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Antioxidants 13 (11): 1368 (2024)
Walton-Raaby, Max
Floen, Tyler
Mora-Diez, Nelaine
Oxidative stress is a biological process that has been linked to many diseases, hence understanding how to prevent and repair it is essential to medicine. The thermodynamics and kinetics of the repair reactions of radically damaged leucine (a lateral chain in a simplified protein environment) by twenty phenolic antioxidants are studied at the M06-2X(SMD)/6-31++G(d,p) level of theory in water and pentyl ethanoate. The two repair mechanisms modelled are formal-hydrogen atom transfer (f-HAT) and single electron transfer (SET). Although all f-HAT reactions are thermodynamically favourable, only one of the phenols produced rate constants in the diffusion limit, exhibiting biological relevance. SET is not suspected to be an important repair pathway for the phenols studied. We show that the Bell–Evans–Polanyi principle, which relates thermodynamics and kinetics properties for a reaction, breaks down when comparing between the solvents, protein repair sites, and the phenolic antioxidants. While thermodynamic data can be used as valuable screening tools, the kinetic calculation of rate constants in solution is crucial for enhancing the biological relevance of theoretical studies.
Citation: Walton-Raaby, M.; Floen, T.;Mora-Diez, N. Modelling the Repairof Carbon-Centered Protein Radicalsby Phenolic Antioxidants.Antioxidants 2024, 13, 1368. https://doi.org/10.3390/antiox13111368Academic Editor: Ruth EdgeReceived: 12 October 2024Revised: 1 November 2024Accepted: 5 November 2024Published: 8 November 2024Copyright: © 2024 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).ArticleModelling the Repair of Carbon-Centered Protein Radicals byPhenolic AntioxidantsMax Walton-Raaby 1,2,† , Tyler Floen 1,3,† and Nelaine Mora-Diez 1,*1 Department of Chemistry, Thompson Rivers University, Kamloops, BC V2C 0C8, Canada;max.walton-raaby@uwaterloo.ca (M.W.-R.); tfloen@student.ubc.ca (T.F.)2 Department of Chemistry, University of Waterloo, Waterloo, ON N2L 3G1, Canada3 Faculty of Pharmaceutical Sciences, University of British Columbia, Vancouver, BC V6T 1Z3, Canada* Correspondence: nmora@tru.ca† These authors contributed equally to the calculations reported and the preparation of the first draft.Abstract: Oxidative stress is a biological process that has been linked to many diseases, hence under-standing how to prevent and repair it is essential to medicine. The thermodynamics and kinetics ofthe repair reactions of radically damaged leucine (a lateral chain in a simplified protein environment)by twenty phenolic antioxidants are studied at the M06-2X(SMD)/6-31++G(d,p) level of theory inwater and pentyl ethanoate. The two repair mechanisms modelled are formal-hydrogen atom transfer(f-HAT) and single electron transfer (SET). Although all f-HAT reactions are thermodynamicallyfavourable, only one of the phenols produced rate constants in the diffusion limit, exhibiting biologi-cal relevance. SET is not suspected to be an important repair pathway for the phenols studied. Weshow that the Bell–Evans–Polanyi principle, which relates thermodynamics and kinetics propertiesfor a reaction, breaks down when comparing between the solvents, protein repair sites, and thephenolic antioxidants. While thermodynamic data can be used as valuable screening tools, thekinetic calculation of rate constants in solution is crucial for enhancing the biological relevance oftheoretical studies.Keywords: DFT; M06-2X; SMD; antioxidants; phenols; leucine; repair; rate constants; HAT; SET;thermodynamics; kinetics1. IntroductionIn biological systems, proteins play an indispensable role in diverse biological pro-cesses. Due to their widespread biological presence, proteins are prone to oxidative damage,a form of biological stress caused by the imbalance between the production and eliminationof free radicals. Free radicals are labile chemical species, capable of oxidizing proteinsat very high rates [1], impairing their functioning. The oxidation of proteins has beenlinked to many diseases such as Alzheimer’s [2–4], diabetes [5,6], and cancer [4,7]; hence,understanding how to mitigate this damage is essential to medicine.Exogenously sourced and endogenously produced, free radicals play a dual rolein health, posing various risks while serving as essential components for maintaininghomeostasis, controlling apoptosis, and regulating gene expression [8,9]. Exogenoussources of free radicals include pollution, certain drugs, UV radiation, heavy metals,and transition metals [2,10,11]. Free radicals are also produced endogenously duringmany biological processes (e.g., oxidative phosphorylation, phagocytosis, and cellularrespiration) [2,10–12]. Notably, the most biologically prominent free radical, the hydroxylradical [13], is capable of attacking virtually any biomolecule (e.g., DNA, RNA, protein,lipids, and cholesterol) within its short half-life (10−9 s) [1,9,12]. Conversely, species suchas the hydroperoxyl and methoxy radicals are less reactive and damage biomolecules moreselectively than the hydroxyl radical. Non-radical mechanisms of oxidative damage, suchas the mechanism of hydrogen peroxide, can also occur [13]; however, free radicals areAntioxidants 2024, 13, 1368. https://doi.org/10.3390/antiox13111368 https://www.mdpi.com/journal/antioxidantsAntioxidants 2024, 13, 1368 2 of 17generally more biologically concerning due to their lability and tendency to initiate chainreactions.Antioxidants are a class of molecules capable of quenching free radicals (primaryactivity), preventing the generation of free radicals (secondary activity), and repairingoxidatively damaged biomolecules (tertiary activity). Enzymatic antioxidants such assuperoxide dismutase, catalase, glutathione peroxidase, and non-enzymatic antioxidantssuch as vitamins A and E, Trolox, and glutathione (GSH) have crucial roles in maintainingthe delicate balance between the production and elimination of free radicals, thus con-tributing to homeostasis [8,9]. More specifically, enzymatic antioxidants are thought to bethe primary line of defense against oxidative damage [14], while non-enzymatic ones arethe secondary line of defense [11]. Despite the many positive effects of antioxidants, thebody cannot differentiate between helpful and deleterious oxidants, hence the excessiveconsumption of antioxidants can block the positive effects of oxidants in the body [15,16].Additionally, high concentrations of some phenolic antioxidants can have pro-oxidantaction [15,17–19]. These conditions are known as antioxidative stress, which has similareffects to oxidative stress [15].Reported studies primarily focused on the harmful reactions of free radicals withDNA and lipids, overlooking the biological significance of their interactions with proteins.Radical damage has the potential to induce protein aggregation, altered turnover rates, andloss of protein functioning [20]. Not all amino acids are equally affected by free radicals.For example, glycine undergoes the slowest reaction with the hydroxyl radical with a rateconstant of 1.7 × 107 M−1s−1, which is less than the diffusion limit (~1 × 108 M−1s−1) [21].Conversely, cysteine and tryptophan exhibit diffusion-controlled reactions, with rate con-stants of 3.4 × 1010 and 1.3 × 1010 M−1s−1, respectively [21]. Leucine is particularly proneto damage due to its long side chain [22] and undergoes diffusion-controlled reactions withthe hydroxyl radical with a rate constant of 1.7 × 109 M−1s−1 [21]. For this reason, we arefocusing on the repair of damaged leucine residues, which have also been studied by ourgroup with other antioxidants such as GSH, Trolox, and dihydrolipoic acid [22–24].N-formyl leucinamide (shown in Figure 1 and referred to as “leucine” in this work)is the tripeptide molecule containing a leucine residue which will be used to representa protein that has been exposed to oxidative stress [25]. This model has been employedsuccessfully in similar theoretical studies [22–24] and correlates well with experimentaldata [26], and it has also been experimentally tested [27]. It contains four main sites ofpotential damage, the α, β, γ, and δ. Only the β, γ, and δ sites are investigated in this studysince a radical at the α site would not be very reactive, and this would also be the leastlikely position to be damaged given its internal placement. Hence, the α site is not expectedto be of biochemical