Antioxidant Properties of Kynurenines: Density Functional Theory Calculations

Kynurenines, the main products of tryptophan catabolism, possess both prooxidant and anioxidant effects. Having multiple neuroactive properties, kynurenines are implicated in the development of neurological and cognitive disorders, such as Alzheimer's, Parkinson's, and Huntington's diseases. Autoxidation of 3-hydroxykynurenine (3HOK) and its derivatives, 3-hydroxyanthranilic acid (3HAA) and xanthommatin (XAN), leads to the hyperproduction of reactive oxygen species (ROS) which damage cell structures. At the same time, 3HOK and 3HAA have been shown to be powerful ROS scavengers. Their ability to quench free radicals is believed to result from the presence of the aromatic hydroxyl group which is able to easily abstract an electron and H-atom. In this study, the redox properties for kynurenines and several natural and synthetic antioxidants have been calculated at different levels of density functional theory in the gas phase and water solution. Hydroxyl bond dissociation enthalpy (BDE) and ionization potential (IP) for 3HOK and 3HAA appear to be lower than for xanthurenic acid (XAA), several phenolic antioxidants, and ascorbic acid. BDE and IP for the compounds with aromatic hydroxyl group are lower than for their precursors without hydroxyl group. The reaction rate for H donation to *O-atom of phenoxyl radical (Ph-O*) and methyl peroxy radical (Met-OO*) decreases in the following rankings: 3HOK ~ 3HAA > XAAOXO > XAAENOL. The enthalpy absolute value for Met-OO* addition to the aromatic ring of the antioxidant radical increases in the following rankings: 3HAA* < 3HOK* < XAAOXO* < XAAENOL*. Thus, the high free radical scavenging activity of 3HAA and 3HOK can be explained by the easiness of H-atom abstraction and transfer to O-atom of the free radical, rather than by Met-OO* addition to the kynurenine radical.

There are multiple mechanisms of kynurenines' action on nervous system. QUIN and KYNA, the ligands of ionotropic glutamate receptors [5,6], modulate neurodegenerative processes in the brain [7]. The autoxidation of 3HOK and 3HAA leads to the hyperproduction of reactive oxygen species (ROS) which damage cellular lipids, proteins, and DNA [8][9][10]. Kynurenine 3-monooxygenase (KMO), an enzyme producing 3HOK from KYN, has been linked to the pathophysiology of HD by a mechanism involving ROS [11]. Accumulation of 3HOK in the central nervous system of Drosophila cardinal mutant leads to the progressive memory loss [12]. Since 3HOK is capable of auto-condensation, the eyes of this mutant, as well as the color of mammalian lens cataract [13] progressively get brown on ageing. The Drosophila eye color mutants are started to be envisioned as a therapeutic tools for HD [14].
At the same time, both 3HOK and 3HAA were shown to be powerful antioxidants scavenging peroxyl radicals [15,16]. Xanthurenic acid (XAA), a product of KYNA hydroxylation, has similar antioxidative properties, but its rate of interaction with free radicals is slower [15]. Tryptophan and its catabolites without aromatic hydroxyl group, such as kynurenine (KYN), KYNA, and anthranilic acid (AA) have no effect on peroxy-mediated oxidation. Thus, phenolic hydroxyl group is important for antioxidant activity of kynurenines. Antioxidants are supposed to beneficially interfere with diseases-related oxidative stress, however, the interplay of endogenous and exogenous antioxidants with the overall redox system is far from clear [17].
Phenolic compounds suppress lipid peroxidation due to their ability to react with free radicals at a faster rate than with the substrate [18,19]. There are two main pathways of phenolic antioxidants quenching free radicals: electron transfer and H-atom transfer. H-atom easily abstracted from the aromatic OH-group interacts with peroxyl radical ROO Ã produced during lipid peroxidation and breaks the chain reaction: There are two pathways of hydrogen transfer: hydrogen atom transfer (HAT) and protoncoupled electron transfer (PCET) [20]. HAT is preferable when electron density of singly The implication of KP in a variety of physiological and pathophysiological processes, including anti-microbial and anti-tumor defense, neuropathology, immunoregulation, and antioxidant activity, has been ever drawing attention to biochemical properties of kynurenines [1]. Kynurenines are considered to be involved in ageing and numerous neurodegenerative diseases, such as Alzheimer's disease (AD), Parkinson's disease (PD), Huntington's disease (HD), amyotrophic lateral sclerosis (ALS), etc. [2][3][4].
doi:10.1371/journal.pcbi.1005213.g001 occupied molecular orbital (SOMO) in the transition structure (TS) lies along the same line as the O. . .H. . .O bond and H is transferred between the oxygens as a whole particle. PCET is preferable when SOMO is orthogonal to O. . .H. . .O bond, as in phenoxyl-phenol complex, and proton is transferred between oxygen σ lone pairs forming hydrogen bonds with them, while the electron is transferred between oxygen π-orbitals.
Also, phenolic antioxidant radicals are able to quench peroxyl radical via its addition to the aromatic ring at ortho-or para-position. In order to trap the radical and not to react with hydrocarbon R-H substrate, an antioxidant should have less value for the homolytic O-H bond dissociation enthalpy (BDE) than ROO-H and R-H. Moreover, antioxidant radical should be kinetically stable to prevent its reaction with substrate [21,19]. Thus, the antioxidant power is not an absolute property of Ar-OH, but depends on the substrate which should be protected.
