Theoretical study of copper complexes with lipoic and dihydrolipoic acids

Abstract

The antioxidant capacity of the deprotonated forms of lipoic and dihydrolipoic acids through their formation of complexes with copper has been theoretically studied. The relative stability of the various Cu(II) complexes considered has been studied at the M06-2X/6-31++G(d, p) level of theory combined with the SMD continuum solvation model in water under physiological pH conditions. The most stable complexes of Cu(II) are those formed with deprotonated dihydrolipoate when coordination involves the carboxylate group and one of the deprotonated thiol groups (in particular the primary one). The most thermodynamically stable Cu(II) complex was found to have antioxidant capacity, since its presence can slow down by two orders the first step of the Haber–Weiss cycle (from 1.29 × 10⁸ M⁻¹ s⁻¹ to 1.33 × 10⁶ M⁻¹ s⁻¹) and reduce the potential damage caused by ˙OH radical formation.

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1. Introduction

Copper, being the cofactor of enzymes involved in processes such as respiration (e.g., cytochrome oxidase) and the removal of reactive oxygen species (e.g., superoxide dismutase), is essential for life. However, since copper ions easily cycle between Cu(II) and Cu(I), some copper complexes could participate in non-enzymatic redox processes. In some cases, these complexes alter the cell status by changing intracellular redox potential. For example, in the presence of molecular oxygen, copper ions catalyze the oxidation of biomolecules and produce reactive oxygen species.^1,2 This induces molecular damage (protein or DNA degradation, membrane peroxidation, etc.), and alters signal transduction cascades.³

Lipoic acid (LA) is an eight-carbon disulfur compound, which is rapidly reduced in cells to dihydrolipoic acid (DHLA),⁴ a species that contains a vicinal dithiol. The acid–base equilibria associated with LA and DHLA are shown in Fig. 1. Under physiological pH conditions these acids are deprotonated. In vitro, LA and DHLA have been shown to have excellent antioxidant activity,⁵ scavenging a number of free radical species⁶ and interacting with other antioxidants. LA has also been used in the treatment of various diseases caused by metal poisoning.

Fig. 1 Acid–base equilibria involving LA (a) and DHLA (b).

Lipoate, the conjugate base of LA, is used in the therapy of a variety of diseases such as liver and neurological disorders. Müller and Menzel⁷ investigated the effects of lipoate and dihydrolipoate on Cd²⁺-induced injuries in isolated rat hepatocytes. They speculated that dihydrolipoate primarily protects cells by extracellular chelation of Cd²⁺, while intracellular reduction of lipoate to the dihydro-compound followed by complexation of both intra- and extracellular Cd²⁺ contributes to the amelioration provided by lipoate. Heavy-metal poisoning has also been treated with lipoic acid, which forms a complex, e.g., with Hg²⁺.⁸ Biliary excretion of Hg²⁺ in rats was enhanced 12- to 37-fold by lipoic acid administration.⁹ It is probable that Hg²⁺ is much more easily excreted in the bile as a dihydrolipoic acid–Hg²⁺ complex. In contrast, the biliary excretion of CH₃Hg⁺, Cd²⁺, Zn²⁺ and Cu²⁺ was diminished by LA administration. Packet et al.⁵ suggested that this might be due to chelation of these metals in the blood stream.

The results above have led researchers to hypothesize that LA and DHLA may exert an antioxidant effect in biological systems through transition-metal chelation,^10,11 and several experimental assays have been carried out to prove this. While the carbonyl group in LA and DHLA, which is considered a hard Lewis base, may coordinate more effectively with hard Lewis acids such as Ca²⁺, Mn²⁺, Co³⁺, Fe³⁺ and As³⁺, the soft Lewis basic sulfur atoms would coordinate more effectively with soft Lewis acids such as Cu⁺, Hg⁺, Pb²⁺, Cd²⁺ and Hg²⁺. However, experimentally, the situation is more complex.

