Copper is both essential and toxic metal for living systems. As an essential trace element, copper participates in physiological processes as a cofactor in redox reactions of many enzymes such as superoxide dismutase, lysyl oxidase, cytochrome c oxidase, tyrosinase, dopamine-beta-hydroxylase [[1], [2], [3], [4]]. Furthermore, copper takes part as a signaling metal in regulating lipolysis, cell growth and proliferation, and autophagy, which are required for iron metabolism, adequate growth, cardiovascular integrity, lung elasticity, neovascularization, and neuroendocrine functions [5]. Imbalances of tightly regulated copper homeostasis and cuproplasia in uptake and export to maintain its adequate supply in reducing toxic effects occurs under condition of increased exogenous exposure or rare genetic metabolic disorders such as Wilson's and Menkes' disease, as well as progression of malignant diseases, inflammation processes, and neurodegenerative disorders in Alzheimer's, Parkinson's, and Creutzfeldt Jakob's diseases [[5], [6], [7], [8], [9]]. Significantly elevated copper levels in blood serum and malignant tumor tissues were reported in cancer patients compared to healthy persons [5,10]. During the last decades, the studies have emerged on the use of chelation therapy for decreasing copper bioavailability as well as copper ion ionophores with cuproptosis-inducing functions for treatment of several types of cancers, and neurodegenerative disorders [4,[11], [12], [13]], including lists of clinical trials for copper ionophores [11], and the principal characteristics of multifunctional chelators with their classification based on the therapeutic efficiency [12,13].

In blood plasma, 65% to 95% of the total copper is bound to ceruloplasmin in a nonexchangeable manner, while the main constituent of exchangeable-bound copper(II) is serum albumin (SA) (about 5–20% Cu) [14]. Up to 5% of total serum Cu comprises low molecular weight (LMW) ligands including amino acids as part of a bioavailable kinetically labile pool for copper [14]. In 1967, electrically neutral copper(II) coordination compounds with two amino acids [Cu(aa)2] were found as predominant copper(II)-amino acid species in blood plasma, preferentially bound with l-histidine (His) in bis(l-histidinato)copper(II) [Cu(His)2], and ternary copper(II)–l-amino acid complexes containing His [Cu(His)(aa)] favorably with l-asparagine (Asn), l-threonine (Thr), and l-glutamine (Gln) [[15], [16], [17]]. These amino acids have a polar side-chain group specific for each amino acid as follows: imidazole in His, hydroxyl –OH in Thr, and amido –CONH2 in Asn and Gln. Kirsipuu et al. [18] estimated from experimentally determined dissociation constants and total blood concentration of His and other free amino acids in the blood, that in average 0.04% and 0.20% of total copper in serum was in Cu(His)2 and Cu(His)(aa) compounds, respectively. In solutions, the formation of LMW copper(II) amino acid compounds depends on the amino-acid and metal concentrations, solvent composition, and the thermodynamically directed forces that control the formation of the metal complex. The most recent modeling of complicated multicomponent equilibrium system of the LMW components in human blood plasma predicted the distribution of copper(II) to be predominantly in the neutral compounds Cu(His)(Gln), Cu(His)2, and Cu(His)(Thr) with 25%, 14%, and 9% of total copper(II), respectively [19]. Although the counterions, such as sodium and chloride ions, were explicitly included in the model of blood plasma, the chloride coordination to the copper(II) was negligible because of the relatively low NaCl(aq) concentration in this biofluid [19]. Similar modeling of the speciation of LMW compounds with trace transition metals, including copper(II), in phloem sap (which is the fluid that transport sugars, amino acids and metal ions from leaves to other plant parts) yielded that 40% of copper(II) was bound with nicotianamine, while 60% of the total copper consisted of a mixture of Cu(His)(aa) ternary compounds [20]. Alike the blood plasma LMW speciation [19], the ternary Cu(His)(Gln) was among the predominant copper(II) species since Cu(His)(aa) with Asn, Gln, and serine accounted for 12.0%, 9.6%, and 7.8% of total Cu(II), respectively [20].

