A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness

Arabian Journal of Chemistry (2017) xxx, xxx–xxx

King Saud University

Arabian Journal of Chemistry www.ksu.edu.sa www.sciencedirect.com

ORIGINAL ARTICLE

A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness Claudia Sandoval-Yan˜ez a, Carolina Mascayano b,*, Jorge I. Martı´ nez-Araya c,1 a Theoretical and Computational Chemistry Center, Engineering Faculty, Universidad Autonoma de Chile, El Llano Subercaseaux 2801, Santiago, Chile b Departamento de Ciencias del Ambiente, Facultad de Quı´mica y Biologı´a, Universidad de Santiago de Chile (USACH), Av. Libertador Bernardo O’Higgins 3363, Santiago, Chile c Departamento de Ciencias Quı´micas, Facultad de Ciencias Exactas, Universidad Andres Bello (UNAB), Av. Repu´blica 498, Santiago, Chile

Received 26 July 2017; accepted 29 October 2017

KEYWORDS Flavonoids; Antioxidant capacity; Ferric reducing antioxidant power; Anodic oxidation potential; Local hypersoftness

Abstract A theoretical reactivity descriptor to estimate local reactivity on molecules was tested to assess the antioxidant capability of some flavonoids. It was validated by comparison with experimental precedents published already by Firuzi et al. (2005). The aforementioned reactivity index is called local hyper-softness (LHS). This parameter was applied on HO- substituent groups on the same set of flavonoids within each subclassification: flavones (apigenin and baicalein), flavonols (fisetin, galangin, 3–OH flavone, kaempferol, myricetin, and quercetin), flavanones (hesperetin, naringenin, taxifolin) and isoflavones (daidzein and genistein). Experimental values of both techniques, ferric reducing antioxidant power (FRAP) and anodic oxidation potential (Eap) were retrieved from Firuzi et al. (2005) with the purpose of validating the calculated LHS values. Excepting myricetin, the LHS values of all these compounds matched in a similar order relationship experimentally obtained by means of Eap and FRAP from Firuzi et al. (2005). Our results revealed that LHS is a suitable theoretical parameter to get an insight concerning to the antioxidant capacity of these compounds, in particular, LHS allows explaining experimentally obtained values of FRAP along with Eap values in terms of reactivity of HO- substituent groups belonging these molecules theoretically computed without including experimental parametes. Ó 2017 Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

* Corresponding author. E-mail addresses: [email protected] (C. Mascayano), [email protected] (J.I. Martı´ nez-Araya). 1 Principal corresponding author. Peer review under responsibility of King Saud University

Production and hosting by Elsevier

1. Introduction 1.1. Relevance of flavonoids Flavonoids are polyphenols of varied structure that can be found as aglycones or glycosides. They are secondary metabolites present in many fruits and vegetables. In plants, they play different functions as protection of UV light, defense of abiotic

https://doi.org/10.1016/j.arabjc.2017.10.011 1878-5352 Ó 2017 Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

2 tensions, bacterial phytopathogens, and fungi; the most recently properties found revealed they can act as the endogenous regulator of the movement of auxins in plants (Brunetti et al., 2013; Jansen et al., 1998). Flavonoids have been studied due to their many pharmacological activities such as antioxidants, antibacterial, antimutagenic, antiangiogenic, anti–inflammatory, antiallergic, modulators of enzymatic activity and anticancer activity (Cushnie and Lamb, 2011; Ribeiro et al., 2013; Kawai et al., 2007). Several studies have shown that flavonoids can interact with different therapeutic targets, this ability to interact is principally influenced by their chemical structure and REDOX capacity (Garcı´ a-Lafuente et al., 2009). Some examples of enzymes that may be inhibited are NADH oxidases, polyphenol oxidases, peroxidases, lipoxygenase, cellulases, xylanases, pectinases, glutathione-Stransferases, glycoproteins, and kinases (Ravishankar et al., 2013). Considering the importance flavonoids is that in our group has been interested in last years in the study of interaction and inhibition of important enzymes involved in the arachidonic acid cascade as are the lipoxygenases (LOX). Therefore, flavonoids appear as attractive molecules because they possess many of the desired structural characteristics aforementioned, for instance: genistein, luteolin, apigenin or kaempferol (Peterson and Dwyer, 1998) and all of them have an important antioxidant capacity. On the other hand, we can mention that biological studies of flavones and isoflavones carried out by our group showed that exist a direct relationship between the structure of inhibitors and LOX inhibition (Mascayano et al., 2011; Mascayano et al., 2015; Ribeiro et al., 2014). Also, results of antioxidant of some natural flavonoids were previously published by Firuzi et al. (2005) and taken into account in this work with the aim to obtain relevant electronic information by quantum chemistry, which could provide an explanation of the structure–activity relationship between flavonoids. According to the latter, our purpose is to reveal locally and theoretically the reactivity on different sites on a molecule. Although a typical local reactivity index corresponds to the net charges coming from a population analysis, as the latter has demonstrated to be not too well connected with an experimental parameter (Martı´ nez-Araya et al., 2015), through the Conceptual DFT (Parr and Yang, 1989; Geerlings et al., 2003), a local reactivity descriptor to assess the antioxidant capability of some flavonoids was proposed by Morell et al. (2005) to get insights concerning to the antioxidant capacity and that local reactivity descriptor is known as the local hyper–softness (LHS) and its definition will be given in the next subsection. 1.2. Local hyper–softness There are many indexes to estimate reactivity theoretically from quantum chemical calculations coming from the field of the Density Functional Theory (Hohenberg and Kohn, 1964; Kohn and Sham, 1965) (DFT) and as a consequence chemists can find a plethora of reactivity descriptors (Chermette, 1999) so giving rise to the Conceptual DFT (Parr and Yang, 1989; Geerlings et al., 2003) under the hypothesis that the total energy E of a system depends upon the total number of electrons N and the external potential tðrÞ, so that the application of successive ordinary and functional derivatives yields a wide range of reactivity descriptors which are divided into three

