A DFT study on the scavenging activity of curcumin toward methyl and ethyl radicals

Abstract The curcumin is a well-known antioxidant that can scavenge free radicals efficiently. The methyl free radicals, generated by the metabolism of various genotoxic compounds such as hydrazines and peroxides, can methylate various sites in DNA. Herein, we have carried out density functional theory calculations to investigate the scavenging activity of curcumin toward the methyl and ethyl radicals through radical adduct formation (RAF), hydrogen atom transfer (HAT) and single electron transfer (SET) mechanisms. The SET mechanism is found to be highly endergonic and so not viable. Our calculations show that the curcumin can scavenge methyl radicals through both RAF and HAT mechanisms but RAF would be preferred over the HAT. Further, it is found that the curcumin can scavenge methyl radicals more efficiently as compared to ethyl radicals through RAF mechanism.


Introduction
Oxidative stress is considered to be the main contributor to the development of five main chronic diseases viz. cancer, cardiovascular disease (CVD), chronic obstructive pulmonary disease (COPD), type II diabetes (T2D) and Alzheimer's disease (AD), which caused about 60% of the total global death in 2018 (World Health Organisation data, 2018) [1]. Oxidative stress occurs due to the over production of pro-oxidants than antioxidants in living organisms, thereby disturbing the normal homeostatic condition. Lipid peroxidation, protein degradation and the DNA damage are three main ill effects of oxidative stress [2]. The free radicals such as hydroxyl (HO·), peroxy (ROO·), alkoxy (RO·) and alkyl (R·) as well as ozone, sulfur dioxide, nitrogen dioxide, O 2 ·− , and H 2 O 2 play a critical role in the damage of lipid, protein and DNA [2].
Antioxidants have the ability to alleviate the inflammation and immunotoxicity caused due to oxidative stress either by inhibiting the formation of free radicals or by interrupting the propagation of free radicals [3]. It is reported that antioxidants can act as radical scavengers, enzyme inhibitors, peroxide decomposers, singlet oxygen quenchers, and synergists as metal-chelating agents [4]. Out of the several dietary antioxidants that we consume regularly, curcumin exhibits potent antioxidant properties [1]. The IUPAC name of curcumin, also known as diferuloylmethane, is (1E,6E)−1,7-bis(4hydroxy-3-methoxyphenyl)−1,6-heptadiene-3,5-dione. It is the major constituent of the spice turmeric, which is derived from the rhizome of the plant, Curcuma longa [5]. Apart from curcumin, demethoxy-curcumin and bisdemethoxycurcumin are also the constituents of turmeric. All together these classes of compounds are known as curcuminoids. But curcumin, which is the principal curcuminoid, is responsible for the yellow colour of the turmeric and majority of its therapeutic effects [6]. In recent past, over hundreds of research articles on the antioxidant, anti-inflammatory, anti-mutagenic, anti-microbial and anticancer properties of curcumin were reported [7][8][9][10][11]. The curcumin is considered to be safe even if it is taken in high amounts (4000-8000 mg/day) [12]and has been approved by the US Food and Drug Administration (FDA),making it appropriate for therapeutic use.
