Quantum chemical treatment of β-sitosterol molecule

Abstract

β-Sitosterol is used as a dietary supplement for lowering plasma cholesterol, and has atherosclerosis preventive, anti-inflammatory, antimicrobial, antipyretic, induced apoptosis, and anticancer effects. In order to understand the effect of the molecule we have investigated the molecule theoretically. The structural, vibrational, and electronic properties of the β-sitosterol molecule have been investigated theoretically by performing molecular mechanics (MM+ force field), semiempirical self-consistent-field molecular-orbital (PM3), and density functional theory (B3LYP) calculations. The geometry of the considered molecule has been optimized; the vibrational dynamics and the electronic properties have been calculated in its ground state in the gas phase. The optimized structure of the molecule is not planar, and its heat of formation is exothermic. The calculated infrared spectrum for β-sitosterol agrees well qualitatively with the experimentally determined FTIR spectrum. The interfrontier molecular orbitals are localized mainly on the double C-C bond, and the energy difference of the corresponding orbitals is relatively small, which makes the molecule kinetically stable. According to the calculated dipole moment, β-sitosterol is a polar molecule. The calculated results for the β-sitosterol molecule in the present study will aid in elucidation of the mechanism of action and may further be used in lipid metabolism drug design studies.

Keywords::

• β-Sitosterol
• density functional theory method
• MM method
• semiempirical PM3 method

Introduction

Epidemiological studies have shown that the consumption of a diet rich in vegetables and fruits reduces the incidence of various types of cancer, diabetes, and cardiovascular and other chronic diseases, with a possible contribution from plant sterols (Ling & Jones, 1995; Pegel, 1997; Stone & Van Horn, 2002; Leitzmann, 2005; Rudkowska, 2008).

Plant sterols are found in large amounts in vegetables, in unrefined plant oils, seeds, nuts, and legumes, and enter the mammalian body only via the diet. Animals can synthesize only cholesterol, whereas plants produce little cholesterol but β-sitosterol, stigmasterol, and campesterol as the major sterols. About half of the dietary cholesterol and merely 5% to sometimes 12.5% of plant sterols are absorbed and are detectable in the blood (Heinemann et al., 1993; Pegel, 1997; Bosner et al., 1999; Gylling & Miettinen, 2005; Ryan et al., 2007; Vecka et al., 2007). A specific and regulatory transporter system (ABCG5 or ABCG8) functions in absorption and resecretion back into the enteric lumen. Sitosterol binds selectively to the transporters. Genetic mutations may lead to an accumulation of plant sterols in different tissues with different biological effects. Since plant sterols are not metabolized, their plasma concentrations depend on their intestinal absorption and biliary elimination rates. Consumption of large quantities of plant sterols inhibits cholesterol absorption and reduces total serum cholesterol and low density lipoprotein cholesterol by 10% and 15%, respectively (Ling & Jones, 1995; Awad & Fink, 2000; Berge et al., 2000; Duester, 2001; Ovesná et al., 2004; Fernandez & Vega-López, 2005; Gylling & Miettinen, 2005; Jansen et al., 2006;Hazard & Patel, 2007; Vecka et al., 2007; Kidambi & Patel, 2008; Reynolds et al., 2008; Rudkowska, 2008; Patch et al., 2006).

β-Sitosterol is the major phytosterol in higher plants such as olive, avocado, and soya bean, and is abundant in vegetable oils, nuts, and fruits. It is found in the serum and tissues of healthy individuals at concentrations 800–1000 times lower than that of endogenous cholesterol. β-Sitosterol differs from cholesterol only in an extra ethyl group on the C-24 in the side chain, providing more bulk (volume) to the molecule in comparison to cholesterol, making the molecule more hydrophobic than cholesterol and poorly soluble in water and oil phases. Recently, β-sitosterol alone and in combination with similar phytosterols has been considered as a dietary supplement for lowering plasma cholesterol, and for its atherosclerosis preventive, anti-inflammatory, antimicrobial, antipyretic, induced apoptosis, and anticancer effects. However, certain individuals with a higher absorption rate of sitosterol should use sitosterol with caution (Bouic & Lamprecht, 1999; Awad & Fink, 2000; Gerber, 2002; Jourdain et al., 2006; Jayaprakasha et al., 2007; Moon et al., 2007; Awad et al., 2008).

The objective of this work was to investigate theoretically the β-sitosterol molecule, due to its biological and medical importance, and to provide information for further studies. To the knowledge of the authors there is no detailed theoretical study of the molecule, apart from that considered here. Theoretical (quantum chemical) approaches are good tools to investigate small molecules; we have investigated the structural features and electronic properties theoretically in this work.