concern. Furthermore, the repair of the α site with Trolox, GSH,and dihydrolipoic acid (DHLA) has been shown to produce small rate constants [22–24].Our previous studies showed the biochemical effectiveness of DHLA and GSH to repairradically damaged leucine residues in proteins [22–24]. It would be of interest to comparetheir antioxidant repair activity with that of other compounds.Antioxidants 2024, 13, x FOR PEER REVIEW 2 of 17 mechanism of hydrogen peroxide, can also occur [13]; however, free radicals are generally more biologically concerning due to their lability and tendency to initiate chain reactions. Antioxidants are a class of molecules capable of quenching free radicals (primary ac-tivity), preventing the generation of free radicals (secondary activity), and repairing oxi-datively damaged biomolecules (tertiary activity). Enzymatic antioxidants such as super-oxide dismutase, catalase, glutathione peroxidase, and non-enzymatic antioxidants such as vitamins A and E, Trolox, and glutathione (GSH) have crucial roles in maintaining the delicate balance between the production and elimination of free radicals, thus contrib-uting to homeostasis [8,9]. More specifically, enzymatic antioxidants are thought to be the primary line of defense against oxidative damage [14], while non-enzymatic ones are the secondary line of defense [11]. Despite the many positive effects of antioxidants, the body cannot differentiate between helpful and deleterious oxidants, hence the excessive con-sumption of antioxidants can block the positive effects of oxidants in the body [15,16]. Additionally, high concentrations of some phenolic antioxidants can have pro-oxidant ac-tion [15,17–19]. These conditions are known as antioxidative stress, which has similar ef-fects to oxidative stress [15]. Reported studies primarily focused on the harmful reactions of free radicals with DNA and lipids, overlooking the biological significance of their interactions with proteins. Radical damage has the potential to induce protein aggregation, altered turnover rates, and loss of protein functioning [20]. Not all amino acids are equally affected by free radi-cals. For example, glycine undergoes the slowest reaction with the hydroxyl radical with a rate constant of 1. × 107 M−1s−1, which is less than the diffusion limit (~1 × 108 M−1s−1) [21]. Conversely, cysteine and tryptophan exhibit diffusion-controlled reactions, with rate con-stants of 3.4 × 1010 and 1.3 × 1010 M−1s−1, respectively [21]. Leucine is particularly prone to damage due to its long side chain [22] and undergoes diffusion-controlled reactions with the hydroxyl radical with a rate constant of 1.7 × 109 M−1s−1 [21]. For this reason, we are focusing on the repair of damaged leucine residues, which have also been studied by our group with other antioxidants such as GSH, Trolox, and dihydrolipoic acid [22–24]. N-formyl leucinamide (shown in Figure 1 and referred to as “leucine” in this work) is the tripeptide olecule containing a leucine residue which will be used to represent a protein that has been exposed to oxidative stress [25]. This model has been employed suc-cessfully in similar theoretical studies [22–24] and correlates well ith experimental data [26], and it has also been experimentally tested [27]. It contains four main sites of potential damage, the α, β, γ, and δ. Only the β, γ, and δ sites are investigated in this study since a radical at the α site would not be very reactive, nd this would also be the least likely position to be damaged given its internal pl cement. Hence, the α site is not expect d to be of biochemical con ern. Furthe mo e, th repair of the α site with Trolox, GSH, and dihy rolipoic acid (DHLA) has been shown to produce small rate constant [22–24]. Our previous st dies showed th biochemical effectiveness of DHLA and GSH to repair rad -c lly damaged leucine residues in proteins [22–24]. It would be of interest to compare their ant oxidant repai act vity w h that of o her compounds. Figure 1. Structure of the N-formyl leucinamide protein model with labelled sites. A wide range of phenolic antioxidants are investigated in this study: butylated hy-droxyanisoles (BHA) (1–2), tocopherols (3–7), aminophenols (8–11), stilbenes related to resveratrol (12–13 and 19–20), propyl gallate (14), nordihydroguaiaretic acid (15), and the substructures of epigallocatechin-3-gallate (EGCG) (16–18). The structures and names of these molecules are shown in Figure 2 and Table S1 of the Supplementary Materials, . .A wide range of phenolic antioxidants are investigated in this study: butylated hy-droxyanisoles (BHA) (1–2), tocopherols (3–7), aminophenols (8–11), stilbenes related toresveratrol (12–13 and 19–20), propyl gallate (14), nordihydroguaiaretic acid (15), and thesubstructures of epigallocatechin-3-gallate (EGCG) (16–18). The structures and names ofthese molecules are shown in Figure 2 and Table S1 of the Supplementary Materials, respec-tively. BHA is a synthetic, lipid-soluble molecule that is commonly used as a preservativeAntioxidants 2024, 13, 1368 3 of 17in foods to scavenge hydroperoxyl and alkyl peroxy radicals, preventing the oxidation offats and oils [28,29]. The tocopherols are a family of four lipid-soluble molecules (α-, β-,γ-, and δ-tocopherol, with the α form being vitamin E) able to scavenge similar radicals asBHA in both biological and industrial contexts [29–31]. The aminophenols are syntheticmolecules commonly used in cosmetics, dyes, and photographic developers [32,33]. Thestilbenes are secondary metabolites produced by numerous types of plants [19,34] andhave shown promise in treating cancers, Alzheimer’s, and heart diseases [15,18,35]. Propylgallate and nordihydroguaiaretic acid, together with BHA, are used as food preservatives.EGCG is a famous antioxidant that is abundant in green tea with the potential for treatingAlzheimer’s disease [36]. A relationship between the structural properties of these phenolicantioxidants and their ability to repair oxidatively damaged proteins will be established.These phenols were selected from a publication by Wright et al. [37] in which the authorsdeveloped a procedure for calculating their gas-phase bond dissociation enthalpies andionization potentials and used these values to interpret relative rates for the reactionsof these antioxidants with free radicals. As this study only considered two gas-phaseproperties of the antioxidants to make kinetic conclusions about their antioxidant activitywhen reacting with free radicals, we were motivated to perform the kinetic study of theirrepair reactions in a biologically relevant setting to establish comparisons.Antioxidants 2024, 13, x FOR PEER REVIEW 3 of 17 respectively. BHA is a synthetic, lipid-soluble molecule that is commonly used as a pre-servative in foods to scavenge hydroperoxyl and alkyl peroxy radicals, preventing the ox-idation of fats and oils [28,29]. The tocopherols are a family of four lipid-soluble molecules (α-, β-, γ-, and δ-tocopherol, with the α form being vitamin E) able to scavenge similar radicals as BHA in both biological and industrial contexts [29–31]. The aminophenols are synthetic molecules commonly used in cosmetics, dyes, and photographic developers [32,33]. The stilbenes are secondary metabolites produced by numerous types of plants [19,34] and have shown promise in treating cancers, Alzheimer’s, and heart diseases [15,18,35]. Propyl gallate and nordihydroguaiaretic acid, together with BHA, are used as food preservatives. EGCG is a famous antioxidant that is abundant in green tea with the potential for treating Alzheimer’s disease [36]. A relationship between the structural prop-erties of these phenolic antioxidants and their ability to repair oxidatively damaged pro-teins will be established. These phenols were selected from a publication by Wright et al. [37] in which the authors developed a procedure for calculating their gas-phase bond dis-sociation enthalpies and ionization potentials and used these values to interpret relative rates for the reactions of these antioxidants with free radicals. As this study only consid-ered two gas-phase properties of the antioxidants to make kinetic conclusions about their antioxidant activity when reacting with free radicals, we were motivated to perform the kinetic study of their repair reactions in a biologically relevant setting to establish com-parisons. Figure 2. Structures of the phenolic antioxidants studied. In the present work, we aim to study the