Insight into Tetramolecular DNA G-Quadruplexes Associated with ALS and FTLD: Cation Interactions and Formation of Higher-Ordered Structure

The G4C2 hexanucleotide repeat expansion in the c9orf72 gene is a major genetic cause of familial amyotrophic lateral sclerosis (ALS) and frontotemporal lobar degeneration (FTLD), with the formation of G-quadruplexes directly linked to the development of these diseases. Cations play a crucial role in the formation and structure of G-quadruplexes. In this study, we investigated the impact of biologically relevant potassium ions on G-quadruplex structures and utilized 15N-labeled ammonium cations as a substitute for K+ ions to gain further insights into cation binding and exchange dynamics. Through nuclear magnetic resonance spectroscopy and molecular dynamics simulations, we demonstrate that the single d(G4C2) repeat, in the presence of 15NH4+ ions, adopts a tetramolecular G-quadruplex with an all-syn quartet at the 5′-end. The movement of 15NH4+ ions through the central channel of the G-quadruplex, as well as to the bulk solution, is governed by the vacant cation binding site, in addition to the all-syn quartet at the 5′-end. Furthermore, the addition of K+ ions to G-quadruplexes folded in the presence of 15NH4+ ions induces stacking of G-quadruplexes via their 5′-end G-quartets, leading to the formation of stable higher-ordered species.