The toxicity of 3HOK depends mainly on the products of its oxidative dimerization, such as hydrogen peroxide, xanthommatin (XAN), 4,6-dihydroxyquinolinequinonecarboxylic acid (DHQCA), their active free radical forms, and o-aminoquinone [22]. Ommochromes XAN and dihydroxanthommatine (DXAN), the brown eye pigments, easily transform into each other under physiological conditions [23,24]. DXAN is synthesized from 3HOK by phenoxazinone synthetase (PHS)-the process disturbed by the cardinal mutation [23]. PHS catalyzes two consecutive abstractions of H-atoms from the hydroxyl group of o-aminophenols, 3HOK or 3HAA, followed by their non-enzymatic condensation to phenoxazinone [25]. The formation of ommochromes can also result from non-enzymatic oxidation of 3HOK [26]. High concentration of 3HOK catabolite hydrogen peroxide induces apoptotic cell death in neuronal cell cultures [27]. 3HOK and 3HAA generate superoxide anion and hydrogen peroxide in the presence of copper-the process leading to the formation of a quinoneimine structure [28]. Both amino and hydroxyl aromatic groups are important for lowering 3HOK and 3HAA oxidation potential. Initially, they can be two-electron donors with antioxidant activity, but their quinoneimine products are highly reactive and damage cell structures. Pro-and antioxidant power of o-aminophenols depends on the whole activity of the redox systems in cell [29].
Other kynurenine metabolites also possess pro-and antioxidant activity [4]. In particular, KYNA is able to scavenge hydroxyl radicals, superoxide anion radicals, and peroxynitrite, decreasing lipid peroxidation and ROS formation [30]. QUIN affects the ROS level only together with iron ions; the pro-and antioxidant effects of QUIN are concentration-dependent [31]. Free radicals scavenging mechanisms shown for non-o-aminophenol kynurenines include electron transfer, metal ion chelation, destruction of carbon skeleton, and radical addition to the aromatic ring [4].
Whereas experimental data regarding chemical and physiological properties of kynurenines are abundant and diverse, there are few computational studies on kynurenines. Quantum chemical calculations could provide a better understanding of the mechanisms of kynurenines' antioxidant activity. In this study, the redox properties of kynurenines and several synthetic phenolic antioxidants were investigated computationally using density functional theory (DFT) approach. The validity of B3LYP methods to model phenolic antioxidants and free radical reactions has already been proved [18,32]. The methodology was similar to that of [18,33]: the energies of frontier highest occupied and lowest unoccupied molecular orbitals (E HOMO , E LUMO ), phenolic O-H bond dissociation enthalpy (BDE), and ionization potential (IP) were calculated and compared for structures fully optimized in the gas phase. We also studied the influence of water solvation on the chemical properties of antioxidants. Finally, we modeled the kinetic behavior of hydroxykynurenines interaction with phenoxyl and peroxyl radicals.

Phenolic antioxidants and hydroxykynurenines; BDE, IP, and frontier orbital energies
Optimal geometries for kynurenines and synthetic antioxidants with substituted phenolic groups were calculated at different levels (Table 1). Six compounds with experimentally known BDE values are used as standards for the estimation of the validity of computational methods. Despite high diversity of chemical structures, Pearson correlation coefficient R is high for level II (0.870 and 0.867 for BDE and BDE COR , respectively; p<0.05) and III (0.865, 0.863; p<0.05), being less for level I (S1 Table) (0.717, 0.710; p > 0.1). Total spin <S2> shows small spin contamination ranging from 0.75 to 0.80 for all free radicals (II, III), being abnormally high for some radicals calculated at level I. Thus, (I) computational data were omitted from further analysis. BDE and BDE COR (II, III) for phenol are greatly higher than the experimental value and the value previously calculated at the same level of theory; the cause is explained in Methods section. With the exception of phenol, the correlation of BDE/BDE COR with experimental values is very strong (R = 0.959 and 0.974 for level II and III, respectively; p < 0.05, n = 5). The goal of this study was not the precise calculations of energy values, but rather the comparison of such values for different antioxidants. Thus, DFT calculations at level II or III can be used to predict the relative antioxidant power of the studied compounds.
The values of E HOMO , E LUMO , BDE, and BDE COR at level II are highly correlated with those calculated at level III (R = 0.98-1.00) In general, level III gives a slightly higher BDE/BDE COR than level II. BDE/BDE COR calculated at B3LYP and HCTH/407 levels of DFT (basis set II) are strongly correlated (R = 0.999 and 0.998, respectively; p < 0.05, n = 16, without phenol). HCTH/ 407 gives slightly lower values of BDE than B3LYP (S1 Table; [38]. L-3HOK and D-3HOK optical isomers have almost equal BDE values. 3HOK and 3HAA are characterized by the decreased energies of H abstraction compared to phenol and its derivatives DIBP and DTBP, both native and modified by propenoic acid (DIBA, DTBA). Total energy for XAA oxo form is lower by 7.4 kcal/mol than for enol form (level III); therefore, we used the oxo form in the majority of calculations. XAA OXO is close to phenolic antioxidants in its H donating properties.