Solid state Hg²⁺ complexes with LA and DHLA have been prepared,¹² as well as the LA–phenyldichloroarsine adduct in methanol.¹³ IR and NMR measurements have shown that both sulfur atoms of the 1,2-dithiolane group in LA participate in complexation.

Ou et al.¹⁴ determined that LA inhibits ascorbic acid oxidation by Cu²⁺ and facilitates the partition of copper ions into octanol, which led them to suggest that LA in its oxidized form may be an antioxidant via its ability to form a complex with Cu²⁺. These authors also showed the inhibitory effect of LA (via metal complexation of Cu²⁺ in the active site of the enzyme) on erythrocyte catalase inactivation produced by ascorbic acid, but they were not able to exclude the possibility that DHLA, which could be formed from intracellular reduction of LA, might protect catalase.

Sigel et al.^11,15 studied the complexes of LA with Mn²⁺, Cu²⁺, Zn²⁺, Cd²⁺ and Pb²⁺. In these complexes, the stability constant values can be related to the basicity of the carboxyl group in the same way as shown in a series of linear carbonic acids. This observation led them to suggest that only the carboxylic group is involved in chelation. However, Sigel et al. proposed that in the complexes of bisnor- and tetranorlipoic acid (metabolites of LA) with Cu²⁺, Zn²⁺ and Pb²⁺ the coordination of one sulfur atom of the disulfide group contributes to their stability because these complexes have larger stability constants than predicted.

DHLA is able to chelate Co²⁺, Ni²⁺, Zn²⁺, Pb²⁺ and Cu²⁺.¹² Cornaro et al. suggest that DHLA forms the Fe₂(DHLA)₄ complex with Fe³⁺.¹⁶ Moreover, evidence has shown that the DHLA complex with Fe³⁺ is more stable than with Fe²⁺.¹⁷ Furthermore, Lodge et al. suggest that the formation of DHLA–Cu²⁺ complexes can prevent human low-density lipoprotein peroxidation.¹⁸

In this paper, we perform the theoretical study of the antioxidant capacity of the deprotonated forms of LA and DHLA through their formation of complexes with copper. After optimizing the geometries of various combinations of complexes with Cu(II) in aqueous media, we aim at investigating which ligand leads to the most thermodynamically stable complexes under physiological pH conditions, and which are the most likely coordinating atoms of the organic ligand. Furthermore, we are interested in exploring whether these complexes have antioxidant capacity by slowing down the formation of hydroxyl radicals that follows the reduction of Cu(II) to Cu(I).

2. Computational details

Geometry optimizations, frequency and single-point energy calculations have been carried out using the M06-2X functional¹⁹ and the 6-31++G(d, p) basis set. All calculations have been performed in solution using the SMD²⁰ continuum solvation model and water as a solvent. This combination of DFT method, basis set, and continuum model was found to be one of the most suitable for the study of radical–molecule reactions is solution.²¹ Calculations were performed with the Gaussian 09 software package.²²

The formation constants (K_f) of the copper complexes were calculated using eqn (1), where R is the universal gas constant and T is temperature (298.15 K). represents the standard Gibbs free energy change for the reaction of forming the complex from its infinitely-separated ligand and solvated central ion , and it is calculated from the standard absolute G values of the products and reactants of the equilibrium considered , which are listed in Table S1 of the ESI.†

Rate constants (k) were calculated applying conventional transition state theory (TST),^23–25 as shown in eqn (2), where k_B and h are Boltzmann and Planck constants, respectively, and ΔG^≠ is the standard Gibbs free energy of activation.

For single electron-transfer (SET) reactions, ΔG^≠ was estimated applying Marcus theory.^26,27 Using eqn (3), the SET activation barrier (ΔG^≠_SET) calculation depends on the standard Gibbs free energy of reaction (ΔG⁰_SET) and the nuclear reorganization energy (λ).