Introduction
Guanine-rich nucleic acid segments have the ability to form non-canonical, fourstranded G-quadruplex structures, which consist of at least two G-quartets.These structures are planar arrays of four guanines held together by eight Hoogsteen hydrogen bonds [1][2][3].In addition to G-quadruplexes, G-rich sequences can also adopt other tetrahelical arrangements [4,5].
Within the human genome, G-rich sequences are predominantly found in telomeres [6] and promoter regions of genes [7].This suggests that G-quadruplex formation may play a role in gene regulation and expression [8][9][10][11].The expansion of the G 4 C 2 hexanucleotide repeat in the c9orf72 gene has been identified as the primary genetic cause of familial amyotrophic lateral sclerosis (ALS) and frontotemporal lobar degeneration (FTLD) [12].Although the exact disease mechanism is still under investigation, three hypotheses have been proposed: RNA toxicity, accumulation of dipeptide repeat proteins, and c9orf72 haploinsufficiency.Despite their differences, all these mechanisms are related to the formation of stable structural features by the expanded G 4 C 2 repeats [13].
Recent research has also demonstrated a correlation between G-quadruplex formation and the development of ALS and FTLD in mice [20,21].It is also known that C9orf72 hexanucleotide repeat expansion interacts with several protein partners, such as DAXX, which drives reorganization of genomic structures and causes epigenetic changes in patient cells [22].Furthermore, it was shown that RNA G 4 C 2 repeats interact with the splicing factor hnRNP H, which leads to elevated insoluble aggregates in patient brains [23], while binding of DEAH-box helicase 36 resolves RNA G 4 C 2 G-quadruplexes and as such is essential in regulating the repeat-associated non-AUG translation [24,25].Furthermore, C-rich antisense DNA d(G 2 C 4 ) and RNA (G 2 C 4 ) repeats can form stable non-canonical structures, such as i-motifs and protonated hairpins [16,26,27], which adds another layer of complexity to the association between c9orf72 and ALS/FTLD.Additionally, ions that are present in the cells at different concentrations may also influence the formation of DNA/RNA structures.
G-quadruplexes can differ in the number of G-quartets, strand stoichiometry and their progression, types of loops, and loop orientation [28].Furthermore, a recent study showed that even a single mutation in the G-tract prevents formation of G-quadruplexes [29].Unimolecular G-quadruplexes formed by d(G 2 C 4 ) n repeats exhibit a high degree of structural polymorphism in solution, and sequence modifications are typically needed to reduce the number of structures formed in solution [19].The topology and thermal stability of G-quadruplexes are known to be significantly influenced by cations [30][31][32][33][34][35][36].Cations play a crucial role in G-quadruplex formation by reducing repulsion between guanine carbonyl oxygen atoms and promoting the stacking of G-quartets [37].Among the various cations that promote G-quadruplex formation, K + ions are the most effective inducers, followed by NH 4 + and Na + ions [38,39].Cations are typically located between two G-quartets, within the plane of a G-quartet, or between the outer G-quartet and loop residues [40].The specific cation binding site in G-quadruplexes is influenced by factors such as the synand anti-orientation of guanine residues in a G-quartet.Additionally, cations are not static and can move between binding sites and exchange with cations in the bulk solution [41][42][43][44][45][46]. 15  NH 4  + ions have been utilized in nuclear magnetic resonance spectroscopy (NMR) studies as a non-metallic substitute for K + ions, enabling the identification of cation binding sites and the study of their exchange kinetics [41][42][43][44][45][46][47].Previous research has demonstrated that the strand stoichiometry and loop topology influence the kinetics of cation movement [44][45][46]48].Furthermore, the presence of syn-quartets significantly decreases the rate of cation exchange [45,49].
In this study, our primary interest was to investigate the interaction between different cations and the G-quadruplex structure formed by the short hexanucleotide repeat d(G 4 C 2 ), where a single repeat was chosen to eliminate the structural polymorphism that prevents the analysis of cation binding sites within G-quadruplexes formed by longer (G 4 C 2 ) n repeats.We expected that the mentioned oligonucleotide, in the presence of 15 NH 4 + ions, would form a tetramolecular G-quadruplex, which could have a parallel or antiparallel orientation of strands.In the former case, G-quartets would be formed, and possibly C-quartets, while in the case of antiparallel strands, we would expect the presence of GC-quartets or GC base pairs in addition to G-quartets.The localization of cations would depend on the resulting 3D structure, and it may not be restricted to residing solely between the G-quartets.We also expected certain binding sites to exhibit a preference for cation binding, leading to their higher occupancy.Additionally, we anticipated that the kinetics of cation exchange between individual binding sites within the structure and the cations from the bulk solution would be strongly influenced by the structural elements of the formed structure.This could manifest in preferential movement of cations in specific directions.Moreover, we expected that the addition of biologically relevant K + ions would cause the replacement of 15 NH 4 + ions within the G-quadruplex with K + ions, potentially resulting in changes in the folding topology and, possibly, formation of higher-order structures.In the case of higher-order structure formation, the question arose as to how many 15 NH 4 + ions need to be replaced by K + ions to achieve such formation.Initially, the folding of d(G 4 C 2 ) was assessed using 1 H NMR spectra.At low cation concentrations, a single set of signals corresponding to aromatic and sugar protons of guanine and cytosine residues was observed, along with a broad signal at approximately δ 10.9 ppm.This signal indicated the formation of GG N1 carbonyl symmetric base pairs in the pre-folded species, while no signals indicating Watson-Crick base pairs were detected (Figures 1A and S1A).

2
many 15 NH4 + ions need to be replaced by K + ions to achieve such

d(G4C2) Forms Tetramolecular G-Quadruplex in the Presence of 15
Initially, the folding of d(G4C2) was assessed using 1 H NM concentrations, a single set of signals corresponding to aromatic a nine and cytosine residues was observed, along with a broad si 10.9 ppm.This signal indicated the formation of GG N1 carbonyl the pre-folded species, while no signals indicating Watson-Crick (Figures 1A and S1A).S3).The NMR data obtained from various 2D NMR experiments (Figures S4-S6) consistently supported the formation of a parallel tetramolecular G-quadruplex with a C 4 symmetry axis and four G-quartets (Figure 2A), with G1 having a synand G2-G4 an anticonformation of their glycosidic torsion angle (Figure S7).The size and strand orientation of the G-quadruplex structure were supported by the translation diffusion coefficient (D t ) of 1.41 ± 0.05 × 10 −6 cm 2 s −1 and the CD spectrum (Figure S8).In the presence of 100 mM 15 NH 4 Cl, [d(G 4 C 2 )] 4 also exhibits a remarkable thermodynamic stability, with unfolding occurring only at 83