During the last few decades, many researchers have given emphasis on the treatment of cancer using curcumin [8]. Interestingly, Dorai and Aggarwal [13] reported that due to regular intake of curcumin, and other dietary agents derived from fruits and vegetables, there were less incidences of cancer and cancer related deaths in Asia as compared to the western countries. It is reported that curcumin can inhibit the initiation and progression of cancer through various cellular and molecular mechanisms [5,14]. Studies on curcumin showed that it could inhibit lipid peroxidation by scavenging various reactive oxygen species (ROS) such as superoxide anions, hydrogen peroxide and nitrite radicals produced by activated macrophages [15]. Agnihotri and Mishra [16] had investigated in details the scavenging mechanisms of curcumin toward the hydroxyl radical theoretically using the BHandH-LYP/aug-cc-pVDZ and B3LYP/aug-cc-pVDZ levels of density functional theory (DFT) in both gas phase and aqueous media. Recently Brenda et al. [17]reported that curcumin, caffeic acid, phenethylester, and chicoric acid could act as potent oxidative stress scavengers by studying theoretically their antiradical properties towards OH • , NO 2 • , HOO • and CH 3 O • free radicals. The methyl free radicals (CH 3 • ), generated by the metabolism of various genotoxic compounds like hydrazines and peroxides, can methylate various sites in DNA [18]. In vitro and in vivo studies have demonstrated the formation of methyl radicals from the environmental chemicals [19,20]. The C8methylguanine (C8mG), N2-methylguanine (N2mG), C8methyladenine (C8 mA), N2-methyladenine (N2 mA) and C5-methylcytosine (C5mC) are the methylated adducts formed by methyl radical generating species [21][22][23]. Hix et al. [24] showed that the C8mG are produced by the treatment of calf thymus DNA with BuOOH in the presence of Fe(II) at pH 7.0. The C8mG is reported to be a mutagenic lesion that can cause G C and G T transversion mutations and deletion [25]. Hyper methylation of CpG island of DNA causes silencing of tumour suppressor genes leading to cancer [26,27]. In vivo formation of ethylated adducts by ethyl free radicals (CH 3 CH 2 • ) generated from tert-butyl hydroperoxide and cumene hydroperoxide was reported by Taffe et al. [28]. The N2edG, an ethylated adduct formed at the N2 site of 2'-deoxyguanosine (dG), was observed in the WBC of alcoholic abusers [29].
Furthermore, it is observed experimentally that alkyl radicals can react with many organic molecules such as curcumin, toluene, arenes and certain drug molecules via direct addition or H-atom abstraction reactions [30][31][32][33]. For example, CH 3 • radicals was found to abstract H-atoms from curcumin [31]. In a reaction of CH 3 • radicals with toluene, it was found that it can react with toluene via both H-atom abstraction as well as addition reactions but the addition reactions occurred only in the liquid phase [30]. The direct alkylation of heteroarenes caused by alkyl radicals generated using stable organic peroxides activated by visible-light photo-redox catalysis was reported by DiRocco and co-workers [32]. Xu et al. [34] reported the methylation of N-arylmethacrylamides and isonitriles by using dicumyl peroxide (DCP) as the CH 3 • radical source. Wang et. al. [35] reported a Re-catalyzed decarboxylative oxymethylation of alkene, where hypervalent iodine(III) acts as both oxygenation and CH 3 • radical source. It may be pertinent to mention here that the alkylation of drug molecules by alkyl radical-mediated photo/electro catalysis are in use nowa-days [33].
Herein, we have investigated theoretically the scavenging activity of curcumin towards methyl radicals via three mechanisms viz. hydrogen atom transfer (HAT), single electron transfer (SET) and radical adduct formation (RAF) that have been extensively studied by many researchers previously for understanding the scavenging activity of antioxidants [36,37]. The reaction of curcumin with ethyl radical via RAF mechanism is also studied to explore its ability to scavenge larger alkyl radicals. The enol form of curcumin ( Figure 1) has been considered for the present study as it exists predominantly in solution [16,38,39].

Computational details
The reactants, products and transition states (TSs) involved in different reactions studied here are fully optimised without any constraints at the M06-2X/6-31G(d) [40,41] level of DFT employing the Gaussian09 suite in gas phase [42]. It is reported that the M06-2X/6-31G(d) yield best cost/performance compromise results for this system [17]. To further refine energies, single-point energy calculations are done at M06-2X/6-311 + G(d,p) level in gas and aqueous phases. For aqueous phase calculation, the polarisable continuum model (PCM) was used [43]. For all the optimised stationary points, we carried out vibrational frequency analysis at the M06-2X/6-31G(d) level in gas phase to determine thermal corrections to Gibbs free energy as well as to ensure that there is no presence of imaginary frequency at the reactants/products and there is the presence of only one imaginary frequency at the TS. For each of the reactants, products and TSs, we have applied the thermal energy corrections obtained at the M06-2X/6-31G(d) level in gas phase to the total energy obtained at the M06-2X/6-311 + G(d,p) level in both gas and aqueous phases to obtain the Gibbs free energy at 298.15 K and 1 atm. All the structure and the vibrational frequencies were visualised using the GaussView 5.0 software [44].
