Kinetic Reaction Mechanism of Sinapic Acid Scavenging NO2 and OH Radicals: A Theoretical Study

The mechanism and kinetics underlying reactions between the naturally-occurring antioxidant sinapic acid (SA) and the very damaging ·NO2 and ·OH were investigated through the density functional theory (DFT). Two most possible reaction mechanisms were studied: hydrogen atom transfer (HAT) and radical adduct formation (RAF). Different reaction channels of neutral and anionic sinapic acid (SA-) scavenging radicals in both atmosphere and water medium were traced independently, and the thermodynamic and kinetic parameters were calculated. We find the most active site of SA/SA- scavenging ·NO2 and ·OH is the –OH group in benzene ring by HAT mechanism, while the RAF mechanism for SA/SA- scavenging ·NO2 seems thermodynamically unfavorable. In water phase, at 298 K, the total rate constants of SA eliminating ·NO2 and ·OH are 1.30×108 and 9.20×109 M-1 S-1 respectively, indicating that sinapic acid is an efficient scavenger for both ·NO2 and ·OH.


Introduction
Sinapic acid (SA, 3,5-dimethoxy-4-hydroxycinnamic acid) is a naturally-occurring and widespread phenolic acid in the plant kingdom, and can be obtained from various fruits and vegetables such as rye [1], orange, grapefruit, and cranberry [2]. Especially, SA accounts for over 73% of all free phenolic acids in rapeseed [3]. SA is a bio-active compound reported as anti-inflammatory and anxiolytic ingredient [4,5]. In addition, SA is a widely-investigated antioxidant, and because of the peroxynitrite (ONOO -) scavenging activity [6], it can be utilized to promote the cellular defense activity against the diseases involving ONOO - [7].

Radical adduct formation (RAF):
SA þ ÁR ! ÁðSA À RÞ ð 2Þ Single-electron transfer (SET): SA þ ÁR ! ÁSAðÀHÞ þ þ RH À ð3Þ The previous theoretical studies on the homologous phenolic compounds such as gallic acid, caffeic acid, and sinapic acid have shown that SET mechanism dose not play a relevant role in the reactions with free radicals [31,[38][39][40]. Hence, in the present work, we are focused on HAT and RAF as the most probable reaction mechanisms.
The contribution of two mechanisms were analyzed. All possible reaction/attack sites were examined, and the corresponding channels were identified by thermodynamic and kinetic calculations. Rate constants and branching ratios for different channels were also estimated. To simulate the water-dominated cellular environment, we also took into account the effect of aqueous solution. Then the theoretical and experimental results were compared.