All syn G-Quartet Directs Cation Movement between [d(G4C2)]4 G-Quadruplex and Bulk Solution
The 2D 1 H-15 N HSQC NMR spectrum provided evidence of three distinct binding sites for 15 NH4 + ions within the [d(G4C2)]4 G-quadruplex.These binding sites were found to be located between pairs of adjacent G-quartets, as confirmed by the analysis of 2D NOESY and ROESY spectra (Figures 2 and S11).Binding site O5 (δH 7.27 ppm) corresponds to the binding site between G1 and G2 G-quartets, binding site I (δH 6.98 ppm) is located between G2 and G3 G-quartets, while binding site O3 (δ 7.02 ppm) is located between G3 and G4 G-quartets.The volume integrals ratio of the autocorrelation cross-peaks O5, I, and O3 was 2:1:1, indicating unequal occupancy of the binding sites (Figure 2B).
A series of 2D 1 H-15 N NzExHSQC spectra with mixing times ranging from 13 ms to 3 s was acquired to evaluate the kinetics of 15 NH4 + ion movement between binding sites within the G-quadruplex and with ions in the bulk solution.Movements of 15 NH4 + ions between binding sites along the central core of the [d(G4C2)]4 G-quadruplex were observed as the exchange cross-peaks O5I, IO5, IO3, and O3I, while ion movement from binding site O3 into the bulk solution was characterized by the exchange cross-peak O3B (Figure 2C).No resolved cross-peak corresponding to 15 NH4 + ion movement from the bulk solution to binding site O3 was observed, possibly due to overlap of a weak cross-peak with autocorrelation cross-peak B. No ion movement between binding site O5, characterized by an allsyn G-quartet, and the bulk solution was detected.However, the 2D 1 H-15 N HzExHSQC experiment showed that protons are able to exchange between 15 NH4 + ions at binding site O5 and those in the bulk solution (Figure 2C), but the quantitative analysis was not possible due to the low peak intensity.

All syn G-Quartet Directs Cation Movement between [d(G 4 C 2 )] 4 G-Quadruplex and Bulk Solution
The 2D 1 H-15 N HSQC NMR spectrum provided evidence of three distinct binding sites for 15 NH 4 + ions within the [d(G 4 C 2 )] 4 G-quadruplex.These binding sites were found to be located between pairs of adjacent G-quartets, as confirmed by the analysis of 2D NOESY and ROESY spectra (Figures 2 and S11).Binding site O 5 (δ H 7.27 ppm) corresponds to the binding site between G1 and G2 G-quartets, binding site I (δ H 6.98 ppm) is located between G2 and G3 G-quartets, while binding site O 3 (δ 7.02 ppm) is located between G3 and G4 G-quartets.The volume integrals ratio of the autocorrelation cross-peaks O 5 , I, and O 3 was 2:1:1, indicating unequal occupancy of the binding sites (Figure 2B).
A series of 2D 1 H-15 N NzExHSQC spectra with mixing times ranging from 13 ms to 3 s was acquired to evaluate the kinetics of 15 NH 4 + ion movement between binding sites within the G-quadruplex and with ions in the bulk solution.Movements of 15 NH 4 + ions between binding sites along the central core of the [d(G 4 C 2 )] 4 G-quadruplex were observed as the exchange cross-peaks O 5 I, IO 5 , IO 3 , and O 3 I, while ion movement from binding site O 3 into the bulk solution was characterized by the exchange cross-peak O 3 B (Figure 2C).No resolved cross-peak corresponding to 15 NH 4 + ion movement from the bulk solution to binding site O 3 was observed, possibly due to overlap of a weak cross-peak with autocorrelation cross-peak B. No ion movement between binding site O 5 , characterized by an all-syn G-quartet, and the bulk solution was detected.However, the 2D 1 H-15 N HzExHSQC experiment showed that protons are able to exchange between 15 NH 4 + ions at binding site O 5 and those in the bulk solution (Figure 2C), but the quantitative analysis was not possible due to the low peak intensity.
The apparent rate constants of cation exchange were obtained by fitting the integrals of autocorrelation and exchange cross-peaks (Figures S12 and S13, Tables S1 and S2) and were in the order of 2 s −1 or slower.The fastest exchange was observed for movement of ions from O 3 to I, and from O 3 to the bulk solution.The observed differences in the apparent rate constants imply the existence of temporarily vacant cation binding sites within [d(G 4 C 2 )] 4 , which is in agreement with the different binding site occupancies observed in the 2D 1 H-15 N HSQC spectrum.+ ions was calculated using NMR restraints (Table S3).Ten final structures were selected based on their lowest energy and the smallest number of violations of experimentally derived structural restraints.The resulting structure that best fit all the experimental restraints was a tetramolecular, parallel G-quadruplex with four G-quartets (ID 8C7B, Figure 3A).In Figure 3A, the 5 -end G-quartet is formed by G1 guanine residues that adopt a syn-orientation around the glycosidic bond, while all the other G-quartets consist of guanine residues in the anti-conformation.The hydrogen bonds within the all-syn and all-anti G-quartets have anticlockwise and clockwise orientations, respectively.The well-defined core of the G-quadruplex has a pairwise heavy-atom RMSD of 0.80 Å.The 5-member rings of G1 and G2 residues overlap, which agrees with the syn-anti sequential step.Stacking interactions between the G2-G3 and G3-G4 residues occur through the partial overlap of both the five-and six-member rings of guanine residues, as expected for the anti-anti sequential step (Figure 3A).All four grooves have a medium width, as all the guanine residues within each individual G-quartet exhibit the same antior syn-orientation around the glycosidic bonds.The C5 residues form a well-defined C-quartet, stabilized by hydrogen bonds in the amino-O2 geometry, that overlaps with the 6-member ring of G4 residues (Figure 3A) and the presence of the cations.The well-defined C-quartet is reflected in a slight increase in RMSD to 0.97 Å compared to the RMSD obtained for the G-quartet core.The C6 residues do not exhibit any stacking interactions.

