Molecular models
A likely structure of arabinoxylans in finger millet was proposed by Subba Rao & Muralikrishna21 following the isolation of purified arabinoxylans from finger millet through a series of methods—methylation, 13C NMR, 1H NMR, FTIR, GLC-MS, oligosaccharide analysis, periodate oxidation and Smith degradation. They revealed that the backbone of the structure was a β-d (1-4)-xylan, with arabinose residues being both mono- and di-substituted at the C3 and C2 positions of the xylose sugar rings. Additionally, the study indicated that the majority of arabinose substitutions were mono substitutions at the C3 position, while the prominence of doubly substituted arabinose was low21. The presence of uronic acid residues, found to be glucuronic acid substituted at the C2 position of the xylose rings, was also detected.
Three simplified variations of the models proposed by Subba Rao & Muralikrishna21 were created using CrystalMaker®45 as seen in Fig. 1a–c. Geometry optimisation using CASTEP29 followed, to create highly accurate representations of the arabinoxylan structures. The first model (Fig. 1a) featured the xylan backbone with an arabinose residue substituted at the C3 position of the xylose ring. The second model (Fig. 1b) featured the xylan backbone with both an arabinose residue and a glucuronic acid residue substituted at the C3 and C2 positions of the xylose rings, respectively. The final model (Fig. 1c) featured the xylan backbone with two glucuronic acid residues substituted at the C2 positions of the xylose rings. From here on, these structures will be referred to as PolyXA (Fig. 1a), PolyXGA (Fig. 1b) and PolyXGG (Fig. 1c).
a PolyXA arabinoxylan consisting of the xylan backbone with one arabinose residue. b PolyXGA arabinoxylan consisting of the xylan backbone with one arabinose and one glucuronic acid residue. c PolyXGG arabinoxylan consisting of the xylan backbone and two glucuronic acid residues. Carbon atoms are shown in black, hydrogen in pink and oxygen in red. Residues (arabinose (A) and glucuronic acid (G)) are also labelled.
All systems were optimised in a fully charge-saturated state. To this end, glucuronic carboxylic acid groups were deprotonated, as were hydroxyl groups if required. For the PolyXA system, hydroxyl ions on the arabinose and xylan backbone were deprotonated, while for the PolyXGA systems, hydroxyl hydrogen atoms were removed solely for the +2 cations (Ca2+, Mg2+). However, it should be noted that these OH groups are unlikely to be deprotonated either in the growing millet or within the gastrointestinal tract. By contrast, with a pKa of 2.9328, the glucuronic carboxylic acid groups are expected to be fully deprotonated under the same conditions. In this respect, the PolyXGG systems represent the most realistic structures for the doubly charged cations, although it should be noted that quantum mechanical calculations rarely return atomic charges that correspond exactly to the assumed electronic model.
Cation interaction with the PolyXA structure
Binding sites
The removal of a hydrogen atom from O2 (Fig. 2) formed an RCO– group, which proved to be a stable binding position for both the K+ and Ca2+ ions following geometry optimisation (Fig. 2a, b). In the K+ PolyXA complex, the K+ ion also formed a bond with the hydroxyl group of the xylan backbone (Fig. 2a), while the Ca2+ ion formed a second ionic bond to the deprotonated OH group of the xylan backbone (Fig. 2b). The observations of the preferential binding positions for K+ and Ca2+ ions were coherent with other studies. Sharma et al.46 analysed the interaction of mono and divalent metal ions with fructose using DFT, and revealed that hydroxyl groups acted as the preferred binding sites for the metal ions. A review on calcium-carbohydrate complexes also showed the ability of calcium ions to bind to multiple oxygen atoms within a polysaccharide complex47. From Fig. 2c, it is clear that Zn2+ ions do not bind to the PolyXA structure. This result differs from previous work by Sharma et al.46, who revealed that zinc was capable of binding to hydroxyl groups of other sugar molecules such as α-fructose and β-fructose.
a K+, b Ca2+ and c Zn2+. Ionic bonds to the cations are shown with dotted lines and populations are marked. Atoms with a formal charge are marked with an asterisk (*). Calcium is shown in blue, potassium in purple, zinc in grey, oxygen in red, carbon in black and hydrogen in pink.
Bond architecture
The coordination number (CN) for both K+ and Ca2+ions was found to be 2 (CN = 2), both bonds being to oxygen atoms. This is expected given that there are no other accessible oxygen atoms surrounding the potassium and calcium ions besides O20 and O2 (Fig. 2). This result aligns well with the work of Sharma et al.46 who showed that both potassium and calcium ions were bi-coordinated to two hydroxyl groups of α-fructose and β-fructose, in a coordination geometry that is similar to those of Fig. 2a, b.