The reorganization energy (λ) has been calculated using eqn (4), where ΔE_SET is the non-adiabatic difference from single-point energy calculations between reactants and vertical products. This approach is similar to the one previously used by Nelsen and co-workers²⁸ for a large set of self-exchange reactions.

λ = ΔE_SET − ΔG⁰_SET (4)

This computational protocol has been previously validated by comparison with experimental results, and its uncertainties have been shown to be no larger than those arising from experiments.²⁹

3. Results and discussion

The pK_a of LA and the first pK_a of DHLA are 4.76 and 4.85, respectively, in aqueous solution at 298.15 K.³⁰ Therefore, at physiological pH (7.40) the concentrations of the neutral forms are negligible (see Fig. 1, S1 and S2 of the ESI†). From now on, our use of the acronyms LA⁻ and DHLA⁻ will refer to their anionic forms. Both LA⁻ and DHLA⁻ could coordinate with one (CO) or both (COO) oxygen atoms of the carboxylate group, and/or with one or both sulfur atoms (S1, S2). Numeric labels will be used to identify the different complexes calculated, together with the indication of the coordinating atoms in the organic ligand and their geometric distribution (cis or trans), when applicable. Complexes in each group will be labelled in sequence starting with the most thermodynamically stable.

3.1. Complexes with Cu(II)

The complexes of copper with 2+ oxidation state are square planar in aqueous media.^31,32 Therefore, we will study the formation of complexes with this geometry involving one organic ligand molecule (LA⁻ or DHLA⁻). Several possible complexes between Cu²⁺ and one LA⁻ species were calculated according to the reaction shown in eqn (5). The structures of these complexes are shown in Fig. 2, and their , K_f and log K_f values are displayed in Table 1. In addition to the complex formed in each case according to eqn (5), a solvated cluster of no more than three water molecules (identified as (4 − n)H₂O) is the other product species. This way, each equilibrium considered has an equal number of aqueous reactant and product species. This has been the procedure followed when considering the different complex formation equilibria in this study.

Fig. 2 Optimized geometries of 1 : 1 complexes of Cu(II) with LA⁻ (bond distances in Å).

Table 1 Standard Gibbs free energy change and formation constant (K_f, log K_f) for the chelation of Cu(II) with LA⁻ (as per eqn (5)) in aqueous solution at 298.15 K^a

Complex [CuLA(H2O)n]^+		Kf Cu^2+–LA^−	log Kf Cu^2+–LA^−
a Coordinating atoms in the organic ligand are shown in parentheses for each complex.
[1] Cu^2+–LA^− (CO)	−13.10	4.04 × 10^9	9.61
[2] Cu^2+–LA^− (COO)	−10.25	3.25 × 10^7	7.51
[3] Cu^2+–LA^− (CO, S2 trans)	−0.97	5.16	0.71
[4] Cu^2+–LA^− (CO, S1 cis)	−0.28	1.59	0.20
[5] Cu^2+–LA^− (CO, S2 cis)	1.82	4.06 × 10^−2	−1.34
[6] Cu^2+–LA^− (S1)	10.35	2.57 × 10^−8	−7.59
[7] Cu^2+–LA^− (S2)	1.54	1.20 × 10^−10	−9.92

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Of the seven complexes calculated, the four most stable, [1] to [4], are exergonic. The most stable complex has only one oxygen atom coordinating the central ion. The second most stable complex has both oxygen atoms of the carboxylate group coordinating, and this complex has a K_f that is almost 100 times smaller than that of the most stable complex. Once the sulfur atoms coordinate the metal ion, the stability of the complex is significantly reduced. The least stable complexes are those in which only one sulfur atom of the organic ligand coordinates to the metal ion. In agreement with the conclusions of Sigel et al.,¹¹ our calculations show that the stability of the Cu²⁺–LA⁻ complex is solely determined by the coordination of the carboxylate group.