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The apparent rate constants of cation exchange were obtained by fitting the integrals of autocorrelation and exchange cross-peaks (Figures S12 and S13, Tables S1 and S2) and were in the order of 2 s −1 or slower.The fastest exchange was observed for movement of ions from O3 to I, and from O3 to the bulk solution.The observed differences in the apparent rate constants imply the existence of temporarily vacant cation binding sites within [d(G4C2)]4, which is in agreement with the different binding site occupancies observed in the 2D 1 H-15 N HSQC spectrum.

C5 Residues Form a Well-Defined C-Quartet within [d(G4C2)]4 G-Quadruplex
A set of G-quadruplex structures formed by the d(G4C2) sequence in the presence of 15 NH4 + ions was calculated using NMR restraints (Table S3).Ten final structures were selected based on their lowest energy and the smallest number of violations of experimentally derived structural restraints.The resulting structure that best fit all the experimental restraints was a tetramolecular, parallel G-quadruplex with four G-quartets (ID 8C7B, Figure 3A).In Figure 3A, the 5′-end G-quartet is formed by G1 guanine residues that adopt a syn-orientation around the glycosidic bond, while all the other G-quartets consist of guanine residues in the anti-conformation.The hydrogen bonds within the all-syn and all-anti G-quartets have anticlockwise and clockwise orientations, respectively.The well-defined core of the G-quadruplex has a pairwise heavy-atom RMSD of 0.80 Å.The 5-member rings of G1 and G2 residues overlap, which agrees with the syn-anti sequential step.Stacking interactions between the G2-G3 and G3-G4 residues occur through the partial overlap of both the five-and six-member rings of guanine residues, as expected for the anti-anti sequential step (Figure 3A).All four grooves have a medium width, as all the guanine residues within each individual G-quartet exhibit the same anti-or syn-orientation around the glycosidic bonds.The C5 residues form a well-defined C-quartet, stabilized by hydrogen bonds in the amino-O2 geometry, that overlaps with the 6-member ring of G4 residues (Figure 3A) and the presence of the cations.The well-defined C-quartet is reflected in a slight increase in RMSD to 0.97 Å compared to the RMSD obtained for the G-quartet core.The C6 residues do not exhibit any stacking interactions.