C. Sandoval-Yan˜ez et al. types: global, local and non–local, all of them based on two essential physical observable quantities: energy, electronic density or both. Among of the endless type of local reactivity descriptors that are possible to conceive, there is one defined at a third order (Geerlings and De Proft, 2008) that has had becoming more and more popular among some researchers interested in measuring local reactivities; this alluded descriptor is the so–called dual descriptor (Morell et al., 2005; Fuentealba and Parr, 1991; Morell et al., 2006) which has demonstrated to be a more robust tool than Fukui functions (Morell et al., 2008; Morell et al., 2008; Martı´ nez-Araya, 2015). But certain limitations (Ca´rdenas et al., 2009) prevent its use to compare reactivity among different molecular systems. In fact, it can only be used to reveal nucleophilic and electrophilic sites on a molecule in order to understand its intrinsic reactivity without expecting to compare that reactivity with the local reactivity of another molecular system even using exactly the same reactivity descriptor. However, dual descriptor allows to define a more useful descriptor, so that in order to overcome the aforementioned limitation of dual descriptor, such an descriptor contains the dual descriptor in its definition along with a global reactivity descriptor giving rise to the local hyper–softness (LHS), this being the local reactivity descriptor that has assumed the role of dual descriptor when a comparison of local reactivities among different molecules is carried out (Martı´ nez-Araya et al., 2015; Ca´rdenas et al., 2009; Martı´ nez-Araya, 2013). LHS is represented by sð2Þ ðrÞ and it is defined by the following operational formula: sð2Þ ðrÞ  fð2Þ ðrÞ S2 ¼

qðrÞLUMO  qðrÞHOMO ðeLUMO  eHOMO Þ2

:

ð1Þ

The use of Eq. (1) implies to assume that global and local reactivity of a molecule is driven by frontier molecular orbitals (details about deduction of this operational formula are described in Supplementary Material). This is a good first approach to get an insight into a family of molecules. Previous studies focused on the local reactivity of flavonoids through the use of the Conceptual DFT revealed information concerning to susceptible sites on a molecule to undergo nucleophilic and electrophilic attacks, in particular one flavonoid like naringenin was the main subject of analysis (Martı´ nez-Araya et al., 2013; Glossman-Mitnik, 2013) and isonaringin (Glossman-Mitnik, 2014), however these works did not broach a family of flavonoids. Even so, that led us to take LHS into account whose operational formula given by Eq. (1) includes energies and electronic densities of frontier molecular orbitals under the hypothesis that reactivity is ruled by these molecular orbitals mainly and as a consequence the electron donor and electron acceptor capabilities of molecules can be computed through that descriptor, so that the antioxidant capacity can be attributable to the electron donor capacity of the molecule under study. Some molecules of biological interest like oxicams have been studied by means of the LHS descriptor (Martı´ nez-Araya et al., 2013), thus revealing the most susceptible sites of these molecules to undergo nucleophilic and electrophilic attacks. Nevertheless there was no an intention to find a possible link with an experimental parameter. According to this precedent, our work points towards to explore a possible link between experimental parameters designed to measure antioxidant capacity of

