Computational Design of Copper Ligands with Controlled Metal Chelating,Pharmacokinetics,and Redox Properties for Alzheimer’s Disease

Abstract

Background:

Redox active metal cations, such as Cu^2 +, have been related to induce amyloid plaques formation and oxidative stress, which are two of the key events in the development of Alzheimer’s disease (AD) and others metal promoted neurodegenerative diseases. In these oxidative events, standard reduction potential (SRP) is an important property especially relevant in the reactive oxygen species formation.

Objective:

The SRP is not usually considered for the selection of drug candidates in anti-AD treatments. In this work, we present a computational protocol for the selection of multifunctional ligands with suitable metal chelating, pharmacokinetics, and redox properties.

Methods:

The filtering process is based on quantum chemical calculations and the use of in silico tools. Calculations of SRP were performed by using the M06-2X density functional and the isodesmic approach. Then, a virtual screening technique (VS) was used for similar structure search.

Results:

Protocol application allowed the assessment of chelating, drug likeness, and redox properties of copper ligands. Those molecules showing the best features were selected as molecular scaffolds for a VS procedure in order to obtain related compounds. After applying this process, we present a list of candidates with suitable properties to prevent the redox reactions mediated by copper(II) ion.

Conclusion:

The protocol incorporates SRP in the filtering stage and can be effectively used to obtain a set of potential drug candidates for AD treatments.

Keywords

Alzheimer’s disease antioxidants computer-aided drug design density functional theory (DFT) calculations drug discovery metal complexes redox

INTRODUCTION

Alzheimer’s disease (AD) is the most common form of dementia, associated with loss of memory, cognitive decline, physical disability, and behavioral instability finally leading to death [1]. One of the most important hallmarks of the disease is the presence of extracellular deposits formed by the aggregation of small peptides in the brain [2, 3]. Experimental evidences have shown that this peptide (amyloid-β, Aβ) can form complexes with some metals, which can triggered oxidative stress events [4]. Moreover, metal ions such as Cu^+/2 +, Fe^2 +/3 +, and Zn^2 + have been found in the Aβ deposits and have been related to reactive oxygen species (ROS) formation [5 –8]. From them, copper is an important metal due to its intermediate Lewis acid behavior with high affinity toward N and O atoms. Hence, it can coordinate to Aβ peptide and form stable metal-Aβ complexes [9].

Copper cations have been intensively studied in the context of AD due to their abundance in the cerebral medium and their high redox activity [10, 11]. In the oxidative stress processes, ROS are generated with the participation of Cu^2 +-Aβ complexes [12]. The process begins with the reduction of copper complexes by natural reducing agents presents in the cerebral medium. Then, the oxygen dissolved reacts with the reduced Cu⁺-Aβ complex leading to the formation of H₂O₂ and Cu^2 +-Aβ. This oxidized species could generate excess of peroxide by successive reduction in a catalytic way. The global reaction is the following: $2 C u^{+} A β + O_{2} + 2 H^{+} \to 2 C u^{2 +} + A β + H_{2} O_{2}$ (1)

As can be seen in Fig. 1, hydrogen peroxide reacts with free metal ions through Fenton-like reactions and produce ROS in solvent exposed cellular environments [13, 14].

Fig. 1

Schematic representation of the catalytic cycle responsible of the ROS generation. Figure adapted from reference [16].

According to this catalytic cycle, key steps depend on the standard reduction potentials (SRP) of the copper complexes. This means that formation of H₂O₂ could be thermodynamically favored if SRP for the Cu-Aβ complex is lower than the corresponding for the O₂/H₂O₂ couple and higher than the corresponding for the natural reducing agents. These natural reducing agents are compounds present in the cerebral medium such as ascorbic acid (vitamin C), cytochrome b, and myoglobine, among others. The SRP values of these relevant biological species are given in Table 1. From them, the NAD⁺/NADH couple has an SRP of –0.32 V which represent the lower limit for the designed ligands [15]. The SRP of Cu^2 +-Aβ/Cu⁺-Aβ complexes are in the range of 0.28 V to 0.34 V [16] and the O₂/H₂O₂ reaction that has an SRP of 0.30 V at physiological pH, both values versus standard hydrogen electrode (SHE). All SRP data in this work are calculated against the SHE.

Table 1

Standard reduction potential (SRP) values of redox species with biological relevance

System	SRP (V versus SHE)	Reference
O₂/H₂O₂	0.30	[53]
Cytochrome a	0.29	[15]
Cu² ⁺ Aβ/ Cu⁺Aβ	0.28–0.34	[54, 55]
Cytochrome c	0.25	[15]
Cu² ⁺ /Cu⁺	0.16	[56]
Vitamin C	0.06	[57]
Cytochrome b	0.04	[15]
Fumarate/Succinate	0.03	[53]
Myoglobine	0.01	[15]
Oxaloacetate/Malate	–0.17	[53]
Pyruvate/Lactate	–0.19	[53]
NAD⁺/NADH	–0.32	[15]

SHE, standard hydrogen electrode.

Anti-AD drug design research has recently focused on the development of metal chelators with additional properties (multifunctional ligands) [17, 18]. These chelators must have a higher metal affinity than the Cu-Aβ complex to capture copper ions from it, but not excessively higher to remove this metal from essential metalloproteins. It has been shown that this strategy reduces the levels of Aβ deposits in in vitro experiments [19, 20]. Rational drug design strategies consider metal chelator as molecular scaffold and includes some functionalizations that may include additional interactions with other AD targets (anti Aβ, acetylcholinesterase inhibition, ROS, etc.) [21, 22]. Furthermore, Opare and Rauk included redox regulation activity in multifunctional ligands to obstruct ROS production [23, 24].

In those protocols, SRP is not considered as a filter even though it is a relevant property in ROS generation. For that reason, in this work we propose to include the SRP values as a filter to select ligands able to prevent redox reactions involved in the development of the AD. According to this, two different mechanisms of action for multifunctional ligands with controlled SRP values are proposed: 1) a ligand can behave as an antioxidant when the SRP of the Cu-ligand complex is higher than 0.30 V. Thus, the reduction of metal complex is favored over oxygen reduction and ROS formation is disrupted; 2) ligands acting as copper distributor when Cu^2 +-ligand complex is generated, thus they could penetrate into the neuron and once inside, get reduced by some of the reducing agents present in the intracellular medium (Table 1). For the latter, the proposed ligand must have low affinity to Cu⁺ in order to facilitate the cleavage processes and detach the metal from the ligand moiety. After this, Cu⁺ could be oxidized by species with higher SRP than the corresponding value of the copper reduction semi-reaction; for instance, cytochrome a or cytochrome c, leading to the less toxic Cu^2 + species. Based on this mechanism, ligand moiety could exit the neuron and repeat the process; this might help to regulate the excess of extracellular copper which is one of the neurological hallmarks of AD [25]. A graphic representation of distributor compounds mechanism is shown in Fig. 2.