thermodynamics and kinetics of the formal-hydrogen atom transfer (f-HAT) and single electron transfer (SET) repair reactions at the β, γ, and δ leucine radical sites with phenolic antioxidants. Wright et al. [37] predicted Figure 2. Structures of the phenolic antioxidants studied.In the pr sent work, we aim to stu the thermody amics and kinetics of the formal-hydrogen atom transfer (f-HAT) and single electron t ansfer (SET) repair r actions at theβ, γ, an δ leucine radical sites with phenolic ant oxidants Wright et al. [37] predictedthat most of these phenols primarily react through f-HAT, except for molecules 10 and11, which may react primarily through SET. We will also evaluate the reliability of theBell–Evans–Polanyi principle which suggests that the more thermodynamically favourableAntioxidants 2024, 13, 1368 4 of 17a reaction, the faster it should be [38,39]. We study the repair reactions of leucine usingthe same methodology as other studies by our group to develop a relative ranking ofantioxidants [22–24]. Our methodology does not differentiate between f-HAT and proton-coupled electron transfer reaction; however, this distinction between reactions can be madeby including a natural population analysis of atomic charges and a Hirshfeld partitionscheme to analyze spin densities along the reaction coordinate [40]. Studying f-HATand SET reactions will also provide insights into the viability of non-concerted repairmechanisms such as sequential proton loss electron transfer, sequential electron-protontransfer, and sequential proton loss hydrogen atom transfer, all of which include eitherf-HAT or SET reaction steps [41].2. Computational MethodologyCalculations were performed at the M06-2X(SMD)/6-31++G(d,p) level of theory at298.15 K using the Gaussian16 package [42]. The M06-2X functional is strongly recom-mended by its developers for main group thermochemistry and kinetic studies [43]. Geom-etry optimizations were followed by frequency calculations at the same level of theory. Thereactants and products were confirmed to be energy minima, and the transition states (TSs)were confirmed to have only one imaginary frequency in which the correct TS is animated.Doublet systems were tested for spin contamination and all <S2> values were very closeto 0.75 after annihilation (see Tables S2 and S3), indicating that spin contamination is nota concern in this study [44]. The standard absolute energies, enthalpies, and Gibbs freeenergies of all optimized species are provided in Tables S4 and S5 along with the Cartesiancoordinates for all optimized geometries.Solvent effects were considered in geometry optimizations and frequency calculationsusing the SMD continuum solvation method [45], which has been widely used in otherthermodynamic and kinetic studies of antioxidant activity [22–24,46–48]. Water and pentylethanoate (PE) were the solvents utilized to simulate hydrophilic and hydrophobic (lipid)microenvironments, respectively. These two microenvironments were chosen since thedamaged protein may be exposed to the solvent or buried within the structure of theoverall protein.The M06-2X functional combined with the SMD solvent model was one of the bestperforming combinations in a benchmark study that compared experimental and calculated(using the same methodology followed in our study) rate constants for a significant collec-tion of radical–molecule reactions in solution [49]. We used the 6-31++G(d,p) basis set tokeep consistency with our previous antioxidant studies of DHLA, GSH, and Trolox [22–24].In the f-HAT repair reactions, a hydrogen atom is transferred from the hydroxyl groupin the phenolic antioxidant to the damaged site of the leucine radical (Reaction R1). Rateconstants were calculated applying conventional transition state theory using Equation (1),where σ represents the reaction path degeneracy (σ = 2 for the f-HAT reactions studied); κ isthe tunnelling factor which was calculated for f-HAT reactions assuming a one-dimensionalasymmetrical Eckart barrier using the Brown’s numeric integration program [50], kB is theBoltzmann’s constant, T is the absolute temperature, h is Plank’s constant, and R is theideal gas constant. The standard Gibbs free energies of activation (∆G ̸=) were converted tothe 1 M reference state and the solvent cage effects were taken into account according toOkuno [51], which applies the free volume theory [52].Phenol-OH + Leucine•⇌ Phenol-O• + Leucine (R1)k = σκkBThe−∆G ̸=RT (1)Reactions in solution are constrained by how quickly the reactants can diffuse to eachother, which is known as the diffusion limit in the solvent considered. If the calculatedrate constant exceeds 108 M−1s−1, the apparent rate constant (kapp) can be calculatedaccording to Kimball–Collins theory [53] using Equation (2). In Equation (2), kD is theAntioxidants 2024, 13, 1368 5 of 17steady-state Smoluchowski rate constant for an irreversible diffusion-controlled bimolecu-lar reaction [54], which can be calculated using Equation (3).kapp =kDkkD + k(2)kD = 4πRDABNA (3)In Equation (3), R is the distance between the atoms involved in the hydrogen atomtransfer (reaction distance), NA is Avogadro’s number, and DAB is the mutual diffusioncoefficient of the reactants, which is given as the sum of DA and DB, which are calculatedusing the Stokes–Einstein approach [55,56] with Equation (4). In Equation (4), η is theviscosity of the solvent (8.91 × 10−4 Pa s for water and 8.62 × 10−4 Pa s for PE) and α isthe radius of spherical solute A or B.DA or B =kBT6πηαA or B(4)In the SET repair reactions, a deprotonated phenol donates an electron to the damagedleucine residue (Reaction R2). Hence, calculating k for the SET reaction requires the pKavalue of the phenolic antioxidant. Given the limited availability of experimental aqueouspKa values for molecules 1 to 20, predicted values were obtained from a recent publicationby our group [57]. These values allow the calculation of the molar fraction of the anionicform of the antioxidants at physiological pH (7.4), which needs to be multiplied by thecalculated SET rate constants using Equation (1), setting σ and κ to 1. The SET activationbarriers (∆G ̸=SET) were calculated applying Marcus theory [58,59] using Equation (5), where∆G0ET is the Gibbs free energy of reaction, and λ is the nuclear reorganizational energywhich defines the nonadiabatic transfer of an electron from reactants to vertical products. λis calculated using Equation (6).Phenol-O− + Leucine•⇌ Phenol-O• + Leucine− (R2)∆G ̸=SET =λ4(1 +∆G0ETλ)(5)λ ≈ ∆EET − ∆G0ET (6)As carried out in previous studies, if a reaction is exergonic, it is further studied froma kinetic point of view. The methodology described has been widely applied in the kineticstudy of reactions in solution, including studies of antioxidant activity [22–24,26,46–48,60].3. Results and Discussion3.1. Investigating the Formal-Hydrogen Atom Transfer (f-HAT) Repair ReactionsThe f-HAT reactions studied involve the transfer of a hydrogen atom from a phenol’shydroxyl group. It is worth noting that molecules 1–13 have one hydroxyl group, whereasmolecules 14–20 have multiple hydroxyl groups, thus multiple main sites of f-HAT reac-tivity. It is worth noting that molecules 14–20 may be capable of quenching multiple freeradicals per antioxidant molecule. The contribution of other sites to f-HAT reactivity isconsidered negligible in this study. The predicted order of stability of the leucine radi-cal is γ > β > δ, corresponding to tertiary, secondary, and primary radicals, respectively,which should be opposite to the thermodynamic favourabilities of their correspondingrepair reactions.Although many different orientations of the substituent groups were tested whensearching for the optimized geometries of the various stationary points in this study, weare unable to guarantee that they are the lowest possible Gibbs energy conformations.Nevertheless, the calculations reported refer to the most thermodynamically favourableconformation identified, with particular attention to the polyphenols. The TSs were builtAntioxidants 2024, 13, 1368 6 of 17using the optimized geometries of the corresponding reactants while maximizing thepossibility of stabilizing interactions such as the formation of intermolecular hydrogenbonding and minimizing steric repulsions.3.1.1. Thermodynamic Study of f-HAT ReactionsThe changes in free energy for the f-HAT reactions are listed in Table 1. Additionally,∆H◦ values are provided in Tables S6 and S7 for the calculations