The activation free energy (ΔG b ) and the reaction free energy (ΔG f ) of a reaction were calculated using the following expressions: Where, G TS , G reactants and G products represent the Gibbs free energy of TS, Gibbs free energy of the sum of reactants and the Gibbs free energy of the sum of products, respectively. The natural bonding orbital (NBO) [45,46] analysis available in Gaussian09 was performed to determine the spin densities associated with the reactants, TSs and products at the M06-2X/6-311 + G(d,p) level of theory in gas phase.

Single electron transfer (SET) reaction
The scavenging of CH 3 • radical by curcumin (Cur) through SET mechanism was studied using the following reaction: Since the SET reaction proceeds without any TS, the feasibility of the reaction is explored on the basis of reaction free energy (ΔG f ). The ΔG f of above reaction is found to be 182.72 kcal/ mol at the M06-2X/6-311 + G(d,p) level of theory in gas phase. Thus, the SET reaction is highly endergonic in gas phase. In going from gas phase to aqueous media, the ΔG f is appreciably decreased but it is still very high (70.58 kcal/ mol) and endergonic. Thus, the large positive values of ΔG f obtained in both gas phase and aqueous media indicate that scavenging of methyl radicals by curcumin through SET mechanism would not take place. This is in agreement with the previous studies where SET mechanism was found unfeasible with respect to the HAT and RAF mechanisms for scavenging activities of some anti-oxidants having phenolic group toward OH• and other radicals [36,47].

Hydrogen atom transfer (HAT) reactions
The optimised geometry of curcumin (Cur) along with atomic numbering scheme is shown in Figure 1. The scavenging activity of curcumin toward the methyl radical through HAT mechanism has been studied using the following reaction [ Figure 2]: where, Hx = H1, H3, H4, H6-8, H10-13, H15-17 and H19 are the H-atoms considered for abstraction reactions.
In total, abstraction of H-atoms from the 14 sites of curcumin has been studied. The optimised geometries along with bond-breaking and bond-forming distances (Å) of transition states (TS-Hx) are presented in Figure 2. The activation free energies (ΔG b ) and reaction free energies (ΔG f ) determined at different levels of theory in gas and aqueous phases are listed in Table 1. It is found that the ΔG b for H-atom abstractions increase in the following order: H8 < H17 < H4 < H13 < H16 < H3 ≈ H7 < H15 < H6 ≈ H12 < H19 < H10 < H1 < H11 at the M06-2X/6-311 + G(d,p) level of theory in gas phase (Table 1). We note that on going from the 6-31G(d) to 6-311 + G(d,p) basis set, the ΔG b are increased by 1.9 − 3.6 kcal/mol in gas phase but they follow almost the similar trend. The ΔG b for abstractions of the H8 and H11 atoms are 19.14 and 30.93 kcal/mol, respectively, as obtained at the M06-2X/6-311 + G(d,p) level in gas phase (Table 1). Further, the ΔG b for abstraction of H17 (19.25 kcal/mol) computed at the same level of theory is found to be comparable to that of H8 (Table 1). The ΔG b involved in the abstractions of the H8 and H17 atoms are also found to be lowest in aqueous media, their values being 19.16 and 19.27 kcal/mol, respectively ( Table 1). The corresponding bond-breaking and bondforming distances at TSs for the H8 and H17-atoms abstractions are found to be same, their values being 1.15 and 1.38 Å, respectively ( Figure 2). This is in consistent with the almost equal ΔG b at these sites ( Figure 2 and Table 1). Moreover, the ΔG b values for the abstractions of H8 and H17 atoms may also be identical because of their same chemical environment and symmetrical positions ( Figure 1). The bond-breaking distance at TS − H 11 for H11 abstraction (1.23 Å) is greater than that at TS − H 8 or TS − H 17 whereas bond-breaking distances at TSs for other sites are even larger (1. 