Vacant Cation Binding Sites Impede Cation Movement within [d(G 4 C 2 )] 4 G-Quadruplex
Since NMR experiments showed that binding sites I and O 3 had lower occupancy by 15 NH 4 + ions compared to O 5 , MD simulations were conducted to gain further insights into the localization of ammonium ions.Initially, MD simulations were performed with three NH 4 + ions present at binding sites O 5 , I, and O 3 within the [d(G 4 C 2 )] 4 G-quadruplex, with a total cation concentration of 115 mM (Figure S14).After 7 ns of simulation, the NH 4 + ions at binding site O 3 moved to the cavity between the G-quartets defined by G4 and C5 residues and remained there for the rest of the 200 ns MD simulation (Figure S15).Despite the absence of cations at binding site O 3 , the structure of the [d(G 4 C 2 )] 4 G-quadruplex remained stable during the MD simulation (Figure S14).This binding site between G4 and C5 residues was designated as O GC .Another 15 NH 4 + ion was trapped between C5 and C6 residues, but due to the flexibility of C6 residues, this cation binding site was not well defined (Figure S15).MD simulations where NH 4 + ions were absent at the beginning of the simulations from binding site O 5 showed that the NH 4 + ion at binding site I immediately moved to binding site O 5 (Figure S15) and remained there for the rest of the simulation.In contrast, MD simulations with NH 4 + ions absent at binding sites I or O 3 demonstrated that, in both cases, the G-quartet core of the [d(G 4 C 2 )] 4 G-quadruplex remained stable, and cation movement was not observed (Figure S15).The unexpectedly slow cation movements observed for the tetramolecular G-quadruplex, as noted from NMR data, are, therefore, a result of vacant cation binding sites I or O 3 , in addition to the all-syn G-quartet at the 5 -end.
The syn-anti and anti-anti steps within the [d(G 4 C 2 )] 4 G-quadruplex lead to distinct stacking modes between the corresponding G-quartets.The binding of cations between two G-quartets is directly influenced by the negative charges of the O6 atoms within the G-quartet.Therefore, the alignment of the negative charge centers of the G-quartet core could affect the binding affinity for cations.The geometric parameter d represents the distance between the center of the first G-quartet, e.g., composed of G3 residues, and the projection of the center of the adjacent G-quartet, e.g., composed of G4 residues, onto the plane defined by the first G-quartet (Figure 4).Different values of d influence the octahedral coordination geometries of cations and, consequently, their binding affinity.The values of d between G-quartets consisting of G1 and G2, G2 and G3, and G3 and G4 residues in [d(G 4 C 2 )] 4 in the presence of 15 NH 4 + ions are 0.4, 0.5, and 0.6 Å, respectively.Since the most populated binding site, O 5 , is characterized by the smallest d, perfect alignment of the negative charge centers would result in the strongest binding affinity for cations.