Fig. 2

Proposed mechanism of action for distributor-like compounds.

In the proposed protocol, we carried out computational evaluation of copper chelating properties for a set of copper ligands. These metal-ligand affinities were calculated by means of quantum chemical calculations based on the density functional theory (DFT).

Drug likeness assessment of the chelating compounds was carried out by using available in silico tools from PubChem database. Therefore, SRP calculations for the corresponding copper complexes were calculated for the set of ligands. Finally, a virtual screening (VS) search was performed using compounds which showed the best results in the previous filtering steps. Derivatives molecules were obtained and the computational strategy was applied for this new set of structures. On the whole, the selection process proposed in this work allowed to find molecules with potential application in AD treatments with chelating, pharmacokinetics and controlled redox properties.

METHODS

In the first part of this section, we present the protocol used to calculate the blood-brain barrier (BBB) permeability. Then, we described the methodological aspects to calculate the copper-ligand affinities and standard reduction potentials. In the last part, we show the details of the computations.

Drug likeness and BBB permeability prediction

Drug likeness are important parameters for appropriate pharmacokinetic properties in multifunctional ligands. These properties are usually evaluated by Lipinski’s rule of five [26], which establishes that is ideal for drug-like compounds fulfill the following requirements: 1) molecular weight (MW) less than 500 Da, 2) ≤5 hydrogen bond donor atoms, 3) ≤10 hydrogen bond acceptor atoms and, 4) logarithm of the octanol-water partition coefficient (log P) less than 5. Moreover, for molecules to be used in the brain, the candidates should ensure BBB permeability. This last parameter is commonly evaluated by the estimation of its blood-brain partition coefficient value (log BB). Molecules with log BB< -1.0 are expected to be poorly distributed into the brain [27].

There are some models that estimates log BB values. One of the most commonly used is the proposed by Clark [28]. Clark’s equations are quantitative structure activity relationship (QSAR) models which combine polar surface area and log P descriptors (clog P and Mlog P). Other alternative models for log BB prediction are also reported in the literature [29, 30], but those use descriptors which increase the computation time. In this sense, new simple models that allows fast calculation of log BB for large set of compounds could be helpful.

On the other hand, the PubChem database has free programs to extract information from large libraries of molecules, allowing to evaluate the Lipinski’s rule of five in an efficient way. Additionally, this database has recent techniques and algorithms to calculate topological polar surface area (TPSA) and the log P descriptors (XlogP), which are important molecular properties related to BBB permeability.

However, Clark’s models use logP descriptors which are different from XlogP. In order to use the PubChem database, we developed a new QSAR model for the log BB determination. The model was built by making multilinear regressions between TPSA and XlogP descriptors with experimental log BB values. We used the same training set of 55 molecules used by Clark in his original model. In addition, we evaluated the performance of this new model in two test sets of compounds [31, 32] and compared the results with the obtained by using Clark’s model.

Metal affinities calculations

The copper-ligand affinity is an essential property in the design of multifunctional agents. Computationally, it can be calculated as the displacement free energy of water molecules from a copper-water complex, according to the following reaction:

$C u^{2 + / +} {(H_{2} O)}_{x} + nL \to C u^{2 + / +} L_{n} + x H_{2} O$ (2)

where n is the number of ligands coordinating the copper cation. We selected the most stable form of the [Cu(H₂O)x] complexes being x = 4 for Cu^2 + and x = 3 for Cu⁺.

From this reaction, the stability constant (logβ_n) in terms of concentrations can be expressed as: $log β_{n} (C u^{2 + / +}) = \frac{[C u^{2 + / +} L_{n}]}{[C u^{2 + / +} {(H_{2} O)}_{x}] {[L]}^{n}}$ (3)

For the free energy determination we added an energy correction of 2.4 kcal/mol (RT ln(55.34)) corresponding to the molar concentration of water [33]. In addition, some of the chelating ligands could deprotonated upon copper coordination, leading to a proton concentration of 1×10^–7 M [34]. Thus, the free energies of reaction in aqueous solution ΔG_s for those reactions can be expressed as follows: $Δ G_{s} = Δ G_{s}^{*} + RT ln (55.34) + RT ln Q$ (4)

where $Δ G_{s}^{*}$ represents the computed free energy in aqueous solution at 298 K, Q is the reaction quotient that can be simplified to [H +] since the rest of species are calculated at 1 M concentration.

Relative chelating ability of ligands can be examined by calculating the stability constants at 298 K as: $log β_{n} = - \frac{Δ G_{s}}{2.303 RT}$ (5)

Standard reduction potential calculations

The calculation of SRP for metal complexes is challenging due to the limitations in the computational methodology. These errors include limitations in the electronic structure treatment for open-shell systems with DFT methods, geometry relaxation produced by change on the copper oxidation state and description of the solute-solvent interactions when implicit solvation models are used on charged systems.

In a previous work, we adapted the isodesmic approach to calculate SRPs of copper complexes [35]. The isodesmic reactions are those where the number and type of bonds are conserved in both sides of the reaction. This methodology allowed to calculate this property in water for a set of 64 copper complexes with a wide variety of coordination spheres with an accuracy comparable with the experimental uncertainty (mean unsigned error of 0.08 V for the set of complexes examined). These calculations were carried out by using the M06-2X density functional and the solvent effect were included with the SMD implicit solvation model. This method estimates the free energy change for one of the semi-reactions involved in the redox process, depends on whether the complex of interest is reduced or oxidized by a reference couple with an SRP experimentally reported: ${Cu}_{(sol)}^{2 +} + {Cu}_{(sol)}^{+, ref} \to {Cu}_{(sol)}^{+} + {Cu}_{(sol)}^{2 +, ref}$ (6) ${Cu}_{(sol)}^{2 +, ref} + {Cu}_{(sol)}^{+} \to {Cu}_{(sol)}^{+, ref} + {Cu}_{(sol)}^{2 +}$ (7)

According to the semi-reaction selected as reference, one of the following equations can be used to calculate the SRP of the global reaction: $SRP = {SRP}_{exp}^{ref} + Δ {SRP}_{ox}$ (8) $SRP = {SRP}_{exp}^{ref} - Δ {SRP}_{red}$ (9)

where ${SRP}_{exp}^{ref}$ is the experimental value of the reference couple and ΔSRP is the difference between the calculated SRPs for the reference and complex of interest. This difference was calculated by using Nernst’s equation of global reaction between reference and interest couple. Properly cancellation of errors is carried out by adding ΔSRP_ox or subtracting ΔSRP_red to the experimental value of the reference ligand, against the SHE.