B3LYP, as well as most DFT methods, is known to give E HOMO and E LUMO in a very poor agreement with experiment, significantly underestimating H-L gap. Using of tuned range-separated hybrid functionals can solve this problem [39,40]. We have computed E HOMO , E LUMO , H-L gap, and IP for five compounds optimized at level III, B3LYP (L-3HOK, 3-HAA, XAA OXO , 2-aminophenol, and DTBP) using tuned LC-BLYP range-separated functional. Indeed, LC-BLYP gives significantly higher absolute values for H-L gap (ΔE LC-BLYP-B3LYP = -69.849±8.135 kcal/mol), and IP values are close to -E HOMO (ΔE -HOMO-IP = -3.333 ±2.929 kcal/ mol). The optimal range-separation parameter μ values are close for four aminophenols (~0.20) and differ from that for phenolic antioxidant DTBP. At the same time, E HOMO , E LUMO , and H-L gap values calculated by III(LC-BLYP) and III(B3LYP) are highly correlated (R = 0.911, 0.989 and 0.955, respectively), thereby the rankings for electron donating power are virtually the same in both cases. XAA OXO has the highest values for IP and -E HOMO , whereas L-3HOK is the best electron donor among the uncharged hydroxykynurenines. There is a moderate negative correlation between E HOMO and BDE/BDE COR (levels II, III) (S2 Table). The correlation between H-L gap and BDE/BDE COR is even stronger. Hence the ability of O-H bond homolytical dissociation tends to increase along with the lowering of E HOMO and H-L gap absolute values. The correlation between E LUMO and BDE/BDE COR is not significant at all levels. For the compounds with an ionized group, such as 3HAA CO2-, XAA CO2-, and L3HK NH3+ , E HOMO significantly differ from those of uncharged compounds. 3HAA CO2 -and XAA OXO/CO2-are more powerful H donors than the uncharged forms. On the contrary, protonation of NH 2 group in L-3HOK phenolic ring significantly complicates O-H dissociation. This is in agreement with the fact that electron-donating groups reduce O-H BDE, thus enhancing antioxidant activity, whereas electron-withdrawing substitutions raise it [41,42,18]. DIBP and DTBP, the substances with skeletal isomerism, have similar BDEs. However, for each of them, BDE is closer to that of its propenoic derivative than to BDE of its isomer. Hence the side chain isomerism significantly affects the H-donating properties of phenolic group. DXAN has the least stable O-H bond among the uncharged compounds, making it a potent anioxidant with the high H donating ability.
In order to check the possible effect of the basis set superposition error (BSSE) on BDE, BSSE correction was performed for phenol, DIBP, and DXAN with a small, intermediate, and large hydrocarbon moiety of a radical. The values of BSSE (III) are -0.722, -0.832 and -1.45 kcal/mol, respectively, being small and similar in all compounds. The decrease of BDE for bulky antioxidants cannot be explained by the growth of BSSE.

Kynurenines and phenolic antioxidants; frontier molecular orbitals and spin-orbits
The geometry of frontier molecular orbitals and spin-orbits was calculated at level III for hydroxykynurenines and their precursors, as well as for their derivatives without an aromatic hydroxyl group. The highest occupied molecular orbital (HOMO) of phenolic antioxidants and kynurenines is localized mainly on the phenolic ring. HOMO is divided into two parts: the first part occupies phenolic OH group and three approximate C atoms, and the second part occupies the opposite two or three C atoms (Fig 2). HOMO also occupies unsaturated and polar groups attached to the phenolic ring, such as the aromatic NH 2 group of L-3HOK and 3HAA, which HOMO's and spin-orbit's geometry is virtually the same as that for 2-aminophenol. Together with the aromatic rings, OH and NH 2 groups form a π-conjugated systems known to decrease IP [43]. DXAN has the largest conjugated system allocated mainly to phenoxazinone structure, which possibly facilitates H-atom and electron abstraction. For the ionized compounds, HOMO is moved from the aromatic hydroxyl group to the charged group.
H-atom and electron donating power of kynurenines and phenolic antioxidants in the gas phase and water solution BDE, IP and frontier orbital energies for compounds optimized at level III were calculated at level IV (B3LYP/6-311+(O)+G(d)) in the gas phase and water solution ( Table 2, Fig 3A and 3B). A moderate negative correlation between BDE and E HOMO /H-L gap values was observed, as well as for levels I-III, both in the gas phase and in water solution (S2 Table, second part). A strong correlation between adaibatic IP and -E HOMO or the so called vertical IP can be seen. This is in accordance with Koopmans' theorem, applicable in high approximation for outer valence Kohn-Sham orbitals [44]. The difference between IP and -E HOMO is 36.7±3.3 kcal/mol in the gas phase, in agreement with the fact that B3LYP underestimates the absolute values for E HOMO [39]. In water solution, IP becomes slightly lower than the negative of E HOMO . BDE is positively correlated with IP; thereby the electron and H donating capacities of the studied compounds are interrelated. BDE of aromatic antioxidants is strongly correlated with standard deviation of Mulliken spin density (δ SD ) on radical (R GAS = 0.879, R WATER = 0.917; p < 0.05, n = 14) and spin density (SD) on radical O Ã atom (R GAS = 0.910, R WATER = 0.951; p = 0.05, n = 14) after H abstraction. BDEs for phenol and DTBP were not considered due to significant deviations from experimental values. Also, BDE is strongly correlated with SD on radical C PARA aromatic atom after H abstraction (R GAS = 0.849, R WATER = 0.876; p < 0.05, n = 13, without KYNA ENOL which has N instead C PARA ).
There is no significant correlation between IP and δ SD for kynurenine radicals after single electron abstraction. Thus, electron delocalization on kynurenines seems to be more important for H-atom donation activity than for the electron donation activity.
