond is 2.87 ± 0.07 Å. In the absence of an appropriate solvent, progesterone cannot form any hydrogen bond.