Similar conclusions are obtained when studying the complexes between Cu²⁺ and one DHLA⁻ species according to the reaction shown in eqn (6). The structures of these complexes are shown in Fig. 3, and their , K_f and log K_f values are displayed in Table 2. The two most stable complexes of Cu²⁺ with LA⁻ and DHLA⁻ (with equivalent coordinating groups) have K_f values that are about 100 times larger when LA⁻ is the ligand.

Fig. 3 Optimized geometries of 1 : 1 complexes of Cu(II) with DHLA⁻ (bond distances in Å).

Table 2 Standard Gibbs free energy change and formation constant (K_f, log K_f) for the chelation of Cu(II) with DHLA⁻ (as per eqn (6)) in aqueous solution at 298.15 K^a

Complex [CuDHLA(H2O)n]^+		Kf Cu^2+–DHLA^−	log Kf Cu^2+–DHLA^−
a Coordinating atoms in the organic ligand are shown in parentheses for each complex.
[8] Cu^2+–DHLA^− (CO)	−10.29	3.47 × 10^7	7.54
[9] Cu^2+–DHLA^− (COO)	−7.17	1.80 × 10^5	5.25
[10] Cu^2+–DHLA^− (CO, S2 cis)	−3.91	7.37 × 10^2	2.87
[11] Cu^2+–DHLA^− (CO, S2 trans)	0.72	2.95 × 10^−1	−0.53
[12] Cu^2+–DHLA^− (CO, S1 cis)	4.71	3.50 × 10^−4	−3.46
[13] Cu^2+–DHLA^− (CO, S1 trans)	5.04	2.04 × 10^−4	−3.69
[14] Cu^2+–DHLA^− (S1)	11.17	6.48 × 10^−9	−8.19
[15] Cu^2+–DHLA^− (CO, S1, S2)	12.02	1.54 × 10^−9	−8.81
[16] Cu^2+–DHLA^− (S2)	14.29	3.32 × 10^−11	−10.48
[17] Cu^2+–DHLA^− (S1, S2 cis)	19.47	5.34 × 10^−15	−14.27

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Coordination between Cu²⁺ and the negatively charged oxygen atoms of the carboxylate group of DHLA⁻ leads to a more thermodynamically stable complex than when coordination involves the sulfur atoms of the thiol units, which are much weaker bases. After considering coordination with both oxygen atoms of the carboxylate group (the second most stable complex), the most distant (primary) thiol group (containing the sulfur atom labelled S2; see Fig. 1(b)) leads to more stable bidentate complexes than the secondary thiol group (containing the sulfur atom labelled S1). The same situation is observed with the Cu²⁺–LA⁻ complexes. The CO–S2 (cis) bidentate complex [10] has a K_f that is about 10⁵ times smaller than that of the most stable complex [8].

Of the ten complexes calculated, only complexes [8] to [10] are exergonic. The tridentate complex that involves one oxygen atom of the carboxylate group, S1 and S2, is one of the least stable, which indicates that the enthalpy decrease does not compensate the entropy loss when forming it.

To further explore the coordinating ability of the sulfur atoms in DHLA⁻, neutral complexes between a deprotonated dihydrolipoate species (DHLA²⁻) and Cu²⁺ were studied following the equilibrium shown in eqn (7). The second deprotonation of DHLA⁻ involves one of the thiol groups; hence, complexes in which S1 (the closer one to the COO⁻ group) and S2 are deprotonated were considered (see Fig. 1(b)). These two acid dissociations of DHLA⁻ have been identified as equivalent, having the same pK_a value of 10.70.³³ The structures of these complexes are shown in Fig. 4 and 5, and their , K_f and log K_f values are displayed in Tables 3 and 4, for S1 and S2 deprotonations, respectively. The Cartesian coordinates of all the calculated structures in this work are reported in the ESI,† together with their absolute standard enthalpies and Gibbs free energies.

Fig. 4 Optimized geometries of 1 : 1 complexes of Cu(II) with S1-deprotonated DHLA²⁻ (bond distances in Å).