35-1.41 Å) indicating that TSs at the H11 and other Hatoms resemble reactant-like structures ( Figure 2). The atomic spin densities of TSs for HAT reactions listed in Table S2 of Supporting Information reveal that delocalisation of the unpaired electron from methyl radical to curcumin moieties are 0.  (Table S2). Similarly at TS − H 17 , atomic spin density of curcumin moiety is broadly delocalised involving C12, C14, C16, C18, O17 and O18 atoms (Table S2). At TSs for HAT reactions at other sites, this stability is not observed as the atomic spin density of curcumin moiety is mainly localised near the reacting sites. Thus, the ΔG b and properties of TSs show that methyl radical can abstract H8 and H17 atoms more readily than other Hatoms from curcumin, in both gas phase and aqueous media. Furthermore, we note that the H8 and H17 atoms are the Hatoms present in the phenolic groups of curcumin and our finding that abstractions of H8 and H17 atoms are favourable  over other H-atoms from curcumin by methyl radical is in line with the previous reports where H-atom abstraction from phenolic groups was also found to be favourable in comparison to that from other groups in some natural polyphenolic compounds [48,49]. For instance, the phenolic O8 and O17 sites of curcumin were found to be favourable sites for H-atom abstraction by OH• radical in a previous study [16]. An examination of the reaction free energies (ΔG f ) obtained at the different level of theory in gas phase and aqueous media reveal that the abstraction reactions for the H8, H17 and H11 atoms only are exergonic (Table 1). However, we note that although the abstraction of H11 atom is thermodynamically favourable, the ΔG b for HAT at this position is higher than that for H8/ H17 atom in both gas phase and aqueous media (  (Figure 1). Thus, the H-atom abstraction from the phenolic O8 and O17 sites would be easier than from the O11 site. It is clearly evident from Figure 3, where the activation free energies and reaction free energies of different HAT reactions obtained at the M06-2X/6-311 + G(d,p) level of theory in aqueous media are plotted, that the abstractions of H8, H17 and H11 atoms only would occur. Thus, our calculations show that curcumin can scavenge the methyl radical through HAT mechanism from its O8, O17 and O11 sites and the H-atom abstraction from the phenolic O8 and O17 sites would be faster than that from O11 site.

Radical adduct formation (RAF) reactions
To explore the scavenging action of curcumin (Cur) toward CH 3 • radicals through RAF mechanism, the addition of CH 3 • radical at its 19 carbon sites has been studied as follows: Where, X = 1-19 are the different carbon sites of curcumin. The optimised structures of TSs and adducts along with bond forming distances (Å) involved in different RAF reactions are shown in Figure 4 and Fig. S1 (Supporting Information), respectively. The activation free energies (ΔG b ) and reaction free energies (ΔG f ) of adducts involved in RAF reactions computed both in gas and aqueous phases, are listed in Table 2. The computed ΔG f values reveal that RAF reactions at all the sites excepting C2, C5, C7, C9, C14, C16 and C18 sites are exergonic (i.e. spontaneous) in both gas and aqueous phases ( Table 2). The ΔG f of exergonic RAF reactions at the different sites obey the following trend in aqueous media: C12 < C1 < C3 < C13 < C4 < C17 < C15 < C8 < C6 < C19 < C10 < C11, the ΔG f at the C12 and C11 sites being −17.77 and −2.16 kcal/mol, respectively (Table 2). However, it is interesting to note that ΔG f values at the C12, C1, C3 and C13 sites lie within a range of ∼1 kcal/mol in aqueous media. This indicates that RAF reactions at the C12, C1, C3 and C13 sites are thermodynamically nearly equally favourable in aqueous media, which is biologically more important.