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

A theoretical assessment of antioxidant capacity of flavonoids flavonoids and LHS which is capable to unveal the most electron donor and acceptor sites on a molecule. 2. Computational methods The following flavonoids were grouped and studied in families: flavones (apigenin and baicalein), flavonols (fisetin, galangin, 3–OH flavone, kaempferol, myricetin and quercetin), flavanones (hesperetin, naringenin, taxifolin) and isoflavones (daidzein and genistein). All possible stereoisomers for those molecules presenting one o more chiral carbons, were taken into account. All molecular structures were geometrically optimized at the B3LYP (Becke, 1993; Lee et al., 1988; Miehlich et al., 1989; Vosko et al., 1980) level of theory by using the 6-311G(d) basis set in aqueous phase through the use of the self-consistent reaction field (Tapia and Goscinski, 1975) method called Polarizable Continuum Model (Scalmani and Frisch, 2010). Frequency calculations were then performed to identify the stationary points as minima (Schlegel, 1982). All calculations were carried out using the Gaussian 09 (Frisch et al., 2009) software package. Flavanones are molecules presenting one or two chiral centers thus implying that all possible estereoisomers were taken into account under the assumption that the presence of each estereoisomer is ruled by a statistical Boltzmann distribution. According to the latter and being vi the mole fraction of the ith stereoisomer of a molecule, this quantity is estimated through the use of a Boltzmann distribution whose details are included in the Supplementary Material. In order to obtain condensed values of LHS on the kth – ð2Þ atom (sk ), the AOMix software has been employed (Gorelsky, 2013; Gorelsky and Lever, 2001). The procedure is the following: under the assumption that frontier molecular orbitals rule the reactivity among molecules, we have supposed the antioxidant capacity of flavonoids is of covalent nature or it is initiated through a covalent interaction. In such a case, nucleophilic and electrophilic Fukui functions [fþ ðrÞ and f ðrÞ] are integrated on each atom (Contreras et al., 1999; Fuentealba et al., 2000; Chamorro and Pe´rez, 2005), the integration within the kth –atomic domain Xk (Contreras et al., 1999; Fuentealba et al., 2000; Galva´n et al., 1988; Zielinski et al., 2012) turns LHS into a local reactivity index associated to the kth –atom because there is no more dependence upon r, the vector position. The latter means: Z Z Z ð2Þ sð2Þ ðrÞ dr ¼ fð2Þ ðrÞ  S2 dr ¼ S2  fð2Þ ðrÞ dr ¼ sk : ð2Þ Xk

Xk

Xk

Notice that Z Xk

fð2Þ ðrÞ dr ¼

Z Xk

fþ ðrÞ dr 

Z Xk

 f ðrÞ dr  fþ k  fk ;

so that AOMix can perform these couple of integrations through the following algorithm: fþ k ¼

M XX cm LUMO cl LUMO Sml

ð3Þ

m2k l¼1

f k ¼

M XX cm HOMO cl HOMO Sml : m2k l¼1

ð4Þ

3 R

where Sml ¼ drvm ðrÞvl ðrÞ is the overlap integral and vl ðrÞ is an atomic basis function; vm ðrÞ is a conjugate atomic basis function in which m 2 k thus indicating that the sum runs over all of the atomic basis functions that are centered on atom k under the assumption that there are M atomic basis functions. As indicated by Eqs. (3) and (4), this software works under the frontier molecular orbital approximation so that the condensation scheme is explained as follows: fþ ðrÞ ¼ qðrÞNþ1  qðrÞN M X M X  jwðrÞj2LUMO ¼ cm LUMO cl LUMO vm ðrÞvl ðrÞ

ð5Þ

m¼1 l¼1 

f ðrÞ ¼ qðrÞN  qðrÞN1 M X M X cm HOMO cl HOMO vm ðrÞvl ðrÞ:  jwðrÞj2HOMO ¼

ð6Þ

m¼1 l¼1

Integration of Eqs. (5) and (6) leads to Eqs. (3) and (4). Since dual descriptor is the arithmetic difference between fþ ðrÞ and f ðrÞ, the condensed value of fð2Þ ðrÞ is the arithmetic difference between Eqs. (3) and (4): ( ) M M X X X ð2Þ   fk ¼ cm LUMO cl LUMO Sml  cm HOMO cl HOMO Sml : m2k

l¼1

l¼1

ð7Þ Finally, the condensed value of local hyper–softness is simð2Þ ð2Þ ply obtained by the following multiplication: S2 fk ¼ sk . 3. Results and discussion The selected flavonoids as depicted by Figs. 1–3 come from the article written by Firuzi et al. (2005). In order to keep the same criterium of chose, we have selected some of them and grouped in the same classes with some exceptions: the singleton group of flavanols was discarded because it is composed by just one flavonoid (catechin); from the flavones class, 5-OH flavone and 7-OH flavone were discarded because their FRAP values are zero; from the flavonols group, the rutin molecule or quercetin-3-O-rutinoside was discarded due to it is a glucoside and away structurally from the other compounds studied. The negative phase of LHS reveals all those electron–donating atoms on a molecule. However, since oxygen atoms belonging to the OH groups are the responsible of providing antioxidant capacity for these molecules, then it makes sense to relate such property with the electron donor capability of hydroxyl oxygen atoms. According to the latter, the summation of LHS condensed values on hydroxyl oxygen atoms were taken into account and the absolute value of the resulting total for each molecule was depicted as bar graphics along with bar graphics of FRAP and Eap values. Readers interested in identifying specific atoms, values of other local reactivity descriptors and the way of use of the Boltzmann distribution, should please read Supplementary Material. Firuzi et al. (2005) proposed an assay called ferric reducing antioxidant power (FRAP) to evaluate the antioxidant capacity of flavonoids. FRAP was suggested by Benzie and Strain (1996) with the aim of assessing the total antioxidant capacity of a molecule. Since the results obtained by Firuzi et al. (2005) are in agreement with the gathered knowledge about the antioxidant capacity of these flavonoids through the measure

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

4

C. Sandoval-Yan˜ez et al.

Fig. 1 Flavones and Flavonols: The computation of their antioxidant capacity through the use of LHS is extensively explained in Supplementary Material.

