C.
Nieuwland
a,
F.
Zaccaria
a and
C.
Fonseca Guerra
*ab
aDepartment of Theoretical Chemistry and Amsterdam Center for Multiscale Modelling, AIMMS, Vrije Universiteit Amsterdam, De Boelelaan 1085 NL-1081HV Amsterdam, The Netherlands. E-mail: c.fonsecaguerra@vu.nl
bLeiden Institute of Chemistry, Leiden University, Einsteinweg 55 NL-2333 CC Leiden, The Netherlands
First published on 10th September 2020
To gain better understanding of the stabilizing interactions between metal ions and DNA quadruplexes, dispersion-corrected density functional theory (DFT-D) based calculations were performed on double-, triple- and four-layer guanine tetrads interacting with alkali metal cations. All computations were performed in aqueous solution that mimics artificial supramolecular conditions where guanine bases assemble into stacked quartets as well as biological environments in which telomeric quadruplexes are formed. To facilitate the computations on these significant larger systems, optimization of the DFT description was performed first by evaluating the performance of partial reduced basis sets. Analysis of the stabilizing interactions between alkali cations and the DNA bases in double and triple-layer guanine quadruplex DNA reproduced the experimental affinity trend of the order Li+< Rb+ < Na+ < K+. The desolvation and the size of alkali metal cations are thought to be responsible for the order of affinity. Nevertheless, for the alkali metal cation species individually, the magnitude of the bond energy stays equal for binding as first, second or third cation in double, triple and four-layer guanine quadruplexes, respectively. This is the result of an interplay between a decreasingly stabilizing interaction energy and increasingly stabilizing solvation effects, along the consecutive binding events. This diminished interaction energy is the result of destabilizing electrostatic repulsion between the hosted alkali metal cations. This work emphasizes the stabilizing effect of aqueous solvent on large highly charged biomolecules.
However, in order to rationally design these so-called GQ-ligands, it is crucial to fully understand the physical principles behind the formation of GQs and the role of the alkali cations in the stabilization of these structures.
Previous work by Fonseca Guerra et al.13,14 has shown that the hydrogen bonding in G4 relies on cooperativity. These synergistic effects originate from charge separation occurring upon hydrogen bonding, due to donor–acceptor interactions of the σ-electron system.15 It contradicts previous assumptions that the enhancement of the hydrogen bonds was solely caused by resonance of the π-electrons. In addition, Fonseca Guerra and co-workers demonstrated that although the presence of alkali metal cations between the G4 layers weakens the hydrogen bonds, the synergy remains in telomeric structures.16–19
The alkali metal cation that is located between two quartets was long believed to generate cation–dipole interactions with the eight interacting guanines and thereupon reducing the repulsion of the central oxygen atoms.20–22 This would enhance the hydrogen bonding strength and stabilize the GQ formation. This idea was rationalized by the presence of significant negative charge located at the central cavity of the G4.21 In 2016, work by Zaccaria et al.23 revealed that the central cation is not needed to reduce repulsion between the oxygen atoms, but rather provides additional stability of the quadruplex by electrostatic and donor–acceptor interactions between the oxygens and the cation. Later work showed that inclusion of the metal cation into the quadruplex significantly lowers the Gibbs free energy of formation of the cationic species compared to the formation of the empty scaffold.24 This led to the insight that the actual need for the cation is to overcome the entropic penalty.
Guanine quadruplexes can host different alkali metal cations, and many experimental studies have revealed an overall affinity sequence of K+ > Na+, Rb+ ≫ Li+, Cs+ in water.25–27 Research has been devoted to finding an explanation of this affinity trend.28–30 Williamson et al.28 suggested in 1989 that the overserved ion specificity was related to the snug fit of the alkali cations into the cavity of the quadruplex, thus the size of the cations. Later, Hud and co-workers30 claimed that the Gibbs free energy of solvation of the alkali metal cations was the determining factor, since cations have to be desolvated completely before they can access the inner channel of GQs. This idea was supported by the theoretical work of Gu and Leszczynski.29
Zaccaria et al.23 showed that both the ionic radius, as well as the Gibbs free energy of solvation, are of equal importance in determining the order of cation affinity in GQ structures. These results were obtained from extensive computational analysis of the electronic properties of double-layer GQ structures interacting with the different alkali metal cations. These computations were based on dispersion-corrected density functional theory (DFT-D).31–36 The study of Zaccaria and co-workers involved double-layer quadruplexes (Fig. 1c). However, natural occurring GQ structures can be encountered as multiple stacks of G4.4,7,37 Therefore, we have investigated if our previous results and conclusions can be extended to larger systems which include interactions between adjacent cations.
