Theoretical assessment of the mechanisms involved in the cholesterol biosynthesis from lanosterol

A theoretical approach to describe the mechanisms of the isomerization and reduction of a double bond, involved in the lanosterol conversion to cholesterol was undertaken. Also, the 14α-demethylation and 4α-demethylation in this biosynthesis were studied, and some similarities were found between the two; however they are different and their mechanisms have not been explained yet. Ab initio calculations were performed in order to prove these mechanisms. Two different characteristics involved in this biosynthesis were explained, namely (i) the stability of each molecule during this reaction using total energy, hardness and dipole moment, and (ii) the explanation of proposed mechanisms [Steroid Biochemistry and Pharmacology, 1970, p. 57] of the two different reactions, using frontier orbitals and atomic charges. For this sequence of reactions, the hardness and dipole moment indicate the hydro-solubility of the molecules, which means that carrying properties change through cell membrane. It is possible to explain the reaction mechanisms using frontier molecular orbitals theory and the atomic charge. The localization of highest occupied molecular orbital, lowest unoccupied molecular orbital and the flow of atomic charge are in agreement with reported mechanisms [Steroids 8 (1966) 353; Medicinal Natural Products, 1997, p. 218; Biochemistry of Steroid Hormones, 1975.

1. Introduction Cholesterol is the main sterol in animal tissues and is an important constituent of membrane lipids. It is biosynthesized from acetate via mevalonic acid, going through squalene to produce lanosterol. Almost all known animal tissues synthesize cholesterol, including liver, gastrointestinal tract, adrenal cortex and artery walls among others. Biologically, cholesterol plays an important role within the cell membrane controlling its fluidity, membrane architecture, supporting both the membrane proteins and the correct arrangement of phospholipid hydrocarbon chains. Hypercholesterolemia and other imbalances in lipid metabolism, including atherosclerosis with its consequent hypertension are important pathophysiological disorders involving failures in cholesterol biosynthesis and metabolism. Lanosterol and desmosterol are natural precursors of cholesterol, which finally is the essential material to produce progesterone and all the steroid hormones. Although the pathway of cholesterol biosynthesis has been described, many possibilities still arise and the biosynthesis may follow several intermediate steps. Actually, we are not aware of complete molecular studies showing the reaction pathways, or preferential thermodynamic biochemical mechanism to achieve cholesterol biosynthesis. Previously we reported, based on frontier orbitals analysis and hardness parameter, that the mechanism of the 14α-demethylation of lanosterol toward cholesterol biosynthesis, is basically through the formyloxy pathway which is preferred to the carboxylic acid pathway. Many authors have proposed several possible routes, among which one was studied by Briggs. This report is a further step dealing with the particular biosynthetic route from lanosterol to cholesterol exploring demethylations, interchange and reduction of double bonds, the role of frontier orbitals and energy parameters among others. The ab initio theory is suitable to calculate the electronic structure of small molecules. Therefore, we applied the RHF method at 6-31G* level to assess the feasible reactions from lanosterol to cholesterol. 2. Methods The molecules studied in this report are those represented in Fig. 1. They are named according to IUPAC nomenclature: (1) lanosta-8,24-diene-3β-ol or lanosterol; (2) 4,4-dimethyl-5α-cholesta-8,24-dien-3β-ol or norlanosterol; (3) 4α-methyl-5α-cholesta-8,24-dien-3β-ol; (4) 4α-methyl-5α-cholesta-7,24-dien-3β-ol; (5) 4α-methylcholesta-5,24-dien-3β-ol; (6) cholest-5,24-dien-3β-ol or desmosterol and (7) cholest-5-en-3β-ol or cholesterol.

Fig. 1. Possible pathway of biosynthesis of the cholesterol.