Fig. 2 Flavanones: The computation of their antioxidant capacity through the use of LHS is extensively explained in Supplementary Material.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

A theoretical assessment of antioxidant capacity of flavonoids

5

Fig. 3 Isoflavones: The computation of their antioxidant capacity through the use of LHS is extensively explained in Supplementary Material.

of anodic oxidation potential, we have decided to test if local hyper–softness can provide a similar qualitative information that was revealed by FRAP. FRAP and LHS were compared against Eap. Our hypothesis lies in the fact that LHS can explain the origin of the antioxidant capacity from the point of view of local reactivity and in consequence, it can also be used to estimate the antioxidant capacity as FRAP does it. The bar graphics involving comparisons between Eap, LHS and FRAP values are exhibited from Figs. 4 until 7. Bar graphics comparing Eap and LHS deserve a more detailed explanation. The absolute value of LHS on chosen O atoms is shown as a red bar and it is measured in millielectronvolt raised to the power of minus two ½mðeVÞ2 . Notice that only eV is raised to the power of 2 and not the milli prefix. The anodic oxidation potentials again are represented as blue bars and expressed in centivolts units (cV). The information reported by Firuzi et al. (2005) reveals that FRAP can be used as a suitable experimental procedure to assess the antioxidant capacity of flavonoids. Values of FRAP and Eap reported by them are contrasted and represented in bar graphics. Oxygen atoms mainly forming part of an hydroxyl group have the most important electron donor capacity, so that condensed LHS values on these atoms are expected to be the most negative and as a consequence they should be responsible for the antioxidant capacity that characterizes these molecules. 3.1. Flavones Fig. 4(a) indicates that baicalein exhibits a more electron– donor capacity in comparison with apigenin because    ð2Þ ð2Þ  2 sO11 þ sO12  ¼ 19:40 mðeVÞ meanwhile the apigenin molecule    ð2Þ ð2Þ ð2Þ  has sO11 þ sO13 þ sO20  ¼ 6:61 mðeVÞ2 thus revealing that baicalein donates electrons coming from these hydroxyl groups easier than apigenin does. The reader can check these values in the Supplementary Material. So, according to the latter, the experimental measurements given by FRAP, as depicted

in Fig. 4(b), can be explained in terms of local reactivities given by the reactivities of the aforementioned oxygen atoms and as a result, FRAP values are supported by this theoretical tool. Consistency in these order relationship is confirmed through Eap values which provide that baicalein < apigenin. Notice that the third OH group attached to the A ring in baicalein establishes a hydrogen bond with the oxygen that belongs to the carbonyl group, so that the catechol group of baicalein is not perturbated by this third OH. So far, we can state that the presence of the carbonyl group highlights the antioxidant capacity of baicalein provided by the catechol group. The latter suggests that the absence of this group would lead to contrary effect, but to make sure this statement is true, we must to find an example where the presence of a third free OH group diminishes the antioxidant capacity that is provided by a neighbor catechol group into a flavonoid. Myricetin is a good candidate to demonstrate this proposal. 3.2. Flavonols This is a more challenging set of flavonoids due to its number of compounds. The condensed values of LHS on the selected oxygen atoms on each flavonol (please see Supplementary Material) provide the following order relationship as depicted in Fig. 5(a): fisetin > quercetin > kaempferol > galangin > myricetin > 3 OH–flavone. On the other hand, FRAP values exhibit the following order relationship as observed in Fig. 5 (b): quercetin > fisetin > myricetin > kaempferol > galangin > 3 OH–flavone and Eap: myricetin < fisetin ¼ quercetin < kaempferol < galangin < 3 OH–flavone.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

6

C. Sandoval-Yan˜ez et al.

Fig. 4 Flavones group involves baicalein and apigenin. Blue bars correspond to Eap, the anodic oxidation potential is given in centivolt units (cV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 5 Flavonols group involves 3 OH-flavone, fisetin, quercetin, galangin, kaempferol and myricetin. Blue bars correspond to Eap, the anodic oxidation potential is given in centivolt units (cV).

After deleting the myricetin molecule, we obtain that: LHS: fisetin > quercetin > kaempferol > galangin > 3 OH– flavone. FRAP: quercetin > fisetin > kaempferol > galangin > 3 OH–flavone. Eap: fisetin ¼ quercetin < kaempferol < galangin < 3 OH– flavone.

Since Eap values are considered as more stable values, we can notice that fisetin and quercetin have the same antioxidant capacity (see Fig. 5) and that is why their FRAP and in particular LHS condensed values are very close one each other, but LHS reveals clearer this similarity because of a difference of DLHS ¼ 0:77 mðeVÞ2 ; FRAP values between these two molecules are lightly farther one each other so providing a difference value of DFRAP ¼ 9:5 lM.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