In this work we investigate the electronic interactions of double, triple and four-layer GQ structures (with and without sugar-phosphate backbone) with the different alkali metal cations in aqueous solution by computational analysis using DFT-D based calculations. To facilitate the computations on these significant larger systems, optimization of the DFT description was performed at first by evaluating the performance of partial reduced basis sets. In case of the triple-layer systems, the computational geometries involve quadruplex structures occupied by one potassium cation, to which a second alkali metal cation is introduced. The four-layer GQ comprises a structure hosting three potassium cations. The calculations simulate the situation of quadruplexes under supramolecular and biological conditions in aqueous solution.
No geometrical constraints were imposed on the optimized geometries. This also applied to the guanine quadruplexes without backbone (129 atoms (2-layer), 194 atoms (3-layer) and 259 atoms (4-layer)) and the guanine quadruplex with backbone (265 atoms (2-layer) and 402 atoms (3-layer)). The guanine quadruplexes in this work are parallel stranded righthanded GQ structures with anti-glycosidic torsion angles at all guanines. Biological GQ structures are also constituted by loop regions with dangling nucleobases. However, dangling nucleobases do not have significant influence on binding properties of the shielded interior of the quadruplex and are therefore omitted in the model systems.
Optimized geometries of the double-layer GQ structures at the ZORA-BLYP-D3 (BJ)/TZ2P level of theory of Zaccaria et al. were used as starting point for the calculations of the triple-layer systems.23,24 Solvent effects in water have been taken into account with the conductor-like screening model (COSMO), as implemented in the ADF program.36,44–46 Radii of the cations have been determined by reproduction of the solvation energy of the cation according to the procedure presented in ref. 36 (see ESI,† Table S1). In ADF releases after ADF2016 an improved method to construct the solvation surface in COSMO (Delley cavity construction instead of the Solvent-Excluding-Surface (SES) method) was implemented that led to more reliable geometry optimizations when using the COSMO solvation model.40 To compare the results of the double-layer quadruplexes with the triple-layer systems, the results of Zaccaria et al. were reproduced using the improved solvation model. Energies regarding the double-layer GQs where calculated as formulated by Zaccaria and co-workers.23
The energy of formation, ΔEform, of the triple-layer guanine quadruplex structures is defined by eqn (1a) and (1b), for the GQ without and with sugar-phosphate backbone, respectively (see also Fig. 2).
ΔEform = E(G4–K+–G4–M+–G4) − 12·E(G) − E(K+) − E(M+) | (1a) |
ΔEform = E(GQ–K+–M+) − 4·E(GGG) − E(K+) − E(M+) | (1b) |
Fig. 2 Definition of the formation energy (ΔEform) of the triple-layer guanine quadruplex structures without (G4, top scheme) and with sugar-phosphate backbone (GQ, bottom scheme). |
ΔEbond = E(G4– K+–G4– M+–G4)aq − E(G4–K+–G4–[ ]–G4)aq − E(M+)aq | (2a) |
ΔEbond = E(GQ–K+–M+)aq − E(GQ–K+–[ ])aq − E(M+)aq | (2b) |
In order to understand the different components that determine the trend in bond energy (i.e. cation affinity) the bond energy was partitioned as formulated by eqn (3) (see also Fig. 3).