in water and PE, respec-tively. All of the f-HAT repair reactions studied were exergonic in both solvents and wereslightly more exergonic in PE than in water in all 13 cases except for the nitrogen-containingmolecules (8–11). Unsurprisingly, the order of the repair site exergonicity was alwaysδ > β > γ, which is a result of many factors, including the radical’s distance from theprotein backbone, the primary, secondary, or tertiary (respectively) nature of the repairsite, and the degree of hyperconjugation. Considering molecules 1–13, the δ and β repairshave very similar ∆G◦ values with average differences of 0.86 and 1.15 kcal/mol in waterand PE, respectively. However, the ∆G◦ values for the γ repairs are around 5.0 kcal/molless negative than the δ repairs in both solvents. These values reflect the Gibbs energydifferences between the various radicals to be repaired. The order of exergonicity will becompared to the kinetics results in the next section to test the Bell–Evans–Polanyi principle,which has already been shown to break down in previous antioxidant studies [22–24]. TheBell–Evans–Polanyi principle correlates the thermodynamics of a reaction with its kinetics:the more exergonic a reaction, the faster it should be.Table 1. Standard Gibbs free energies of reaction (∆G◦) and activation (∆G ̸=), and rate constants (k)for the f-HAT repair reactions of the corresponding damaged (dmg) N-formyl leucinamide (Leucine)in water and pentyl ethanoate (PE) at 298.15 K.∆G◦ (kcal/mol) ∆G ̸= (kcal/mol) k (M−1s−1) ∆BDE cReactants Water PE Water PE Water PE Overall (PE) GasLeucine-β-dmg + 1 −19.6 −20.7 10.9 10.4 4.57 × 105 3.04 × 105−8.9Leucine-γ-dmg + 1 −14.6 −15.9 14.2 13.7 9.32 × 103 1.59 × 104Leucine-δ-dmg + 1 −20.4 −21.9 11.3 8.2 2.29 × 105 1.22 × 107Leucine-β-dmg + 2 −17.4 −18.0 15.5 13.0 5.74 × 103 3.00 × 104−6.1Leucine-γ-dmg + 2 −12.4 −13.2 14.5 14.5 1.19 × 104 1.01 × 104Leucine-δ-dmg + 2 −18.3 −19.2 12.7 11.8 1.86 × 105 3.69 × 105Leucine-β-dmg + 3 −17.6 −18.3 14.8 10.5 9.86 × 103 1.27 × 106−7.2Leucine-γ-dmg + 3 −12.6 −13.5 15.1 14.1 4.80 × 103 1.64 × 104Leucine-δ-dmg + 3 −18.5 −19.5 12.9 11.8 1.31 × 105 4.40 × 105Leucine-β-dmg + 4 −18.4 −18.7 11.4 11.6 4.98 × 105 3.25 × 105−7.3Leucine-γ-dmg + 4 −13.4 −13.9 15.2 13.6 4.46 × 103 3.80 × 104Leucine-δ-dmg + 4 −19.3 −19.9 12.9 11.6 1.28 × 105 6.14 × 105Leucine-β-dmg + 5 −20.0 −20.3 10.7 10.6 5.66 × 105 3.53 × 105−9.4Leucine-γ-dmg + 5 −15.0 −15.5 13.5 13.2 4.67 × 104 5.63 × 104Leucine-δ-dmg + 5 −20.9 −21.4 12.3 11.1 7.85 × 104 4.98 × 105Leucine-β-dmg + 6 −19.9 −20.1 11.2 11.0 3.34 × 105 2.75 × 105−8.9Leucine-γ-dmg + 6 −14.9 −15.3 13.9 12.8 2.37 × 104 1.21 × 105Leucine-δ-dmg + 6 −20.8 −21.3 12.7 11.1 1.36 × 105 1.00 × 106Leucine-β-dmg + 7 −22.3 −22.4 9.0 8.5 3.18 × 106 6.86 × 106−11.3Leucine-γ-dmg + 7 −17.3 −17.5 13.0 12.3 5.43 × 104 1.57 × 105Leucine-δ-dmg + 7 −23.2 −23.5 11.3 8.0 4.60 × 105 1.66 × 107Leucine-β-dmg + 8 −23.7 −22.6 11.4 11.1 1.32 × 106 7.63 × 105−9.4Leucine-γ-dmg + 8 −18.7 −17.7 13.8 12.9 3.86 × 104 9.97 × 104Leucine-δ-dmg + 8 −24.5 −23.7 12.5 9.9 1.84 × 105 6.78 × 106Antioxidants 2024, 13, 1368 7 of 17Table 1. Cont.∆G◦ (kcal/mol) ∆G ̸= (kcal/mol) k (M−1s−1) ∆BDE cReactants Water PE Water PE Water PE Overall (PE) GasLeucine-β-dmg + 9 −25.0 −23.6 12.1 11.5 5.07 × 105 3.08 × 105−10.3Leucine-γ-dmg + 9 −20.0 −18.7 13.0 11.9 1.40 × 105 5.16 × 105Leucine-δ-dmg + 9 −25.9 −24.7 12.2 9.2 3.69 × 105 1.45 × 107Leucine-β-dmg + 10 −29.9 −27.7 6.9 6.6 9.34× 107 a 1.38× 108 a−14.6Leucine-γ-dmg + 10 −24.9 −22.9 9.8 11.3 1.93 × 106 2.34 × 105Leucine-δ-dmg + 10 −30.7 −28.9 9.3 6.7 1.92 × 106 1.23× 108 aLeucine-β-dmg + 11 −27.5 −26.6 10.0 9.6 2.30 × 106 1.21 × 106−11.8Leucine-γ-dmg + 11 −22.5 −21.8 12.8 11.8 2.34 × 105 4.14 × 105Leucine-δ-dmg + 11 −28.3 −27.8 12.2 8.9 1.85 × 105 1.15 × 107Leucine-β-dmg + 12 −15.7 −16.1 14.3 13.0 3.18 × 104 7.01 × 104−7.7Leucine-γ-dmg + 12 −10.7 −11.2 16.1 15.3 1.01 × 103 3.04 × 103Leucine-δ-dmg + 12 −16.5 −17.2 14.6 13.5 1.34 × 104 4.73 × 104Leucine-β-dmg + 13 −14.5 −15.6 15.8 13.0 2.96 × 103 6.87 × 104−8.5Leucine-γ-dmg + 13 −9.5 −10.8 16.9 15.0 2.49 × 102 4.85 × 103Leucine-δ-dmg + 13 −15.4 −16.8 15.7 13.3 2.26 × 103 7.46 × 104Leucine-δ-dmg + 14 (1) −15.9 8.9 3.94 × 1061.12 × 107 −11.2Leucine-δ-dmg + 14 (2) −21.9 8.9 4.03 × 106Leucine-δ-dmg + 14 (3) −16.3 9.0 3.23 × 106Leucine-δ-dmg + 15 (1) −20.9 8.3 9.47 × 1063.44 × 107 −11.1Leucine-δ-dmg + 15(2) −22.4 8.1 1.37 ×107Leucine-δ-dmg + 15 (3) −23.6 8.6 6.48 × 106Leucine-δ-dmg + 15 (4) −20.9 8.8 4.74 × 106Leucine-δ-dmg + 16 (1) −14.0 10.9 1.38 × 1052.39 × 105 −2.3−1.3Leucine-δ-dmg + 16 (2) −13.6 11.3 1.01 × 105Leucine-δ-dmg + 17 (1) −23.9 7.9 2.10 × 1072.14 × 107 −14.1Leucine-δ-dmg + 17 (2) −18.0 11.0 1.98 × 105 bLeucine-δ-dmg + 18 (1) −16.4 8.8 4.69 × 1061.34 × 107 −11.6Leucine-δ-dmg + 18 (2) −21.9 8.7 4.95 × 106Leucine-δ-dmg + 18 (3) −15.9 8.9 3.80 × 106Leucine-δ-dmg + 19 (1) −16.1 13.1 9.36 × 1042.91 × 105 −8.2Leucine-δ-dmg + 19 (2) −11.5 11.8 6.52 × 104Leucine-δ-dmg + 19 (3) −11.7 11.3 1.33 × 105Leucine-δ-dmg + 20 (1) −19.8 9.7 1.05 × 1062.49 × 106 −15.6Leucine-δ-dmg + 20(2) −23.0 10.2 1.26 × 106Leucine-δ-dmg + 20 (3) −11.6 11.7 3.20 × 104Leucine-δ-dmg + 20 (4) −12.3 11.3 1.52 × 105a These are apparent rate constants (kapp); b This value represents the rate constant for both degenerate sitescombined; c Calculated bond dissociation enthalpy changes (relative to the value of phenol, in kcal/mol) in thegas phase reported in [37].When considering the food additive molecules 1 and 2, 1 reacts more exergonicallywith leucine in both solvents, which is consistent with the predicted change in bonddissociation energy values, ∆BDE (O-H BDE relative to phenol), by Wright et al. [37] andthe preferential use of 1 in industry [61,62]. At equivalent sites, reactions with molecule1 are 2.1 to 2.2 kcal/mol more exergonic in water and 2.7 kcal/mol more exergonic in PEthan with molecule 2. The tert-butyl group increases the electron density in the phenolicring and can stabilize the oxygen radical better when in ortho relative to it. Furthermore,the hydroxyl group in ortho-substituted BHA faces much more steric repulsion than in themeta-substituted case [63].Antioxidants 2024, 13, 1368 8 of 17In the family of vitamin E molecules, 3–7, molecule 7, the most bioactive form, pro-duced the most exergonic repair reactions with leucine (−22.4,−17.5,−23.5 kcal/mol at theβ, γ, and δ sites in PE, respectively). In agreement with previous publications which studiedBDE and ∆BDE, β-tocopherol (5) had slightly more exergonic reactions than γ-tocopherol(6) with leucine in both solvents [29,37,64]. Not surprisingly, the least exergonic moleculewas the tocol model (3) due to the lack of substitution present relative to molecules 4–7.Overall, the order of tocopherol exergonicities is 7 > 5 > 6 > 4 > 3, which is consistent withthe number of ortho methyl groups present, as well as the total number of substituentmethyl groups.For the four aminophenols studied (8–11), consistent trends in ∆G◦ between bothsolvent models and reaction sites were found. Molecule 10 produced the most exergonicrepair reactions seen in this study (−29.9, −24.9, and −30.7 kcal/mol at the β, γ, and δsites in water, respectively). As previously mentioned, these were the only molecules thatproduced more exergonic reactions in the hydrophilic environment than in the hydrophobicone. The f-HAT reactions of the stilbenes (12, 13) were the least exergonic in both solventsstudied when considering the monophenolic antioxidants.Based on the results of the monophenolic antioxidants, we decided to examine only δrepair in PE for the polyphenolic antioxidants (14–20). This is because this site and solventconsistently produced the most exergonic reactions and largest repair rate constants (seeSection 3.1.2.) for almost all of the monophenolic antioxidants. The other sites and solventproduced rate constants that were sometimes multiple orders lower; therefore, we deemedtheir contribution to the overall repair rate constants to be negligible.As seen in Figure 2, molecules 14, 17, and 18 are structurally similar, each presentingthree adjacent hydroxyl groups. As previously noted [37], when three hydroxyl groups areadjacent, the HAT reaction of the “internal” group is the most thermodynamically favoured.The “internal” oxygen radical is stabilized by hydrogen bonds from both “external” hy-droxyl groups, whereas the “external” oxygen radical is only stabilized directly by the“internal” hydroxyl group. Our results follow this trend (Table 1). The stabilization of the“internal” oxygen radicals is also coupled with the electron-withdrawing (and stabilizing)effect of the ester groups in molecules 14 and 18. Interestingly, despite the lack of additionalresonance or electron delocalization relative to molecules 14 and 18, molecule 17 producedthe most exergonic reaction in PE of this study at its “internal” site (−23.9 kcal/mol). Thisbehaviour of molecule 17, relative to molecules 16 and 18, is corroborated by the activityof EGCG, which is typically associated with the molecule 17 substructure and has shownsimilar results in other publications [37,65].Molecules 19 and 20 are also structurally similar, with 20 having an additional hydroxylgroup. In molecule 19, the 19(2) and 19(3) reactions have similar exergonicities (0.2 kcal/moldifference), about 4.5 kcal/mol less negative when compared to the 19(1) site, which issupported by previous work [65,66]. A similar trend is seen in the 20(3) and 20(4) sites (witha difference of 0.7 kcal/mol). The Gibbs energy of the reaction is 9.0–10.0 kcal/mol morenegative for the ortho-related hydroxyl groups, 20(1) and 20(2).There are also common substituent effects observed among the polyphenolic antioxi-dants. The sites 14(2), 18(2), 19(1), and 20(2) are all para relative to electron withdrawing (byresonance and/or induction) substituents. Unsurprisingly, these hydroxyl sites producethe most exergonic reactions of these molecules.3.1.2. Kinetic Study of Hydrogen Atom Transfer ReactionsThe kinetic study of a reaction should provide the best assessment of reactivity andshould give us better tools for the comparison of antioxidant activity between differentspecies when following a given methodology and with experimental results, when avail-able. The experimental evaluation of specific types of antioxidant activity is challenging andmost studies analyze the total antioxidant capacity of their samples. However, assigningindividual antioxidant activities has been suggested as more important than determiningthe total antioxidant activity of a system [67], especially when designing synthetic antioxi-Antioxidants 2024, 13, 1368 9 of 17dants based on natural antioxidants. While theory gains insight by studying antioxidantsin isolation, it also loses key information such as agonist and antagonist activities of speciesin the chemical environment.N-formyl leucinamide has been used experimentally as a protein model, but thekinetics of its repair reactions with the phenols in this study have not been performedexperimentally. However, the theoretical calculation of the rate constant of these reactionscan allow the reactivity comparison between these phenols, and with previously studiedantioxidants, in order to assess their tertiary antioxidant activity.Following the thermodynamic study of the f-HAT repair reactions, the correspondingTSs were calculated. All the reactions were studied because they are exergonic. The degreeof inter-molecular hydrogen bonding in the TS was generally consistent with its stability,but TSs leading to reactions with small Gibbs energies of activation were also found withoutthese additional stabilizing interactions. The δ site repair generally had the lowest Gibbsenergy of activation, followed by the β site. The γ site repair faced a large amount ofsteric repulsion, hence these TSs were built to minimize this and generally showed nointer-molecular hydrogen bonding. Nevertheless, many other factors, such as the presenceof electron-withdrawing (EWG)/electron-donating (EDG) groups, local and through-bondeffects, conjugation, hyperconjugation, solvent effects, and quantum tunnelling, contributeto the stability of the TS and the rate constant (k) of the reaction.Table 1 displays the calculated Gibbs energy of activation (∆G ̸=) and k values inwater and PE. The ∆G ̸= values are always larger in water than in PE for equivalent repairpositions of molecules 1–13 except for 4(β) and 10(γ). In general, k values in PE werelarger than in water, except for seven of the β repairs (those of molecules 1, 4–6, 8, 9, and11) and two of the γ repairs (for molecules 2 and 10). Hence, a general observation fromour calculations is that these antioxidants might be more effective in repairing damagedleucine (and perhaps other aliphatic amino acid residues) in proteins within hydrophobicpockets than in a more solvent-exposed (hydrophilic) environment. Our discussion in thissection will mainly focus on the magnitudes of k (instead of ∆G ̸=) since it includes theeffects of quantum tunnelling (κ values between 1.0 and 113.3 were calculated as shown inTables S6 and S7)), reaction path degeneracy, and the reaction temperature.The food additive antioxidants (1 and 2), behave somewhat consistently with theresults from the thermodynamic study, as seen in Table 1. Molecule 1 (with more exergonicrepair reactions) has a larger rate constant than molecule 2 in all cases except at the γ site inwater, with the fastest repair corresponding to the δ site in PE (k = 1.2 × 107 M−1s−1).The tocopherol molecules (3–7) present a similar overall trend to the thermodynamicstudy; the rate constant increases with the degree of substitution of the phenol, partic-ularly with ortho substitutions. The fastest repair is produced by molecule 7(δ) in PEwith k = 1.7 × 107 M−1s−1. It should be noted that the overall repair rate constant ofmolecule 7 is three orders of magnitude larger than the experimental radical lysozymerepair rate constant of 2.6 × 104 M−1s−1 in sodium dodecyl sulphate (SDS) micelles [68].Nevertheless, this comparison is indirect, as we are studying radically damaged leucineand the radical lysozyme mentioned in the study seems to be related to the presence ofdamaged tryptophan residues. Other fast repairs correspond to 3(β), 6(δ), and 7(β) in PEwith k values in the (1.0–6.9) × 106 M−1s−1 range. One surprising observation regardingmolecules 3–7 is that the β sites had larger rate constants than the δ sites in water, whichdisagrees with the thermodynamic predictions.The aminophenol antioxidants (8–11) also present similar overall trends to the thermo-dynamic study. As predicted, the molecule exhibiting the most exergonic f-HAT repairsof all the phenols studied, 10(β) and 10(δ), shows the largest k values seen in this study,(1.2–1.4) × 108 M−1s−1 in PE, which are also the only rate constants in the diffusion limit.These are the only effective f-HAT repair reactions studied, and they are proposed toquench the radical damage and compete with alternate protein radical mechanisms, suchas peroxidation [69]. The structure of the TS leading to the fastest repair (β) by molecule 10is displayed in Figure 3, with important bond distances indicated. This TS did not exhibitAntioxidants 2024, 13, 1368 10 of 17additional stabilizing interactions from inter-molecular hydrogen bonding between thereacting units.Antioxidants 2024, 13, x FOR PEER REVIEW 10 of 17 The aminophenol antioxidants (8–11) also present similar overall trends to the ther-modynamic study. As predicted, the molecule exhibiting the most exergonic f-HAT re-pairs of all the phenols studied, 10(β) and 10(δ), shows the largest k values seen in this study, (1.2–1.4) × 108 M−1s−1 in PE, which are also the only rate constants in the diffusion limit. These are the only effective f-HAT repair reactions studied, and they are proposed to quench the radical damage and compete with alternate protein radical mechanisms, such as peroxidation [69]. The structure of the TS leading to the fastest repair (β) by mol-ecule 10 is displayed in Figure 3, with important bond distances indicated. This TS did not exhibit additional stabilizing interactions from inter-molecular hydrogen bonding be-tween the reacting units. Similar to molecule 7, molecule 10 presents the most substitution among the amino-phenols and has the largest rate constant. The other aminophenols produced the largest k values when repairing the δ site in PE. While this site selection corresponds to the ther-modynamic prediction, it contradicts the prediction that water would be a more suitable solvent for repair by aminophenols. Repair by the stilbenes (12–13) produced the smallest f-HAT rate constants in agree-ment with these reactions being the least exergonic. One inconsistency was found in mol-ecule 12, where the largest repair k value occurred in PE at the β site instead of the δ site (the most exergonic). A few inconsistencies in trends between the thermodynamic and the kinetic study of the