Fig. 5 Optimized geometries of 1 : 1 complexes of Cu(II) with S2-deprotonated DHLA²⁻ (bond distances in Å).

Table 3 Standard Gibbs free energy change and formation constant (K_f, log K_f) for the chelation of Cu(II) with S1-deprotonated DHLA²⁻ (as per eqn (7)) in aqueous solution at 298.15 K^a

Complex [CuDHLA(H2O)n]		Kf Cu^2+–DHLA^2−	log Kf Cu^2+–DHLA^2−
a Coordination atoms in the organic ligand are shown in parentheses for each complex.
[18] Cu^2+–DHLA^2− (CO, S1 trans)	−19.27	1.34 × 10^14	14.13
[19] Cu^2+–DHLA^2− (CO, S1 cis)	−17.86	1.24 × 10^13	13.09
[20] Cu^2+–DHLA^2− (S1)	−14.05	2.01 × 10^10	10.30
[21] Cu^2+–DHLA^2− (CO)	−11.05	1.26 × 10^8	8.10
[22] Cu^2+–DHLA^2− (COO)	−8.10	8.74 × 10^5	5.94

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Table 4 Standard Gibbs free energy change and formation constant (K_f, log K_f) for the chelation of Cu(II) with S2-deprotonated DHLA²⁻ (as per eqn (7)) in aqueous solution at 298.15 K^a

Complex [CuDHLA(H2O)n]		Kf Cu^2+–DHLA^2−	log Kf Cu^2+–DHLA^2−
a Coordination atoms in the organic ligand are shown in parentheses for each complex.
[23] Cu^2+–DHLA^2− (CO, S2 cis)	−26.26	1.79 × 10^19	19.25
[24] Cu^2+–DHLA^2− (CO, S2 trans)	−22.76	4.85 × 10^16	16.69
[25] Cu^2+–DHLA^2− (CO)	−22.54	3.33 × 10^16	16.52
[26] Cu^2+–DHLA^2− (COO, S2)	−18.55	3.99 × 10^13	13.60
[27] Cu^2+–DHLA^2− (S2)	−13.81	1.33 × 10^10	10.12
[28] Cu^2+–DHLA^2− (COO)	−8.70	2.38 × 10^6	6.38

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All these complexes are exergonic relative to DHLA²⁻ and the hydrated central ion. Complexes where the primary thiol group, S2, is deprotonated have significantly larger K_f values than complexes with equivalent coordinating atoms in which the secondary thiol group, S1, is deprotonated (e.g., [18] and [24], [19] and [23], [21] and [25], and [22] and [28]), with the exception of the complexes [20] and [27] where only the deprotonated S1 or S2 atom coordinates. These two complexes, which are not the most thermodynamically stable in each group, have similar K_f values, with less than 1 kcal mol⁻¹ difference in their values.

The much greater basic strength of the negatively charged sulfur atoms in DHLA²⁻ (relative to their basic strength as –SH groups in DHLA⁻) when coordinating to the central ion leads to stronger bonds between S and Cu(II), which is also manifested in the geometries of these complexes. When sulfur is one of the coordinating atom, the S–Cu bond distances with DHLA⁻ are 2.46–2.60 Å, while with DHLA²⁻ these distances, 2.34–2.40 Å, are smaller.

The two sets of Cu²⁺–DHLA²⁻ complexes are significantly more thermodynamically stable with respect to the organic ligand (DHLA²⁻) and the hydrated Cu(II) species, than the Cu²⁺–LA⁻ and Cu²⁺–DHLA⁻ complexes, with the exception of the least stable complexes in each group ([21], [22] and [28]), which are less stable by about an order in K_f relative to the corresponding Cu²⁺–LA⁻ complexes.

To better compare the thermodynamic stability of the complexes listed in Table 2 with those listed in Tables 3 and 4, the same starting point (DHLA⁻ + [Cu(H₂O)₄]²⁺) is needed. In doing so, we properly account for the Gibbs free energy cost of forming DHLA²⁻ under physiological pH (7.40) conditions since a very small proportion of this species would be found (see Fig. S2†).