The selected reference couple must have the same coordination sphere, similar size of the ligand and equal charge on the metal cation than those of the complex of interest. Moreover, the number and type of bonds have to be the same for the reduced and the oxidized references complexes as well as for the complexes of interest.

Virtual screening application

In order to expand and optimize the selection process, we followed the similarity based principle [36] (structurally similar compounds are more likely to exhibit similar properties). To do that, we used the power user gateway (PUG REST) web interface of PubChem database [37]. This tool allows to perform a VS process on the obtained molecular scaffolds. From this database we also get information on the molecular properties of the ligands, which can be combined simultaneously with VS procedures. This methodology was used to extract molecular descriptors of each compound, such as molecular weight, hydrogen bond donor/acceptor counting, TPSA [38], and XlogP [39]. In addition, we calculated the log BB values for each ligand, and candidates with the best values in these properties were selected for the DFT calculation of their copper complexes. A schematic representation of the proposed methodology is presented in Fig. 3.

Fig. 3

Computational methodology for SRP controlled drug design protocol.

Computational details

We carried out DFT geometry optimizations and frequency calculations with the M06-2X functional [40] to calculate copper affinities of the ligands and SRP of the copper complexes. For better exploration of the potential energy surface, we performed an initial optimization and conformational analysis prior to the DFT optimizations using molecular mechanics with the universal force field (UFF). M06-2X functional provides good metal coordination description and accurate copper second ionization energies [41]. LANL2DZ pseudopotential and its associated basis set for copper (5s5p5d)/[3s3p2d] [42] and the standard 6–31++G(d,p) basis set for the rest of the atoms were used, both in optimization and frequency calculations. Pseudopotentials have been shown to reduce computational cost in transition metal containing systems with a proper energy and geometry description [43]. Real frequencies were obtained for all complexes and structures. In order to reduce basis set superposition errors, we carried out single-point energy calculations, on the optimized geometries, employing the larger LANL2TZ (5s5p5d)/[5s5p3d] basis set for Cu [44] augmented with an f function [45] and the 6–31++G(d,p) for the rest of the atoms.

All the optimizations were performed in aqueous solution considering the solvent as a continuum through the SMD model [46]. The calculated free energies were used to calculate the SRPs with the isodesmic method using these molecular scaffolds as references. All calculations were carried out with the Gaussian09 and Gaussian16 suite of programs [47]. A schematic representation of the computational strategy used in the present work is presented in Fig. 3.

RESULTS

Results section is organized as follows: first, we present the new computational model to calculate log BB and its evaluation. Second, we show the protocol for the molecular scaffold selection considering chelating and redox properties. Finally, we present the results of the multifunctional ligand selection based on the virtual screening procedure.

QSAR model for log BB prediction

The log BB is an essential parameter to design drug candidates with a potential action in the brain. We made a multilineal regression between TPSA and XlogP descriptors extracted from PubChem to propose a new computational model to calculate BBB permeability. From this regression, the following QSAR model was generated: $log BB = - 0.011 (\pm 0.001) TSPA$ (10) $\begin{matrix} + 0.156 (\pm 0.038) X log P + 0.053 (\pm 0.124) \\ n = 55, r = 0.849, s = 0.404 \end{matrix}$

where n is the number of examined compounds, r is the correlation coefficient and s is the standard deviation. When compared the results of our models with those obtained with the two Clark’s models (DEC-I and DEC-II), the values are quite similar, as well as the statistic parameters. The following coefficients of determination were obtained for the three models: (R²) DEC-I = 0.787, DEC-II = 0.767 and 0.722 for the new model. All predicted values of log BB from equation 10 and correlation plots are presented in the Supplementary Material. According to these results, the performance of the three models in the training set is similar.

To determine the accuracy of the model, we evaluate it with molecules other than the training set and compare the results with those obtained with Clark’s equations. Table 2 shows log BB prediction of the three QSAR models. All the chemical structures on Table 2 are presented in Supplementary Material. For test set 1, only five of the original seven compounds were considered since they are outliers due to the particular experimental difficulties and large deviations when predicting log BB values [31]. The mean absolute errors were: DEC-I = 0.158, DEC-II = 0.135, and 0.163 for the new model. About test set 2, there is a large experimental uncertainty for compound 36, but the log BB of the designed model is within the range. The mean absolute errors for this set were: DEC-I = 0.234, DEC-II = 0.232 and 0.261 for equation 10. According to these results, the proposed model has a similar performance in predicting BB partition coefficients compared to Clark’s models, but the main advantage is the inclusion of the XlogP descriptor and the application of PubChem tools which allows to extract information in an efficient way for the selected set of copper ligands.

Table 2

Log BB values and parameters of QSAR models in training sets

Compounds	PSA (Å²)	TPSA (Å²)	clogP	MlogP	XlogP	log BB exp	log BB DEC-I	log BB DEC-II	log BB New
Test set 1
Y-G14	29.3	24.9	–0.1	0.6	0.4	–0.3	–0.30	–0.18	–0.15
Y-G15	18.8	16.1	–0.3	1.0	0.8	–0.06	–0.19	0.03	0.01
Y-G16	43.1	67.2	–0.6	–0.3	0.3	–0.42	–0.59	–0.55	–0.61
SKF89124	67.5	52.6	2.7	2.6	2.3	–0.43	–0.45	–0.39	–0.15
SKF101468	44.1	32.3	2.0	2.6	2.7	0.25	–0.21	–0.06	0.13
Test set 2
31	46.7	46.3	2.0	3.1	2.5	0	–0.25	–0.01	–0.05
32	62.7	58.9	0.3	2.4	1.3	–0.34	–0.75	–0.36	–0.37
33	76.1	77	1.9	3.4	2.4	–0.3	–0.70	–0.38	–0.39
34	98.5	97.3	0.4	2.7	1	–1.34	–1.26	–0.83	–0.82
35	120.4	118	–0.9	2.0	0	–1.82	–1.78	–1.28	–1.20
36	5.4	3.2	4.6	4.3	5	0.76–0.98	0.76	0.80	0.80

PSA, polar surface area; TPSA, topological polar surface area.