repair reactions of molecules 1–13 have already been pointed out when discussing the results of the four groups of phenols. In addition to these, we can observe that the ther-modynamic study predicted that repairs at the δ site would have the largest rate constants in both PE and water; however, this was not always the case, with the β site producing a larger rate constant in 14 cases. Furthermore, the solvent producing the more thermody-namically favoured reactions did not lead to the fastest repairs in 13 cases. Figure 3. Structure of the f-HAT TS corresponding to the β repair of N-formyl leucinamide with molecule 10, the fastest repair reaction studied (important bond distances shown in Å). Based on the thermodynamic results in PE (δ repair), the predicted order of rate con-stants would have been 10 > 11 > 9 > 8 > 7 > 1 > 5 ≈ 6 > 4 > 3 ≈ 2 > 12 > 13, compared to the calculated order of 10 > 7 > 9 > 1 > 11 > 8 > 6 > 4 > 5 > 3 > 2 > 12 > 13. These differences in thermodynamic and kinetic antioxidant activity predictions indicate a breakdown of the Bell–Evans–Polanyi principle. This is expected since thermodynamic calculations ignore structural and stability aspects of the TS and other kinetic features such as quantum tun-nelling and reaction path degeneracy. Because the fastest repair reaction for molecules 1–13 was for the δ position in PE, we decided to focus on this specific repair reaction when studying the tertiary antioxidant activity of the polyphenolic antioxidants (14–20). Overall rate constants that result from adding the site-specific k values for each molecule are displayed in Table 1. The largest overall k value (3.4 × 107 M−1s−1) is produced by molecule 15. For these molecules, none of f -f l ilec le 10, t e fastest re air reacti st ie (i rta t bon distances sho n in ).Similar to molecule 7, molecule 10 presents the most substitution among the aminophe-nols and has the largest rate constant. The other aminophenols produced the largest kvalues when repairing the δ site in PE. While this site selection corresponds to the ther-modynamic prediction, it contradicts the prediction that water would be a more suitablesolvent for repair by aminophenols.Repair by the stilbenes (12–13) produced the smallest f-HAT rate constants in agree-ment with these reactions being the least exergonic. One inconsistency was found inmolecule 12, where the largest repair k value occurred in PE at the β site instead of the δsite (the most exergonic).A few inconsistencies in trends between the thermodynamic and the kinetic studyof the repair reactions of molecules 1–13 have already been pointed out when discussingthe results of the four groups of phenols. In addition to these, we can observe that thethermodynamic study predicted that repairs at the δ site would have the largest rateconstants in both PE and water; however, this was not always the case, with the β siteproducing a larger rate constant in 14 cases. Furthermore, the solvent producing the morethermodynamically favoured reactions did not lead to the fastest repairs in 13 cases.Based on the thermodynamic results in PE (δ repair), the predicted order of rateconstants would have been 10 > 11 > 9 > 8 > 7 > 1 > 5 ≈ 6 > 4 > 3 ≈ 2 > 12 > 13, compared tothe calculated order of 10 > 7 > 9 > 1 > 11 > 8 > 6 > 4 > 5 > 3 > 2 > 12 > 13. These differencesin thermodynamic and kinetic antioxidant activity predictions indicate a breakdown ofthe Bell–Evans–Polanyi principle. This is expected since thermodynamic calculationsignore structural and stability aspects of the TS and other kinetic features such as quantumtunnelling and reaction path degeneracy.Because the fastest repair reaction for molecules 1–13 was for the δ position in PE, wedecided to focus on this specific repair reaction when studying the tertiary antioxidantactivity of the polyphenolic antioxidants (14–20). Overall rate constants that result fromadding the site-specific k values for each molecule are displayed in Table 1. The largestoverall k value (3.4 × 107 M−1s−1) is produced by molecule 15. For these molecules, noneof the repair rate constants were in the diffusion limit, indicating that these repair reactionsare not biologically relevant. This is corroborated for molecule 14 whose experimentalrepair rate constant of the lysozyme radical (in SDS micelles, a hydrophobic environment)is (9.9 ± 1.0) × 106 M−1s−1 [68], in close proximity to our calculated rate constant of1.12 × 107 M−1s−1 for the repair of the δ position in leucine.Many of the general thermodynamic predictions are reflected in the kinetic results.For example, the “internal” hydroxyl groups of 14, 17, and 18 (14(2), 17(1), and 18(2), seeFigure 2) had larger rate constants than the “external” hydroxyl groups. As seen in thethermodynamic calculations, this is due to the stabilization of the radical via the “external”Antioxidants 2024, 13, 1368 11 of 17hydroxyl groups on either side which was also observed in the TSs. One interestingobservation is that 17(1) produced a rate constant that is two orders larger (2.1× 107 M−1s−1)than its other hydroxyl group, while 14(2) and 18(2) produced rate constants in the sameorder as its other hydroxyl groups, (3.2–5.0) × 106 M−1s−1, in general agreement withBrigati et al. [70] where the BDE of similar molecules were investigated. When an estergroup is placed para relative to the hydroxyl group, the strength of the O-H bond increases,hence producing smaller rate constants. The larger rate constants of molecule 17 are alsoexpected since this ring is typically associated with the activity of EGCG and has shownsimilar results in other publications [37,71], in agreement with our thermodynamic results.Molecule 19(1) was predicted to have the largest repair rate constant when consideringthe thermodynamic study; however, 19(3) had a slightly larger rate constant which is likelydue to the shorter inter-molecular hydrogen bonding that stabilizes its TS. Molecule 20has its thermodynamic predictions reflected in its kinetic results, as previously describedfor molecules 14, 17, and 18. As predicted, 20(3) and 20(4) had smaller rate constants than20(1) and 20(2), with 20(2) having the largest repair rate constant (1.3 × 106 M−1s−1). Thisis likely due to the stabilization of the radical from the ortho hydroxyl group and theconjugated system in the para position. This indicates that the TS stabilization from theortho hydroxyl group in 20 is relevant in producing a larger rate constant, and althoughthe para conjugated system may have led to a more exergonic reaction, it did not affect therate constant to the same extent.The thermodynamic results reported in Section 3.1.1., led us to believe that parasubstituents relative to the reacting hydroxyl group correspond to larger rate constants(14(2), 18(2), 19(1), and 20(2)). However, it is worth noting that 14(2), 18(2), and 20(2) alsohave ortho hydroxyl groups to stabilize the radical. Given the kinetic results obtained,we propose that the presence of an ortho hydroxyl group is a better predictor of kineticbehaviour than para electron-withdrawing substituents.Further examining the thermodynamic and kinetic data for molecules 14–20, additionalviolations of the Bell–Evans–Polanyi principle can be observed. Inspecting each moleculeindividually, this principle is not followed by molecules 15 and 19 (e.g., the most exergonicsite does not produce the largest rate constant). This principle breaks down even furtherwhen comparing exergonicities and rate constants between molecules. For instance, thereaction of 20(2) was the third-most exergonic reaction in this study (∆G◦ =−23.0 kcal/mol),yet it produced a rate constant smaller than all of the sites in molecules 14, 15, and 18.Other breakdowns of this principle can be found within our data, which indicates thatthermodynamic data are insufficient to predict kinetic results, in agreement with previouswork [22,24].To investigate the correlation between our rate constant calculations and the relativeantioxidant activity of the phenolic antioxidants under study with the calculated gas-phaseproperties by Wright et al. [37], we plotted −∆BDE versus the logarithm of the largest kvalue for each compound in both solvents (see Figure 4). With respect to the ∆BDE bars,the relative heights of the rate constants corresponding to both solvents are widely variable.In some cases, as with molecule 10, the –∆BDE value matches quite closely with the log(k)values; the two approaches predict this molecule to be very reactive