To transform eqn (7) into (8) (in the complex [CuDHLA(H₂O)_n], DHLA stands for DHLA²⁻), we must take into account the second acid dissociation of DHLA (by deprotonation of S1 or S2, see Fig. 1) and combine eqn (7) with (9).

DHLA⁻ ⇆ DHLA²⁻ + H⁺ (9)

The equilibrium constant expression, K_a(2), associated with the equilibrium of eqn (9) is shown in eqn (10), where ΔG⁰ is the standard aqueous Gibbs free energy change of this acid dissociation. The experimental aqueous pK_a(2) is 10.7,^30,33 at 298.15 K and it can be calculated using eqn (11).

Under physiological conditions pH is buffered to 7.40 and [H⁺] remains unchanged ([H⁺] = 10^−pH = 3.98 × 10⁻⁸ M). Under these conditions, a conditional equilibrium constant (K′) can be defined according to eqn (12). From eqn (12)–(14) can be obtained to calculate the Gibbs free energy change of the acid dissociation at a particular buffered pH, ΔG′. From eqn (14), the Gibbs free energy cost, ΔG′, for forming DHLA²⁻ from DHLA⁻ in water at pH = 7.40 and at 298.15 K is calculated to be 4.50 kcal mol⁻¹.

ΔG′ = ΔG⁰ − pHRT ln 10 (13)

ΔG′ = (pK_a(2) − pH)RT ln 10 (14)

Adding the Gibbs free energy change of eqn (9) (ΔG′ = 4.50 kcal mol⁻¹) to the previously calculated Gibbs free energy change of eqn (7) (, values listed in Tables 3 and 4), allows us to calculate the Gibbs free energy change of eqn (8) for each case (because eqn (8) = (7) + (9)). The new values, , are displayed in Tables 5 and 6, together with the corresponding K′_f and log K′_f values.

Table 5 Standard Gibbs free energy change and equilibrium constant (K′_f, log K′_f) for the chelation of Cu(II) with S1-deprotonated DHLA²⁻ from DHLA⁻ and the hydrated central ion (as per eqn (8)) in aqueous solution at 298.15 K^a

Complex [CuDHLA(H2O)n]		K′f Cu^2+–DHLA^2−	log K′f Cu^2+–DHLA^2−
a Coordination atoms in the organic ligand are shown in parentheses for each complex.
[18] Cu^2+–DHLA^2− (CO, S1 trans)	−14.77	6.71 × 10^10	10.83
[19] Cu^2+–DHLA^2− (CO, S1 cis)	−13.36	6.23 × 10^9	9.79
[20] Cu^2+–DHLA^2− (S1)	−9.55	1.01 × 10^7	7.00
[21] Cu^2+–DHLA^2− (CO)	−6.55	6.31 × 10^4	4.80
[22] Cu^2+–DHLA^2− (COO)	−3.60	4.38 × 10^2	2.64

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Table 6 Standard Gibbs free energy change and equilibrium constant (K′_f, log K′_f) for the chelation of Cu(II) with S2-deprotonated DHLA²⁻ from DHLA⁻ and the hydrated central ion (as per eqn (8)) in aqueous solution at 298.15 K^a

Complex [CuDHLA(H2O)n]		K′f Cu^2+–DHLA^2−	log K′f Cu^2+–DHLA^2−
a Coordination atoms in the organic ligand are shown in parentheses for each complex.
[23] Cu^2+–DHLA^2− (CO, S2 cis)	−21.76	9.00 × 10^15	15.95
[24] Cu^2+–DHLA^2− (CO, S2 trans)	−18.26	2.43 × 10^13	13.39
[25] Cu^2+–DHLA^2− (CO)	−18.04	1.67 × 10^13	13.22
[26] Cu^2+–DHLA^2− (COO, S2)	−14.05	2.00 × 10^10	10.30
[27] Cu^2+–DHLA^2− (S2)	−9.31	6.65 × 10^6	6.82
[28] Cu^2+–DHLA^2− (COO)	−4.20	1.19 × 10^3	3.08