ΔEbond = ΔEdesolv + ΔEprep + ΔEint + ΔEsolv | (3) |
ΔEdesolv = E(G4–K+–G4–[ ]–G4)gas − E(G4–K+–G4–[ ]–G4)aq + E(M+)gas − E(M+)aq | (4a) |
ΔEdesolv = E(GQ–K+–[ ])gas − E(GQ–K+–[ ])aq + E(M+)gas − E(M+)aq | (4b) |
ΔEsolv = E(G4–K+–G4–M+–G4)aq − E(G4–K+–G4–M+–G4])gas | (5a) |
ΔEsolv = E(GQ–K+–M+)aq − E(GQ–K+–M+)gas | (5b) |
Finally, the interaction energy (ΔEint) can be computed in the gas phase for the geometries of the solvated state (eqn (6a) and (6b)).
ΔEint = E(G4–K+–G4–M+–G4)gas − E(G4–K+–G4–[ ]–G4)gas − E(M+)gas | (6a) |
ΔEint = E(GQ–K+–M+)gas − E(GQ–K+–[ ])gas − E(M+)gas | (6b) |
The interaction energy is further decomposed based on the Kohn–Sham molecular orbital theory using a quantitative energy decomposition analysis (EDA), which divides the total interaction energy (ΔEint) into electrostatic interaction (ΔVelstat), Pauli repulsion (ΔEPauli), orbital interaction (ΔEoi) and dispersion correction (ΔEdisp) components (eqn (7)).47
ΔEint = ΔVelstat + ΔEPauli + ΔEoi + ΔEdisp | (7) |
(8) |
TZ2P | TZP/DZ | |
---|---|---|
a The energies (in kcal mol−1) were computed with the DFT-D method at the ZORA-BLYP-D3(BJ) level of theory in the gas phase. b Average distance (in Å) between the oxygen atoms and the midpoint of the eight oxygen atoms. c Difference in the average z-coordinate (in Å) of the upper and lower oxygen atoms. d Average outer hydrogen bond distance N2(H)⋯N7 (in Å). e Average inner hydrogen bond dissonance N1(H)⋯O6 (in Å). f Average OPO angle (in degrees) of bridging two sugar molecules of the backbone. | ||
Calculated ΔEforma | −277.3 | −277.0 |
Relative average calculation time/geometry optimization cycle | 1 | 0.3 |
d[O–K+]b | 2.81 | 2.81 |
R | 3.12 | 3.11 |
N2(H)⋯N7d | 2.90 | 2.90 |
N1(H)⋯O6e | 2.81 | 2.80 |
∠OPOf | 107.0 | 106.1 |
System | M + | d[O–M+]b | R | N2(H)⋯N7d | N1(H)⋯O6e | ΔEforma |
---|---|---|---|---|---|---|
a All energies (in kcal mol−1) were computed with the DFT-D method at the ZORA-BLYP-D3(BJ)/TZP(/DZ) level of theory with COSMO to simulate water. b Average distance (in Å) between the oxygen atoms and the second alkali metal cation. For the empty cavities the midpoint of the eight adjacent oxygen atoms was taken. In the case of Li+ the average distance to the oxygen atoms is taken of the quartet where Li+ lies in the center. c Difference in the average z-coordinate (in Å) of the upper and lower oxygen atoms. d Average outer hydrogen bond distance N2(H)⋯N7 (in Å). This value is not presented in the case of Li+, since Li+ lies in the center of one of the quartets. e Average inner hydrogen bond dissonance N1(H)⋯O6 (in Å). | ||||||
G4–M+–G4 | No metal | 2.86 | 3.35 | 2.88 | 2.80 | −102.4 |
Li+ | 2.14 | 3.10 | — | — | −128.2 | |
Na+ | 2.68 | 2.90 | 2.85 | 2.81 | −144.1 | |
K+ | 2.81 | 3.23 | 2.88 | 2.82 | −144.3 | |
Rb+ | 2.94 | 3.56 | 2.90 | 2.83 | −137.7 | |
GQ–M+ | No metal | 2.92 | 3.57 | 2.89 | 2.81 | −83.2 |
Li+ | 2.12 | 3.41 | — | — | −109.3 | |
Na+ | 2.70 | 3.01 | 2.86 | 2.81 | −122.6 | |
K+ | 2.84 | 3.36 | 2.89 | 2.83 | −123.9 | |