Selection of molecular scaffolds

For the initial molecular scaffolds selection, we used a set of 62 copper complexes with experimental SRP values reported by Rorabacher [48] and Tabbi et al. [49]. We determined the chelating and drug-like properties of the ligands on these complexes. In addition, we determined the log BB by using the model proposed above. Some representative examples of these ligands are presented in Fig. 4.

Fig. 4

Examples of the ligands used in copper affinity determination a) polypyridyl derivatives, b) polythiaethers, and c) mixed donor atoms ligands. Figure taken from reference [35].

Assessment of chelating and redox properties

Metal affinities were calculated for the set of 62 copper complexes in aqueous solution. This set consists in three groups of copper chelating agents that can be classified as: 1) polypiridyl derivatives, 2) polythiaethers, and 3) mixed-donor atoms. These ligands cover a wide variety of coordination spheres: 4N, 4S, 3N1O, 3O1S, 3S1O, 3N1S, 4S1N, 2N2O, 2O2S, and 2N2S arrangements. Some representative ligands for each group are presented in Fig. 4 and all chemical structures, name abbreviations, and computed affinities are given in Supplementary Material.

The determination of stability constants of the corresponding copper complexes is an important step in the process to filter out potential drug candidates. These molecules should have intermediate affinity for Cu^2 + in order to compete with Cu-Aβ complex but no with essential metalloproteins. In this sense, the molecules were divides into two groups, antioxidants and distributor-like compounds. In the first group are the molecules with log β_n(Cu^2 +) value within the range of 10–26 [11, 50]. Additionally, for distributors-like compounds we establish that log β_n(Cu⁺) must be lower than the corresponding Cu^2 + value in at least two units, to increase metal regulation ability.

In the first group, polypiridil derivatives ligands form stable copper complexes through 4N coordination spheres. These complexes are rigid due to ligand’s structure. As a consequence, these complexes exhibit high stability constants (logβ_n= 15–30) for both oxidized and reduced forms. This range of values is appropriate for antioxidants ligands but not for distributors compounds, in which it is required a lower affinity for Cu⁺ ion to induce bond cleavage after complex reduction process (see Fig. 2).

For the group of polythiaethers, their complexes exhibit a 4S coordination arrangement. The electronic treatment of Cu-S bonds is quite different compared to the other systems. Some DFT functionals tend to underestimate the stability of the Cu^2 + complexes by partially oxidizing the ligand fragments and reducing the copper center [35, 41]. The last was verified with copper’s spin densities values for the complexes. However, these limitations can be overcome by controlling the spin density in the copper center and by using the isodesmic method to calculate the SRP. Overall, the stability of the reduced complexes is favored over the oxidized ones. This fact agrees with the high experimental SRP values reported for these complexes. As a result, low stability constants were determined for Cu^2 + complexes, hence this kind of ligands are inappropriate to capture copper from Cu^2 +-Aβ toxic species.

The ligands with different coordinating atoms enclose the remaining variety of coordination sphe-res, due to this there is not a general trend as in the previous groups and a wide range of computed stability constants was obtained. When more than two sulfur atoms are involved in complex formation, this is associated with poor chelating ability of the ligand. Conversely, in 2N2O arrangements high logβ_n(Cu^2 +) and low logβ_n(Cu⁺) affinity values were obtained, which makes them potential candidates for distributor ligand scaffolds.

Stability constants and SRP of selected lead molecules are shown in Table 3. For a proper application of the isodesmic method for SRP calculations, a careful selection of the reference complex is required. In Table 3, these references are shown in parenthesis for each compound of interest. Computed SRP for the set of study are listed in the Supplementary Material with their corresponding reference couples. From previous data, it can be seen that clioquinol (CQ) has a low SRP value in order to participate in the catalytic generation of ROS. This 8-hydroxyquinoline derivative chelator has been evaluated in terms of amyloid deposits desegregation with relative success and it is included among selected molecules for the sake of comparison [51]. The performance of the computational protocol was evaluated by comparing the experimental logβ₂ of CQ (21.91) [20] with the computed value (21.15).

Table 3

Classification of lead molecules according to coordination spheres (CS), chelating ability and computed SRP of the corresponding copper complex

Ligand	CS	logβ_n(Cu^2 +)	logβ_n(Cu⁺)	SRP (V)
Antioxidants
tta (3dta)	2O2S	19.62	21.31	0.4
3dta (tta)	2O2S	19.42	19.29	0.4
BPEMEA (PMAS)	3N1S	16.05	17.76	0.5
2,9-Me₂phen (pyim)	4N	14.52	16.27	0.5
Distributors
Leu (CQ)	2N2O	25.07	8.47	–0.2
IDA (Gly)	2N2O	24.48	12.75	–0.3
CQ (Gly)	2N2O	21.15	7.27	–0.4
4,4’-Me₂bpy (bpy)	4N	18.62	9.96	0.1
terpy (dipa)	3N1O	15.87	7.87	0.1

Complexes in brackets represent the reference couple used in the isodesmic method.

The chemical structures of the lead molecules are shown in Fig. 5. 3D optimized geometries of the corresponding oxidized and reduced copper complexes for these molecules are presented in Supplementary Material. Three sulfur containing molecules (tta, 3dta, and BPEMEA) have adequate affinities for Cu^2 +. These ligands can form highly rigid structures in the corresponding copper complexes. These geometrical constraints increase complex stability and compensate the presence of sulfur atoms in the coordination sphere.

Fig. 5

Chemical structures of lead molecules with the most appropriate chelating and redox properties.

Drug likeness requirements

The second step in the filtering process consists of the assessment of the drug-like properties of the selected molecules. We determined the molecular descriptors of the compounds with the best chelating and redox properties using the PubChem database services and applying the new designed QSAR model for log BB prediction (equation 10). The pharmacokinetic properties of the chelating ligands are presented in Table 4.

Table 4

Drug likeness determination of molecular scaffolds. The most appropriate values of log BB are highlighted in bold

Ligand	MW	HBA	HBD	Xlog P	TPSA (Å²)	log BB
Antioxidants
tta	298.4	4	2	0.92	74.6	–0.594
3dta	224.3	4	2	0.12	74.6	–0.719
BPEMEA	301.5	3	0	2.13	29.02	0.078
2,9-Me₂phen	208.3	2	0	2.01	25.78	0.093
Distributors
Leu	131.2	3	3	–1.38	63.32	–0.833
IDA	133.1	5	3	–3.59	86.62	–1.425
CQ	305.5	2	1	3.62	33.12	0.267
4,4’-Me₂bpy	184.2	2	0	2.24	25.78	0.129
terpy	233.3	3	0	2.19	38.68	–0.015

MW, molecular weight; HBA, hydrogen bond acceptors; HBD, hydrogen bond donors; TPSA, topological polar surface area.

