Molecular modeling is made to predict the cholesterol molecule behavior in gas phase and in solution. In gas phase, molecule's geometry is optimized and its dipole moment is studied at MP2/6-31g, B3LYP/6-31g, HF/6-31g, HF/6-31g*, and HF/6-31+g (d,p) levels. Also, Partial atomic charges of cholesterol molecule were computed with the B3LYP of DFT and HF methods at the 6-31G basis set level of theory. The self-consistent reaction field theory (SCRF) based on polarizable continuum model (PCM) has been employed at B3LYP/6-31g and HF/6-31g levels to optimize the geometry and to calculate the solute-solvent interaction and dipole moment of the cholesterol molecule in different solvent environments (water, ethanol, acetone and octanol, benzene and heptane). It was found that the dipole moment of the cholesterol molecule was increased and the geometry of the molecule was strongly affected as a result of solute-solvent interactions (solvent effects). The free energy of transfer of cholesterol from aqueous phase to hydrocarbons and alcohols was estimated accurately using solvation data acquired from modeling.
Keywords: Cholesterol, Solvent effects, Polarizable continuum model, DFT, Dipole moment, Sublimation energy.
Introduction
Cholesterol, an important biological amphiphile, is found in mammalian cell membranes and in various classes of serum lipoproteins. It has a paradoxical nature in mammalian life; on one hand it is essential for mammalian life because it controls the fluidity of the cell membranes and it affects the activities of enzymes that act adjacent to membranes. On the other hand, crystallization of cholesterol in bodily fluids is the main cause of heart attack and gallstone development [1].
In mammalian cells cholesterol is present in water-lipid-protein solutions such as micelles, vesicles and microemulsion. Knowledge of cholesterol-cholesterol and cholesterol-solvent interactions is essential for understanding these complex systems. However, little is known about the physical properties of cholesterol in solutions even in binary systems [2].
The physicochemical properties of dissolved molecules are influenced by their close environment. Determination of the character and magnitude of these effects is crucial in studying the structure and properties of molecules in solutions. Experimental study on these parameters is very expensive and time consuming but several theoretical methods have been developed to model the solvent effects. They can be roughly divided into two types, discrete methods and continuum models. In discrete methods the solvent molecules as well as solute molecules are treated implicitly by means of Monte Carlo (MC) or molecular dynamics (MD) simulations as the solute molecule needs to be embedded in a large number of solvent molecules. This allows for rigorous treatment of molecular interactions; however continuum models are less computation expensive because they consider the solvent as a continuous dielectric medium represented by macroscopic properties of the solvent (dielectric constant) Error: Reference source not found.
In this study the cholesterol molecule behavior in gas phase is studied thoroughly and its structure, dipole moment and partial atomic charges were predicted. Then, the effect of different solvent environments on these parameters was investigated based on Polarizable continuum model (PCM) model. Finally, solvation of cholesterol in aqueous phase is discussed in details and the free energy of transfer of cholesterol from aqueous phase to hydrocarbon and alcoholic solvents is estimated. Although experimental data were not available, agreement between results of the two models
Computational details
2.1. Geometry Optimization
Each species was initially optimized with PM3 method and, then the optimized structures were again optimized with DFT and HF methods [4-8]. The molecular were optimized and calculated by the Hartree-Fock of ab initio method and Becke's three- parameter Error: Reference source not found combined with gradient corrected correlation functional of Lee-Yang-Parr (LYP) Error: Reference source not found of DFT method by implementing the 6-31G atomic basis set, using GUASSIAN 2003 Error: Reference source not found computational package. Error: Reference source not found shows the optimized cholesterol structure.
Full geometry optimizations and frequency calculations were performed and each species was found to be minima by having no negative values in the frequency calculation. The calculations gave internal energies at 0 K. In order to obtain gas phase free energies at 298.15 K, it is necessary to calculate the zero-point energies and thermal corrections together with entropies to convert the internal energies to Gibbs energies at 298.15 K.
<Fig. 1>
Partial atomic charges of cholesterol molecule were computed using Gaussian 03 package with B3LYP of DFT and HF methods at the 6-31G basis set level, given in (Table 1). The net atomic charges of hydrogen atoms in the hydrophobic-hydrophilic segments are positive while those of carbon atoms are negative indicating the existence of electrostatic interactions within cholesterol molecule.
<Table 1>
Cholesterol is predominantly a hydrocarbon compound with one polar functional group which gives it a dipole moment of approximately 1.9 D Error: Reference source not found. Table 2 shows that the dipole moment of cholesterol molecule in vacuo calculated by B3LYP and HF methods are in good agreement with the experimental value.
<Table 2>
2.2. Contribution to Gibbs free energy
The self-consistent reaction field theory (SCRF) based on Tomasi's polarized continuum model Error: Reference source not found have been employed at B3LYP/6-31g and HF/6-31g levels to calculate the solute-solvent interactions in different solvent environments (water, ethanol, acetone, octanol and heptane). The calculated energitical parameters in polar and apolar environments are given in Table 3. Analysis of the geometrical parameters indicates a significant strain in the cholesterol structure due to a change in environment. Figure 2 depicts the dielectric dependence of the dipole moment of the cholesterol molecule.
<Table 3>
Dipole moments determine intermolecular interactions in substances. For polar liquids, intermolecular interactions increase as dipole moments increase. From Figure 2, the dipole moment of the cholesterol molecule increases as the dielectric constant increases.