The transformation of Fig. 1 requires three general processes: removal of the three extra methyl groups, the shift of the nuclear double bond from Δ8 to the Δ5 position and reduction of a double bond. The two types of demethylations are given from structure 1 to 2, from 2 to 3 and from 5 to 6; the last two will be discussed in the following paper. The shifts of the nuclear double bonds, called isomerization, are from 3 to 4 and from 4 to 5. The reduction of the side chain (C24–C25) is carried out from 6 to 7. Therefore in order to know the implied mechanisms of the biological actions of these compounds, it is necessary to have a detailed knowledge of the 3D structures, their electronic structures and the possible ways to obtain these products. The theoretical studies of the 3D structures of these molecules using computational methods allow us to obtain information, not available through experimentation. The results make it possible to know and to comprehend the chemical transformation and the stages between reactants and products. To study these mechanisms the following parameters were calculated: total energy, dipole moment, atomic charge, and frontier molecular orbitals HOMO (highest occupied molecular orbital), SHOMO (second HOMO), LUMO (lowest unoccupied molecular orbital), SLUMO (second LUMO). These orbitals were used to calculate the hardness η with the purpose of measuring molecular reactivity.The optimization of the structures of Fig. 1, were performed using Hartree–Fock (HF) method with the STO-3G basis set. Finally the electronic structures of all the molecules were calculated using the HF and 6-31G basis set including d functions for heavy atoms. The molecules studied in this report were built with Spartan 4.0, a graphical software program for quantum chemical method calculations. Computational calculations were made using the Silicon Graphics Indigo Extreme and DEC ALPHA workstation of the Laboratory of Hormonal Chemistry, from the Biomedical Institute from UNAM. 3. Results and discussion The biological pathway of conversion from lanosterol 1 to cholesterol 7 is enzymatic and requires removal of three methyl groups, a reduction of a double bond between C24–C25 and shifting the nuclear double bond from Δ8 to the Δ5. This report discusses the isomerization and the reduction of side chain double bond. While these reactions are in progress, some molecular properties change as a consequence of different electronic distribution. Thus, hardness and dipole moment for instance, increase along the route of intermediates except hardness of compounds 3 and 6 and dipole moment of compound 5. The total energy increased but showed two plateaus, one composed by intermediates 3, 4, and 5 and the second composed by compounds 6 and 7. The common parameters of all molecules involved in the reaction from lanosterol to cholesterol are presented in Table 1, including energy of frontier orbitals, hardness and dipole moment. Table 1. Total energies and molecular frontier orbital energies in eV, hardness and dipole moment of steroids, involved in the biosynthesis of cholesterol. The data were obtained with RHF/6-31G* calculations (η: hardness; μ: dipole moment; 1 a.u.=627.5 kcal/mol=27.21 eV; 1 eV=3.675 a.u.=2.306 kcal/mol)

HOMO and SHOMO energies showed tendency to decrease along the way from structure 1 to structure 7. This is reasonable because the electrons in orbitals with low energy are more susceptible to receive the electrophilic species and the reactions occur easier. Another finding is that the LUMO energies do not show any linear tendency; however the hardness values increase linearly in good agreement with the principle of maximum hardness, Table 1. The dipole moment for the structures from lanosterol 1 to cholesterol 7, increases in a linear way, because the loss of three non-polar methylenes through the biosynthesis modifies the charge distribution of lanosterol. It must be noticed that when 1 goes to 7, the hydro-solubility of the molecules is increased and at the same time there is a decrease in lipo-solubility. Table 1 shows how dipole moment and hardness increase in the same way implying both increase in hydro-solubility. It is believed that cholesterol 7 has larger dipole moment than desmosterol 6 because its side chain double bond (C24–C25) has a polarization in opposite direction of the C-3 hydroxyl group that nullifies in some extend the electronic density, Fig. 1. Nevertheless, it is observed that structures with the highest dipole moment have the double bond (C5–C6) near the hydroxyl group, because of the existence of inductive and resonance effects. The lowest dipole moment values are for structures with the hydroxyl group, far from the double bond (C8–C9) where there is no possibility to add both effects. In Table 1 it is observed that the hardness values η=(HOMO−LUMO)/2,clearly indicate that the pathway from lanosterol to cholesterol is in agreement with the Pearson reactivity theory, which states, “In any spontaneous reaction, it is necessary for the starting material to have more softness than the product”. In other words, softer is the material, the more reactive it is. This is just what has been observed when the starting material stages 1 (lanosterol) is transformed into the end product 7 (cholesterol) through the intermediates 2, 3, 4, 5, 6. 3.1. Demethylations A common feature of the three demethylations is the change in energy. It has been observed experimentally that each time a sterol undergoes a demethylation, it is possible to waste 40 hartrees corresponding to the loss of one methylene (–CH2) Table 1. This is not an irregular situation because there are reported Hartree–Fock energies for atoms, where it has been observed that energy diminishes when the number of atoms increases. Some features of 14α-demethylation can be classified into two groups: geometric and electronic features. The methyl group must have an alpha orientation. The molecule must have a double bond near the group that will be released. The methyl C-30 (molecule 1, Fig. 1) that will act as a nucleophilic species must have a high electronic density. The carbon bonded with the methyl group that will be released must have increased its electronic density after releasing the methyl. Other reactivity properties of 14α-demethylation were described in. However, it has been observed that 14α-demethylation is different from the 4α-demethylation, because the former has a Baeyer–Villiger rearrangement to obtain formyloxy intermediate and in the latter the methyl group is oxidized to form carboxylic acid. Therefore, these reactions are carried out along different pathways and different intermediates, as well as sets of catalysts or enzymes. Additionally these reactions have different hardness because when 14α-demethylation occurs, the hardness has a positive slope, whereas 4α-demethylation has a negative one, Table 1. 3.2. Isomerization During the biosynthesis of cholesterol there is another reaction, the isomerization of the endocyclic double bond from C8–C9 to C5–C6. This reaction is called allylic isomerization and includes three stages at the same time, and the overall reaction is summarized in Fig. 2.