Computational Methods
DFT calculations were carried out using the GAUSSIAN 09 computational package [41]. Geometry optimization and frequency calculations were performed at the M05-2X level [42] with the basis set 6-311++G(d,p). The M05-2X functional was recommended for kinetic calculation by the developers [43] and was successfully used by independent authors with that purpose [44][45][46][47][48][49][50][51]. It is also one of the best functional for calculating the reaction energy involving free radicals [52].
Unrestricted calculations were used for open shell systems. The nature of stationary points was evaluated by using normal vibration frequencies: all of reactants (R), complexes (C) and products (P) must show positive real frequencies; all of transition states (TSs) must show a single imaginary frequency which corresponds to the expected vibration mode. In addition, the intrinsic reaction coordinates (IRC) at the M05-2X/6-311++G(d,p) level were calculated to obtain the minimum energy path. Solvent effects were introduced using the continuum solvation model based on solute electron density (SMD) [53], which is a universal solvation model due to its applicability to either charged or uncharged solute in any solvent or liquid medium. At the same level of M05-2X/6-311++G(d,p), all reactants and products were optimized in aqueous solution by SMD model. The transition states were also optimized using SMD model in aqueous solution. However, in spite of trying our best, only part of the TS for water-phase pathways were identified. Therefore, the solvation effect on TS were estimation by the single point calculations with SMD model on the basis of the optimized gas-phase geometries. Then, we compared the geometries of TS found in aqueous solution with the corresponding TS optimized in gas phase (see S1 Fig). The results show that the geometries of TS optimized in aqueous solution are very similar with that of TS optimized in the gas phase. Such as, for the bond of readying to form, the biggest difference in bond length is only 0.13Å. We also compared the energy barrier heights obtained by optimization of TS under SMD model with that of obtained by the single point calculation using SMD model based on the gas-phase optimized geometries of TS (see S1 Table). It can be seen that the differences in energy barrier height are also little. Hence, we think that the single energy calculation using SMD model seems to provide a proper estimation of solvent effects for our studied systems. Just as reported in the literature [54][55][56], the results of single point calculations using solvent model were in good agreements with the corresponding experimental results for their systems.
Reaction enthalpy in solution was computed by the difference of enthalpy values between products and reactants optimized in the presence of SMD model. Relative Gibbs energy in solutions was computed using thermodynamic cycle and Hess' law which explicitly include solvation energy. For example, the thermodynamic cycle for the addition reaction between SA and ÁOH is as follows: SA gas þ Á OH gas ! DG gas Á ðSA À OHÞ gas " ÀDGs ðSAÞ " ÀDGs ðÁOHÞ # DGs ÁðSAÀOHÞ With this strategy, the Gibbs energy of reaction in solution (ΔG sol ) can be determined as the sum of the Gibbs energy of reaction in the gas phase (ΔG gas ) and the difference in solvation energies (ΔΔG s ): where ΔΔG s is calculated as: where ΔG s is the solvation energy. The reference state is 1M in all cases. The solvent cage effect was included with Okuno's corrections [57], which take into account the free volume theory. These corrections agree well with those independently obtained by Ardura et al. [58]. In this work the expression used to correct the Gibbs energy as follows: where n is the reaction molecularity. According to Eq 8, the solvent cage effect causes a decrease of 10.63 kJ/mol in ΔG for a bi-molecular reaction at 298.15 K [59]. The theoretical rate constants of all channels were calculated using the theory of improved canonical variational transition state (ICVT) [60] with small-curvature tunneling (SCT) correction [61] on the program POLYRATE 9.7 [62]. We adopted a separable equilibrium solvation (SES) approximation [63] to calculate the rate constants of water-phase reactions. Specifically, we first calculated the gas-phase reaction channels, solved each configuration along the gas-phase IRC (including reactants, products and saddle points), and then calculated the water-phase rate constants through the variational transition state theory with interpolated single-point energy (VTST-ISPE) on POLYRATE.

Results and Discussion
The optimized structure of SA as well as the atomic numbering scheme are shown in Fig 1. Clearly, SA has an approximately planar structure in which the dihedral angle between benzene ring and carbonyl group is about 179.56°. This result is consistent with the reported structure of SA optimized under the B3LYP/6-31+G(d) level [64]. The planar structure of SA implies that the molecule is completely conjugated and lead to an extended spin delocalization [65]. The possibility of excellent delocalization could account for its potential radical scavenging activity [65].

ÁNO 2 scavenging by SA
For reactions of SA with ÁNO 2 , we considered two most possible HAT channels from -OH and -COOH, and defined them as channels O 15 Fig 1); we also considered two RAF channels with addition of the corresponding radical to the carbon-carbon double bond, and defined them as channels C 11 and C 12 , respectively (on sites C 11 and C 12 in Fig 1).