As can be seen, all compounds satisfied the Lipin-ski’s rule of five, thus they have structural characteristics to be considered as drug candidates. However, none of these compounds has a log BB value higher than 0.3, limit commonly used to determinate if a compound is able to cross BBB readily [27]. Nevertheless, log BB is defined as the radio of the steady state concentrations of drug molecule in both brain and blood (log(C_brain/C_blood)). In other words, it can be considered as a partition coefficient hence the 0.3 value should not be considered as a strict limit. Those molecules which approaching the limit value are likely to be distributed into the brain with greatest extent. For instance, CQ has a log BB value of 0.267 and it has been proven its ability to cross BBB. Additionally, molecules with log BB ≥-1 are very likely to have central nervous system activity [52]. In this sense, in this study, those ligands with computed log BB > -0.1 were selected as molecular scaffolds for searching analogues in the VS process. In addition, further functionalizations of resulting derivatives compounds could improve ligand BBB permeability. Consequently, the ligands selected as molecular scaffolds are CQ, 4,4’-Me₂bpy, 2,9-Me₂phen, terpy, and BPE-MEA. These molecules have the best chelating, drug like, and redox properties of the examined set and are a good starting point to apply VS techniques.

The optimized geometries of molecular scaffolds formed with the copper cations are shown in Fig. 6 and the most significant structural parameters are given in Table 5. As expected, square-planar and tetrahedral geometries can be observed for Cu^2 + and Cu⁺ complexes, respectively. However, considerable distortions of the square planar geometry are presented due to repulsion of nearby groups in the ligands. The BPEMEA and terpy ligands have rigid structures and for this reason, the oxidized and the reduced complexes showed similar geometries. Conversely, the other ligands exhibited important changes in bond lengths and bond angles for their copper complexes with different oxidation states.

Fig. 6

M06-2X optimized geometries of the complexes formed between the molecular scaffolds and the Cu^2 + and Cu⁺ ions.

Table 5

Computed M06-2X optimized structural parameters of the complexes formed between Cu^2 + and Cu⁺ ions and the molecular scaffolds

Complex	Cu-N1	Cu-N2	Cu-N3	Cu-N4	Cu-O1	Cu-O2	Cu-S	Θ	Ψ
[Cu(CQ)₂]	2.051	2.051			1.976	1.976		180.0	97.2
[Cu(CQ)₂] ^–	2.138	2.138			2.182	2.182		118.7	127.0
[Cu(4,4’-Me₂bpy)₂]^2 +	2.052	2.060	2.054	2.058				156.3	100.6
[Cu(4,4’-Me₂bpy)₂]⁺	2.169	2.169	2.169	2.169				125.0	131.1
[Cu(2,9-Me₂phen)₂]^2 +	2.189	2.189	2.182	2.182				139.5	117.6
[Cu(2,9-Me₂phen)₂]⁺	2.179	2.189	2.174	2.161				137.2	116.1
[Cu(BPEMEA)]^2 +	2.001	2.090	2.007				2.728	163.9	99.1
[Cu(BPEMEA)]⁺	2.110	2.270	2.128				2.512	125.1	99.5
[Cu(terpy)H₂O]^2 +	2.099	2.002	2.119		2.009			156.9	78.7
[Cu(terpy)H₂O]⁺	2.283	2.179	2.285		2.142			146.4	73.7

Θ refers to the angle between two opposite coordination atoms, whereas Ψ is the angle between two adjacent coordination atoms. Bond lengths in angstroms and angles in degrees.

Derived multifunctional ligands selection

The VS technique was applied for each molecular scaffold presented in Fig. 5 in order to find derivative compounds with similar chelating and redox properties while conserving the coordination spheres. Table 6 shows the number of commercial compounds found in PubChem database with the proper values in the successive filters, but this time with and additional restriction of log BB >0.25, to improve BBB permeability. As can be seen from this table, a high number of derivatives with the desired drug likeness descriptors were obtained from the searching process, except for the BPEMEA scaffold which present no coincidences.

Table 6

Number of commercial compounds that fulfill imposed constrains in the filtering process

Ligand	VS	Lipinski’s rule	log BB
CQ	223	96	21
4,4’-Me₂bpy	12336	10262	3629
2,9-Me₂phen	902	346	224
terpy	1820	1025	109
BPEMEA	0	0	0

From these derivatives, we selected the best candidates to evaluate the SRP by quantum mechanical calculations. This selection process was based on pharmacokinetics requirements. Thereby, those compounds that satisfied Lipinsky’s rule and presented higher values of log BB were selected. For the SRP determination, the respective molecular scaffolds of derived molecules were used as reference couple, since they have experimental reported values. Pharmacokinetic molecular descriptors and chemical structure of derived candidates are presented in Table 7 and in Fig. 7, respectively. Optimized geometries of copper complexes formed with some of the derivatives are presented in Fig. 8 and their structural parameters are given in Table 8.

Table 7

Drug likeness determination of derived multifunctional ligands

Ligand	MW	HBA	HBD	Xlog P	TPSA (Å²)	log BB
2,9-Me₂phen1	242.71	2	0	4.2	25.8	0.435
2,9-Me₂phen2	277.15	2	0	4.5	25.8	0.482
CQ1	249.7	2	1	4.7	33.1	0.435
CQ2	381.6	2	1	4.7	33.1	0.435
4,4’-Me₂bpy1	302.42	2	0	4.9	25.8	0.543
4,4’-Me₂bpy2	268.40	2	0	4.8	25.8	0.528
terpy1	317.44	3	0	4.5	38.7	0.345
terpy2	317.44	3	0	4.3	38.7	0.314
terpy3	336.60	3	0	4.0	38.7	0.267

MW, molecular weight; HBA, hydrogen bond acceptors; HBD, hydrogen bond donors; TPSA, topological polar surface area.

Table 8

Computed M06-2X optimized structural parameters of the complexes formed between Cu^2 + and Cu⁺ ions and some of the derivatives ligands

Complex	Cu-N1	Cu-N2	Cu-N3	Cu-N4	Cu-O1	Cu-O2	Θ	Ψ
[Cu(CQ1)₂]	2.053	2.048			1.966	1.973	178.9	98.1
[Cu(CQ1)₂] ^–	2.143	2.139			2.163	2.180	124.8	135.1
[Cu(4,4’-Me₂bpy1)₂]^2 +	2.064	2.057	2.060	2.063			158.5	79.8
[Cu(4,4’-Me₂bpy1)₂]⁺	2.146	2.207	2.170	2.170			143.4	77.1
[Cu(2,9-Me₂phen1)₂]^2 +	2.018	2.214	2.214	2.018			117.5	108.7
[Cu(2,9-Me₂phen1)₂]⁺	2.222	2.231	2.156	2.158			127.8	122.0
[Cu(terpy1)H₂O]^2 +	2.105	2.002	2.104		2.001		156.5	78.2
[Cu(terpy1)H₂O]⁺	2.302	2.166	2.267		2.131		146.2	73.4

Θ refers to the angle between two opposite coordination atoms, whereas Ψ is the angle between two adjacent coordination atoms. Bond lengths in angstroms and angles in degrees.