Fig. 2. (a) Allylic isomerization mechanism, formation of 4 intermediate. (b) Dehydrogenation mechanism, formation of the 4B intermediate. (c) Mechanism of the reduction of the double bond (C7–C8), formation of 5 intermediate.
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3.2.1. Allylic isomerization, formation of 4 intermediate
The first step of this reaction is carried out from molecule 3 to 4 of Fig. 1 and implies the migration of the endocyclic double bond; this is found between C8 and C9 and after the transformation it will be localized between C7 and C8 Fig. 2a. According to the proposed chemical mechanism, it is necessary that β hydrogen of C-7 releases like a proton, and then the electrons form a π bond between C7 and C8. After that, taking a proton back to C-9 from the environment breaks the double bond between C8 and C9. To carry out this mechanism, it is necessary to have a HOMO between C8 and C9 and a virtual orbital (LUMO) between C7 and C8. The analysis of the frontier orbital in Fig. 2a shows that this molecule has the orbital just on the reactive part as it was predicted. This mechanism is in agreement with the changes in atomic charges of Table 2 because the polarization of each bond follows the order proposed by the mechanism Fig. 2a. It is observed that the C-7 of structure 3 has −0.335 ues, indicating that C-7 with higher charge could share more electronic charge to C-8 because of its lack of atomic charge (0.001 ues).
[pic]Table 2. Electrostatic potential charges of some atoms of structures 3, 4, 4A+ and 4B involved in the biosynthesis reaction, data were obtained with RHF/6-31G* calculations

3.2.2. Formation of the carbocation 4A+ intermediate The second step of isomerization occurs when molecule 4 is dehydrogenated (Fig. 1). This happens when an α-hydride belonging to C-6 in structure 4 is eliminated to obtain a carbocation called 4A+. The hydride goes away by the aid of NADP+ (nicotinamide adenine dinucleotide phosphate). After this step the only proton that could be eliminated belongs to C-5, to get an endocyclic conjugate diene on ring B called the 4B intermediate. This reaction is possible because of the presence of NADPH and the resonance stability of the diene, Fig. 2b. This reaction is possible if molecule 4 has a HOMO on the reactive part of C-6 and H-6α. Likewise it is possible to obtain 4B if the intermediate 4A+ has one LUMO on C-6. Analysis of Fig. 2b displays each of the necessary frontier orbitals and exactly on the reactive positions to satisfy the proposed mechanisms. Using atomic charges the mechanism is completely explained. The H-6α of molecule 4 from Fig. 2b is released to produce the carbocation 4A+. This hydrogen has small atomic charge (0.174, Table 2), which makes it difficult to release as hydride. Nevertheless this transformation is successful if NADP+ is present in the medium. Since NADP+ is a cationic species with a great deficiency of electrons may compel the hydrogen to leave the rest of the molecule as hydride. The reaction continues forming carbocation 4A+, this intermediate must eliminate one proton. The proton is eliminated from C-5 successfully because C-5 has greater atomic charge (−0.054 ues) than hydrogen H-5 (0.086 ues), and due to this negative charge could be transferred from C-5 to C-6, to obtain the endocyclic double bond between C5 and C6. At the same time 4A+ can be formed because H-5 can be released as a proton because of its small atomic charge. Another reason to consider this reaction favorable is that the double bond can be stabilized because of the conjugation effect, promoted by the presence of another double bond endocyclic (C7–C8), which is observed in the HOMO of structure 4B from Fig. 2b.