<Fig. 2>
Thermodynamics model for cholesterol dissolution in water
The dissolution of cholesterol in water is divided into three steps (Figure 3). At first step one molecule of cholesterol is removed from the crystal lattice. Next, a cavity is formed in water and finally the molecule is transferred to the cavity. For dissolution to take place, the magnitude of the energy gain in third step has to be larger than the total energy cost at previous steps Error: Reference source not found.
(1)
Each step is associated with a change in total Gibbs free energy and summation of these changes will result in the free energy of dissolution. In the rest of this section the various terms involved to calculate the free energy are discussed.
<Fig. 3>
3.1. Thermodynamics of sublimation
The enthalpy of sublimation is the energy that is absorbed when one mole of molecules is removed from the crystal lattice and transferred to the gaseous state. The value of the enthalpy of sublimation is calculated by the Clausius-Claperon equation:
(2)
Where P is vapor pressure, T is the absolute temperature and R is the universal gas constant.
The experimentally determined vapor pressure data were described by the following equation
(3)
Gibbs free energy and entropy of sublimation of cholesterol at a given temperature T can be calculated from the following relations:
(4)
(5)
Using appropriate values for constants A and B the enthalpy, Gibbs free energy and entropy of sublimation for cholesterol molecule can be calculated using equations 3 to 5. When temperature ranges from 386 to 414 K, ∆Hsub=142.5±0.89 KJ/mol, ∆Gsub=-44.945 KJ/mol and ∆Ssub=0.453 KJ/mol K Error: Reference source not found.
3.2. Free energy of solvation
The interaction energy of a solute molecule with the statistically averaged solvent molecule is expressed as sum of electrostatic (), and non-electrostatic () contributions. Neglecting the entropy contribution due to molecular motions, can thus be written
(6)
The electrostatic contribution can be found from an SCRF calculation. The non-electrostatic contribution can be split into dispersion, repulsion and cavitation free energies.
(7)
Electrostatic and non-electrostatic contributions to the Gibbs free energy of solvation were presented in Table 3.
Transfer of cholesterol from aqueous phase to another phase
The free energy of the transfer of linear molecule from the water phase to the hydrocarbon phase can be readily estimated at any temperature using expressions developed by Nagarajan, R. and Ruckenstein, E. Error: Reference source not found. But similar expression is not available for almost all of the cyclic molecules such as cholesterol.
In this section, an accurate estimation of for the transfer of cyclic molecules is made using solvation free energy data. The Gibbs energy of solvation is defined as the change in Gibbs free energy when a solute molecule is transferred from a fixed position in the ideal gas phase to a fixed position in the solution at constant pressure and temperature Error: Reference source not found. Considering the thermodynamics cycle was depicted in Figure 4.
<Fig. 4>
The free energy of transfer of the solute molecule from solvent 1 to solvent 2 can be obtained by subtracting the solvation energy of solvent 1 from that of the solvent 2; that is:
(8)
The formation of micellar and vesicular structures (and monolayers or bilayers, too) is a consequence of the hydrophobic effect. The large hydrocarbon tails aggregate in the center of the particle excluding water from contact with the non-polar structures (dielectric constant D=2, similar non-polar hydrocarbons Fig. 5). The polar head groups form the particle's surface making it perfectly soluble in water (dielectric constant D=80), and the water surrounding the two sides of the membrane.
<Fig. 5>
The causes of favorable partitioning of a cholesterol molecule from water into a membrane are non-polar (np) interactions due to expulsion of non-polar compounds from water (hydrophobic effect), and electrostatic (elec) effects arising from differences in the dielectric constants of the water and membrane Error: Reference source not found. One way to estimate the free energy changes of the transfer of cholesterol between the aqueous and membrane phases is to consider a bilayer (membrane) as a nonpolar hydrocarbon.
Table 5 shows the calculated free energies of transfer of cholesterol from water phase to hydrocarbon or a bilayer (membrane) calculated with the two methods.
<Table 5>
Conclusion
We have used a reliable self-consistent reaction-field method, which combines a polarisable continuum model of the solvent with both DFT and HF for the cholesterol molecule, to calculate the solvation Gibbs free energies and the electronic properties of cholesterol molecule in water and another organic solvents. Since there are no experimental data available to compare with these techniques, rendering a value judgement on the accuracy of one technique over another is really impossible. Yet, the comparison itself is of interest. A continuum model like self consistent reaction field (SCRF) theory allows us to take into account the long range interactions between solute molecule and solvent along with the adjustment of molecular geometry and dipole moment of the solute that reflects the interactions within polar medium. In addition, the SCRF model is easy to implement and computationally efficient for prediction of general structure and stability trends in aqueous phase.
The dipole moment of the cholesterol molecule, computed at B3LYP/6-31G and HF/6-31G levels of theory in different solvents was greater than its dipole moment in the gaseous state. This can be attributed as follows: the dipole moment of a solute molecule induce a dipole moment on each nearby solvent molecule that adds to permanent dipole. The net result of these orientation and induction effects is that the solvent acquires a bulk polarization in the region of each solute molecule. The polarized solvent generates an electric field called the reaction field, around each solute molecule. The reaction field distorts the solute's molecular electronic wave function from what it has been in the gaseous phase, thereby producing an induced dipole moment that adds to the permanent gaseous phase dipole moment. The increased dipole moment further polarizes the solvent, and so forth. Because of the additional dipole moment induced by the solvent's reaction field, a polar molecule will have a larger dipole moment in a polar solvent than in the gaseous phase, which in turn will increase the stability of the molecular system.