when interactingwith a radical via an HAT reaction. However, in other cases, the thermodynamic-kineticreactivity predictions are very different. The ∆BDE values for molecules 10 and 20 are verysimilar and the thermodynamic approach predicts these molecules to be the most reactiveof all; however, compound 20’s k value is unimpressive in terms of its reactivity. Anotherexample of contradictions found are the stilbenes (molecules 12 and 13) which producedthe smallest f-HAT rate constant values in both solvents, though their calculated gas-phase∆BDE values are on par with those of molecules 3–6, which have k values that are an orderor larger than the k values of the stilbenes.Antioxidants 2024, 13, 1368 12 of 17Antioxidants 2024, 13, x FOR PEER REVIEW 12 of 17 kinetic reactivity predictions are very different. The ΔBDE values for molecules 10 and 20 are very similar and the thermodynamic approach predicts these molecules to be the most reactive of all; however, compound 20’s k value is unimpressive in terms of its reactivity. Another example of contradictions found are the stilbenes (molecules 12 and 13) which produced the smallest f-HAT rate constant values in both solvents, though their calculated gas-phase ΔBDE values are on par with those of molecules 3–6, which have k values that are an order or larger than the k values of the stilbenes. Figure 4. Comparison of −∆BDE values in the gas phase (from [37]) with our largest HAT log(k) values for the 20 compounds in water and PE. In summary, only molecule 10 produced rate constants in the diffusion limit for the f-HAT repair reaction showing biological significance. Important violations of the Bell–Evans–Polanyi principle have been discussed, which indicate that thermodynamic data are insufficient to properly predict kinetic antioxidant activity. However, thermodynamic data can be used as valuable screening tools [40,60]. Thermodynamic results also indicate the extent of products formed; however, it should be noted that endergonic reactions can still be viable antioxidant pathways if the products are consumed rapidly in subsequent reactions. From our experience, the kinetic calculation of rate constants is a valuable tool for predicting antioxidant activity and greatly increases the biological relevance of theo-retical studies. We also discussed some of the contradictions between the calculated rate constants in solution and calculated gas-phase ΔBDE values when attempting to make reactivity predictions for the f-HAT reactions between these phenols and radicals. 3.2. Investigating the Single-Electron Transfer Repair Reaction Multiple forms of SET reactions exist and can considerably contribute to a molecule’s overall antioxidant activity. We consider the case where the antioxidant has been depro-tonated before the SET reaction. Since this type of SET reaction is only thermodynamically feasible in protic media, this study was only performed in water. Table S8 displays the calculated Gibbs energy of reaction (∆G°) and activation (∆G≠), and the k values for the SET reactions. As can be observed, these reactions are highly en-dergonic and are not expected to contribute to the overall antioxidant activity of these molecules. In addition, their pKa values are quite large [57], indicating that only a small molar fraction of the anionic form is available for this reaction at pH 7.4. In the case of the polyphenolic (polyprotic) molecules, the aqueous pKa value for the most stable monoan-ion was calculated, as this represents the most dominant anion at pH 7.4 (see Table S9). The pKa values for the monoanions were calculated using the ∆G°-pKa correlation Figure 4. Comparison of −∆BDE values in the gas phase (from [37]) with our largest HAT log(k)values for the 20 compounds in water and PE.In summary, only molecule 10 produced rate constants in the diffusion limit for thef-HAT repair reaction showing biological significance. Important violations of the Bell–Evans–Polanyi principle have been discussed, which indicate that thermodynamic dataare insufficient to properly predict kinetic antioxidant activity. However, thermodynamicdata can be used as valuable screening tools [40,60]. Thermodynamic results also indicatethe extent of products formed; however, it should be noted that endergonic reactions canstill be viable antioxidant pathways if the products are consumed rapidly in subsequentreactions. From our experience, the kinetic calculation of rate constants is a valuable tool forpredicting antioxidant activity and greatly increases the biological relevance of theoreticalstudies. We also discussed some of the contradictions between the calculated rate constantsin solution and calculated gas-phase ∆BDE values when attempting to make reactivitypredictions for the f-HAT reactions between these phenols and radicals.3.2. Investigating the Single-Electron Transfer Repair ReactionMultiple forms of SET reactions exist and can considerably contribute to a molecule’soverall antioxidant activity. We consider the case where the antioxidant has been deproto-nated before the SET reaction. Since this type of SET reaction is only thermodynamicallyfeasible in protic media, this study was only performed in water.Table S8 displays the calc lated Gibbs energy of reaction (∆G◦) and activation (∆G ̸=),and the k values for t SET reactions. As can be observed, these reactions are highlyendergonic and are not expected to contribute to th overall antioxidant activity of thesemolecules. In addition, their pKa values ar qui e larg [57], indicati g that only a smallmolar fraction of the anionic form is available for this reaction at pH 7.4. In the case of thep yphenolic (polyprot c) molecule , the aqu ous pKa v lue for he most stabl mon anionwas calculated, as this repres nts the most dominant anion at pH 7.4 (see Table S9). ThepKa values for he monoanions were calculated using the ∆G◦-pKa correlation equation att M06-2X(PCM)/6-311++G(d,p) level of theory reported in a recent publication by urgroup [57].The calculated SET rate constants are extremely small and this result is in contradictionwith the predictions of Wright et al. [37] based on calculated gas-phase ionization potentialsand BDE values. They reported that the phenols studied primarily react with radicalsthrough f-HAT, except for molecules 10 and 11, which may react primarily through SET.While the SET reactions with radically damaged leucine are not predicted to be a viablerepair mechanism, this does not reflect the ability of these molecules to engage in SETrepair mechanisms with other free radicals (see Ref. [72], for example).Antioxidants 2024, 13, 1368 13 of 17It is important to note that our SET rate constant calculations focus on the anionicspecies of each phenol as a reactant in aqueous solution, while the gas-phase adiabatic IPvalues calculated by Wright et al. [37] refer to the formation of the cation from the neutralphenol and account for the geometry changes upon removal of the electron. These IP valuesmight have a better correlation with the rate constant of an SET reaction that focuses on theneutral phenol as a reactant, but this reaction would be of less biochemical relevance thanthat which we considered [73,74].Similar to the way that we proceeded with the f-HAT reactions, the calculated gas-phase –∆IP values (calculated relative to the value of phenol) by Wright et al. [37] versusthe largest log(k) values calculated for the SET reactions in water were plotted for eachcompound (see Figure 5). A better overall agreement between relative changes in the twoproperties could be appreciated for the set of molecules relative to our discussion on the−∆BDE versus the largest f-HAT log(k) values. However, large differences that breaktrends can be observed for molecules 1, 8, 17, 18, and especially molecule 19. Perhaps inthe cases where the trends are kept, no significant geometry changes are produced betweenthe neutral and the cation species in the gas phase. This might be the case because our kcalculations for the SET process use vertical energy differences (no geometry relaxation isconsidered). In either type of ionization, the solvent presence should have an effect but wedid not explore this further.Antioxidants 2024, 13, x FOR PEER REVIEW 13 of 17 equation at the M06-2X(PCM)/6-311++G(d,p) level of theory reported in a recent publica-tion by our group [57]. The calculated SET rate constants are extremely small and this result is in contradic-tion with the predictions of Wright et