3.2.3. Reduction of double bond between C7 and C8, formation of 5 intermediate Subsequently, the intermediate 4B yields molecule 5 through reduction of the double bond between C7 and C8. This reaction is NADPH dependent. Here it is necessary to find one HOMO between C-7 and C-8 in order to have electrons that allow attracting a proton from the environment. In other words the proton interacts with the rich electronic bond of C7–C8; that is why, it is necessary to have one LUMO on the C-7 so that it can accept the electrons that are given by the hydride arising from NADPH. The presence of these orbitals is shown in Fig. 2c. Finally the formation of molecule 5 of Fig. 1 occurs because C-7 (−0.207 ues) has a large atomic charge, Table 2, part of which is given to C-8 (−0.016 ues). C-8, which does not have such large atomic charge, will use the charge of C-7 to form a bond with a proton from the environment. When the C-7 loses charge, it instantly becomes susceptible to be attacked by any hydride, forming product 5.
3.3. Hydrogenation of double bond between C24 and C25, formation of 7 intermediate In accord with the mechanism proposed Fig. 3, the double bond of the side chain (C24–C25) is reduced by the reductase enzyme dependent on NADPH. The necessary hydride, which causes the reaction, comes from the coenzyme and is added to C-25, while C-24 takes one proton from the water. Due to the fact mentioned previously, it could be said that the reaction occurs only if both HOMO and LUMO are located on C24–C25. This has been observed from the frontier orbital represented in Fig. 3 of the molecule 6 of desmosterol. According to the ab initio calculations, the HOMO exists in that place along with an equivalent LUMO namely SLUMO. However, the hydrogenation of the double bond is feasible since both LUMO and SLUMO are quasi-degenerated with 0.1836 and 0.1902 eV, respectively (Table 1).

Fig. 3. Mechanism of the reduction of the side chain double bond (C24–C25), formation of 7 intermediate. It can be concluded that the reduction is possible because of the existence of occupied and unoccupied orbitals, although it could not be proved, with this information, where the reaction begins. The reaction might initiate if the first species to attack was the hydride, or if the first reaction was the protonation of the π system. An alternative possibility exists if the reaction is simultaneous, Fig. 3. 4. Conclusions This study was done to prove theoretically proposed mechanisms of the biosynthesis of cholesterol from lanosterol, with a detailed analysis of local properties such as atomic charges and frontier orbitals. Besides, a general analysis of the molecules was made using global parameters, as total energy, hardness and dipole moments. From the hardness and dipole moment parameters, it is possible to provide a logical explanation of the nature in which reactions occur. For this sequence of reactions, the hardness increases linearly and the dipole moment increases too when the cholesterol is obtained. Both quantities indicate the hydro-solubility of the molecules is increased and at the same time its lipo-solubility decreases, which may have biological importance, mainly for cell membrane biophysics and biosynthesis of steroid hormones. It is worth to emphasize that the tendencies of hardness, dipole moment and energy, Table 1, increase in the same way, and a constant change in energy has been observed when the number of electrons changes. And there is almost the same energy when there is only an internal rearrangement but not in the number of electrons. In spite of these observations, energy gives us information about stability of the structures, but not necessarily about reactivity. It is possible to explain the mechanisms of reaction of the cholesterol biosynthesis starting from lanosterol, using the theory of the frontier molecular orbitals. It does not matter which reaction is considered; any electrophilic species attracts a nucleophilic one. In the same way a HOMO can react with a LUMO. Therefore, frontier orbitals and atomic charge were used to explain the isomerization and reduction mechanisms. The localization of the HOMO, LUMO and the flow of atomic charge are in agreement with the reported mechanisms. There are some common features of the demethylations. It was found that there was a constant value for the total energy as a consequence of release of a methylene. However, it might be possible to establish some differences between 14α-demethylation and 4α-demethylation and to prove such differences, hardness criteria is used. Nevertheless, with the data obtained till now, it has not been possible to explain and differentiate clearly between the mechanisms of the 14α-demethylation and the 4α-demethylation. In order to detect factors to prove that these two reactions are completely different, the next goal is to study 4α-demethylation in detail, as well as other demethylations.

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