The effects of biologically important divalent and trivalent metal cations on the cyclization step of dopamine autoxidation reaction: A quantum chemical study

2.1 Quantum chemical calculations

Gaussian 16 software package (Frisch et al., 2016) was used to perform all the quantum chemical calculations to study the organometallic complexes of metal cations and dopamine o-quinone, and to determine the effect of metallic cations on the reaction mechanism of dopamine o-quinone cyclization step. The initial structures of dopamine o-quinone and dopamine o-quinone complexed with various metallic cations were built using the Molden v5.9 software package (Schaftenaar and Noordik, 2000). To decrease computational cost, a 1:1 M ratio of metal cation to dopamine o-quinone was considered for all studied complexes. All the structures were optimised at the M06/Def2-TZVPP level of theory because M06 functional and Def2-TZVPP basis set are recommended for organometallic chemistry and for noncovalent interactions (Weigend and Ahlrichs, 2005; Zhao and Truhlar, 2008). Solvent effects were considered by the universal solvation model, based on density (SMD) (Marenich et al., 2009), which is a solvent reaction field model that describes the solute as a composite of interlocking spheres and the solvent as a dielectric continuum. A dielectric constant of water (ε = 78.3) was applied to represent an aqueous solution. While studying reaction kinetics, the same procedure was applied to optimize geometries of products after cyclization. The transition state search started from the manually set initial geometries. Analysis of harmonic vibrational frequencies was performed for all stationary points. Calculated frequencies were used for thermodynamic corrections of relative free energies at 298.15 K. The reactant and product minima have only real frequencies, while the transition states have one imaginary frequency and visualisation of its eigenvector corresponds to the reactive motion. Atomic charges were calculated by the Merz–Singh–Kollman scheme. For metal atoms, the corresponding universal force field radii scaled by 1/1.2 were applied (Rappé et al., 1992). Frontier molecular orbital analysis was performed at the same level of theory and the solvation model to assess the chemical reactivity of studied complexes. Where applicable, high-spin (HS), intermediate-spin (IS), and low-spin (LS) states were considered. Described quantum chemical methods with the inclusion of solvent effect represent an established tool for studying binding and reactivity and can provide important knowledge and insight into properties of otherwise unattainable systems (Dalla Torre et al., 2019; Khan et al., 2018; Kržan et al., 2020).

2.2 Electron density analysis

To perform a topological analysis of the electron density between metal cations and dopamine o-quinone, we used a quantum theory of atoms in molecules (QTAIM) (Bader, 1991) that provides critical points of the electron density and the atomic boundaries. The bond critical points (BCPs) are saddle points of the electron density between two bonded atoms and provide information about the nature of bonding. Small electron density values, charge depletion, and positive energy densities are characteristic for van der Waals, ionic and hydrogen bonds, and metal–metal interactions, while large electron densities, charge concentration, and negative energy densities are characteristic for covalent interactions. The topological parameters at the BCPs were calculated using the multiWFN3.1 software package (Lu and Chen, 2012) on the previously optimized structures. Wavefunction files derived by Gaussian 16 at M06/Def2-TZVPP/SMD level of theory served as input files.

2.3 Calculation of pKa values

The pKa values of organometallic complexes of metal cations and dopamine o-quinone were calculated using the thermodynamic cycle shown in Fig. 1 (Liptak et al., 2002). If acid donates a proton to bulk water, there is an analytical relation between the free energy for the process, acid dissociation constant (K_a), and pH value of water (Bronsted, 1928). For the deprotonation reaction

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Fig. 1

Thermodynamic cycle used for pKa calculations. $\mathrm{\Delta }$ G_gas – free energy of deprotonation in gas-phase; $\mathrm{\Delta }$ G_s – solvation free energy; $\mathrm{\Delta }$ G_aq – free energy of deprotonation in an aqueous solution.