SRP values of derivatives do not change drastically respect to the reference couples. This can be explained by the fact that the coordination spheres and molecular geometries are similar when the electron transfer processes takes place (Figs. 7 and 8). Moreover, the bond lengths and angles of these compounds are close to the present in the complexes with the scaffolds, with exception for the Me₂phen1 ligands which have a chlorine atom near to the coordination sphere in their structures and this produces additional interactions and geometrical variations. By contrast, the terpy1 complexes do not show important changes since terpy scaffold has a rigid geometry and no substitutions were made near to the copper center. Summarizing, the calculated SRPs are appropriate for the design of antioxidants and distributors molecules, with the exception of CQ2 which have a low SRP value. Thermodynamic data obtained from DFT calculations for derived ligands are reported in the Supplementary Material.

Fig. 7

Chemical structures of derived ligands. The SRP value of each derived compound is presented, as well as the value of the corresponding reference used in the isodesmic method.

Fig. 8

M06-2X optimized geometries of the complexes formed between some of the derivatives ligands and the Cu^2 + and Cu⁺ ions.

About the SRP results, it is observed that when substituents of derivatives are more electron withdrawing (EW), the SRP of the complexes increases compared to references values, due to a tendency to reduce the copper cation. On the other hand, electron donating (ED) groups avoid the reduction of the metal center by decreasing the positive charge in the copper atom, in consequence lower SRP were obtained. In some cases, this phenomenon is not observed. For instance, in the 2,9-Me₂phen derivatives, a compensation of EW and ED effects is observed in 2,9-Me₂phen2 with a slightly SRP variation and in 2,9-Me₂phen1 a dominating ED effect it was expected due to greater presence of ED groups, but this does not agree with the obtained higher SRP. These results suggest that electronic substitution nature is not always the only aspect that determine SRP values.

The number of substitutions in the ligands are another aspect that affects the reduction potentials. For example, terpy’s derivatives (terpy1 and terpy2) both have the same number of atoms but different number of substituents with terpy2 being more substituted by six methyl groups compared to three ethyl groups on terpy1. These groups have a weak electronic donating effect, but an increase of substitution number reduce the SRP value. The position in the substitution is also relevant. Thus, groups closer to the coordinating atom have bigger effect in SRP value with important contributions of ortho substitutions. This could explain why large SRP changes were observed in CQ-like compounds.

DISCUSSION

AD currently represents a major public health issue. Unfortunately, no success has been reached from clinical trials to obtain a cure or preventive treatment. This can be explained by the difficult of conducting experiments, lack of information in some processes related to AD, and the multifactorial nature of the disease. Nowadays, it is known that metal ions also play an important role in AD development since there are sufficient experimental evidences on their role on ROS production. For this reason, we think that it is possible to obtain better ligands aimed at targeting copper ions if redox activity is included among their desirable properties (along with copper chelation, BBB permeability, selectivity and low toxicity).

This work presents a new computational protocol that includes standard reduction potential as a parameter in drug design for AD. The proposed in silico strategy allows the identification of compounds that exhibit suitable coordination, pharmacokinetics and redox properties. The basic steps in the protocol are: 1) evaluation of chelating and redox properties of scaffolds by quantum mechanical calculations, 2) drug likeness scaffold determination using simple molecular descriptors, 3) searching commercial compounds with similar structure with the previous selected molecular scaffolds through database virtual screening, 4) filtering derivative molecules according to drug-like requirements, and 5) SRP determination of the final candidates by quantum chemical methods. After the application of the protocol for a set of 62 copper chelates, we obtained five different scaffolds with N, O, and S donor atoms. Once derived molecules were filtered by evaluating their drug likeness properties, the SRPs of the selected ligands were calculated. These molecules presented proper anti-AD parameters in eight of the nine final candidates.

The log BB prediction is particularly useful in the design of potential drugs against neurodegenerative diseases, but its calculation depends on the predictive model selection. In this sense, a careful review of available molecular descriptors, size, and type of compound set should be made before model application. Present work describes the derivation of a simple QSAR model for fast log BB estimation, based on TPSA and XlogP descriptors. This model uses the tools available in PubChem database to make the process efficient in the evaluation of this property in a large set of compounds.

Incorporation of SRP as drug design filter requires a reliable computational method for the accurate determination of this property. The isodesmic method allows a proper cancellation of errors when a similar complex of reference with known experimental value is used. This strategy should be applied when at least one reference couple of the molecular scaffold is available and for derivatives that satisfied isodesmic method requirements (e.g., molecular size, charge, etc.). Moreover, rational group substitutions in a potential candidate could be made in order to modifying SRP of corresponding copper complex and obtain a desired value, this could improve the specificity and efficiency of anti-AD drug candidates.

Footnotes

ACKNOWLEDGMENTS

A. F-G. thanks Universidad Militar Nueva Granada for financial support (Project INV-CIAS-2535).

Authors’ disclosures available online ().

The supplementary material is available in the electronic version of this article: .

References

McKhann

, Knopman

, Chertkow

, Hyman

, Jack

Jr , Kawas

, Klunk

, Koroshetz

, Manly

, Mayeux

, Mohs

, Morris

, Rossor

, Scheltens

, Carrillo

, Thies

, Weintraub

, Phelps

(2011) The diagnosis of dementia due to Alzheimer’s disease: Recommendations from the National Institute on Aging-Alzheimer’s Association workgroups on diagnostic guidelines for Alzheimer’s disease. Alzheimers Dement7, 263–269.

Glenner

, Wong

(1984) Alzheimer’s disease: Initial report of the purification and characterization of a novel cerebrovascular amyloid protein. Biochem Biophys Res Commun120, 885–890.

Masters

, Simms

, Weinman

, Multhaup

, McDonald

, Beyreuther

(1985) Amyloid plaque core protein in Alzheimer disease and Down syndrome. Proc Natl Acad Sci U S A82, 4245–4249.

Markesbery

(1997) Oxidative stress hypothesis in Alzheimer’s disease. Free Radic Biol Med23, 134–147.