and O 22, respectively (on sites O 15 and O 22 in
The optimized geometries of TSs and product complexes (PCs) of all channels are shown in Figs 2 and 3. The reaction enthalpy (ΔH), ΔG and energy barrier height (ΔE) including zeropoint energy (ZPE) corrections obtained for each channel were collected in Table 1.
According to the values of ΔG (Table 1), only HAT channels in water phase are exergonic (ΔG<0), meaning they could spontaneously occur. On the contrary, the RAF channels are all endergonic (ΔG>0) wherever in gas or water phase. Such, we conclude that the RAF mechanism is not thermodynamically feasible for SA scavenging ÁNO 2 .
As showed in Fig 2, (44.84 kJ/mol) >O 22 (117.18 kJ/mol) in water phase. Thus, the medium does not seem to affect the order of reaction energy barrier or activity. In this case, channel O 15 is the major channel for all reactions of SA with ÁNO 2 . In addition, the waterphase channel O 15 with negative ΔE+ZPE is a barrierless reaction, meaning a pre-reactive complex (IM) is formed in the entrance of the reaction, which energy is lower than that of the reactants, and the "real" energy barrier height between IM O 15   The spin density is another important parameter to characterize the stability of free radicals formed from phenolic acids, because the energy of a free radical can be efficiently decreased if the unpaired electron is highly delocalized through the conjugated system [66]. The phenolic acid radical having higher spin density delocalization, easier is the formation of product and then higher radical-scavenging activity of the group. Atomic spin densities plots for the product radicals of all water-phase channels in S3  The rate constant and branching ratio of each channel, as well as the total rate constants at 298 K in both gas and water phases, were calculated out and listed in Table 2. We assumed that neither mixing nor crossover between different channels occurs and therefore calculated the total rate constants of HAT and RAF reactions for SA scavenging ÁNO 2 as follows: The rate constant of each mechanism was estimated by summing up the rate constants of different channels: As showed in Table 2, channel O 15 possesses the largest rate constant which is several orders of magnitude higher than other channels. The RAF channels C 11 and C 12 have similar rate constants, but which are much lower than HAT channels. In addition, for the same channel, the k in water phase is always higher than in gas phase, which is particularly evident on the channel O 15 , indicating that aqueous solutions can enhance the ÁNO 2 scavenging activity of SA.  To quantify the contribution of each channel to the total reaction, we calculated the branching ratio (Γ), representing the percent of each channel in the total rate constant, as follows: Also in Table 2, channel O 15 contributes more than 98% capacity of scavenging ÁNO 2 , indicating it accounts for almost the whole activity of SA. And the rest channels are very rarely used. Summarily, channel O 15 , combined with its thermodynamic superiority, is the absolutely dominant pathway for SA scavenging ÁNO 2 . As for the RAF channels, since their total branching ratio is very little and they are significantly endergonic, it is reasonable that the RAF mechanism is irrelevant for the ÁNO 2 scavenging activity of SA in gas or water phase.
To better understand the kinetic mechanisms of the studied reactions, we calculated the temperature dependence of rate constant for each channel and plotted it against the reciprocal   of temperature in Figs 6 and 7. Clearly, the HAT channel O 15 is always keeping its superiority in the range of 200-600 K, which further confirms its leading role. The lower lines k O22 , k C11 and k C12 are nearly overlapped, especially at lower temperature. The rate constant of channel O 15 presents a negative temperature dependence, as its negative energy barrier (Fig 7). The total rate constants at 298 K, as well as the experimentally-determined rate constant [67], are also listed in Table 2. In aqueous environment, the calculated total rate constant of SA scavenging ÁNO 2 is 1.30×10 8 M -1 S -1 , which is at the same order of magnitude as the experimental result (7.20×10 8 M -1 S -1 ). This agreement validates the reliability of our calculations. Furthermore, it is important to compare the rate constant of SA scavenging ÁNO 2 with the rate constants of ÁNO 2 damaging unsaturated fatty acids in vivo. As reported, the rate constants in ÁNO 2 -based oxidations of tyrosine, fumaric acid and linoleic acid are (M -1 S -1 ): k = 3.20×10 5 [68], 1.30×10 7 and 5.00×10 4 [69], respectively, which are much smaller than the rate constant of SA eliminating ÁNO 2 predicted here. Thus, we conclude that SA is able to efficiently prevent cell damage by directly trapping ÁNO 2 .