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For the thermodynamic cycle used

For calculations of gas-phase reaction energies and solvation free energies ( $\mathrm{\Delta }$ G_s) the M06/Def2-TZVPP level of theory and SMD reaction field model were used. The latter was chosen because it was found to be the most accurate in predicting catecholamine o-quinone pKa values (Umek, 2020). The solvation free energy of a proton $\mathrm{\Delta }$ G_s(H⁺) = −264.0 kcal mol⁻¹ and the gas phase standard free energy of a proton G_gas(H⁺) = −6.287 kcal mol⁻¹ at 298.15 K were adopted from the literature (Ho and Coote, 2009; Liptak et al., 2002). Please note, that value of G_gas(H⁺) includes reaction free energy of hydronium ion formation and is hydration free energy. For conversion of $\mathrm{\Delta }$ G_gas, for which the 1 atm reference state is used for calculation, to 1 M reference state, which is used for $\mathrm{\Delta }$ G_s calculation, the following equation was used:

The pKa values were therefore calculated using the equation:

The latter equation was derived by combining Eqs. (4)–(7) and experimental values for $\mathrm{\Delta }$ G_s(H⁺) and G_gas(H⁺).

Free energy differences of proton transfer from the ionizable group with a certain pKa value to bulk water with a certain pH value were calculated using the equation:

It is worth stressing that pKa calculations are extremely demanding since deprotonation is equivalent to SN1 reaction (Perdan-Pirkmajer et al., 2010; Sham et al., 1997).

3.1 Binding affinities of metal cation-dopamine o-quinone complexes

For 1:1 complexes, the equilibriums between divalent (M²⁺) and trivalent (M³⁺) metal cations with neutral (DAQ) and protonated (DAQ⁺) dopamine o-quinones are shown by the following equations respectively:

The stability constant values (log K₁) are given as:

The binding free energies and stability constant values are shown in Table 1. All studied complexes between divalent and trivalent metal cations and dopamine o-quinone except complex with Mn²⁺ had negative binding free energies, suggesting that complexation of most studied metal cations and dopamine o-quinone is thermodynamically favourable. The complexation of Mn²⁺ with dopamine o-quinone is thermodynamically not favourable, which is also supported by experimental kinetic data where Mn²⁺ did not significantly affect the mechanism and kinetics of dopamine o-quinone cyclization (Lloyd, 1995). Moreover, the trivalent cations Al³⁺ and divalent cation Ni²⁺ had the largest biding affinities and stability constants, followed by Fe³⁺, Pb²⁺, Cu²⁺, Co²⁺, Fe²⁺, Cd²⁺ and Zn²⁺. The binding affinities of all studied metal cations complexed with protonated dopamine o-quinones were smaller than for neutral dopamine o-quinones, suggesting that the positively charged amino tail has an electron withdrawal effect, which is mediated by electron attracting behaviour of positive charge. In the study by Dalla Torre et al., a similar observation was noted for complexes of Al³⁺ and catecholamines. For Al³⁺ cation, it was also shown that in aqueous solution at physiological pH the formation of ${\mathrm{A}\mathrm{l}(\mathrm{O}\mathrm{H})}_4^{-}$ is more favourable than complexation with catecholamines (Dalla Torre et al., 2019). However, since the free energy of hydroxide ion formation which is given by $k_{B}Tln(10)(15.7-pH)$ , where 15.7 is pKa of a water molecule (Bronsted, 1928), is very high at acidic pH, the formation of hydroxide ion becomes thermodynamically less favourable making the complexation with catecholamines more likely.

Our results also show that the stability constants of the complexes between divalent and trivalent metal cations and dopamine o-quinone are the highest for high spin, intermediate for intermediate spin and the lowest for low spin states (Table 1), suggesting that the low- and intermediate spin state complexes are thermodynamically less favourable. Accordingly, only high spin state complexes were investigated further.