al. [37] based on calculated gas-phase ionization potentials and BDE values. They reported that the phenols studied primarily react with radicals through f-HAT, except for molecules 10 and 11, which may react primarily through SET. While the SET reactions with radically damaged leucine are not predicted to be a viable repair mechanism, this does not reflect the ability of these molecules to en-gage in SET repair mechanisms with other free radicals (see Ref. [72], for example). It is important to note that our SET rate constant calculations focus on the anionic species of each phenol as a reactant in aqueous solution, while the gas-phase adiabatic IP values calculated by Wright et al. [37] refer to the formation of the cation from the neutral phenol and account for the geometry changes upon removal of the electron. These IP val-ues might have a better correlation with the rate constant of an SET reaction that focuses on the neutral phenol as a reactant, but this reaction would be of less biochemical rele-vance than that which we considered [73,74]. Similar to the way that we proceeded with the f-HAT reactions, the calculated gas-phase –ΔIP values (calculated relative to the value of phenol) by Wright et al. [37] versus the largest log(k) values calculated for the SET reactions in water were plotted for each compound (see Figure 5). A better overall agreement between relative changes in the two properties could be appreciated for the set of molecules relative to our discussion on the −ΔBDE versus the largest f-HAT log(k) values. However, large differences that break trends can be observed for molecules 1, 8, 17, 18, and especially molecule 19. Perhaps in the cases where the trends are kept, no significant geometry changes are produced be-tween the neutral and the cation species in the gas phase. This might be the case because our k calculations for the SET process use vertical energy differences (no geometry relax-ation is considered). In either type of ionization, the solvent presence should have an effect but we did not explore this further. Figure 5. Comparison of −∆IP in the gas phase (from [37]) with our largest SET log(k) values for the 20 compounds in water. 4. Conclusions This paper evaluates the tertiary antioxidant activity of a family of phenols. The f-HAT and SET repair of oxidatively damaged N-formyl leucinamide was investigated at its β, γ, and δ sites with twenty phenolic molecules. Thermodynamic and kinetic quanti-ties were calculated at the M06-2X(SMD)/6-31++G(d,p) level of theory in water and pentyl Figure 5. Comparison of −∆IP in the gas phase (from [37]) with our largest SET log(k) values for the20 compounds in water.4. ConclusionsThis paper evaluates the tertiary antioxidant activity of a family of phenols. The f-HATand SET repair of oxidatively damaged N-formyl leucinamide was investigated at its β, γ,and δ sites with twenty phenolic molecules. Thermodynamic and kinetic quantities werecalculated at the M06-2X(SMD)/6-31++G(d,p) level of theory in water and pentyl ethanoateto simulate the hydrophilic and hydrophobic microenvironments where a damaged leucineresidue may be found.SET is not an effective repair mechanism in water for the antioxidants studied, andwhile all the f-HAT repair reactions were exergonic, only one phenol (molecule 10) pro-duced rate constants in the diffusion limit showing biological significance at the level ofdihydrolipoic acid and GSH [22,24]. A general observation from our calculations is thatthese antioxidants might be more effective at repairing damaged leucine (and perhapsother aliphatic amino acid residues) in proteins within hydrophobic pockets than in a moresolvent-exposed (hydrophilic) environment. It is possible that our simplified protein modelis not able to capture additional stabilizing intermolecular interactions involving othersites of the protein and the phenolic antioxidants, which would lead to the calculation ofAntioxidants 2024, 13, 1368 14 of 17larger rate constants. This could be tested by modelling the leucine residue repair withinsolvent-exposed and hydrophobic sites of a protein which could be compared to previousexperimental data [68,75]. Quantum mechanics/molecular mechanics (QM/MM) studiesof leucine (in lysozyme) repair reactions with Trolox and GSH are the focus of anotherstudy currently in preparation by our group. In general, the conclusions derived from thesmaller protein model [22] are validated by the QM/MM study.While the results of the kinetic study were predicted by the thermodynamic calcu-lation of Gibbs energies in some cases, several important inconsistencies were discussedthat indicate the breakdown of the Bell–Evans–Polanyi principle. These breakdowns werefound when comparing the solvents, protein repair sites, and the phenolic antioxidants.We also compared the trends between our calculated rate constants in solution and theantioxidant reactivity predictions made by Wright et al. [37] based on their calculatedgas-phase thermodynamic quantities (O-H BDE and adiabatic IP values). Important in-consistencies were highlighted in this comparison for the radicals considered in this study.The evaluation of the primary antioxidant activity of this group of phenols when reactingwith a simpler but biochemically relevant radical could be performed in a future studyfollowing the methodology applied in this work for comparison. Our experience in theevaluation of antioxidant activity indicates that while thermodynamic data can be usedas valuable screening tools, the kinetic calculation of rate constants in solution is a morevaluable approach and thus greatly increases the biological relevance of theoretical studies.Supplementary Materials: The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/antiox13111368/s1. The names of the molecules studied (Table S1);spin contamination values for doublet systems in water and PE (Tables S2 and S3, respectively); theabsolute energies, enthalpies, and Gibbs free energies of all stationary points at the M06-2X(SMD)/6-31++G(d,p) level of theory in water and PE (Tables S4 and S5, respectively); the standard enthalpiesof reaction and activation, imaginary frequencies, and tunnelling factors in water and PE (Tables S6and S7, respectively); standard Gibbs free energies of reaction and activation, and rate constants forthe SET reactions (Table S8); the standard Gibbs free energies for neutral and anionic forms in water,molar fractions for monoanionic forms, and predicted pKa values for the polyphenolic antioxidantspecies (Table S9); optimized structures at the M06-2X(SMD)/6-31++G(d,p) level of theory in waterand PE.Author Contributions: Conceptualization, N.M.-D.; methodology, M.W.-R., T.F. and N.M.-D.; soft-ware, M.W.-R. and T.F.; validation: M.W.-R. and T.F.; formal analysis: M.W.-R. and T.F.; investigation:M.W.-R., T.F., and N.M.-D.; resources: N.M.-D.; data curation: M.W.-R. and T.F.; writing—originaldraft preparation: M.W.-R. and T.F.; writing—review and editing: M.W.-R. and N.M.-D.; visualization:M.W.-R. and T.F.; supervision: N.M.-D.; project administration: N.M.-D.; funding acquisition: N.M.-D.All authors have read and agreed to the published version of the manuscript.Funding: This research was funded by the Natural Sciences and Engineering Research Council ofCanada (NSERC) and Thompson Rivers University (TRU). M.W.-R. and T.F. acknowledge NSERCUSRA funding and additional funding received from the TRU Student Union (TRUSU), TRU UREAP(M.W.-R.), and TRU Apprenticeship (T.F.). M.W.-R. acknowledges NSERC CGSM and NSERCPGSD scholarships.Institutional Review Board Statement: Not applicable.Informed Consent Statement: Not applicable.Data Availability Statement: Data available upon request.Acknowledgments: We gratefully acknowledge the financial support received from NSERC and TRU,and the computing resources provided by the Digital Research Alliance of Canada (www.alliancecan.ca).We appreciate Paula Jofily’s (paula.jofily@gmail.com) work in designing the graphical abstract. Ourthanks also to Information Technology Services at TRU.Conflicts of Interest: The authors declare no conflicts of interest.Antioxidants 2024, 13, 1368 15 of 17References1. Davies, M.J. The oxidative environment and protein damage. Biochim. Biophys. Acta Proteins Proteom. 2005, 1703, 93–109.[CrossRef] [PubMed]2. 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Modelling the Repair of Carbon-Centered Protein Radicals by Phenolic Antioxidants
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