Shannon & Prewitt48 provided a set of effective ionic radii that serve to study bond lengths between cations and oxygen. For the ions considered in this study, the ionic radii trend follows K+(1.38 Å) > Ca2+ (1.00 Å) > Zn2+(0.60 Å). Here, the average bond length of the K+-oxygen bond is 2.505 Å, which is greater than the average bond length of the Ca2+-oxygen bond (2.024 Å), following the trend in ionic radii. Tehrani et al.49 revealed that when potassium was involved in a bidentate bond with oxygen in sugar molecules, bond lengths ranged from 2.45 to 2.69 Å, a result that is representative of the present study.
The bond length between K+-O2 (2.298 Å) is shorter than the bond length between K+-O20 (2.711 Å), which is to be expected given the formal charge of O2 and its increased electronegativity. The bond lengths of Ca2+-O2 (2.045 Å) and Ca2+-O20 (2.003 Å) are comparable, which is also expected given that the calcium ion was bonded to the same RCO– functionality.
Mulliken bond populations (Fig. 2) suggest that all cation-oxygen bonds are ionic, as defined by cation-oxygen bond populations <0.4 |e|. The weak bond populations of the K+-O bonds (0.01 |e| and 0.02 |e|), are considerably smaller than the average bond population of Ca2+-O (0.30 |e|). This can be explained by the greater charge density of Ca2+ compared to K+, resulting in considerably stronger electrostatic forces of attraction with the oxygen atom.
Thermodynamic stability
The thermodynamic stabilities of the resulting complexes were determined by calculating the formation energy (Eq. 1, Table 1). It is evident that calcium (Ef = −1.06 eV) formed the most stable structures with PolyXA, followed by potassium (Ef = −0.19 eV). The zinc complex, however, remained thermodynamically unfavourable (Ef = 4.85 eV). Given that the charge density trend follows the order of Zn2+ > Ca2+ > K+, it is evident that the stability of the resulting cation-arabinoxylan complex is not solely due to charge density factors. Debon & Tester50 noted that zinc ions have no affinity for neutral polysaccharides. However, the removal of hydrogen atoms from the O2 and O20 atoms presented two RCO− groups that might have been expected to bind to the positive zinc ion if charge density alone were the driver for chemical bonding. Therefore, it is necessary to consider other factors such as effective ionic radius, that can have an effect in determining the stability of the resulting cation-arabinoxylan complex. This will be discussed further in the following sections.
Cation interaction with the PolyXGA structure
Binding sites
In the PolyXGA structure, the removal of hydrogen atoms from O28 and O4 created adjacent RCOO– and RCO– groups, which provided a stable binding pocket for both the Ca2+ and Zn2+ ions (Fig. 3b, c). In the K+ PolyXGA complex, the RCOO– group provides the stable binding site (Fig. 3a), with the only bond to K+ formed in this group. It should be noted that the deprotonation of the RCOOH group of glucuronic acid results in charge resonance effects upon optimisation, such that both oxygen atoms in this group have almost equal charge. These observations corroborate the DFT work of Hills et al.51 who revealed that the RCOO– and hydroxyl groups were favourable binding positions for mono and divalent metal ions (Na+, Ca2+, Mg2+) within bacterial alginate (mannuronate-guluronate) extracellular matrix complexes. Furthermore, Agulhon et al.30 demonstrated, also through a DFT study, that transition metals bonded to the hydroxyl or RCOO– groups in metal-diuronate complexes.
a K+, b Ca2+ and c Zn2+. Ionic bonds to the cations are shown with dotted lines and the one covalent bond from Zn2+ to O4 is shown as a solid green line. Atoms with a formal charge are marked with an asterisk (*). Note that due to resonance effects, the formal charge has become equally split between O27 and O28 upon optimisation. Bond lengths and populations are provided in Table 2. Calcium is shown in blue, potassium in purple, zinc in grey, oxygen in red, carbon in black and hydrogen in pink.
Bond architecture
Bond populations and lengths are shown in Supplementary Table 1. K+ was bonded to just one oxygen atom in the PolyXGA complex (CN = 1), making this the lowest CN when compared to Ca2+ (CN = 5) and Zn2+ (CN = 4). While the Zn2+ ion has a greater charge density than the Ca2+ ion, the difference in CN between the two cations can be explained by their respective sizes (ionic radii of Ca2+ > Zn2+), whereby larger cations are able to form more bonds within complexes52. Hills et al.51 also noted that alkaline earth ions were capable of forming five or six bonds with oxygen atoms of hydroxyl and carboxylate groups in other (alginate) polysaccharides, a result that was mirrored in the present study.