Rb+ | 2.95 | 3.65 | 2.90 | 2.84 | −118.1 | |
G4–K+–G4–M+–G4 | No metal | 2.88 (2.80) | 3.42 (3.19) | 2.87 (2.87) | 2.80 (2.81) | −212.3 |
Li+ | 2.14 (2.81) | 3.06 (3.23) | — | — | −241.4 | |
Na+ | 2.67 (2.81) | 2.92 (3.32) | 2.83 (2.85) | 2.81 (2.82) | −255.8 | |
K+ | 2.82 (2.81) | 3.31 (3.27) | 2.85 (2.87) | 2.82 (2.83) | −255.3 | |
Rb+ | 2.94 (2.81) | 3.63 (3.23) | 2.86 (2.88) | 2.83 (2.83) | −247.2 | |
GQ–K+–M+ | No metal | 2.96 (2.84) | 3.68 (3.45) | 2.87 (2.86) | 2.81 (2.79) | −205.9 |
Li+ | 2.14 (2.84) | 3.35 (3.49) | — | — | −229.7 | |
Na+ | 2.71 (2.85) | 3.07 (3.28) | 2.83 (2.84) | 2.80 (2.80) | −242.8 | |
K+ | 2.86 (2.86) | 3.43 (3.34) | 2.86 (2.86) | 2.82 (2.80) | −245.0 | |
Rb+ | 2.97 (2.90) | 3.73 (3.48) | 2.88 (2.87) | 2.84 (2.78) | −238.8 |
System | M+ | ΔEbond | ΔEdesolv | ΔEprep | ΔEint | ΔEsolv | ΔEdesolv + ΔEsolv | ΔEprep + ΔEint |
---|---|---|---|---|---|---|---|---|
a All energies were computed with the DFT-D method at the ZORA-BLYP-D3(BJ)/TZP(/DZ) level of theory. | ||||||||
G4–M+–G4 | Li+ | −25.8 | 208.1 | 10.4 | −159.4 | −85.0 | 123.1 | −149.0 |
Na+ | −41.8 | 182.1 | 8.0 | −149.9 | −81.9 | 100.2 | −141.9 | |
K+ | −41.9 | 164.4 | 3.3 | −126.9 | −82.7 | 81.7 | −123.6 | |
Rb+ | −35.3 | 160.3 | 2.6 | −114.2 | −84.1 | 76.2 | −111.5 | |
GQ–M+ | Li+ | −26.1 | 286.2 | 9.4 | −163.6 | −158.2 | 128.0 | −154.2 |
Na+ | −39.5 | 260.2 | 8.4 | −154.2 | −153.8 | 106.4 | −145.8 | |
K+ | −40.7 | 242.5 | 4.0 | −133.0 | −154.2 | 88.3 | −129.0 | |
Rb+ | −34.9 | 238.4 | 3.0 | −121.3 | −155.0 | 83.4 | −118.3 | |
G4–K+–G4–M+–G4 | Li+ | −29.1 | 235.4 | 9.6 | −119.1 | −155.0 | 80.4 | −109.5 |
Na+ | −43.4 | 209.4 | 8.4 | −105.1 | −156.1 | 53.3 | −96.7 | |
K+ | −42.9 | 191.7 | 4.7 | −81.2 | −158.2 | 33.5 | −76.5 | |
Rb+ | −34.8 | 187.6 | 5.1 | −67.6 | −159.9 | 27.7 | −62.5 | |
GQ–K+–M+ | Li+ | −23.8 | 330.1 | 9.9 | −132.7 | −231.1 | 99.0 | −122.8 |
Na+ | −37.0 | 304.1 | 9.6 | −118.0 | −232.6 | 71.5 | −108.4 | |
K+ | −39.2 | 286.4 | 5.1 | −96.9 | −233.7 | 52.7 | −91.8 | |
Rb+ | −32.9 | 282.2 | 4.4 | −85.0 | −234.5 | 47.7 | −80.7 |
Fig. 5 Partitioning of the bond energy (in kcal mol−1) between the alkali metal cations (M+) and GQ–[ ] (dashed lines) and GQ–K+–[ ] (solid lines). |
In all cases, the bond energy is mainly the sum of a strong interaction energy, compensated by a large desolvation energy. The preparation energy does not vary much for the different cations and decreases upon increasing the size of the cation. This trend can be explained by looking at the cation–oxygen distance (d[O–M+]) and interplanar distance (R) (Table 2) that determine the size of the cavity hosting the second cation. The values of the geometrical parameters d[O–M+] and R come closer to the values of the empty cavity going from Li+ to Rb+. For the guanine bases to interact with the smaller cations (Li+ and Na+), the cavity should shrink. This leads to a higher preparation energy than in the case of the larger cations (K+ and Rb+), which give rise to less distortion of the empty cavity.