3.2 Properties of metal–oxygen atom bonds in metal cation-dopamine o-quinone complexes

To characterise metal–oxygen atom bonds, the QTAIM analysis at BCPs was performed for each studied metal cation-dopamine o-quinone complex shown in Fig. 2. Each complex forms two metal–oxygen atom bonds, for which the topological parameters are reported in Table 2. The electron density (ρ(r)) at BCP is a measure of the strength of the bond. Metal–oxygen atom bonds involving divalent cations Fe²⁺ and Ni²⁺ had the largest ρ(r), followed by Cu²⁺, Fe³⁺, Al³⁺, Co²⁺, Zn²⁺, Cd²⁺, Pb²⁺ and Mn²⁺. The Laplacian of the electron density (∇2ρ(r)) at BCP characterizes a bond in terms of negative (covalent bond) or positive (electrostatic interactions, hydrogen bond or van der Waals interactions) values, while the nature of the bond is denoted by the negative ratio of kinetic to potential energy density (–G(r)/V(r)) at BCP. The positive values of ∇²ρ(r) and the values of -G(r)/V(r) near 1 (Table 2) indicate that the interactions between the oxygen atoms and metal cations are electrostatic and partially covalent (Crisponi and Nurchi, 2011; Grabowski, 2011). The bond ellipticity (ε) at the BCP, a derivative of the Hessian matrix of the electron density, demonstrated that the predominant character of the metal–oxygen atom bond is the σ-type character (Silva Lopez and R. de Lera, 2011). The heterogeneity in our results suggests that because of their dative nature, metal–oxygen atom bonds are mainly electrostatic with some degree of covalency (Gervasio et al., 2004). A similar finding was recently shown for Al-oxygen atom bonds in complexes of Al³⁺ and catecholamines and for metal–oxygen atom bonds in some other organometallic complexes such as Fe³⁺-hydroxypyridinones (Dalla Torre et al., 2019; Kaviani et al., 2018).

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Fig. 2

Metal cation-dopamine o-quinone complex with unprotonated amino group with marked bond critical points. Carbon atoms are represented with grey, oxygen atoms with red, hydrogen atoms with white, nitrogen atoms with blue, and metal cation with yellow colour. Numbers 1 and 2 denote specific bond critical points which electronical density analyses are presented in Table 2.

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3.3 Chemical reactivity of metal cation-dopamine o-quinone complexes

Chemical reactivity of metal cation-dopamine o-quinone complexes was assessed using frontier molecular orbital analysis and quantum chemistry reactivity indices such as HOMO-LUMO energy gap, electronic chemical hardness, electronic chemical potential, and electrophilicity index. The HOMO-LUMO energy gap (ΔE_gap = E_LUMO − E_HOMO) correlates with the charge transfer interaction within the molecule (Aihara, 1999). Global chemical hardness η and electronic chemical potential µ describe the charge transfer within a system in the ground state and are calculated as:

Results presented in Table 3 show that during a complex formation, the electronic hardness and electronic chemical potential decreased while electrophilicity increased, suggesting that metal cation-dopamine o-quinone complexes are more reactive than dopamine o-quinone. Moreover, dopamine o-quinone complexes with Ni²⁺, Cu²⁺, Al³⁺ and Pb²⁺ exhibited the highest chemical reactivity among the studied complexes.

3.4 The pKa values of metal cation-dopamine o-quinone complexes

Since the cost in terms of free energy for deprotonation of the amino group of dopamine o-quinone is necessary for the cyclization reaction to occur, we investigated the effect of complexation of metal cations and the dopamine o-quinone on its pKa values. The calculated pKa values of dopamine o-quinone and metal cation-dopamine o-quinone complexes are shown in Table 4. The complexation with metal cations causes a decrease of pKa values from 0.47 to 3.46. This suggests that the positive charge of metal cation electrostatically affects the protonated amino group of the dopamine o-quinone. Since the free energy differences of proton transfer from the ionizable group with a certain pKa value to bulk water with a certain pH bears the following relation $\mathrm{\Delta }G=k_{B}T\ln \left(10\right)\left(pKa-pH\right)$ , the complexation of dopamine o-quinone with metal cations thermodynamically favours the amino group deprotonation by decreasing the energy of proton transfer from the amino group to bulk water for 0.64–4.51 kcal mol⁻¹ at any given pH value. Such influence of a charge on the pKa value of a nearby ionizable group has already been established in proteins (Pace et al., 2009). The apparent decrease in pKa value of dopamine amino group in the presence of Fe³⁺ and Cu²⁺ ions was also indirectly observed by Salomäki et al. while studying the dopamine autoxidation rates at different pH values with and without the presence of the forementioned metal cations. It was also theoretically predicted that the pKa value of the dopamine amino group would decrease by approximately 0.45 per unit of positive charge (Salomäki et al., 2018).