The bond length of the K+-oxygen bond was 2.634 Å, which is greater than the average bond length of the Ca2+-oxygen bonds (2.364 Å) and Zn2+-oxygen bonds (2.040 Å). The differences in bond lengths can be explained by charge density where Zn2+ > Ca2+ > K+, and a greater charge density would result in stronger electrostatic forces of attraction with the oxygen atom, and hence, a shorter bond length49. Agulhon et al.30 reported DFT-calculated average bond lengths of Ca2+ to oxygen of around 2.4 Å, which are very similar to the results presented here. Earlier, using X-ray diffraction, Bugg53 reported that the bond lengths of calcium to oxygen were between 2.38 to 2.54 Å in a calcium-lactose complex. Moving to the zinc-oxygen bonds, in two alternative saccharide monomer complexes (α-fructose and β-fructose), calculated using DFT, Zn2+-oxygen distances were found to be in the region of 2.0 Å. These previous results correspond well with the results presented here.
In the PolyXGA-calcium system, the bond length of Ca2+-O28 (2.384 Å) was similar to that of Ca2+-O27 (2.355 Å), despite O28 being the formally charged atom. This can be explained by resonance effects at the RCOO– group, where the delocalisation of electrons has resulted in the negative charge being shared between the O28 and O27 atoms. The bond lengths of the Ca2+-RCOO− bonds were, however, greater than the bond length between Ca2+-O4 (2.056 Å). This suggests that the interaction between Ca2+ and the RCO– functionality of the arabinose residue was stronger than the RCOO− functionality of the glucuronic acid residue. The favouring of the monodentate (RCO– group) over the bidentate (RCOO−) bond was also seen with Zn2+, where the shortest bond length between Zn2+ and oxygen was between Zn2+ and O4 (1.82 Å). Once again, this suggests that the RCO– functionality interacted most strongly with the cations. By contrast, Hills et al.51 noted that the cation and RCOO− interactions in models of Pseudomonas aeruginosa bacterial alginate were the strongest and formed the shortest bonds compared to other oxygen groups. However, it should be noted that at physiological pH, the arabinose RCOH group would not be expected to be deprotonated. This is further explored in the PolyXGG section below.
Mulliken bond populations (Supplementary Table 1) suggest that all cation-oxygen bonds are ionic, except for the Zn2+-O4 bond (0.49 |e|). The ability of zinc to form covalent bonds with oxygen was also highlighted by Agulhon et al.30, who showed that both zinc and a number of transition metals, were able to form covalent bonds with oxygen in cation-sugar complexes. The bond population of the K+-O bond (0.01 |e|) is much weaker than the average bond population of both the Ca2+-O bonds (0.12 |e|) and the Zn2+-O (0.22 |e|) bonds, due to the greater charge densities of Zn2+ and Ca2+.
Thermodynamic stability
The thermodynamic stabilities of the resulting complexes (Table 1) were determined by calculating the formation energy (Eq. 1). It is evident that Ca2+ ions (Ef = −2.96 eV) formed the most stable structures with PolyXGA followed by K+ (Ef = −1.49 eV), which is also thermodynamically stable, and Zn2+ (Ef = 0.62 eV), which is unfavourable. A study by Hills et al.51 also revealed that Ca2+, compared to other mono (Na+) and divalent (Mg2+) cations, formed the most stable complexes amongst bacterial alginates. Given that the charge density of Zn2+ ions is greater than both potassium and calcium ions, one would expect Zn2+ to have formed the most stable complexes. Therefore, it is evident that the stability of the resulting cation-arabinoxylan complex is not solely due to charge density factors. Steric factors appear to play a much greater role; due to their smaller size, zinc ions have to get closer to other atoms or groups to be within the bond-forming range, which limits the number of bonds that can be formed. Therefore, it is likely that the zinc ions have to induce greater torsional changes in the PolyXGA structure to create stable chelation sites for binding, which results in an unstable complex.
Cation interaction with the PolyXGG structure
Binding sites
The deprotonation of O24 and O31 atoms created two adjacent RCOO– groups, which formed a stable binding position for both the potassium and calcium ions (Fig. 4a, b). For charge balance, two potassium ions were included in this simulation. In the potassium PolyXGG complex, the RCOO– and hydroxyl groups provided a stable binding position for the K1 ion, while the K2 ion failed to bind despite being situated in a similar environment. As for calcium, the RCOO– groups alone were involved in bonding. Similar observations were noted by DeLucas et al.54 where, using X-ray diffraction, the carboxyl and hydroxyl groups of glucuronate residues were bonded to the calcium ions. Hills et al.51 also demonstrated that cations were capable of forming bonds to two RCOO– groups in a cross-linked alginate complex. Additionally, Saladini et al.55 stated that in sugar acids, the oxygen from both the carboxylic and hydroxyl functionality were involved in the binding of cations. The observations from previous studies align well with the data of the present study.
a K+, b Ca2+ and c Zn2+. Ionic bonds to the cations are shown with dotted lines. Atoms with a formal charge are marked with an asterisk (*). Note that due to resonance effects, upon optimisation, the formal charge has become equally split between O23 and O24, and O30 and O31. Bond lengths and populations are provided in Supplementary Table 2. Calcium is shown in blue, potassium in purple, zinc in grey, oxygen in red, carbon in black and hydrogen in pink.