To investigate the contributions of geometrical effects and solvation effects, the sum of the interaction and preparation energy (ΔEint + ΔEprep) is displayed in Table 3, as well as the sum of the solvation and desolvation energy (ΔEdesolv + ΔEsolv), The former combination follows almost the exact same trend as the interaction energy alone. Table 3 shows that both summations are of counteracting and almost of equal importance to the order of cation affinity, resulting in small differences in bonding energy for the different alkali cations. The results of the double-layer GQs in Table 3 are consistent with the results found by Zaccaria et al.23 With this we would like to emphasize that the improved COSMO version results in different absolute energies, but yields the same relative energies and trends. The trends of the bond energy and the partitions are the same for both the double and triple-layer quadruplexes (Fig. 5). Remarkably, the magnitude of the bond energy decreases only little, going from the first to the second binding event. That the overall bond energy stays approximately the same for the first and second binding event of alkali metal cations of the same kind is the result of two counteracting effects: (1) the interaction energy (ΔEint) is less stabilizing for the interaction of the second metal cation (M+) with the cavity of the GQ than for the first metal cation; (2) the sum of solvation effects (ΔEdesolv + ΔEsolv) is less destabilizing for the second binding event. The latter is because the stabilizing ΔEsolv term increases more than the destabilizing ΔEdesolv term, going from the first to the second binding cation. In other words, the gain in solvation energy (ΔEsolv) for going from a GQ of charge 1+ (GQ–M+) to 2+ (GQ–K+–M+) is larger, than the increase of desolvation energy (ΔEdesolv) for going from an neutral GQ (GQ–[ ]) to a positively charged species (GQ–K+–[ ]). This can be explained by the fact that in the 2+ species the charge is more localized, resulting in more polarization of the solvent and thereupon to stronger interactions than in the case of 1+ species. It must be examined if this effect will be even stronger in highly charged systems (3+, 4+, etc.).
System | M+ | ΔEint | ΔVelstat | ΔEPauli | ΔEoi | ΔEdisp |
---|---|---|---|---|---|---|
a All energies were computed with the DFT-D method at the ZORA-BLYP-D3(BJ)/TZP (G4) or at the ZORA-BLYP-D3(BJ)/TZP/DZ (GQ) level of theory. | ||||||
G4–M+–G4 | Li+ | −159.4 | −108.2 | 11.6 | −54.8 | −8.0 |
Na+ | −150.0 | −105.3 | 11.2 | −43.0 | −12.9 | |
K+ | −127.2 | −102.1 | 30.9 | −40.8 | −15.2 | |
Rb+ | −114.3 | −96.0 | 36.6 | −38.4 | −16.5 | |
GQ–M+ | Li+ | −163.6 | −111.0 | 12.9 | −58.0 | −7.4 |
Na+ | −154.2 | −106.8 | 10.3 | −44.6 | −13.1 | |
K+ | −133.1 | −103.6 | 28.4 | −42.3 | −15.6 | |
Rb+ | −121.5 | −99.2 | 34.8 | −40.1 | −16.9 | |
G4–K+–G4–M+–G4 | Li+ | −119.1 | −66.0 | 11.7 | −56.1 | −8.7 |
Na+ | −105.2 | −56.8 | 11.8 | −45.3 | −14.9 | |
K+ | −81.3 | −51.3 | 30.9 | −42.7 | −18.2 | |
Rb+ | −68.2 | −46.7 | 37.1 | −40.3 | −18.2 | |
GQ–K+–M+ | Li+ | −132.7 | −78.6 | 11.8 | −57.9 | −8.0 |
Na+ | −118.0 | −66.7 | 10.1 | −46.4 | −15.0 | |
K+ | −96.9 | −62.1 | 27.4 | −43.7 | −18.5 | |
Rb+ | −84.9 | −57.6 | 33.4 | −41.6 | −19.1 |
Fig. 6 Energy decomposition of the interaction energy (in kcal mol−1) between the alkali metal cations (M+) and GQ–[ ] (dashed lines) and GQ–K+–[ ] (solid lines). |