In order to compare the reactivity of different sites for RAF reactions, rate constant (k) at all the sites were calculated using the following expression.
Where, G(T) is the quantum mechanical tunnelling factor obtained using the method suggested by Skodje and Truhlar [50];k b is the Boltzmann constant; T is the absolute room temperature i.e. 298.15 K, h is the Planck's constant and R is the gas constant. The rate constant of RAF reactions at the C3 and C14 sites in gas phase (aqueous media) are found to be3.28 × 10 2 (1.23 × 10 2 ) and 3.71 × 10 −5 (1.22 × 10 −5 ) s −1 , respectively (Table S1 (Supporting Information)). In gas phase, the reactivity of C3 site is 2.67, 2.85, 4.07, 75.19 and 1111.11 times that of C13, C12, C4, C1 and C19 sites, respectively(Table S1 (Supporting Information)). In aqueous media, it is 1.93, 2.94, 4.06, 51.02 and 588.24 times the reactivities of C13, C12, C4, C1 and C19 sites, respectively (Table S1 (Supporting Information)). The reactivities of remaining sites are even lower than the C19 site(Table S1 (Supporting Information)). It indicates that addition of methyl radical at the C19 and other sites where ΔG b is very high would be significantly less favourable as compared to the most reactive C3 site. An examination of the TS structures for different RAF reactions reveals that TSs at the C3, C13, C12, C4 and C1 sites resemble to the reactant-like structure as their bond-forming distances are significantly large (2.31 − 2.34 Å) whereas TSs at the C19 and other sites resemble to the product-like structures as their bond-forming distances are small (1.15 − 2.24 Å) (Figure 4). The atomic spin densities of TSs for RAF reactions listed in Table S3 show that delocalisation of the unpaired electron from methyl radical to the curcumin moiety is less (0.22-0.24) for TSs at the C3, C13, C12, C4 and C1 sites as compared to that for TSs at the C19 and other sites (0. 26-0.44) implying that TSs at the C3, C13, C12, C4 and C1 sites retain the reactant-like structure. Thus, properties of TSs again indicate that reactions at the Table 2. The activation free energy (ΔG b ) and the reaction free energy (ΔG f ) involved in different RAF reactions, as obtained at different levels of theory in gas and aqueous phases. The energies are expressed in kcal/mol. C19 and other sites would be less favourable as compared to the C3, C13, C12, C4 and C1 sites. It is clearly apparent from the activation free energies and reaction free energies of different RAF reactions, as obtained at the M06-2X/6-311 + G(d,p) level of theory in aqueous media, plotted in Figure 5 that addition of CH 3 • radical would occur mainly at the C3, C12, C13, C1, C4 and C19 sites of curcumin. Considering both the HAT and RAF mechanisms together, it is found that ΔG b at the most reactive C3 site for RAF mechanism is 14.01 (14.59) kcal/mol whereas the ΔG b for the most reactive site O8 for HAT mechanism is 19.14 (19.16) kcal/mol, as obtained at the M06-2X/6-311 + G(d,p) level of theory in gas phase (aqueous media) (Tables 1 and 2). Thus, it shows that the scavenging activity of curcumin toward the CH 3 • radical through RAF mechanism would be more probable as compared to the HAT mechanism.