Computational methods

The geometry of the β-sitosterol molecule has been optimized using different levels of quantum chemical calculations. Preoptimization was performed by applying the molecular mechanics (MM) method (Burkert & Allinger, 1982) using the MM+ force field (Allinger, 1977). The high computational speed of molecular mechanics makes it easier to perform better optimization using a higher level of computational method. The preoptimized structure was taken, and the semiempirical self-consistent-field molecular-orbital (SCF-MO) method (Stewart, 1990) at PM3 (Stewart, 1989) level within the restricted Hartree–Fock (RHF) formalism (Roothaan, 1951) was applied to fully optimize the structure and calculate the vibrational spectra. Geometrical optimization was carried out using a conjugate gradient method (Polak–Ribiere algorithm) (Fletcher, 2000). The root mean square (RMS) gradient of 10⁻⁵ was set to obtain sufficient structural optimization. Harmonic frequency analysis indicated that all stationary points were true minima (there was no imaginary frequency). At the final stage, the geometry taken from PM3 was used to perform single point calculation with density functional theory (DFT) (Kohn & Sham, 1965) using Becke’s three-parameter exchange functional (Becke, 1993) with the Lee–Yang–Parr correlation functional (B3LYP) (Lee et al., 1988). DFT calculation was realized using a 6-31G* basis set (Hehre et al., 1972). The calculations MM and PM3 were carried out with the HyperChem 7.5 program package (2002), whereas the DFT/B3LYP/6-31G* calculation was carried out with the Gaussian-03 program package (2004).

Results and discussion

Optimized structure

The chemical formula of β-sitosterol is C₂₈H₄₈O. Preoptimization by the MM method using the MM+ force field is quite fast and gives a reliable optimized structure. In the second stage of the optimization procedure, the PM3 method has been applied by taking care of relatively fine criteria. Figure 1 shows the final form of the optimized structure (ball and stick model with labels) of β-sitosterol. PM3 optimization has not changed the MM optimized structure much. As seen from Figure 1, β-sitosterol appears non-planar in the middle. The energy contributions after MM optimization are given in Table 1. It can be seen from Table 1 that all types of energy contribution are positive; the dominant contributions are due to dihedral, van der Waals (vdW), and angle interactions. The remaining contributions (bond, stretch-bend, and electrostatic) are relatively small. Some of the calculated energy values after PM3 optimization are given in Table 2. According to PM3 calculations, the heat of formation of β-sitosterol is exothermic and has a value around–124 kcal/mol; the binding energy is about–7469 kcal/mol. The bond lengths of the optimized structure are displayed in Figure 2, which includes only the C-C bonds. There is only one double bond in the β-sitosterol molecule, which is located in the middle ring. The C-C double bond is ∼1.34 Å, whereas the C-C single bonds vary between 1.48 and 1.55 Å. There is one oxygen atom in the present system; the C-O single bond length is ∼1.41 Å. C-H bonds are almost the same, ∼1.11 Å, and the O-H bond is ∼0.95 Å. We should note that the structure and bond lengths are valid for the case that the molecule is electronically in its ground state and isolated, namely in the gas phase.

Figure 1.  Ball and stick model with labels of optimized structure of the β-sitosterol molecule. Red: oxygen; dark gray: carbon; light gray: hydrogen (PM3 result).

Figure 2.  Bond lengths between carbon atoms in β-sitosterol molecule; hydrogen atoms are not displayed (PM3 result).

Table 1.  Energy contributions (in kcal/mol) after molecular mechanics (MM) method with MM+ force field.

Contribution	Value
Bond	3.766
Angle	11.258
Dihedral	28.137
vdW	17.822
Stretch-bend	0.904
Electrostatic	0.286
Total	62.172

Note. vdW, van der Waals.

Table 2.  Calculated energies (in kcal/mol) after PM3 method.

Quantity	Value
Total energy	−100,434.922
Binding energy	−7469.436
Isolated atomic energy	−92,965.486
Electronic energy	−1,031,581.063
Core–core interaction	931,146.141
Heat of formation	−124.061

Vibrational analysis

The vibrational spectrum of β-sitosterol, namely the infrared spectrum (IRS) (in harmonic approximation), has been calculated within the PM3 level. The IRS, including both frequencies and the corresponding intensities, is shown in Figure 3. There are 225 normal modes (harmonic vibrations) for the molecule studied. The first 16 modes with relatively larger intensity are given in Table 3. The vibration directions with relative intensities are displayed in Figure 4. The vibration with the largest intensity takes place in the ring to which the oxygen atom is bonded. This vibration is due to the stretching of the C-C single bond close to the oxygen. The calculated IRS for β-sitosterol agrees well qualitatively with the experimentally determined Fourier transform infrared (FTIR) spectrum (Sigma Aldrich Co., 2009). However, PM3 harmonic frequencies should be scaled by 0.976 for comparison with the experimental values (Scott & Radom, 1996).