From Fig. 6, it can be seen that the significant drop in interaction energy going from Na+ to K+ is due to the increase in Pauli repulsion that increases by almost 20 kcal mol−1. We want to emphasize this counterintuitive observation that K+ results in less deformation of the GQ, although it is accompanied by a higher Pauli repulsion than Na+. From the energy decomposition analysis (EDA) follows that the bonding interaction of the second alkali cation to GQ–K+–[ ] is a combination of mainly electrostatic interaction, followed by orbital interaction and dispersion. These trends are also in line with the results found by Zaccaria et al.23 In fact, the trendlines of the energy terms ΔEPauli, ΔEoi and ΔEdisp do exactly overlap for the double- and triple-layered GQs. It turns out that only the decrease in electrostatic interaction (ΔVelstat) is responsible for the observed decrease in interaction energy in the second binding event.
The observed decrease in electrostatic interaction (ΔΔVelstat) for binding of the second alkali cation can be the result of the repulsion between the two present cations in the quadruplex or the diminished electron density available on middle guanine quartet to bind the second cation. The presence of the first potassium ion in GQ–K+–[ ] leads to extraction of electron density from the oxygen atoms. Thereupon, the oxygen atoms in the middle guanine quartet layer of GQ–K+–M+ are likely to become less electronegative, potentially leading to less stabilizing electrostatic interaction with the second alkali cation M+.
In order to identify the effect of electron depletion of the middle guanine stack upon binding of the first alkali cation, it was examined whether there is diminished charge-transfer from the guanine bases to the second metal cation. Therefore, the VDD change in atomic charge to the second metal cation (ΔQM+) was calculated for the triple-layer GQs and compared to the values found for the two-layer GQs (eqn (8) and Table 5). As presented in Table 5, the charge-transfer interaction between the GQ and the second cation is equal to the values found for binding of the first alkali cation in two-layer GQ. This indicates that there is sufficient electron density left on the middle guanine quartet to donate the same number of electrons to the second cation. This observation is supported by the overlapping of ΔEoi (green lines in Fig. 6) for the binding of the first and second cation in the double-layer and triple-layer GQ systems, respectively.
To investigate the contribution of repulsive interactions as cause of the diminished electrostatic interaction, an EDA of the interaction energy between the two alkali cations in GQ–K+–M+ was performed at the inter-atomic distance within the GQ (see Table 6). The results demonstrate that a large destabilizing interaction is present between the alkali cations in the quadruplex with interaction energies of ca. +80 kcal mol−1. Table 6 shows that this destabilizing interaction is almost exclusively due to repulsive electrostatic interactions between the two cations. The electrostatic interaction is less stabilizing by approximately +40 kcal mol−1 (ΔΔVelstat) for all the different cations in GQ–K+–M+ compared to the two-layered quadruplexes (see difference in ΔVelstat in Fig. 6 for the triple-layer (solid line) and double-layer GQ (dashed line)). Therefore, it is expected that the large repulsive interaction energy between the two alkali cations contributes significantly to the observed decrease in bond energy of the second alkali metal cation but is reduced by electronic shielding of the guanine bases.