Drew

, Barnham

(2011) The heterogeneous nature of Cu2+interactions with Alzheimer’s amyloid-β peptide. Acc Chem Res44, 1146–1155.

Alí-Torres

, Mirats

, Maréchal

J-D

, Rodríguez-Santiago

, Sodupe

(2015) Modeling Cu2+-Aβ complexes from computational approaches.92402. AIP Adv5, 1–11.

Talmard

, Yona

, Faller

(2009) Mechanism of zinc (II)promoted amyloid formation: Zinc (II) binding facilitates the transition from the partially α-helical conformer to aggregates of amyloid β protein (1–28). J Biol Inorg Chem14, 449–455.

Huang

, Atwood

, Moir

, Hartshorn

, Tanzi

, Bush

(2004) Trace metal contamination initiates the apparent auto-aggregation, amyloidosis, and oligomerization of Alzheimer’s Aβ peptides. J Biol Inorg Chem9, 954–960.

Pearson

(1963) Hard and soft acids and bases. J Am Chem Soc85, 3533–3539.

10.

Barnham

, Bush

(2014) Biological metals and metal-targeting compounds in major neurodegenerative diseases. Chem Soc Rev43, 6727–6749.

11.

Kepp

(2012) Bioinorganic chemistry of Alzheimer’s disease. Chem Rev112, 5193–5239.

12.

Gaggelli

, Kozlowski

, Valensin

(2006) Copper homeostasis and neurodegenerative disorders (Alzheimer’s, prion, and Parkinson’s diseases and amyotrophic lateral sclerosis). Chem Rev106, 1995–2044.

13.

Barnham

, Masters

, Bush

(2004) Neurodegenerative diseases and oxidative stress. Nat Rev Drug Discov3, 205–214.

14.

Das

, Wati

, Fatima-Shad

(2015) Oxidative stress gated by Fenton and Haber Weiss reactions and its association with Alzheimer’s disease. Arch Neurosci2, 1–8.

15.

Dryhurst

, Kadish

, Scheller

, Renneberg

(1982) Biological electrochemistry. Academic Press, pp. 406–409.

16.

Alí-Torres

, Mirats

, Maréchal

J-D

, Rodríguez-Santiago

, Sodupe

(2014) 3D structures and redox potentials of Cu2+–Aβ (1–16) complexes at different pH: A computational study. J Phys Chem B118, 4840–4850.

17.

Rodríguez-Rodríguez

, Telpoukhovskaia

, Orvig

(2012) The art of building multifunctional metal-binding agents from molecular scaffolds for the potential application in neurodegenerative diseases. Coord Chem Rev256, 2308–2332basic.

18.

Savelieff

, Nam

, Kang

, Lee

, Lim

(2018) Development of multifunctional molecules as potential therapeutic candidates for Alzheimer’s disease, Parkinson’s disease, and amyotrophic lateral sclerosis in the last decade. Chem Rev119, 1221–1322.

19.

Gomes

LMF

, Vieira

, Jones

, Wang

MCP

, Dyrager

, Souza-Fagundes

, Da Silva

, Storr

, Beraldo

(2014) 8-Hydroxyquinoline Schiff-base compounds as antioxidants and modulators of copper-mediated Aβ peptide aggregation. J Inorg Biochem139, 106–116.

20.

Rodríguez-Rodríguez

, Sanchez de Groot

, Rimola

, Alvarez-Larena

, Lloveras

, Vidal-Gancedo

, Ventura

, Vendrell

, Sodupe

, González-Duarte

(2009) Design, selection, and characterization of thioflavin-based intercalation compounds with metal chelating properties for application in Alzheimer’s disease. J Am Chem Soc131, 1436–1451.

21.

Ritchie

, Bush

, Mackinnon

, Macfarlane

, Mastwyk

, MacGregor

, Kiers

, Cherny

, Li

Q-X

, Tammer

, Carrington

, Mavros

, Volitakis

, Xilinas

, Ames

, Davis

, Beyreuther

, Tanzi

, Masters

(2003) Metal-protein attenuation with iodochlorhydroxyquin (clioquinol) targeting Aβ amyloid deposition and toxicity in Alzheimer disease: A pilot phase 2 clinical trial. Arch Neurol60, 1685–1691.

22.

Esmieu

, Guettas

, Conte-Daban

, Sabater

, Faller

, Hureau

(2019) Copper-targeting approaches in Alzheimer’s disease: How to improve the fallouts obtained from in vitro studies. Inorg Chem58, 13509–13527.

23.

Opare

SKA

, Rauk

(2017) Copper (I) chelators for Alzheimer’s disease. J Phys Chem B121, 11304–11310.

24.

Opare

SKA

, Rauk

(2019) Pseudopeptide designed to inhibit oligomerization and redox chemistry in Alzheimer’s disease. J Phys Chem B123, 5206–5215.

25.

Lovell

, Robertson

, Teesdale

, Campbell

, Markesbery

(1998) Copper, iron and zinc in Alzheimer’s disease senile plaques. J Neurol Sci158, 47–52.

26.

Lipinski

, Lombardo

, Dominy

, Feeney

(1997) Experimental and computational approaches to estimate solubility and permeability in drug discovery and development settings. Adv Drug Deliv Rev23, 3–25.

27.

Abraham

, Takács-Novák

, Mitchell

(1997) On the partition of ampholytes: Application to blood–brain distribution. J Pharm Sci86, 310–315.

28.

Clark

(1999) Rapid calculation of polar molecular surface area and its application to the prediction of transport phenomena. 2. Prediction of blood-brain barrier penetration. J Pharm Sci88, 815–821.

29.

Yan

, Liang

, Chong

, Nie

, Yu

(2013) In-silico prediction of blood–brain barrier permeability. SAR QSAR Environ Res24, 61–74.

30.

Gupta

, Basant

, Singh

(2015) Qualitative and quantitative structure–activity relationship modelling for predicting blood-brain barrier permeability of structurally diverse chemicals. SAR QSAR Environ Res26, 95–124.

31.

Abraham

, Chadha

, Mitchell

(1995) Hydrogen-bonding. Part 36. Determination of blood brain distribution using octanol-water partition coefficients. Drug Des Discov13, 123–131.

32.

Lombardo

, Blake

, Curatolo

(1996) Computation of brain-blood partitioning of organic solutes via free energy calculations. J Med Chem39, 4750–4755.

33.

Bryantsev

, Diallo

, Goddard Iii

(2008) Calculation of solvation free energies of charged solutes using mixed cluster/continuum models. J Phys Chem B112, 9709–9719.