Calculations of pKa values are very demanding and can serve as one of the strictest tests for the efficiency of various solvation models (Kavcic et al., 2021; Repič et al., 2014; Warshel, 1981). Our results show that the calculated pKa value of dopamine o-quinone (pKa^calc = 8.73) is in good agreement with the experimental pKa value of dopamine (pKa^exp = 8.86) (Berfield et al., 1999) showing that the SMD reaction field solvation model with M06/Def2-TZVPP level of theory is sufficiently accurate. Note that because of the topological proximity (six bonds away) of the closest carbonyl group from the amino group, the pKa value of the dopamine amino group was applied as an approximation on account of lack of the exact experimental pKa value for dopamine o-quinone amino group. The latter is not experimentally accessible due to the very fast cyclization rate at alkaline pH and the instability of dopamine o-quinone.

3.5 Mechanism and pH dependence of metal cation-dopamine o-quinone cyclization

Our results show that in contrast to dopamine o-quinone cyclization in aqueous solution where a hydroxide anion must first extract a proton from unprotonated amino group (Fig. 3A) (Umek et al., 2018), a cyclization of 1:1 metal cation-dopamine o-quinone with unprotonated amino group can proceed spontaneously as suggested by negative reaction free energies (Table 5, Fig. 3b). For all the studied complexes a transition state was searched for, and the intrinsic activation free energy ( ${\mathrm{\Delta }G}_i^{\ne }$ ) calculated (Table 5), which was the lowest and basically barrierless for dopamine o-quinone complexes with Al³⁺ and Fe³⁺ cations. Note that at physiological pH values, complete activation free energy ( $\mathrm{\Delta }{G}^{\ne }$ ) that would be comparable to the experimental values also includes the energy of amino group deprotonation. Therefore, the complete activation free energy for cation-dopamine o-quinone cyclization is given by:

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Fig. 3

Dopamine o-quinone cyclization reaction (A) and metal cation-dopamine o-quinone complex cyclization reaction (B) in aqueous solution.

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Inserting the latter into the transition state equation.

The latter is qualitatively fully consistent with experimental pH dependence of dopamine, adrenaline, and noradrenaline autoxidation rate in aqueous solution in the presence of Fe³⁺ ions (El-Ayaan et al., 1998, 1997; Linert et al., 1993). Please note that since bulk water is a proton rich environment, the rearrangement of protons after the cyclization step was not investigated because the proton diffusion rate in an aqueous solution is very fast and does not represent a rate-limiting step (Umek et al., 2018).

Results therefore show that most of the studied metal cations can significantly increase the dopamine o-quinone cyclization rate in aqueous solution, first, by enabling the cyclization to proceed spontaneously without the attack of the unprotonated amino group by hydroxide ion; second by, decreasing the intrinsic activation energy; and third, by decreasing the free energy of protonated amino group deprotonation. It also relatively decreases the protective effect of acidic pH on dopamine autoxidation. This could be biologically important in the aspect of neurodegeneration, since with age and in various pathological conditions, different metals can accumulate in the various tissues, including the brain, and the mechanisms that counteract metal neurotoxicity could become less efficient (Paris and Segura-Aguilar, 2011).

At this point, it is worth stressing that synaptic vesicles, cytosol, and extracellular fluid are very complex environments with many molecules such as citrate that could act as endogenous chelators that could bind metal cations and ameliorate their toxic effect (Chua et al., 2010; Dalla Torre et al., 2019). Moreover, Jiang et al. showed that stabilization of Fe³⁺ by ATP molecule that is abundant in the neurons and also acts as co-transmitter could significantly decrease the ability of Fe³⁺ to catalyse dopamine autoxidation (Jiang et al., 2013). Furthermore, it was also proposed that complexes of catecholamines, Fe³⁺, and ATP are produced in neurons or synaptic clefts as a protective measure against oxidative stress (Kou et al., 2019). Accordingly, further experimental studies examining the role of metal cations in catecholaminergic neurodegeneration are warranted.

The implicit SMD solvation model was used to represent the aqueous solution, therefore, the hydrogen bonds between studied complexes and water molecules were not explicitly considered. Since hydrogen bonds can have a crucial role for the structure and interactions of biomolecules, they could influence the studied reactions (Benmalti et al., 2009; Flakus et al., 2012; Rekik et al., 2015). However, the quantitative theoretical treatment of hydrogen-bonded systems is very demanding, and even the most advanced theories are sometimes not able to sufficiently describe them (Ghalla et al., 2010; Rekik, 2014; Rekik et al., 2016). Therefore, it remains a challenge to address these reactions on multiscale QM/MM level with explicit solvation model.