OH group bonded to the aromatic ring significantly increases the ability of kynurenines to donate H-atom and electron. L-KYN C 3 -H BDE is much higher than L-3HOK O 3 -H BDE: the difference is 40.4 kcal/mol in the gas phase and 40.3 kcal/mol in water solution (level V: B3LYP/6-311++(d,p)). IP value is lower for XAA OXO , L-3HOK, and 3HAA than for KYNA OXO , L-KYN, and AA, respectively (ΔIP GAS = 6.4±2.9 kcal/mol, ΔIP WATER = 5.5±0.6 kcal/mol). However, the relative IP rankings are the same for compounds with and without OH group: KYNA has higher IP compared to L-KYN and AA, as well as XAA compared to L-3HOK and 3HAA. This is in agreement with experimental data: the electrochemical potential E pa for kynurenines has been shown to decrease in the following rankings: KYNA > KYN > AA > 3HOK > 3HAA [29]. There is a strong positive correlation between experimental E pa and IP calculated for non-ionized compounds in water solution at level IV (R = 0.924; p < 0.05, n = 5). For compounds with an ionized CO 2 group, the correlation is not significant (R = 0.804; p > 0.1, n = 5), probably, due to the small sampling. QUIN is the least powerful electron donor among the uncharged kynurenines. IP GAS for XAN is close to that for 3HAA, hence XAN easily abstracts electron, but not H-atom. This possibly makes it a prooxidant with toxic effects [22].
The electron-donating substituents are known to decrease IP and to increase the antioxidant activity [33]. In general, compounds with ionized CO 2 group have lower IP and higher E HOMO values than their neutral forms (ΔIP GAS = -88.5±11.5 kcal/mol, ΔIP WATER = -8.7±9.5 kcal/mol, without KYNA OXO ; ΔE HOMO/GAS = 88.6±8.4 kcal/mol; ΔE HOMO/WATER = 7.4±1.6 kcal/mol). KYNA OXO in water solution has lower IP than KYNA OXO/CO2 . Probably, geometry optimization of charged compounds in the gas phase leads to some distortions in KYNA OXO/ CO2 structure. In water solution, IP becomes lower for the majority of compounds and higher for the anionic forms. This seems to result from a high dielectric capacity which decreases electrostatic interactions, stabilizes anions, and diminishes electron attraction to cations and neutral molecules. The change of gas-water -E HOMO and -E LUMO is correlated with the change of IP. BDE for XAA OXO/CO2-becomes higher than that for 3HAA and only 2 kcal/mol less than that for XAA OXO . The same trend is observed for 3HAA/3HAA CO2-and L-3HOK/L-3HOK NH3+ . Thus, water solution significantly diminishes the influence of charged groups on BDEs and IPs. multiple nodes in the bonding region, mainly localized outside of the OH group (S1 Fig). For the ionized compounds, LUMO is moved from the charged group to the aromatic system; for L-3HOK NH3+ , its form is nearly the same as that of L-3HOK HOMO. The geometry of HOMOs closely resembles the geometry of spin-orbits of cation radicals (S2 Fig). Hence HOMO correctly reproduces the geometry of the electron density in phenolic cations calculated at the DFT level. The main differences are between anion HOMOs and the corresponding spin-orbits after electron abstraction: spin-orbit is localized mainly on aromatic atoms and partly on α-carboxylic group. Spin-orbit of radicals after H-atom abstraction is localized on O*-atom and π-conjugated moiety, including the aromatic system and unsaturated side chains (S3 Fig). Delocalization is low in L-KYN, KYNA ENOL , and phenol radicals. This may explain their lower capability to donate H compared with hydroxykynurenines and substituted phenols.    There are different pathways for ROS inactivation by antioxidants [19]. Most likely, kynurenines quench radicals by donating aromatic hydroxyl H-atom to radical Ã O-group. We have computationally studied the kinetics of this process for the complexes of four hydroxykynurenines, 3HAA, L-3HOK, XAA OXO , and XAA ENOL , with phenoxyl radical (Ph-O Ã ) and methyl peroxy radical (Met-OO Ã ). BDE difference for Met-OO Ã and buthyl peroxy radical is less than 0.7 kcal/mol (levels II, III), hence Met-OO Ã can be used instead of the radicals with long aliphatic chain to simplify calculations. Ph-O Ã -DTBP and Ph-O Ã -DTBA complexes have been also calculated, as well as Met-OO Ã complex with XAA in ionized form. TSs for reaction pathways were located at level II. Reagent and product complex structures are in good agreement with the results of IRC calculations (RMSD = 0.026±0.015 Å for all complexes and 0.019 ±0.008 Å for kynurenines' complexes).
The values for the reaction rate and height of activation barrier were calculated in the gas phase and water solution (Table 3). k(T) values are significantly higher than those experimentally shown for phenolic compounds with BDE values of 70-80 kcal/mol, which are about 10 4 −10 7 M -1 s -1 [19]. This fits the fact that B3LYP underestimates the reaction barrier heights, whereas functional XYG3 is almost as accurate, as the highly precise CCSD(T) method [45].
It is rather difficult to calculate the exact value of the reaction rate, as multiple factors should be considered, and appropriate DFT level should be used [46]. However, the location of TS point calculated for 3HAA-Met-OO Ã and XAA OXO −Met-OO Ã by B3LYP (level II) is similar to that calculated by XYG3 (level V) (S4 Fig). Thus, even B3LYP with the relatively small basis set II correctly describes the geometry of TS structure. ΔE TS-R (XYG3) for XAA OXO complex is higher than that for 3HAA complex.