To understand whether an adduct formed by the reaction of a CH 3 • radical with curcumin can further bind to another CH 3 • radical, the addition of second CH 3 • radical at the different carbon sites of the adduct formed by the addition of a CH 3 • radical at the most reactive C3 site of curcumin, [Cur − CH † 3 ] C3 , has been studied as follows: where, X represents the different carbon sites of curcumin excluding 3. The successive CH 3 • radical binding energies (expressed in kcal/mol) of adducts thus formed are listed in Table 3. The binding energies of these adducts indicate that addition of second CH 3 • radical at the C5, C6, C8 and C10 sites are thermodynamically stable in both gas phase and aqueous media. In fact, the addition of second CH 3 • radical is found to be more favourable than the first CH 3 • radical (Tables 2 and 3). Thus, curcumin may act as a sponge for CH 3 • radicals.

Scavenging of ethyl (C 2 H 5 • ) radicals
As it is found that RAF mechanism would be preferred over the HAT or SET mechanisms for the scavenging of methyl radicals by curcumin, the scavenging of ethyl radicals by curcumin has been studied through RAF mechanism only. The addition of ethyl radicals has been considered at all the 19 sites of curcumin where CH 3 • radical addition was studied. The adducts formed by the addition of ethyl at different sites of curcumin are shown in Fig. S2 (Supporting Information). The binding energy of these adducts computed in both gas and aqueous phases are listed in Table 4. It may be noted that the binding energies of adducts are increased by 0.64 − 2.03 kcal/mol in going from the 6-31G(d) to 6-311 + G(d,p) basis set but they follow the similar trend ( Table 4). The aqueous media binding energies are deviated from the corresponding gas phase values by 0.01 − 1.29 kcal/mol (Table 4). It is evident from Table 4 that ethylated adducts formed at the C1, C3, C13, C12, C4, C17, C8, C15 and C6 sites are appreciably stable in both gas and aqueous phases as their binding energies lie in the range of −14.57 to −3.3 (−15.15 to −2.77) kcal/mol at the M06-2X/ 6-311 + G(d,p) level of theory in gas phase (aqueous media). The binding energy of ethylated adduct formed at the C19 site is only −0.63 (−0.67) kcal/mol in gas phase (aqueous media). However, the adducts formed at the remaining sites are not stable as their binding energies are positive in both gas phase and aqueous media. Thus, the addition of ethyl radicals would mainly occur at the C1, C3, C13, C12, C4, C17, C8, C15 and C6 sites. Further, it is evident from Figure 6 that the aqueous media binding energies of stable methylated adducts are appreciably more negative than the corresponding ethylated adducts. It indicates that the curcumin can scavenge methyl radicals more efficiently as compared to ethyl radicals through RAF mechanism.

Conclusions
In the present contribution, DFT calculations employing the M06-2X functional and the 6-31G(d,p) and 6-311 + G(d,p) basis sets have been carried out to investigate the scavenging activity of curcumin toward the methyl and ethyl radicals through RAF, HAT and SET mechanisms. It is found that for scavenging of methyl radicals, the SET mechanism is not viable (highly endergonic) whereas the RAF mechanism is more favourable than the HAT mechanism. Within RAF mechanism, the addition of methyl radical can occur at the C3, C4, C12, C13, C1 and C19 sites of curcumin with C3 as the most reactive site. And within HAT mechanism, abstractions of H-atoms can occur only from the O8, O17 and O11 sites of curcumin. For reactions of ethyl radicals, binding energies of ethylated adducts show that addition of ethyl radicals can occur at the C1, C3, C13, C12, C4, C17, C8, C15 and C6 sites of curcumin. Further, binding energies of methylated and ethylated adducts indicate that the curcumin can scavenge methyl radicals more efficiently as compared to ethyl radicals through RAF mechanism. The addition of second methyl radical show that curcumin may act as a sponge for CH 3 • radicals.
research work, analysis of the results and writing of the manuscript. All authors read and approved the final manuscript.

Data availability
All data generated or analyzed during this study are included in this published article.

Supporting information
The optimised structures of methylated and ethylated adducts, tables containing rate constants and relative reactivities, atomic spin densities of TSs and the Cartesian coordinates of all the optimised TSs involved in RAF and HAT reactions are provided as Supporting Information.