The Cu(His)(Gln) compound was first isolated in 1967 from an aqueous solution at pH 7.5 using thin-layer chromatography [16]. While His is an essential amino acid, Gln is a non-essential amino acid, that may be essential during pregnancy, lactation, neonatal growth, and during relatively low protein diets [21,22]. In almost every cell, Gln can be used as a substrate and provider of nitrogen atoms for nucleotide synthesis, as well as for many other biosynthetic pathways involved in cell growth and division. In plasma and tissues, the Gln concentration being 10- to 100-fold surplus of any other amino acid has been considered as the most abundant amino acid [21,22].

The ternary Cu(His)(Gln) and binary bis(glutaminato)copper(II) [Cu(Gln)2] compounds were experimentally studied in aqueous solutions by calorimetric [[23], [24], [25], [26], [27]], potentiometric [[23], [24], [25], [26],[28], [29], [30], [31], [32], [33], [34]], polarographic [35,36], and spectroscopic [26,31,33,[35], [36], [37], [38]] methods. Deschamps et al. studied the copper(II)/Gln [35] and copper(II)/Gln/His [36] systems in aqueous solutions using polarography, the ultraviolet/visual (UV/VIS) and electron paramagnetic resonance (EPR) spectroscopy for physiochemical characterization of Cu(His)(Gln) as a potential drug for the treatment of Menkes' disease. The UV/VIS absorption spectra investigated over a large pH range (3 < pH < 10) indicated that Cu(Gln)2 was the major species above pH 6 [35]. The polarographic analysis of Cu(II) aqueous solution with excess of Gln ligand (from 1:10 to 1:70) also showed only Cu(Gln)2 at physiological pH 7 [35]. The polarographic analysis of a copper nitrate solution with His and Gln in a 1:10:10 M ration at pH 7 showed the Cu(His)(Gln), Cu(His)2, and [Cu(His)2(OH)] species to coexist in the same mixed solution at physiological pH, which led to the suposition that the presence of the latter two compounds in the same solution would disable the pharmaceutical formulations of single Cu(His)(Gln) in aqueous solutions [36].

For Cu(Gln)2 in aqueous solutions, the thermodynamic parameters (the Gibbs free-energy change, ΔG, and corresponding enthalpy, H, and entropy, S, contributions) were determined by calorimetric studies [[23], [24], [25], [26], [27]]. The stability constants (log β) of Cu(Gln)2 [23,[25], [26], [27], [28], [29], [30], [31]], Cu(His)2, [[29], [30], [31],39], and Cu(His)(Gln) [23,[31], [32], [33]] were measured in aqueous solutions at different ionic strengths and temperatures using potentiometric titrations [23,34]. The log β of Cu(Gln)2, Cu(His)2, and Cu(His)(Gln) determined under blood plasma conditions of temperature and ionic strength (37 °C, 0.15 M) in an unreactive NaClO4 electrolyte are: 13.586(21) [29], 17.498(21) [29], and 16.703(6) [32], respectively. Hence, the stability constant of the ternary Cu(His)(Gln) is larger than that of the parent Cu(Gln)2. Generally, Cu(His)(aa) stability constants are greater than the values statistically estimated by means of the stability constants of the parent binary compounds [31,33,40,41]. Suggestions which structural properties might produce this enhanced ternary-complex stability include an increased entropy contribution to ΔG due to the copper(II) binding asymmetry [40], and inter-ligand hydrogen-bond interactions between side-chain polar groups, which were assumed to be a factor governing the preferential formation of ternary complexes [33]. However, the stability constants do not reflect significantly the effects of the ligand-ligand interactions as log β of the ternary Cu(His)(aa) species with amino acids having either polar or nonpolar side chains are very close to each other [33]. Bexter and Williams suggested that a greater –ΔG for Cu(His)(Asn) came from the possibility that the ternary-complex formation liberated more water from the solvation sphere of the copper(II), and thus increasing ΔS, but decreasing –ΔH due to more broken aquation bonds [41]. The density functional theory (DFT) conformational analyses performed by us for Cu(His)2 [42], Cu(Thr)2 [43], Cu(His)(Thr) [44], Cu(Asn)2 [45], and Cu(His)(Asn) [45] in aqueous solution revealed that both intra- and inter-ligand hydrogen bonds could be the stabilizing factor, and that the ternary compounds had greater conformational flexibility than the parent binary compounds [44,45]. Considering the results that the ternary Cu(His)(aa) compounds in blood plasma are generally more abundant than the binary compounds [19], we hypothesized that an extent of conformational flexibility and abundance of Cu(His)(aa) in blood plasma might be interrelated [44,45].