A theoretical assessment of antioxidant capacity of flavonoids

7

It is noticeable that neither LHS nor FRAP can quantify the antioxidant capacity of myricetin as Eap quantifies correctly. From the FRAP point of view, we cannot state any analysis because we have not performed those experiments, however from the perspective of LHS we can provide some plausible explanations to understand this discrepancy. In this flavonols family, myricetin is the only structure bearing three OH groups in the B ring (pyrogallol). Our obtained condensed values of LHS showed a better link to the previously reported values of FRAP, but not to Eap which is in agreement with results reported by Firuzi et al. (2005). This anomalous behaviour exhibited by myricetin is attributed by this author to the pyrogallol group aforementioned, being the responsible of steric and electronic effects, however a possible way to confirm or reject that suggested explanation given by Firuzi et al. is including a maximum number of conformations versus condensed values of LHS for all those molecules having the pyrogallol group, the latter should be mandatory in next analyses because of the found structural conformation of myricetin obtained by us could not be the most representative for an assessment of the local reactivity of myricetin. The remaining flavonols show a local reactivity given by LHS which is in good agreement with FRAP and Eap values. Although baicalein has a pyrogallol group on ring A, the results did not show the effect of this group on this flavonoid, unlike the myricetin. This phenomenon can be explained by the presence of the -OH group on carbon 7 (numerical labelling on atoms is defined in Supplementary Material), of the ring A of baicalein, which generates a hydrogen bond with the oxygen of the carbonyl group on the ring C. This justifies the free availability of the catechol group in the ring A of the baicalein. This was reflected in the results of LHS, Eap and FRAP.

and the biggest Eap value, thus revealing that less iron (II) is released by naringenin and more difficult is the oxidation process from iron (II) into iron (III). In other words, we can notice that LHS localized at positions of chosen oxygen atoms (those ones having the best electron donor capability) is able to explain the FRAP and Eap values in terms of reactivities of atoms on each molecule. Concerning the reactivity inter–families, we can remark that flavanones present a lesser antioxidant capacity in comparison with flavanols when FRAP values are compared. This noticeable difference is attributable to the absence of aromaticity in the C ring in all flavanones, thus preventing a suitable electron delocalization among p–electrons between B ring and C ring.

3.3. Flavanones As depicted by Fig. 6, there is no doubt that in this set of flavonoids just one trend is found: LHS: taxifolin > hesperetin > naringenin. FRAP: taxifolin > hesperetin > naringenin. Eap: taxifolin < hesperetin < naringenin. It is evidenced that taxifolin presents a noticeable antioxidant capacity that overcomes that ones of hesperetin and naringenin. And the reasons for that lies in the known fact concerning to the presence of a catechol group along with the presence of an OH group in the C ring and their influence exerted on the molecule to which they are attached. As observed in Fig. 2, the existence of a catechol group attached to the B ring in taxifolin is reinforced with the presence of the OH group bound to the carbon atom number 5 in the C ring. On the contrary, the absence of both, the catechol group in the B ring and the OH group in the C ring, makes naringenin has the lowest electron donor capability, thus making it the worst antioxidant flavanone. This theoretical result supports the experimental information gathered by us through the FRAP and Eap values, thus meaning that naringenin presents the smallest FRAP value

3.4. Isoflavanones We obtain just one trend again from Fig. 7: LHS: daizen  genistein. FRAP: daizen > genistein. Eap: daizen  genistein. Notice that genistein has an Eap value that is 1.3% smaller than the respective value of daidzein; genistein has a LHS value that is 7.4% smaller than the respective value of daizein, thus revealing these values are pretty similar to the case of quercetin whose LHS value is 5.1% smaller than the LHS value of fisetin which makes them a couple of molecules presenting almost the same antioxidant capacity because the respective value of Eap is exactly the same. In terms of a global comparison, we observe that the antioxidant capacity of this couple of flavonoids is overcome by the remaining flavonoids that were analyzed at the present work. As can be noticed, isoflavones exhibit big Eap values thus revealing a difficulty to oxidize them. As a Supplementary Material, their FRAP values are also one of the lowest in the flavonoids studied here, which reveals that small amounts of iron (II) are released in comparison with the remaining flavonoids. The values of these two experimental parameters, Eap and FRAP, can be explained in terms of a small electron donor capability given by the chosen oxygen atoms that presented the highest values of LHS in these two molecules that conform the isoflavones when comparing with the electron donor capability shown by the remaining flavonoids. According to our results, it can be noticed that LHS allows one to explain Eap and FRAP values from the perspective of the reactivity of atoms, specifically from an electron donor capability given by the oxygen atoms of hydroxyl groups. As global perspective, we can remark that the merit of our work lies in the fact the trends found by Firuzi et al. are explained in terms of reactivities of certain oxygen atoms coming from hydroxyl groups of the studied flavonoids. The temporal disadvantage in our analysis is the absence of all possible conformers, even so we used stable conformers taking into account the most favourable hydrogen-bond interactions that are possible to distinguish at a simple glance along with all possible enantiomers whose weighted presence is given by a Boltzmann distribution.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

8

C. Sandoval-Yan˜ez et al.

Fig. 6 Flavanones group involves taxifolin, naringenin and hesperetin. Blue bars correspond to Eap, the anodic oxidation potential is given in centivolt units (cV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7 Isoflavones group involves daidzein and genistein. Blue bars correspond to Eap, the anodic oxidation potential is given in centivolt units (cV). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