The structures of radical complexes with 3HAA, L-3HOK, and XAA OXO are very similar (Fig 4, Table 4). The influence of solvent and partial charges' distribution on antioxidant activity depends on whether HAT or PCET is the dominant mechanism of H transfer. The increase in H-atom charge in the TS compared to the parent antioxidant is specific for PCET [20]. The interaction of phenolic antioxidants with tert-buthyl-peroxy radical is known to occur via PCET [47]. PCET-TS is stabilized by the enhanced spin density (SD) and electron density on radical O 2 and O 3 atoms. Thereby (O 3 +O 2 -O 1 ) negative charge and Δ(O 3 +O 2 -O 1 ) TS-R negative charge correlate with the reaction rate [47]. In our study, positive charge on H-atom increases in all TSs (ΔQ(H) > 0), and the negative charge on O atoms in the gas phase moves towards the free phenol and DTBP. DTBA have much lower BDE, which is in agreement with its high antioxidant power. BDE for DIBP and DIBA are close to those for DTBA and, presumably, the true BDE value for DTBP. For the uncharged kynurenines with the OH group, BDE is maximal for KYNA ENOL and minimal for DXAN, both in the gas phase and in water solution. XAA and KYNA have smaller BDE in oxo form than in enol form.    (Table 5). In the gas phase, there is a strong correlation between ΔE TS-R and SD on O 1 and C PARA atoms of antioxidants. Hence the high SD on these atoms decreases the reaction rate. For Ph-O Ã complexes in water solution, the decrease of the negative charge on radical O atoms (Δ(dQ) TS-R ) correlates with the growth of ΔE TS-R , as it is typical for PCET. There is a negative correlation between ΔE TS-R and E TS-SOMO . Thus, E SOMO may serve to predict the reaction rate, as shown by Nikolic [47].
The Partial charges Q and ΔQ on H are higher, and the negative charge displacement to O 1 is lower for Ph-O Ã complexes than for Met-OO Ã complexes. Thus, PCET seems to be more  preferable for kynurenines' reaction with Ph-O Ã than for their reaction with Met-OO Ã . HAT may also occur in both cases, however, SOMO geometry and charges distribution character indicate that it is not the chief mechanism of H transfer for the studied complexes.
Thermodynamic study of methyl peroxy radical addition to the aromatic ring of kynurenine radicals Another possible way of free radical quenching is its addition to the aromatic ring of the antioxidant radical. We have modeled the products of Met-OO Ã addition to the aromatic ring of phenoxyl and kynurenines radicals at para-position relative to O Ã atom (Fig 6, Table 6). The orientation of side chain Met-OO group varies, being closer for the different forms of XAA than for the different antioxidants. In the gas phase, all reactions are thermodynamically favorable (ΔE P-R/COR < 0), in contrast to H abstraction. In water solution, radical addition to 3HAA and L-3HOK radicals is slightly unfavorable. The rankings of -ΔE P-R and -ΔE P-R/COR are the same at all levels: 3HAA Ã < L- It is reverse to the rankings of -ΔE P-R and k(T) for H-atom donation: the affinity to Met-OO Ã is minimal for 3HAA Ã and maximal for phenoxyl radical. XAA OXO/CO2-Ã is less active than XAA OXO Ã and more active than L-3HOK Ã , both in the gas phase and in water solution. Thus, high Met-OO Ã scavenging activity of L-3HOK and 3-HAA is unlikely to be explained by Met-OO Ã addition to the aromatic rings of kynurenine radicals.

Lipophilicity estimation for kynurenines and phenolic antioxidants
The antioxidant power of a substance depends not only on its chemical properties, but also on its ability to penetrate into the surroundings where it displays its antioxidant activity. To inhibit lipid peroxidation, a substance should have high lipophilicity. It can be measured as a logP value, where P is the octanol-water partition coefficient [48]. We used the Molinspiration method of logP calculation reported to be robust and precious. Among the antioxidants studied, substituted phenols, such as DTBP and DTBA, have maximal lipophilicity, whereas the kynurenines' ions have higher water solubility compared to ASC (Table 7). Lipophilicity decreases in the following rankings: AA > 3HAA> XAA OXO > QUIN > L-3HOK; the rankings are the same for kynurenines' carboxylic anions. Hence XAA should penetrate through lipid bilayer better than 3HOK and 3HAA. This fact does not fit with the lower rate of XAA reaction with peroxy radicals, which is rather explained by the higher rate of H donation.
Topological polar surface area (TPSA) is a molecular descriptor numerically close to PSA which can be used for the prediction of passive transport through membranes in intestines and blood-brain barrier [49]. Drugs that penetrate the brain by passive absorption typically have PSA < 70 Å 2 , while the most non-CNS active drugs have much larger PSA values up to 120 Å 2 [50]. In our study, TPSA is less than 120 Å 2 for all compounds except L-3HOK, so they are more or less capable of penetrating passively through the plasma membrane. TPSA is minimal for phenolic antioxidants, which should be easily absorbed in intestines and penetrate into the brain. It is significantly higher for 3HOK (> 120 Å 2 ) than for 3HAA (< 90 Å 2 ), while XAA has the intermediate TPSA. Hence in the case of absence of specific carriers 3HAA should more actively penetrate through lipid bilayer than 3HOK.

Discussion
A great need in studies of biochemical properties of KP is promoted by the fact that this very pathway plays an overwhelming role in physiology and pathology. Dysregulation of this pathway, resulting in hyper-or hypofunction of active metabolites, is associated with neurodegeneration and other disorders, such as depression and schizophrenia [51], diabetes mellitus [52,53], attention-deficit hyperactivity disorder [54], and cataract [13]. Some KP metabolites are neuroactive, while others are molecules with prooxidant and antioxidant properties [3]. Therefore, it is necessary to understand the molecular and biophysical mechanisms of kynurenines' activity to elaborate the strategy of disorders' prevention and therapy.
In this study, we investigated the antioxidant activity of kynurenines, namely their ability to donate electron and H atom. The hydroxyl group BDE and adiabatic IP are the most important determinants for the radical scavenging activity of substituted phenols [55]. According to our data, the antioxidant properties of 3HOK and 3HAA are determined by their 2-aminophenolic moiety. For the uncharged hydroxykynurenines, BDE and IP are maximal for KYNA ENOL and miminal for DXAN, both in the gas phase and in water solution. 3HOK and 3HAA have lower BDE and IP than XAA, ascorbic acid, and some phenolic antioxidants, such as DTBP and DTBA. Aromatic OH group diminishes IP values for 3HOK, 3HAA, and XAA relative to KYN, AA, and KYNA. Our results confirm the correlation between BDE and IP also shown by Borges [56]. Negatively charged carboxylic group significantly diminishes BDE and IP values, while positively charged amino group enhances them. This phenomenon can be explained by electron-donating and withdrawing effects of substituents [18]. The effects of charged groups are significantly more pronounced in the gas phase than in water solution. Basis set and the type of density functional had a little effect on the rankings for BDE values of kynurenines.