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It can be observed that relative to the same set of reactant species (DHLA⁻ + [Cu(H₂O)₄]²⁺), the Cu²⁺–DHLA²⁻ complexes continue to be exergonic, and with much larger equilibrium constants than most of the corresponding Cu²⁺–DHLA⁻ complexes (see Table 2). For example, the most stable Cu²⁺–DHLA²⁻ complex, [23], has an equilibrium constant of 9.00 × 10¹⁵, while the corresponding Cu²⁺–DHLA⁻ complex (when both S2 and the carboxylate group coordinate in cis geometry) has an equilibrium constant of 7.37 × 10². Only the least thermodynamically stable complexes, where coordination takes place through one of the carboxylate oxygen atoms or through both (complexes [21], [22] and [28]), are less stable than the equivalent Cu²⁺–DHLA⁻ complexes. The most stable Cu²⁺–DHLA²⁻ complexes in both groups are those in which S1 or S2 coordinate, together with one of the oxygen atoms of the carboxylate group. These complexes ([18] to [20] and [23] to [27], see Tables 5 and 6), are also more thermodynamically stable than the exergonic Cu²⁺–LA⁻ complexes ([1] to [4], see Table 1; complex [1] has an equilibrium constant of 4.04 × 10⁹).

In summary, our results indicate that the formation of complexes between Cu(II) and the deprotonated forms of LA and DHLA in water at 298.15 K under physiological pH conditions will be most favourable when the doubly-deprotonated form of DHLA, DHLA²⁻, is involved; especially when any of the thiol groups (and in particular the primary one, S2) is deprotonated and acting as ligand together with one of the oxygen atoms of the carboxylate group. Our findings are in agreement with the results of Dokken et al.,³⁴ who, after studying the Cu(II)–cysteine complexes, concluded that the disappearance of the thiol (SH) stretch at 2552 cm⁻¹ was an indication of the deprotonated state of this group and its coordination to the Cu(II) central ion.

3.2. Reduction of Cu(II) to Cu(I): the Haber–Weiss cycle

In vivo, Cu(II) reduction can lead to the formation of very reactive ˙OH radicals through a sequence of reactions known as the Haber–Weiss cycle. The initial reaction of the Haber–Weiss cycle involves the reduction of Cu(II) to Cu(I) by reaction with the superoxide radical anion, O₂˙⁻ (see eqn (15)). In the next step, known as the Fenton reaction, ˙OH radicals are formed (see eqn (16)).

Cu²⁺ + O₂˙⁻ → Cu⁺ + O₂ (15)

Cu⁺ + H₂O₂ → Cu²⁺ + OH⁻ + ˙OH (16)

A more realistic way of representing eqn (15), in which the copper ions are hydrated while in aqueous solution, is eqn (17). Fig. 6 displays the structures of the most stable hydrated Cu(II) and Cu(I) complexes. The hydrated Cu(II) complex is square planar, while the hydrated Cu(I) complex is linear. When representing the Cu(I) complex using eqn (17), two hydrating solvent molecules are explicity shown to keep the number of reactant and product species constant. This is the most stable hydrated Cu(I) complex with four water molecules.

[Cu(H₂O)₄]²⁺ + O₂˙⁻ → [Cu(H₂O)₂]⁺·2H₂O + O₂ (17)

Fig. 6 Optimized geometries of the most stable hydrated Cu(II) and Cu(I) complexes (bond distances in Å).