4. Conclusions A local reactivity descriptor which is known as local hypersoftness (LHS) was applied on hydroxyl substituent groups on a set of flavonoids: flavones (apigenin and baicalein), flavonols (fisetin, galangin, 3–OH flavone, kaempferol, myricetin and quercetin), flavanones (hesperetin, naringenin, taxifolin) and isoflavones (daidzein and genistein). Stereoisomers were taken into account on each molecule presenting one or more

chiral centers. Condensed values of the negative phase of the LHS on oxygen atoms revealed similar trends as experimental FRAP and Eap values have done for these molecules by Firuzi et al. (2005). According to the condensed aforementioned LHS values, the flavonoids that exhibit the best antioxidant capacities are: baicalein, fisetin, quercetin and taxifolin which are also the same ones as revealed by the respective FRAP and Eap values. The only clear exception given by the myricetin molecule will encourage us to perform an analysis concerning

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

A theoretical assessment of antioxidant capacity of flavonoids

9

to the conformational dependence of LHS in order to find a more suitable conformation of hydroxyl groups for this molecule with the aim of matching with the experimental trend reported in the literature. Even so, in spite of not considering all possible conformers of each flavonoid and only one of their most stable conformations were taken into account, our analysis highlights in the sense that same trends found by Firuzi et al. (2005) are reproduced by us, thus validating our methodology as a theoretical procedure usable on a family of compounds in order to obtain the antioxidant behavior with an additional explanation in terms of local reactivities of oxygen atoms (coming from hydroxyl groups mainly) of strong electron donor behavior which is detected by the use of local hyper-softness.

Agents 38, 99–107. https://doi.org/10.1016/j. ijantimicag.2011.02.014. Firuzi, O., Lacanna, A., Petrucci, R., Marrosu, G., Saso, L., 2005. Evaluation of the antioxidant activity of flavonoids by ferric reducing antioxidant power assay and cyclic voltammetry. Biochim. Biophys. Acta (BBA) – General Subjects 1721 (1–3), 174–184. https://doi.org/10.1016/j.bbagen.2004.11.001 . Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M. A., Cheeseman, J.R., Scalmani, G., Barone, V., Mennucci, B., Petersson, G.A., Nakatsuji, H., Caricato, M., Li, X., Hratchian, H. P., Izmaylov, A.F., Bloino, J., Zheng, G., Sonnenberg, J.L., Hada, M., Ehara, M., Toyota, K., Fukuda, R., Hasegawa, J., Ishida, M., Nakajima, T., Honda, Y., Kitao, O., Nakai, H., Vreven, T., Montgomery Jr., J.A., Peralta, J.E., Ogliaro, F., Bearpark, M., Heyd, J.J., Brothers, E., Kudin, K.N., Staroverov, V.N., Kobayashi, R., Normand, J., Raghavachari, K., Rendell, A., Burant, J.C., Iyengar, S.S., Tomasi, J., Cossi, M., Rega, N., Millam, J.M., Klene, M., Knox, J.E., Cross, J.B., Bakken, V., Adamo, C., Jaramillo, J., Gomperts, R., Stratmann, R.E., Yazyev, O., Austin, A.J., Cammi, R., Pomelli, C., Ochterski, J.W., Martin, R.L., Morokuma, K., Zakrzewski, V.G., Voth, G.A., Salvador, P., Dannenberg, J.J., Dapprich, S., Daniels, A.D., Farkas, Foresman, J.B., Ortiz, J.V., Cioslowski, J., Fox, D.J., 2009. Gaussian 09 Revision E.01, Gaussian Inc. Wallingford CT. Fuentealba, P., Parr, R.G., 1991. Higher-order derivatives in densityfunctional theory, especially the hardness derivative @g=@; n. J. Chem. Phys. 94 (8), 5559–5564. https://doi.org/10.1063/1.460491. Fuentealba, P., Pe´rez, P., Contreras, R., 2000. On the condensed fukui function. J. Chem. Phys. 113, 2544–2551. https://doi.org/10.1063/ 1.1305879. Galva´n, M., Vela, A., Ga´zquez, J.L., 1988. Chemical reactivity in spinpolarized density functional theory. J. Phys. Chem. 92, 6470–6474. https://doi.org/10.1021/j100333a056. Garcı´ a-Lafuente, A., Guillamo´n, E., Villares, A., Rostagno, M.A., Martı´ nez, J.A., 2009. Flavonoids as anti-inflammatory agents: implications in cancer and cardiovascular disease. Inflamm. Res. 58 (9), 537–552. https://doi.org/10.1007/s00011-009-0037-3. Geerlings, P., De Proft, F., 2008. Conceptual dft: The chemical relevance of higher response functions. PCCP 10, 3028–3042. https://doi.org/10.1039/B717671F. Geerlings, P., Proft, F.D., Langenaeker, W., 2003. Conceptual density functional theory. Chem. Rev. 103, 1793–1874. https://doi.org/ 10.1021/cr990029p. Glossman-Mitnik, D., 2013. A comparison of the chemical reactivity of naringenin calculated with the m06 family of density functionals. Chem. Cent. J. 7 (1), 155. https://doi.org/10.1186/1752-153X-7-155. Glossman-Mitnik, D., 2014. Computational chemistry of natural products: a comparison of the chemical reactivity of isonaringin calculated with the m06 family of density functionals. J. Mol. Model. 20 (7), 2316. https://doi.org/10.1007/s00894-014-2316-3. Gorelsky, S.I., 2013. Aomix: Program for molecular orbital analysis; version 6.88, university of Ottawa, . Gorelsky, S.I., Lever, A.B.P., 2001. Electronic structure and spectra of ruthenium diimine complexes by density functional theory and indo/s. Comparison of the two methods. J. Organomet. Chem. 635, 187–196. https://doi.org/10.1016/S0022-328X(01)01079-8. Hohenberg, P., Kohn, W., 1964. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871. https://doi.org/10.1103/PhysRev.136.B864. Jansen, M.A., Gaba, V., Greenberg, B.M., 1998. Higher plants and uvb radiation: balancing damage, repair and acclimation. Trends Plant Sci. 3, 131–135. https://doi.org/10.1016/S1360-1385(98) 01215-1. Kawai, M., Hirano, T., Higa, S., Arimitsu, J., Maruta, M., Kuwahara, Y., Ohkawara, T., Hagihara, K., Yamadori, T., Shima, Y., Ogata, A., Kawase, I., Tanaka, T., 2007. Flavonoids and related compounds as anti-allergic substances. Allergol. Int. 56, 113–123. https://doi.org/10.2332/allergolint.R-06-135.