Adiabatic IP strongly correlates with -E HOMO , confirming that Koopmans' theorem can be used to calculate IP at DFT level [44]. However, B3LYP significantly underestimates the absolute values of E HOMO . We have used the tuned LC-BLYP range-separated functional to compute E HOMO , E LUMO , H-L gap, and IP for several antioxidants, including three hydroxykynurenines. The tuned LC-BLYP gives significantly higher absolute values for E HOMO and H-L gap, also, there is a minor difference between -E HOMO and adiabatic IP. However, the rankings for kynurenines' E HOMO values are the same as for those calculated using B3LYP. Also, BDEs calculated with B3LYP and HCTH/407 are highly correlated. B3LYP is significantly faster than the high quality functionals partly based on perturbation theory, such as XYG3. B3LYP contains less empirical parameters than HCTH/407, thereby it seems to be more universal. B3LYP has been successfully used to model both thermodynamic and kinetic properties of free radicals [18,32,33]. Thus, we used B3LYP in the majority of our calculations. At the same time, using LC-BLYP and other range-separated functionals may be favorable to predict the exact values for frontier orbital energies.
High radical stability and even spin distribution are among the factors predisposing low BDE and IP values [55]. Conjugated bonds system facilitates electron delocalization after HAT or single electron transfer (SET). Standard deviation of SD in kynurenine radicals is correlated with BDE; however, there is no significant correlation between SD and IP. BDE for kynurenines is correlated with SD on O Ã and C PARA atoms. SD on antioxidant O Ã atom in TS complex with Met-OO Ã is also strongly correlated with the height of the activation barrier. The same is true for O PARA atom in phenolic antioxidants [47].
The rate of H-atom donation to phenoxyl and methyl peroxy radicals is correlated with BDE: 3HAA and 3HOK are more active radical scavengers than XAA. Likewise, for phenolic compounds donating H to hydroxyl radical, the rate constant is negatively correlated with O-H bond straight, IP, and SET enthalpy [57]. The rankings for free energies of radical addition to kynurenine radicals in para-position relative to OH group is reverse: 3HAA Ã radical has the lowest affinity to Met-OO Ã . Thus, high antioxidant activity of 3HAA and 3HOK relative to XAA [15] rather can be explained by their lower BDEs and higher rates of H-atom donation to peroxy radical. PCET seems to be the chief mechanism for H donation by kynurenines to phenoxyl radical and, probably, to Met-OO Ã radical. Studies of oxidations of O-H bond usually invoke stepwise oxidation, where the positive and negative charges are transferred separately. Here, there may be a complex dependence of BDE and k(T) on solvent, biochemical surroundings, and pH [58].
Low BDE and IP values are not sufficient for Ant-OH to be a powerful antioxidant without toxic side effects. Some of the necessary conditions include: 1) O 2 should not abstract H from Ant-OH; 2) Ant-OH should react with ROO Ã much faster than ROO Ã with R-H; 3) Ant-O Ã should not abstract H from R-H at an appreciable rate; 4) Ant Ã should not react with O 2 to produce AOO Ã ; 5) Ant-OH and its products should not be toxic [21]. Though we did not concentrate on the study of these properties, our calculations performed for 3HAA at level II have shown that: Hence O 2 can abstract H from 3HAA, but the reaction is dramatically slower than H abstraction by Met-OO Ã (2.2 x 10 11 M -1 s -1 ; Table 3). The aliphatic ethane interacts with Met-OO Ã faster than with 3HAA, and 3HAA interacts with Met-OO Ã dramatically faster than with ethane. Only the reaction of 3HAA with Met-OO Ã is thermodynamically favorable, so O 2 or free radicals must be in high concentration to hinder the protective action of 3HAA. Therefore, it seems to be a potent antioxidant, as well as 3HOK.
At the same time, the ability of 3HAA and 3HOK to form dimers leads to the production of toxic free radicals which damage the cell [23,26,22]. 3HAA undergoes three successive oneelectron oxidative reactions: 1. conversion to semiquinoneimine (hydroxyl H abstraction); 2. conversion to quinoneimine (amine H abstraction); 3. two quinoneimine molecules condensation to cinnabarinic acid [59,60]. The rate of 3HAA oxidation increases exponentially with increasing pH [59]. This corresponds to our data that BDE decreases and k(T) for H-atom donation increases for compounds with ionized carboxylic group. 3HOK autoxidation is similar to that of 3HAA [29]. BDE for 3HOK N-H is significantly higher than for 3HOK O-H, being 99.5 and 77.2 kcal/mol, respectively (level III). Both of them are smaller for semiquinoneimine, becoming 91.8 and 69.4 kcal/mol after the other H-atom abstraction. Hence the first stage of oxidation facilitates the second one. o-Quinoneimine which is synthesized at the second stage may be responsible for the prooxidant effects of 3HOK and 3HAA [29]. The enzymatic oxidation of o-aminophenols leads to the concomitant reduction of oxygen to water [25]. Non-enzymatic oxidation produces the toxic reactive forms of oxygen. Therefore, it may be therapeutically important to enhance the antioxidant power of hydroxykynurenines by inhibiting their non-enzymatic dimerization and/or stimulating the enzymatic dimerization.