Cu(II) complexes with antioxidant capacity could reduce the potential damage caused by ˙OH radical formation by slowing down the first reaction of the Haber–Weiss cycle in which Cu(II) is reduced. It is our intent to investigate if the previously studied Cu(II) complexes with the deprotonated forms of LA and DHLA (LA⁻, DHLA⁻ and DHLA²⁻) have antioxidant capacity. To do this, we chose to focus on the most thermodynamically stable Cu(II) complex, that which is formed with S2-deprotonated DHLA²⁻ (complex [23], shown in Fig. 5), and its reaction with the superoxide radical anion, O₂˙⁻, as shown in eqn (18).

[CuDHLA(H₂O)₂] + O₂˙⁻ → [CuDHLA(H₂O)]⁻·H₂O + O₂ (18)

The main product of eqn (18) is the Cu(I) complex with S2-deprotonated DHLA²⁻, which after optimization starting from complex [23], became a negatively charged linear complex with only two ligands, as shown in Fig. 7. Only the deprotonated primary thiol group (S2) coordinates the central ion in addition to a solvent molecule, which is H-bonded to the carboxylate group. The other initial solvent molecule is part of the solvation sphere and is H-bonded to the solvent molecule acting as ligand.

Fig. 7 Optimized geometry (bond distances in Å) of the Cu⁺–DHLA²⁻ complex obtained from the most thermodynamically stable Cu²⁺–DHLA²⁻ complex [23].

To investigate the antioxidant capacity of the Cu²⁺–DHLA²⁻ complex, i.e., to find out if this complex slows down the Cu(II) reduction according to the first reaction of the Haber–Weiss cycle, we calculate and compare the rate constants of eqn (17) and (18).

The rate constants of eqn (17) and (18), together with the standard Gibbs free energies of reaction and activation, are reported on Table 7. As can be observed, the Cu(II) reduction to Cu(I) is significantly slowed down when Cu(II) is coordinated by DHLA²⁻. The rate constant for eqn (17) is 1.29 × 10⁸ M⁻¹ s⁻¹; it becomes 100 times smaller, 1.33 × 10⁶ M⁻¹ s⁻¹, when DHLA²⁻ coordinates the copper ions.

Table 7 Standard Gibbs free energy of reaction (ΔG°) and activation (ΔG^≠) and rate constant (k) for the initial reaction of the Haber–Weiss cycle (with and without copper complexation with DHLA²⁻) in aqueous solution at 298.15 K

Reaction	ΔG^0 (kcal mol^−1)	ΔG^≠ (kcal mol^−1)	k (M^−1 s^−1)
[Cu(H2O)4]^2+ + O2˙^− → [Cu(H2O)2]^+·2H2O + O2	−3.91	6.39	1.29 × 10^8
[CuDHLA(H2O)2] + O2˙^− → [CuDHLA(H2O)]^−·H2O + O2	−1.01	9.10	1.33 × 10^6

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4. Conclusions

Various Cu(II) complexes with the deprotonated forms of lipoic and dihydrolipoic acids have been calculated at the M06-2X-SMD/6-31++G(d, p) level of theory in water under physiological pH conditions at 298.15 K. The most stable complexes of Cu(II) are those formed with deprotonated dihydrolipoate (DHLA²⁻) when coordination involves the carboxylate group and any of the deprotonated thiol groups (in particular the primary one). The most thermodynamically stable Cu(II) complex was found to have antioxidant capacity, since its presence can slow down by two orders the first step of the Haber–Weiss cycle (from 1.29 × 10⁸ M⁻¹ s⁻¹ to 1.33 × 10⁶ M⁻¹ s⁻¹) and reduce the potential damage caused by ˙OH radical formation.

Acknowledgements

We gratefully acknowledge the financial support received from the Natural Sciences and Engineering Research Council of Canada (NSERC), the National Council on Science and Technology of Mexico (CONACyT, project SEP-CONACyT 167430) and a grant from DGAPA UNAM PAPIIT-IN220215. We would also like to thank Information Technology Services at Thompson Rivers University and the Dirección General de Servicios de Cómputo Académico (DGSCA) of the Universidad Nacional Autónoma de México.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra23553k

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