Acknowledgements C. Sandoval wishes to thank the financial support coming from U. Auto´noma grant DP50-2015, C. Mascayano wishes to thank the financial support coming from DICYT grant 021641MC and FONDECYT grant 1170842 and J.I. Martı´ nez-Araya wishes to thank the financial support coming from FONDECYT grant 1140289 and ICM, Millennium Nucleus Chemical Processes and Catalysis (CPC) grant N 120082. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.arabjc.2017. 10.011. References Becke, A.D., 1993. Density-functional thermochemistry. III. The role of exact exchange. J. Chem. Phys. 98, 5648–5652. https://doi.org/ 10.1063/1.464913. Benzie, I.F., Strain, J., 1996. The ferric reducing ability of plasma (frap) as a measure of antioxidant power: The frap assay. Anal. Biochem. 239 (1), 70–76. https://doi.org/10.1006/abio.1996.0292 . Brunetti, C., Di Ferdinando, M., Fini, A., Pollastri, S., Tattini, M., 2013. Flavonoids as antioxidants and developmental regulators: Relative significance in plants and humans. Int. J. Mol. Sci. 14 (2), 3540–3555. https://doi.org/10.3390/ijms14023540 . Ca´rdenas, C., Rabi, N., Ayers, P.W., Morell, C., Jaramillo, P., Fuentealba, P., 2009. Chemical reactivity descriptors for ambiphilic reagents: Dual descriptor, local hypersoftness, and electrostatic potential. J. Phys. Chem. A 113, 8660–8667. https://doi.org/ 10.1021/jp902792n. Chamorro, E., Pe´rez, P., 2005. Condensed-to-atoms electronic fukui functions within the framework of spin-polarized density-functional theory. J. Chem. Phys. 123, 114107. https://doi.org/10.1063/ 1.2033689. Chermette, H., 1999. Chemical reactivity indexes in density functional theory. J. Comput. Chem. 20, 129–154. https://doi.org/10.1002/ (SICI)1096-987X(19990115)20:1<129::AID-JCC13>3.0.CO;2-A. Contreras, R.R., Fuentealba, P., Galva´n, M., Pe´rez, P., 1999. A direct evaluation of regional fukui functions in molecules. Chem. Phys. Lett. 304, 405–413. https://doi.org/10.1016/S0009-2614(99)00325-5. Cushnie, T.T., Lamb, A.J., 2011. Recent advances in understanding the antibacterial properties of flavonoids. Int. J. Antimicrob.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011