The inhibition of tryptophan 2,3-dioxygenase, the key enzyme of KP, is neuroprotective in Drosophila huntingtin (htt) mutant. Feeding flies by 3HOK alone, in the absence of mutant HTT, did not cause neurodegeneration [14]. Thus, the high level of 3HOK is toxic, yet, it may be not sufficient for neurodegeneration which also requires the additional factors, such as the lack of neuroprotectant KYNA. Both 3HOK and 3HAA inhibit the spontaneous lipid peroxidation in the brain [61]. The dual redox activity of 3HOK makes it prooxidant at low concentrations (5-20 μM) and antioxidant at higher concentrations (100 μM) in the rat striatum slices. 3HOK seems to be a redox modulatory molecule which stimulate the increase in glutathione reductase and glutathione S-transferase activities [62]. Interferon-γ induces TRP degradation along the KYN pathway in mononuclear blood cells and inhibits the oxidation of low density lipoprotein (LDL). 3HAA inhibits LDL oxidation in submicromolar concentrations, probably being a catalyst for the other antioxidants [63]. It is a highly efficient coantioxidant for plasma lipid peroxidation which can be initiated by α-tocopherol radical (α-TO Ã ).
3HAA in low concentration (5μM) inhibits α-TO Ã production and accumulation of lipid peroxides. 3HOK inhibitory efficacy is the same as for 3HAA, but AA lacking the phenolic group can not reduce α-TO Ã [16]. This fits with low BDE for kynurenines having phenolic group. Monocytes in human blood can release 3HAA in concentration up to 30 μM [63]. Thus, 3HOK and 3HAA display the antioxidant activity under physiological conditions, not only in the brain, but also in blood plasma regulating the process of atherogenesis. In contrast to 3HAA, the antioxidant properties of XAA are in relation to its ability to chelate the transition metals which induce LDL oxidation [64]. Thus, kynurenines' action on redox conditions and physiological processes depends on their level in organism. The lack of kynurenines in Drosophila mutant vermilion, as well as the excess of 3HOK in cardinal, leads to the progressive loss of 3 h memory performance under conditioned courtship suppression paradigm [65,12]. The lack of kynurenines redox activity might partially cause these effects.
Not only BDE and IP define the antioxidant power of substances, but also their ability to pass through the biological barriers, mainly the lipid bilayers. The lipophilicity of kynurenines is low, compared to phenolic antioxidants, due to their polar and charged groups. Hence they should rather act in water environment than in membrane. Besides, their surfaces are quite large, that should hamper their penetration through intestine and blood-brain barriers. Indeed, 3HAA, KYNA, and QUIN poorly cross the blood-brain barrier by passive diffusion, but KYN and 3HOK are taken up into the brain by a large neutral amino acid carrier [66]. AA easily penetrates into the brain by passive diffusion that can be explained by its high logP and low TPSA values. Kynurenine pathway enzymes in the brain are preferentially localized in astrocytes and microglia; however, the cerebral pathway is driven mainly by blood-borne KYN [2]. Thus, 3HOK, KYN, and AA may play an important role in the brain both as prooxidants and antioxidants.
In our study, we did not consider several important factors affecting the antioxidant power of kynurenines, such as: 1) thermodynamics and kinetics of 3HOK and 3HAA dimerization; 2) energy and rate of proton abstraction from antioxidant OH group; 3) interaction between solvent and OH group of kynurenines; 4) hydrogen bond formation between functional kynurenine groups; 5) steric effects of side-chain groups on free energy and rate of kynurenine interaction with radicals, etc. Other functional groups of kynurenines can also donate H-atom, such as the 3HOK aromatic NH 2 group, which BDE was shown to be significantly higher than that for OH group. It would be interesting to evaluate the activity of kynurenines and phenolic antioxidants in their native surroundings, such as lipid bilayer, affecting the dielectric capacity and hydrophobic interactions. Consideration of these factors is a task for the future.
The ionic forms for kynurenines with α-carboxylic group (total charge -1) were modeled as well as the uncharged forms. The major forms for 3HAA and XAA at physiological pH (7.4) are the forms with the ionized carboxylic group, while KYN and 3HOK are mainly in zwitterionic form with ionized α-amino and α-carboxylic group [70].

BDE and IP calculations
All quantum chemical calculations were performed using Firefly 8.1.0 partially based on the GAMESS (US) [71] source code. Firefly 8.1.0 was kindly provided by Alex A. Granovsky [72]. The geometries of molecular structures with neutral total charges were fully optimized using density functional theory (DFT) at 6-31G(d) level (I), B3LYP/6-31G(d) level (II), and B3LYP/ 6-311G(d,p) level (III) [73][74][75]. B3LYP1 version of B3LYP was used. Highly parameterized functional HCTH/407 [76] was also used to calculate BDE values for compounds at level II. Closed shell configurations were calculated with restricted Hartree-Fock or DFT methods; open shell configurations were calculated with unrestricted Hartree-Fock or DFT methods. All closed shell molecules were calculated in a singlet state, whereas doublet state was used for free radicals. The symmetry point group was set as C1 for all compounds. Hessian matrix, vibrational frequencies, and thermal corrections to the enthalpy were calculated with the same methods. The enthalpies and free energies were obtained from the vibrational frequency calculations at 298.15 K, using unscaled frequencies. In order to calculate the adiabatic ionization potential (IP), cation-radical forms of corresponding molecules were fully optimized at level III. BSSE correction [77] was performed for several compounds at level III. The nature of all stationary points was determined by evaluating the vibrational frequencies. Standard deviation of Mulliken spin density (δSD) was used as an estimator of electron delocalization on the radicals.