34.

Rickard

, Gomez-Balderas

, Brunelle

, Raffa

, Rauk

(2005) Binding affinities for models of biologically available potential Cu (II) ligands relevant to Alzheimer’s disease: An ab initio study. J Phys Chem A109, 8361–8370.

35.

Chaparro

, Alí-Torres

(2017) Assessment of the isodesmic method in the calculation of standard reduction potential of copper complexes. J Mol Model23, 1–8.

36.

Martin

, Kofron

, Traphagen

(2002) Do structurally similar molecules have similar biological activity?J Med Chem45, 4350–4358.

37.

Kim

, Chen

, Cheng

, Gindulyte

, He

, Li

, Shoemaker

, Thiessen

, Yu

, Zaslavsky

, Zhang

, Bolton

(2019) PubChem 2019 update: Improved access to chemical data. Nucleic Acids Res47, 1102–1109.

38.

Ertl

, Rohde

, Selzer

(2000) Fast calculation of molecular polar surface area as a sum of fragment-based contributions and its application to the prediction of drug transport properties. J Med Chem43, 3714–3717.

39.

Cheng

, Zhao

, Li

, Lin

, Xu

, Zhang

, Li

, Wang

, Lai

(2007) Computation of octanol-water partition coefficients by guiding an additive model with knowledge. J Chem Inf Model47, 2140–2148.

40.

Zhao

, Truhlar

(2008) The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor Chem Acc120, 215–241.

41.

Rios-Font

, Sodupe

, Rodríguez-Santiago

, Taylor

(2010) The role of exact exchange in the description of Cu2+-(H2O) n (}=1-6) complexes by means of DFT methods. J Phys Chem A114, 10857–10863.

42.

Hay

, Wadt

(1985) Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals. J Chem Phys82, 299–310.

43.

Frenking

, Antes

, Böhme

, Dapprich

, Ehlers

, Jonas

, Neuhaus

, Otto

, Stegmann

, Veldkamp

, Vyboishchikov

(2007) Pseudopotential calculations of transition metal compounds: Scope and limitations. In Reviews in Computational Chemistry, Volume 8, Lipkowitz KB, Boyd DB eds. John Wiley and Sons, Indianapolis, pp. 63-144.

44.

Roy

, Hay

, Martin

(2008) Revised basis sets for the LANL effective core potentials. J Chem Theory Comput4, 1029–1031.

45.

Ehlers

, Böhme

, Dapprich

, Gobbi

, HÃűllwarth

, Jonas

, Köhler

, Stegmann

, Veldkamp

, Frenking

(1993) A set of f-polarization functions for pseudo-potential basis sets of the transition metals Sc-Cu, Y-Ag and La-Au. Chem Phys Lett208, 111–114.

46.

Marenich

A V

, Cramer

, Truhlar

(2009) Universal solvation model based on solute electron density and on a continuum model of the solvent defined by the bulk dielectric constant and atomic surface tensions. J Phys Chem B113, 6378–6396.

47.

Frisch

, Trucks

, Schlegel

, Scuseria

, Robb

, Cheeseman

, Scalmani

, Barone

, Mennucci

, Petersson

, Nakatsuji

, Caricato

, Li

, Hratchian

, Izmaylov

, Bloino

, Zheng

, Sonnenberg

, Hada

, Ehara

, Toyota

, Fukuda

, Hasegawa

, Ishida

, Nakajima

, Honda

, Kitao

, Nakai

, Vreven

, Montgomery

Jr. , Peralta

, Ogliaro

, Bearpark

, Heyd

, Brothers

, Kudin

, Staroverov

, Kobayashi

, Normand

, Raghavachari

, Rendell

, Burant

, Iyengar

, Tomasi

, Cossi

, Rega

, Millam

, Klene

, Knox

, Cross

, Bakken

, Adamo

, Jaramillo

, Gomperts

, Stratmann

, Yazyev

, Austin

, Cammi

, Pomelli

, Ochterski

, Martin

, Morokuma

, Zakrzewski

, Voth

, Salvador

, Dannenberg

, Dapprich

, Daniels

, Farkas

, Foresman

, Ortiz

J V

, Cioslowski

, Fox

(2013) Gaussian09 (Revision D.01). Gaussian Inc., Wallingford, CT.

48.

Rorabacher

(2004) Electron transfer by copper centers. Chem Rev104, 651–698.

49.

Tabbí

, Giuffrida

, Bonomo

(2013) Determination of formal redox potentials in aqueous solution of copper (II) complexes with ligands having nitrogen and oxygen donor atomsand comon with their EPR and UV–Vis spectral features. J Inorg Biochem128, 137–145paris.

50.

Rodríguez-Rodríguez

, Rimola

, Alí-Torres

, Sodupe

, González-Duarte

(2011) In silico strategies for the selection of chelating compounds with potential application in metal-promoted neurodegenerative diseases. J Comput Aided Mol Des25, 21–30.

51.

Cherny

, Atwood

, Xilinas

, Gray

, Jones

, McLean

, Barnham

, Volitakis

, Fraser

, Kim

, Huang

, Goldstein

, Moir

, Lim

, Beyreuther

, Zheng

, Tanzi

, Masters

, Bush

(2001) Treatment with a copper-zinc chelator markedlyand rapidly inhibits β-amyloid accumulation in Alzheimer’s disease transgenic mice. Neuron30, 665–676.

52.

Vilar

, Chakrabarti

, Costanzi

(2010) Prediction of passive blood–brain partitioning: Straight forward and effective classification models based on in silico derived physicochemical descriptors. J Mol Graph Model28, 899–903.

53.

Nelson

, Lehninger

, Cox

(2013) Lehninger principles of biochemistry. Macmillan Press, pp. 531.

54.

Guilloreau

, Combalbert

, Sournia-Saquet

, Mazarguil

, Faller

(2007) Redox chemistry of copper–amyloid-β: The generation of hydroxyl radical in the presence of ascorbate is linked to redox-potentials and aggregation state. ChemBioChem8, 1317–1325.

55.

Balland

, Hureau

, Savéant

J-M

(2010) Electrochemical and homogeneous electron transfers to the Alzheimer amyloid-β copper complex follow a preorganization mechanism. Proc Natl Acad Sci U S A107, 17113–17118.

56.

Bard

(2017) Standard potentials in aqueous solution. Routledge, pp. 49.

57.

Loach

(1976) Oxidation-reduction potentials, absorbance bands and molar absorbance of compounds used in biochemical studies. In CRC Handbook of Biochemistry and Molecular Biology, Fasman GD, ed. CRC Press, Waltham, pp. 122-130.