The supposed significance of the conformational flexibility for the exchangeable-bound blood-plasma Cu(His)(aa) components may be supported by a high conformational flexibility proposed for the NH2-terminus of the free SA protein based on the studies using nuclear magnetic resonance, EPR, visual spectroscopy, and the X-ray crystallography of SAs and model peptides having the NH2-terminus motif of the human SA, i.e., the Asp-Ala-His sequence [46,47]. Namely, the NH2-terminus showed no defined structure, and could accommodate for binding specifically Cu(II) by four nitrogen atoms in a plane, as well as for releasing the metal with appropriate ligands [46]. The study of Cu(II)-binding affinities for SA in the presence of competing Cu(II)-binding ligands including His at pH 7.4 showed a fast Cu(SA) demetallation by His (half-life of approx. 1–2 min); a ternary Cu(SA)(His) was supposed to form and act as a ligand-exchange complex which increased the rate of copper release [18]. The studies of Cu(AS)(His) by equilibrium dialysis, absorption spectroscopy and potentiometric titration at pH 7.5 also suggested that the copper(II) exchange between Cu(SA) and Cu(aa)2 was mediated through a ternary Cu(SA)(His) complex [48,49]. This catalytic effect of enhancing the rate of the copper transfer between Cu(SA) and other proteins was found to be specific for His [18]. Therapies based on the copper(II)-His supplementation administered subcutaneously are operative in the treatment of Menkes' disease [50]. The following reactions between copper(II), SA, and His were suggested by in vitro kinetic analyses of copper(II) transport from plasma to rat liver cells: at physiological concentrations, SA inhibited copper(II) uptake by the cells via binding copper(II) and reducing the concentration of free Cu(II) ions in solution; by competing for the copper(II), His mobilized the copper(II) from SA and formed Cu(His)2, which interacted with hepatic copper transport protein, and this protein transported copper ions to the cell [51].

Structure data of Cu(His)(Gln) and Cu(Gln)2 in solutions are rare. For Cu(Gln)2, reliable structural values were obtained by X-ray absorption only for the CuN and CuO distances [(1.96(1) Å] [35]. The EPR spectra obtained separately of Cu(Gln)2, and the Cu(II)/His/Gln mixture in a 1:1:1 M ratio, from a 50% v/v glycerol-water frozen solution (T = 80 K) at pH 7 [35,36] suggested a CuN2O2 coordination and a distorted octahedral geometry of Cu(Gln)2 [35], and an elongated axial geometry with an equatorial N3O copper(II) coordination of Cu(His)(Gln) [36]. Both trans and cis isomers of Cu(Gln)2 were identified by EPR to coexist in a D2O solution at room temperature [37,38].

To complement the experimental findings, this paper computationally investigates the structural properties of Cu(Gln)2 and Cu(His)(Gln) in the gas phase and implicitly modeled aqueous solutions using density functional B3LYP calculations without and with dispersion correction (B3LYP-D). To evaluate if the low-energy conformers are accurately described, the performance of B3LYP and B3LYP-D approaches is corroborated by the high-level domain-based local pair natural orbital implementation of coupled cluster singles doubles and perturbative triples [DLPNO-CCSD(T)] [52,53] calculations. The reliability of predicted low-energy aqueous structures is examined by comparing the DFT calculations of magnetic parameters with the values obtained from the experimental EPR spectra. The X-ray crystal and molecular structure of Cu(Gln)2 [54] is geometry optimized to examine whether noncovalent interactions simulated by implicitly modeled water medium can cause the same effect on the geometry as the crystal lattice effects did. The aim of this study is to gain structural properties and information on effects of intra- and intermolecular interactions on the coordination modes and geometry of physiologically important Cu(aa)2 as part of their physicochemical characterization for potential pharmacological activity and use.