The following energy parameters were estimated: 1. The energies of the highest occupied molecular orbital (E HOMO ) related to electron donating capacity or the ionization potential (IP) and the lowest unoccupied molecular orbital (E LUMO ) related to the electron accepting capacity or the electron affinity.
2. H-L gap: the difference between E HOMO and E LUMO related to the chemical hardness and the ability of compound to participate in oxidation-reducing reactions.
3. Homolytic bond dissociation enthalpy (BDE) and corrected enthalpy (BDE COR ) for O-H bond: where E W is the total energy of the whole molecule, E RAD is the total energy of the radical after H-atom abstraction, E H is the total energy of H radical; where H T is the thermal correction to enthalpy, H RAD , H H , H W are the thermal contributions to enthalpies for the antioxidant radical, H radical, and the whole molecule, respectively. 4. Ionization potential: where E CAT is the energy of cation radical after single electron abstraction (or the neutral form for compounds with ionized carboxylic group), E W is the total energy of the whole molecule. BDEs for methane, water, phenol, 2-aminophenol, water-soluble antioxidant ASC (uncharged form), and phenolic antioxidant DTBP were used as standards and reference points to estimate the relative activities of antioxidants. For symmetric phenol and DTBP radicals, there were significant deviations of BDE from the experimental values. To exclude the possible artefacts, BDE was also calculated for several structural analogues of DTBP-DTBA, DIBP, and DIBA, which are believed to have similar BDE values.
Zwitterionic form is not stable in the gas phase, therefore, the optimization of KYN and 3HOK in the neutral form was performed. To check the influence of positively charged group on BDEs and IPs, calculations were performed for L-3HOK with aromatic NH 3 + group (total charge +1). 3HAA and AA cations with ionized carboxylic group are not stable in the gas phase, therefore, their optimization was performed in water solution at level IV (see below), without cavitation, dispersion and repulsion free energies. NWChem software [78] was used to calculate E HOMO , E LUMO , H-L gap, and IP with the help of the tuned range-separated hybrid functional LC-BLYP for five compounds optimized with B3LYP (III). The tuning of optimal range-separation parameter μ was done as in [40]: the single point energies were calculated using basis set III for antioxidant's cation, anion, and neutral form for different values of μ ranging from 0.05 to 0.9 with increments of 0.05, and then the optimal parameter was obtained by minimizing the following function: where N is the number of electrons in antioxidant. For XAA OXO , J 2 (0.1) and J 2 (0.15) were obtained by spline interpolation due to the problem with DFT convergence. The curves for J 2 (μ) are shown in S5 Fig; the minimum of each curve (optimal μ, see Table 1) was obtained by spline interpolation.
Firefly 8.1.0 and Gaussian 98 [79] give almost equal values of total energy for phenol and significantly different values for phenoxyl radical. Gaussian 98 uses Harris functional for the initial orbital guess by default instead of extended Huckel calculations used by Firefly. Harris functional is a nonself-consistent approximation to Kohn-Sham density functional theory [80], hence electron correlations should be partially taken into account. Nevertheless, the differences between Gaussian 98 (S1 Table) and Firefly (Table 1) BDE values are generally small (0.092±0.03 kcal/mol; p < 0.05, n = 16, without phenol).

Transition structures optimization and reaction rate calculations
For antioxidants in complex with phenoxyl radical (Ph-O Ã ) and methyl peroxy radical (Met-OO Ã ), transition structures (TSs) and corresponding local minima were optimized at level II. Intrinsic reaction coordinates (IRC) calculations [81] were performed for all TS species at the same level to confirm that anticipated reagent (R) and product (P) are connected to TS on potential energy surface. The products of the Met-OO Ã addition to antioxidant radical in paraposition were optimized at level II. ΔE COR is corrected reaction activation energy: where ΔG TS-R and ΔG P-R signify thermal correction to free energy at 298.15 K; E TS , E R, and E P are total energies of TS, R, and P; G TS , G R , and G P are thermal contributions to free energies of TS, R, and P. The rate of reaction (M -1 s -1 ) between antioxidant and radical was calculated as in [32,46] using conventional TS theory: where I is the reaction pathway degeneracy (equal to 1 for the all compounds), k B is Boltzmann's constant, h is Planck's constant, 24.3 is a multiplier used to convert the units from 1 atmosphere standard state to 1 M standard state, and A(T) is a temperature-dependent factor which corresponds to quantum mechanical tunneling, approximated by the Wigner method [82]: where ν i is the imaginary frequency (cm -1 ) whose vibrational motion determines the direction of the reaction. Atom coordinates of the optimized structures are given in S1 Dataset. kynurenines. Single point energy calculations were performed for 3HAA-Met-OO Ã and XAA OXO −Met-OO Ã IRC at level V in the gas phase using XYG3 functional [45]. The values of the total free energy in solvent were used to calculate ΔE for the compounds in water solution. Since the value of the thermal correction to BDE (III) was very similar for different compounds (-6.645±0.260 kcal/mol, p < 0.05, n = 16), it was not considered. Also, the value for the thermal correction to antioxidant IP (III) was small (-0.20±0.25 kcal/mol, p < 0.05, n = 21) and was not considered. For the TSs, the values of ΔG TS-R and ν i obtained at level II were used to calculate the values of ΔE COR and k(T) at level IV.

Single point energy calculations in the gas phase and water solution
Statistical analyses were performed using Social Science Statistics online resource [84]. Illustrations were prepared with the help of MaSK 1.3.0. [85] and VMD [86]. The lipophilicity (logP) of compounds was calculated using the Molinspiration server [87].
Supporting Information S1 Table. BDE