ÁOH scavenging by SA
Like the previous section, in order to investigate the antioxidant activity of SA toward ÁOH, we identified two HAT channels O 15h and O 22h , as well as two RAF channels C 11h and C 12h . Because we concern the application of the antioxidant in vivo, and the obtained rate constants in aqueous solutions are closer to the fact in vivo environment, we only retained the thermodynamic and kinetic data of water phase in this section.
The results of ΔH, ΔG and ΔE including the ZPE corrections calculated under the level of M05-2X/6-311++g(d,p) are listed in Table 3. For scavenging ÁOH, all HAT and RAF channels in aqueous solutions are exothermic and exergonic, indicating they are all thermodynamically feasible. Thus, SA is able to scavenge ÁOH in vivo through both mechanisms of HAT and RAF. According to the spin densities plots in S3 Fig, similar with scavenging ÁNO 2 , HAT channels have more extended delocalization of the unpaired electron, indicating that the HAT mechanism should be more efficient than the RAF mechanism.
As showed in Table 3, channel O 15h has a lower energy barrier height than channel O 22h , it is the major channel of SA scavenging ÁOH within the HAT mechanism. The -O 15 H group has  higher activity mainly because the corresponding H-abstraction product is a more stable semiquinone radical, as the spin density of O 15h atom (0.243) of Product O 15h has lager spin density concentration than O 22h atom (0.016) of Product O 22h . The activities of RAF channels are lower than HAT channels, and channels C 11h and C 12h are very little different in energy barrier heights. As mentioned before, the channels with negative energy barrier heights are barrierless reactions, and the IMs are formed in the entrances of the reactions. The "real" energy barrier heights need to overcome between IM O 15h and TS O 15h, IM O 22h and TS O 22h, IM C 11h and TS C 11h, IM C 12h and TS C 12h are 58.71, 30.74, 7.49 and 1.90 kJ/mol, respectively. The relative energies are plotted in Fig 8. The rate constants and branching ratios of SA scavenging ÁOH were also calculated and listed in Table 4, as well as the available experimental data. As showed in Table 4, the HAT channel O 15h possesses the largest rate constant, followed by the HAT channel O 22h . The RAF channels C 11h and C 12h have similarly lower rate constants. Thus, to the total reaction of SA with ÁOH, the most contributive pathway is channel O 15h (Γ O15h = 62.97%). And different from the case of scavenging ÁNO 2 (Γ O22 = 0.01%), channel O 22h has a considerable contribution (Γ O22h = 36.98%). The contributions of RAF channels (Γ RAF = 0.05%) are estimated to be negligible. The total rate constants of HAT channels are on the 10 9 at 298 K, meaning that the reactions are very fast and diffusion controlled, underlining the excellent antioxidant activity of SA toward ÁOH. The temperature dependence of rate constants against the reciprocal of temperature for each channel and total reaction are sketched in Fig 9. It is clear that channel O 15h always maintains the largest rate constant from 200-600 K. The second channel O 22h is also very important, and its ratio branching is increasingly higher with the temperature rising. In addition, the rate The Activity of Sinapic Acid Scavenging Radicals constants of HAT channels have negative temperature dependence, while the RAF channels have positive temperature dependence. According to the above points of view, thermodynamics and kinetics: among the two feasible mechanisms, HAT is the major mechanism for the antioxidant activity of SA toward ÁOH in vivo. Channel O 15h is the major pathway of all reactions, followed by channel O 22h , which is also not negligible. Although the RAF mechanism is thermodynamically feasible, its contribution to the total reaction is negligible.
The theoretical total rate constant at 298 K computed here (9.20×10 9 M -1 S -1 ) agrees well with the pulse radiolysis experiment about the ÁOH-scavenging capability of SA conducted in neutral solution (k = 9.60×10 9 M -1 S -1 ) [70], which further supports the reliability of the calculations in our work.