From Fig. 4c, it is clear that Zn2+ does not bind to the PolyXGG structure. However, Saladini et al.55 showed that zinc ion was capable of forming complexes with other sugar acids such as galactaric acid and d-aldonic acid.
Bond architecture
In the K+ PolyXGG complex, the CN for K1 is 4, while for K2, the CN is zero, with no bonds formed (Supplementary Table 2). This lack of binding to K2 is likely to be due to repulsive forces between the two potassium ions, preventing co-localisation within the binding pocket. It should be noted, however, that the bond populations are small for the K1-oxygen bonds, and even a minor deviation from an ideal position, results in non-bonding. The CN for the Ca2+ complex is also 4, but the bonding varies considerably between the two structures. In the K+ complex, the one bonding ion forms very weak ionic bonds (0.02 |e|) to one oxygen atom (O23, O30) of each of the deprotonated RCOOH groups on the adjacent glucuronic acid residues. Notably, although it was O24 and O31 that were the formally deprotonated oxygen atoms, following optimisation, and through the establishment of resonance effects, it is O23 and O30 that have the greater negative charge, −0.73 e (O23) compared to −0.67 e (O24), and −0.74 e (O30) compared to −0.69 e (O31). In addition, there are two slightly stronger hydrogen bonds from K1 to a ring oxygen (O25) and a hydroxyl oxygen (O27). Similarly, Tian et al.56 noted that, using FTIR, only one oxygen atom from each RCOO– group was involved in the bonding of K+ ions in a K+-galactarate complex. It is also evident that in this complex, the cation-RCOO− bonds are now shorter and stronger (in contrast to the PolyXGA system), which corresponds more closely to the results of Hills et al.51 who made the same observation in binding pockets composed of at least two carboxylic acid residues. In contrast to the K+ ions, the Ca2+ ion sits squarely in the binding pocket between the two adjacent RCOO– groups, bonding to all four oxygen atoms.
The bond lengths between the calcium ion and oxygen atoms were all within 0.12 Å of each other. This suggests that the interactions between Ca2+ ions and the oxygen atoms of the carboxylic functionality of the glucuronic acid residues were similar in strength. This result can once again be explained by the stabilisation of the RCOO– functionality due to positive steric effects with respect to the size of both the binding pocket and the Ca2+ ion. With regards to the K+ ions, it is interesting to note that although no bonding is predicted to K2 (using Mulliken population analysis), it is nevertheless residing in the vicinity of the second RCOO− group, as illustrated in Fig. 5. It seems likely that the energetics of this position are very similar to that of K1, and the formation energy for the complex overall (−3.82 eV) does indeed suggest favourable binding positions for both ions. It should also be noted that with the two glucuronic acid residues, the K+ now forms its strongest (and shortest) bonds (see Supplementary Table 2).
The Mulliken-predicted bonds to K1 are shown as blue dotted line, and bond distances (not predicted as bonding) to K2 are shown with red dotted lines.
Mulliken bond populations suggest that all cation-oxygen bonds are ionic. The average bond population of K+-O is 0.04 |e|, which is significantly smaller than the average bond population of the Ca2+-O bonds (0.08 |e|). This is expected given that the charge density of Ca2+ is greater than K+, resulting in stronger electrostatic forces of attraction with calcium ions. However, in bacterial alginates (mannuronate/guluronate polysaccharides) average Ca2+-oxygen bond populations as high as 0.14 |e| have been observed51. These higher bond populations were found in binding sites that encompassed not just carboxylic acid groups, but a wider range of oxygen functionality, including hydroxyl and ring oxygen atoms51.
Thermodynamic stability
From Table 1, it is clear that both potassium (−3.82 eV) and calcium (−2.99 eV) formed thermodynamically stable structures with the PolyXGG motif. This is in contrast to zinc (4.82 eV), which proved highly unstable. Given that the charge density trend follows Zn2+ > Ca2+ > K+, it might have been expected that zinc would form the most stable complex within the PolyXGG complex. Indeed, Gianguzza et al.57 indicated that in glucuronate complexes, Zn2+ formed the most stable complex compared to Ca2+ and Na+. Equally, based on charge density arguments alone, Ca2+ ions should have formed more stable complexes with the arabinoxylan structure than potassium ions. However, the lack of stability in zinc binding can be explained using steric factors. Due to its smaller size, Zn2+ ions require a greater torsional change of the PolyXGG backbone structure to create favourable binding sites. K+ and Ca2+ clearly have better steric compatibility with the glucuronate-glucuronate binding pockets likely to be found within finger millet.
