Chapter 4. Development of Novel Solid-electrolyte Material
4.3 G-quadruplex with Various Cations as Single-ion Conductor
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and EM+ is non-bonding energy of the central cation. Subsequently, the formation energy was compared by getting relative energy based on the lowest value among all Efor values (Fig. 4.9a-c). Note that relative energy landscape for LiGQ system was exhibited in Fig. 4.3b. To analyze the effect of central cation central toward ion migration behavior at G-quadruplex ion channel, G-quadruplex ion channel structure with 12 G-quartet layers were constructed. Following the thermodynamically favorable stacking sequence which was previously found, 12 cation-centered G-quartets were stacked into 100 Å
× 100 Å × a Å (a = 12 × optimal stacking distance for each central cations) sized unit cell. To relax the G-quadruplex structure, geometry optimization was carried out until the convergence criteria (1000 kJ·nm mol–1 for the maximum energy change) were satisfied. To calculate energy profile at ion migration inside G-quadruplex channel, interaction energy between cation and G-quadruplex channel was measured, by moving cations in ion channel by 1/10 stacking distance. Then, relative interaction energy at each point was estimated to exhibit energy profile upon ion migration. Furthermore, the non- bonded terms of interaction energy at each point were deconvoluted into electrostatic and van der Waals energy terms, to analyze ion migration behavior more specifically.
Figure 4.9 Contour plot of relative formation energy, with every possible combination of variables for central cation (a) Na+, (b) K+ and (c) Mg2+.
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4.3.2 Results and Discussion
Evidently, the central cation species may play a crucial role in determining the structural parameters of the G-quadruplex, i.e., a different central cation induces electrostatic potential change at the quartet center, which can manipulate the potential energy surface for ion migration. To provide a comprehensive understanding of the effect ofthe central cation on the structure of the G-quadruplex at the molecular level and the cation migration behavior of the complex, a molecular mechanics simulation was conducted. The main factors governing the structure of the G-quartets and their stacking sequence were the valence of the cation and its ionic radius. Therefore, we first investigated the effect of the valence of the cations on the G-quadruplex structure (Fig. 4.10a). The electrostatic interaction between the central cation and an oxygen atom in the carbonyl group of a guanine in Y2 can be relatively weaker for monovalent cations compared to divalent cations. Thus, the distance between the central cation and Y2 motif was estimated to be longer for the monovalent cations than the divalent cations (i.e., Li+, Na+: 2.1−2.2 Å, K+ 2.8 Å, Mg2+: 1.97 Å) in the thermodynamically favorable structures. Due to the long distance, the G-quadruplex with the monovalent cations had enough space for forming HBs between the Y2 molecules at two positions, which are denoted as inner HB (HB between N1–H and carbonyl oxygen) and outer HB (HB between N2–H and N7) in Fig. 4.10a. Conversely, the G-quadruplex with the divalent cations had a narrow space between the central cation and Y2 molecules. Thus, only one type of HB could be formed between N1–H and N7 in this case. The effect of the ionic radius on the coordination properties of the cations in the G-quadruplexes was examined, as shown in Fig. 4.10b. In the thermodynamically favorable structures, the cations with a small ionic radius (i.e., Li+, Na+, and Mg2+) are positioned at the intraplane of the G-quartet and are coordinated by four carbonyl oxygens.
Conversely, in case of K+ with a large ionic radius, the cation is placed at the interplane position of the G-quartets and coordinated by eight carbonyl oxygens. This is because the large ionic radius of the K+ ion induces strong van der Waals repulsion when it is located at the intraplane of the G-quartet, which cannot be compensated by electrostatic attraction.
The HB characteristics of the G-quartets and coordination structure of the G-quadruplexes vary considerably according to the type of the central cation, which eventually affects the potential energy landscape for ion conduction through the G-quadruplexes. To compare the ion migration behaviors, we calculated the relative energy profiles for the ion position in the G-quadruplexes (Fig. 4.10c). The lowest energy was denoted as zero energy for each cation; therefore, the highest relative energy can be regarded as the ion migration barrier, which the cations must overcome in the process of ion migration though the central cation-induced channel in the G-quadruplex. From the profiles, the magnitude of the ion migration barrier was as follows: Li+ < Na+ < K+ Mg2+. The cations with a small ionic radius (i.e., Li+, Na+, and Mg2+) are the most stable when they are located at the intraplane of the G-quartet. Thus,
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assuming the relative ion position at the center of two neighboring G-quartets as 0.0 and 1.0, as depicted in Fig. 4.10b, the cations have the lowest energy at the relative ion positions of 0.0 and 1.0, with the ion migration barrier at the interplane position. Moreover, in case of K+, the ion is most stable at the interplane position. Accordingly, K+ has the lowest energy at the relative ion position of 0.5 with the ion migration barrier at both ends (at the center of the G-quartets). For a deeper understanding of the potential energy surface for ion migration, the relative energy profiles in Fig. 4.10c were deconvoluted into two elements: those originating from the electrostatic interaction (Fig. 4.10d) and the relative energy of the van der Waals interaction (Fig. 4.10e). In terms of electrostatic interaction, all the cations showed the lowest energy at the intraplane position because electrostatic interaction is stabilized at this position due to the short distance between the cations and dipoles at the carbonyl oxygens in the Y2 molecules. The stabilization effect of electrostatic interaction was the strongest for Mg2+ caused by a greater coulombic charge than the monovalent cations, which induces a stronger electrostatic attraction between the central cation and Y2 molecules. Because the overall energy is the sum of two elements, the exceptionally strong electrostatic interaction of Mg2+ governs the overall energy profile, leading to the greatest ion migration barrier at the interplane region. In terms of van der Waals interaction, all the cations showed the lowest energy at the interplane position. This is due to the stronger van der Waals repulsion between the cations and G-quartets at a closer position. Particularly, K+ exhibits a large van der Waals repulsion between the K+ and G-quartets due to the larger ionic radius of K+ compared to the other cations. The large van der Waals repulsion of K+ dominates the overall energy profile, thereby forming an ion migration barrier at the intraplane position despite the stronger electrostatic attraction compared to the other monovalent ions. The coordination structure of K+ is determined due to the same reason. Conclusively, we could identify the factors governing the shape and stacking sequence of the G-quadruplexes with different central cations and energy profiles for ion conduction through the G- quadruplexes in terms of intermolecular interactions based on theoretical analysis.
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Figure 4.10. Structural variations between the G-quadruplexes in terms of (a) the number of valence electrons and (b) ionic size, and (c) the ion conduction barrier of the G-quadruplexes, which can be affected by (d) the electrostatic and (e) Van der Waals interactions of G-quadruplexes.
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