Radicals scavenging by SA -
In the environment of physiological pH (7.4), SA primarily exist in anionic form with a dissociated COOH group [73][74]. In order to provide a detailed investigation on the radical scavenging activity of SA toward ÁNO 2 and ÁOH, also the anionic form of sinapic acid has been taken into account, considering HAT and RAF mechanisms in aqueous.
For each radical, one HAT channel (O 15 for ÁNO 2 ; O 15h for ÁOH) and two RAF channels (C 11 , C 12 for ÁNO 2 ; C 11h , C 12h for ÁOH) were considered. Under the M05-2X/6-311++G(d,p) level, SAalso has a planar stricture, the optimized geometries of SA -, TSs and PCs of all channels are gathered in S5 Fig. The ΔH, ΔG and ΔE+ZPE of all water-phase channels were also calculated and listed in Table 5.
For scavenging ÁNO 2 , according to the Table 5, the channel C 12 has the lowest energy barrier height, but the ΔG of this channel is positive, meaning that it is could not occur spontaneously. While the channel O 15 , with a second lower energy barrier height, is the largest exergonic channel, hence it is the major channel of SA with ÁNO 2 . The ΔG values of 62.16 and 10.43 kJ/mol for the RAF channels C 11 and C 12 indicate that this mechanism is quite unfavored also when the antioxidant is present in the anionic form, and thus it can be concluded that both SA and SAdo not follow the RAF process when scavenging ÁNO 2 radicals.
For scavenging ÁOH, all channels are exothermic and exoergic, indicating both HAT and RAF mechanisms are feasible. Among them, the channel O 15h has a absolute dominance, as it is the most exothermic and exoergic channel, and having the lowest energy barrier height. These results are in agreement with the scavenging activity of neutral SA toward ÁOH.
Considering the largest contribution channel O 15 /O 15h , the energy barrier heights of SAscavenging ÁNO 2 and ÁOH are much higher than those of SA, thus the rate constants of SAscavenging both radicals should be lower than the rate constants of SA scavenging ÁNO 2 and ÁOH.

Conclusions
In this work, we carried out a systematic study on the radical scavenging activities of SA and SAtoward ÁNO 2 and ÁOH in aqueous simulated media using DFT and direct dynamic method.
For SA/SAscavenging,ÁNO 2 , only HAT reactions in water phase are thermodynamically feasible. The H-abstraction reaction from site O 15 is the major channel of all reactions, while the RAF mechanism is not useful.
For SA/SAscavenging ÁOH, both HAT and RAF mechanisms are very feasible thermodynamically and kinetically. In the HAT mechanism, the most active site is also the -O 15 H group in benzene ring. The RAF mechanism is weaker than HAT, and the activities of two channels (C 11h and C 12h ) are similar.
The reactions of SA eliminating ÁNO 2 and ÁOH take place predominantly by the HAT mechanism (Γ>99%), especially via the channel O 15 /O 15h . For the reactions of SA with ÁOH, the site O 22h on the carboxyl group is also a significantly active site. Agreeing with our points, the DFT study from Galano et al. reported that the main mechanism of SA scavenging ÁOOH should be HAT with the largest contribution (Γ%99.9%), and the most important active site is the phenolic group of SA to scavenge ÁOOH [22].
The total rate constants of SA scavenging ÁNO 2 and ÁOH are 1.30×10 8 and 9.20×10 9 M -1 S -1 respectively, in water phase, at 298 K; and are 1.10×10 8 and 8.20×10 9 M -1 S -1 respectively, at 310 K. The rate constants in pulse radiolytic experiments are 7.20×10 8 and 9.60×10 9 M -1 S -1 , respectively. The total rate constant of k total-NO2 is small than k total-OH , due to the high activity of ÁOH, which is a reasonable result, but they are still very fast. Thus we state SA can efficiently scavenge ÁNO 2 and ÁOH radicals in vivo.  Table. The geometry coordinates of all species optimized at M05-2X/6-311++G(d,p) level.

Supporting Information
(DOC)