10 Kohn, W., Sham, L.J., 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138. https://doi.org/10.1103/PhysRev.140.A1133. Lee, C., Yang, W., Parr, R.G., 1988. Development of the colle-salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 37, 785–789. https://doi.org/10.1103/ PhysRevB.37.785. Martı´ nez-Araya, J.I., 2013. Explaining some anomalies in catalytic activity values in some zirconocene methyl cations: Local hypersoftness. J. Phys. Chem. C 117, 24773–24786. https://doi.org/ 10.1021/jp402808k. Martı´ nez-Araya, J.I., 2015. Why is the dual descriptor a more accurate local reactivity descriptor than fukui functions? J. Math. Chem. 53, 451–465. https://doi.org/10.1007/s10910-014-0437-7. Martı´ nez-Araya, J.I., Salgado-Mora´n, G., Glossman-Mitnik, D., 2013. Computational nutraceutics: Chemical reactivity properties of the flavonoid naringin by means of conceptual dft. J. Chem. 2013, 1–8. https://doi.org/10.1155/2013/850297. Martı´ nez-Araya, J.I., Salgado-Mora´n, G., Glossman-Mitnik, D., 2013. Computational nanochemistry report on the oxicams– conceptual dft indices and chemical reactivity. J. Phys. Chem. B 117 (21), 6339–6351. https://doi.org/10.1021/jp400241q. Martı´ nez-Araya, J.I., Grand, A., Glossman-Mitnik, D., 2015. Towards the rationalization of catalytic activity values by means of local hyper–softness on the catalytic site: A criticism about the use of net electric charges. PCCP 17, 29764–29775. https://doi.org/ 10.1039/C5CP03822G. Mascayano, C., Caroli Rezende, M., Rivera, Y., Espinosa, V., 2011. Isoflavans derivatives as inhibitors of soybean lipoxygenase: Invitro and docking studies. J. Chil. Chem. Soc. 56, 935–937 . Mascayano, C., Espinosa, V., Sepu´lveda-Boza, S., Hoobler, E.K., Perry, S., Diaz, G., Holman, T.R., 2015. Enzymatic studies of isoflavonoids as selective and potent inhibitors of human leukocyte 5-lipo-oxygenase. Chem. Biol. Drug Des. 86 (1), 114–121. https:// doi.org/10.1111/cbdd.12469. Miehlich, B., Savin, A., Stoll, H., Preuss, H., 1989. Results obtained with the correlation energy density functionals of becke and lee, yang and parr. Chem. Phys. Lett. 157, 200–206. https://doi.org/ 10.1016/0009-2614(89)87234-3. Morell, C., Grand, A., Toro-Labbe´, A., 2005. New dual descriptor for chemical reactivity. J. Phys. Chem. A 109, 205–212. https://doi.org/ 10.1021/jp046577a. Morell, C., Grand, A., Toro-Labbe´, A., 2006. Theoretical support for using the dfðrÞ descriptor. Chem. Phys. Lett. 425, 342–346. https:// doi.org/10.1016/j.cplett.2006.05.003.

C. Sandoval-Yan˜ez et al. Morell, C., Hocquet, A., Grand, A., Jamart-Gre´goire, B., 2008. A conceptual dft study of hydrazino peptides: Assessment of the nucleophilicity of the nitrogen atoms by means of the dual descriptor dfðrÞ. J. Mol. Struct. (Thoechem) 849, 46–51. https:// doi.org/10.1016/j.theochem.2007.10.014. Morell, C., Ayers, P., Grand, A., Gutie´rrez-Oliva, S., Toro-Labbe´, A., 2008. Rationalization of diels-alder reactions through the use of the dual reactivity descriptor dfðrÞ. PCCP 10, 7239–7246. https://doi. org/10.1039/B810343G. Parr, R., Yang, W., 1989. Density–Functional Theory of Atoms and Molecules. Oxford Univ. Press, New York. Peterson, J., Dwyer, J., 1998. Flavonoids: Dietary occurrence and biochemical activity. Nutrition Res. 18 (12), 1995–2018. https://doi. org/10.1016/S0271-5317(98)00169-9 . Ravishankar, D., Rajora, A.K., Greco, F., Osborn, H.M., 2013. Flavonoids as prospective compounds for anti-cancer therapy. Int. J. Biochem. Cell Biol. 45 (12), 2821–2831. https://doi.org/10.1016/j. biocel.2013.10.004 . Ribeiro, D., Freitas, M., Tome´, S.M., Silva, A.M., Porto, G., Fernandes, E., 2013. Modulation of human neutrophils’ oxidative burst by flavonoids. Eur. J. Med. Chem. 67, 280–292. https://doi. org/10.1016/j.ejmech.2013.06.019 . Ribeiro, D., Freitas, M., Tome´, S.M., Silva, A.M., Porto, G., Cabrita, E.J., Marques, M.M.B., Fernandes, E., 2014. Inhibition of lox by flavonoids: a structure–activity relationship study. Eur. J. Med. Chem. 72, 137–145. https://doi.org/10.1016/j.ejmech.2013.11.030 . Scalmani, G., Frisch, M.J., 2010. Continuous surface charge polarizable continuum models of solvation. I. General formalism. J. Chem. Phys. 132 (11), 114110. https://doi.org/10.1063/1.3359469. Schlegel, H.B., 1982. Optimization of equilibrium geometries and transition structures. J. Comput. Chem. 3, 214–218. https://doi.org/ 10.1002/jcc.540030212. Tapia, O., Goscinski, O., 1975. Self-consistent reaction field theory of solvent effects. Mol. Phys. 29 (6), 1653–1661. https://doi.org/ 10.1080/00268977500101461. Vosko, S.H., Wilk, L., Nusair, M., 1980. Accurate spin-dependent electron liquid correlation energies for local spin density calculations: A critical analysis. Can. J. Phys. 58, 1200–1211. https://doi. org/10.1139/p80-159. Zielinski, F., Tognetti, V., Joubert, L., 2012. Condensed descriptors for reactivity: A methodological study. Chem. Phys. Lett. 527, 67– 72. https://doi.org/10.1016/j.cplett.2012.01.011.

Please cite this article in press as: Sandoval-Yan˜ez, C. et al., A theoretical assessment of antioxidant capacity of flavonoids by means of local hyper–softness. Arabian Journal of Chemistry (2017), https://doi.org/10.1016/j.arabjc.2017.10.011