M+ | ΔEint | ΔVelstat | ΔEPauli | ΔEoi | ΔEdisp | ΔΔVelstatb | d[K+–M+]c |
---|---|---|---|---|---|---|---|
a All energies were computed with the DFT-D method at the ZORA-BLYP-D3(BJ)/TZP(/DZ) level of theory. b Difference in the electrostatic interaction component of the bond energy of GQ–K+–M+vs. the two-layer GQ–M+ of Zaccaria et al.23 (see Fig. 6). c Distance (in Å) between K+ and the second alkali metal cation in GQ–K+–M+. | |||||||
Li+ | 61.8 | 68.5 | 0.0 | −0.3 | −6.4 | 34.2 | 48.5 |
Na+ | 88.1 | 90.2 | 0.0 | −0.9 | −1.2 | 42.6 | 36.8 |
K+ | 86.2 | 88.7 | 0.1 | −1.5 | −1.2 | 44.2 | 37.5 |
Rb+ | 83.4 | 86.1 | 0.2 | −1.7 | −1.1 | 39.5 | 38.5 |
Note that the trend in electrostatic repulsion among the different alkali metal cations is related to the distance between K+ and the second alkali metal cation in the geometry of GQ–K+–M+ (d[K+–M+] in Table 6).
It can be concluded that the strong repulsive interaction between the two alkali metal cations, as found by the results in Table 6, accounts for the decrease in interaction energy of the second binding event in guanine quadruplex systems, rather than electron depletion of the middle guanine layer. This would suggest that in even larger multi-layer guanine quadruplexes, where each cation is adjacent to two other cations, the interaction energy for hosting alkali cations would decrease even further. These results question the role of alkali metal cations in the stabilization of multi-layer guanine quadruplex DNA and whether each cavity hosts an alkali metal cation or that rather an alternating pattern of empty and occupied is preferred. The decreasing importance of the alkali metal cations for the stability of multi-layer quadruplexes is in line with the results find by Kotlyar et al.53 In this work they report G4 DNA wires in the absence of alkali cations that show equal stability as the cation containing G4 structures reported in literature. The high stability is probably the result of the much greater length of these structures.
Fig. 7 Partitioning of the bond energy (in kcal mol−1) for subsequent binding events of K+ in G4–K+–G4, G4–K+–G4–K+–G4 and G4–K+–G4–K+–G4–K+–G4. |
In Fig. 7 the preparation energy stays the same, but the interaction energy decreases for each binding event. In addition, the contribution of solvation effects becomes more significant following this trend. The stabilizing solvation energy increases faster than the destabilizing desolvation energy with each binding event, resulting in an equalized bond energy.
The interaction energy is further decomposed into physical meaningful terms for consecutive binding events in G4–K+–G4, G4–K+–G4–K+–G4 and G4–K+–G4–K+–G4–K+–G4 (see eqn (7) and Fig. 8). Fig. 8 shows that the energy terms ΔEPauli, ΔEoi and ΔEdisp stay the same for the subsequent binding events of K+ in double- and triple- and four-layer quadruplexes. It is only the decrease in electrostatic interaction (ΔVelstat) that is responsible for the observed decrease in interaction energy in sequel binding events. These results show that electrostatic repulsion operates not only locally, but operates also over long range distances.
Fig. 8 Energy decomposition of the interaction energy (in kcal mol−1) for subsequent binding events of K+ in G4–K+–G4, G4–K+–G4–K+–G4 and G4–K+–G4–K+–G4–K+–G4. |
Partitioning of the bond energy between the alkali cation and the cavity of the quadruplexes, showed that the desolvation energy and the size of the cation are of equal importance to the trend. Descending the first group of the periodic table shows a decrease of the desolvation energy of the cation, and a decrease of the attractive interaction between the cation and the quadruplex. Simultaneously, hosting of the larger cations diminishes the deformation of the empty quadruplex cavity. These effects result together in a minimum of the bond energy for K+.
The magnitude of the bond energy stays approximately the same for the subsequent binding events of a first, second and third cation in double, triple and four-layer guanine quadruplexes, respectively. Although the interaction energy decreases for each binding event, the contribution of solvation effects becomes more significant following this trend. The stabilizing solvation energy increases faster than the destabilizing desolvation energy with each binding event, resulting in an equalized bond energy.
Decomposition of the interaction energy into physically meaningful terms showed that electrostatic repulsion between the hosted metal cations is responsible for the diminished interaction energy. This work demonstrates that solvent effects become of increasing importance for the stabilization of highly charged multi-layer guanine quadruplex DNA.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0cp03433a |
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