Figure 3.  Calculated infrared spectrum of β-sitosterol molecule (PM3 result).

Figure 4.  Directions of vibrations in β-sitosterol molecule (PM3 result).

Table 3.  The first 16 relatively larger infrared intensities (in km/mol) and the corresponding harmonic frequencies (in cm⁻¹) after PM3 method.

Intensity	Frequency	Intensity	Frequency
22.71248	367.28	3.43942	1096.41
11.23686	374.00	2.91183	1382.75
7.50335	3071.15	2.61672	600.37
4.87831	1263.91	2.54071	1303.08
4.63438	379.77	2.27232	1343.91
4.62016	1401.09	2.23868	1369.92
3.89302	1403.20	2.23294	877.27
3.83999	1404.16	2.21367	1030.10

Electronic properties

Electronic properties have been obtained by performing single point DFT/B3LYP/6-31G* level calculations using the PM3 optimized structure. Some of the calculated energy values are given in Table 4. Three-dimensional (3D) images of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are displayed in Figure 5. As seen from Figure 5, both the HOMO and the LUMO are localized mainly on the C-C double bond. The HOMO–LUMO energy difference, E_g, has been calculated to be ∼6.8 eV. The HOMO–LUMO energy gap is used as a measure of kinetic stability; a large gap indicates that it is difficult to add electrons to a high LUMO and remove electrons from a deep HOMO (Denis, 2008). However, in some cases the HOMO–LUMO rule fails. For example, it has been demonstrated that for very large molecules it cannot be used as a good indicator of kinetic stability (Yoshida & Aihara, 1999). However, β-sitosterol is a relatively small molecule. The calculated energy gap for β-sitosterol may be considered fairly small. Therefore, one may conclude that β-sitosterol may be considered a kinetically stable molecule.

Table 4.  Some of the calculated quantities after DFT/B3LYP/6-31G* method.

Quantity	Value
Total energy (Hartree)	−1170.769
Electronic kinetic energy (Hartree)	1164.929
eN energy (Hartree)	−8618.648
Nuclear repulsion energy (Hartree)	2952.109
Highest MO (Hartree)	2.559
LUMO (Hartree)	0.022
HOMO (Hartree)	−0.227
Lowest MO (Hartree)	−19.126
HOMO–LUMO difference, Eg (eV)	6.775
Dipole moment, µ (debye)	2.487
Virial (–V/T)	2.005

Note. LUMO, lowest unoccupied molecular orbital; HOMO, highest occupied molecular orbital.

Figure 5.  3D images of highest occupied molecular orbital (HOMO, upper) and lowest unoccupied molecular orbital (LUMO, lower) of β-sitosterol molecule (DFT/6-31G* results).

The calculated dipole moment of β-sitosterol is ∼2.5 debyes (D). This dipole moment value is relatively large. Comparing this value with that of water (exp. 1.85 D, same level of cal. 2.02 D), the β-sitosterol molecule has a relatively large dipole moment, and seems to be polar (hydrophilic). Excess charge (Mulliken charge) on the atoms is displayed in Figure 6. The most interesting feature is the excess charge on the carbon atoms. For instance, a carbon atom bonded to oxygen has a positive excess charge of about +0.092|e|, and one of the double-bonded carbon atoms has a positive excess charge of about +0.139|e|; all the other carbon atoms have a negative excess charge, and vary between about–0.081|e| and–0.424|e|. Positive charge accumulation takes place on hydrogen atoms, and varies between +0.110|e| and +0.147|e|. Another interesting and important feature of charge accumulation is that carbon atoms labeled 7 and 9 and hydrogen atoms bonded to them have a relatively small charge accumulation. These carbon atoms are bonded to each other. This feature may be interpreted by the following. A small charge accumulation on two bonded atoms may cause a relatively weak bond. Therefore, hydrogen atoms bonded weakly to carbons that also form weak bonds may easily be abstracted, and play an important role in radical formation. Tejero and coworkers theoretical analysis for linoleic acid (Tejero et al., 2004) supports our argument. The negatively charged oxygen part of the molecule may also play an important role in the interaction of β-sitosterol with its environment. 3D images of charge density and electrostatic potential are displayed in Figure 7. As seen from the electrostatic potential, the end of the molecule where oxygen is located is an attractive part of β-sitosterol.

Figure 6.  Excess (Mulliken) charge on atoms of β-sitosterol molecule (DFT/6-31G* result).

Figure 7.  3D images of charge density (upper) and electrostatic potential (lower) of β-sitosterol molecule (DFT/6-31G* results).

Declaration of Interest

One of the authors (S.E.) would like to thank the Middle East Technical University (METU) for partial support through the project METU-BAP-08-11-DPT-2002-K120-510.