Vacant Cation Binding Sites Impede Cation Movement within [d(G4C2)]4 G-Quadruple
Since NMR experiments showed that binding sites I and O3 had lower occupan 15 NH4 + ions compared to O5, MD simulations were conducted to gain further insight the localization of ammonium ions.Initially, MD simulations were performed with NH4 + ions present at binding sites O5, I, and O3 within the [d(G4C2)]4 G-quadruplex a total cation concentration of 115 mM (Figure S14).After 7 ns of simulation, the NH at binding site O3 moved to the cavity between the G-quartets defined by G4 and C dues and remained there for the rest of the 200 ns MD simulation (Figure S15).D the absence of cations at binding site O3, the structure of the [d(G4C2)]4 G-quadrupl mained stable during the MD simulation (Figure S14).This binding site between G C5 residues was designated as OGC.Another 15 NH4 + ion was trapped between C5 a residues, but due to the flexibility of C6 residues, this cation binding site was no defined (Figure S15).MD simulations where NH4 + ions were absent at the beginn the simulations from binding site O5 showed that the NH4 + ion at binding site I im ately moved to binding site O5 (Figure S15) and remained there for the rest of the si tion.In contrast, MD simulations with NH4 + ions absent at binding sites I or O3 de strated that, in both cases, the G-quartet core of the [d(G4C2)]4 G-quadruplex rem stable, and cation movement was not observed (Figure S15).The unexpectedly slow movements observed for the tetramolecular G-quadruplex, as noted from NMR dat therefore, a result of vacant cation binding sites I or O3, in addition to the all-syn G-q at the 5′-end.
The syn-anti and anti-anti steps within the [d(G4C2)]4 G-quadruplex lead to d stacking modes between the corresponding G-quartets.The binding of cations bet two G-quartets is directly influenced by the negative charges of the O6 atoms with G-quartet.Therefore, the alignment of the negative charge centers of the G-quarte could affect the binding affinity for cations.The geometric parameter d represents th tance between the center of the first G-quartet, e.g., composed of G3 residues, an projection of the center of the adjacent G-quartet, e.g., composed of G4 residues, on plane defined by the first G-quartet (Figure 4).Different values of d influence the o dral coordination geometries of cations and, consequently, their binding affinity.Th ues of d between G-quartets consisting of G1 and G2, G2 and G3, and G3 and G4 res in [d(G4C2)]4 in the presence of 15 NH4 + ions are 0.4, 0.5, and 0.6 Å, respectively.Sin most populated binding site, O5, is characterized by the smallest d, perfect alignm the negative charge centers would result in the strongest binding affinity for cations   + ion movements, adaptive steered molecular dynamics [50,51] were employed.The potential of mean force (PMF) profile depicted in Figure 5 illustrates that the free-energy barriers for NH 4 + ions to cross the outer G-quartets, consisting of G4 and G1 residues, to the bulk solution were 10.3 and 20.9 kcal/mol, respectively.The significantly higher energy barrier for the G-quartet composed of G1 residues aligns with the NMR observation that 15 NH 4 + ions do not move between the O 5 binding site and the bulk solution.The energy barriers for NH 4 + ion movements through G-quartets composed of G2 and G3 residues were approximately 12.2 and 8.7 kcal/mol, respectively.
atoms of the G-quartets are shown as red sphere models, and centers of the G-quartets are shown in blue.d is the distance between the centers of two adjacent G-quartets.

Free-Energy Barriers of 15 NH4 + Ion Movement Confirm Asymmetry between Binding Sites
NMR experiments revealed that the exchange of 15 NH4 + ions from the central channel of the [d(G4C2)]4 G-quadruplex with the bulk solution occurs through the 3′-end.To investigate the free-energy profiles of NH4 + ion movements, adaptive steered molecular dynamics [50,51] were employed.The potential of mean force (PMF) profile depicted in Figure 5 illustrates that the free-energy barriers for NH4 + ions to cross the outer G-quartets, consisting of G4 and G1 residues, to the bulk solution were 10.3 and 20.9 kcal/mol, respectively.The significantly higher energy barrier for the G-quartet composed of G1 residues aligns with the NMR observation that 15 NH4 + ions do not move between the O5 binding site and the bulk solution.The energy barriers for NH4 + ion movements through G-quartets composed of G2 and G3 residues were approximately 12.2 and 8.7 kcal/mol, respectively.G-quartets composed of G1, G2, G3, and G4 residues are marked as G1-, G2-, G3-, and G4quartets, respectively.

[d(G4C2)]4 G-Quadruplex Dimerizes into Higher-Order Structures in the Presence of K + Ions
Upon gradual titration of KCl into a solution of [d(G4C2)]4 G-quadruplex, folded in the presence of 15 NH4Cl alone, the imino region of 1 H NMR spectra exhibited additional signals, indicating the presence of various G-quadruplexes in the solution (Figure 6).At 80 mM of KCl, a single G-quadruplex species was observed again, albeit different from the initial one.NMR and CD data revealed the formation of a parallel tetramolecular Gquadruplex with a C4 symmetry axis, with the G1 residue in the syn-conformation (Figures S16-S19).Furthermore, the Dt value gradually decreased upon the addition of KCl, reaching 1.19 ± 0.05 × 10 −6 cm 2 s −1 at 80 mM of KCl, indicating the dimerization of two tetramolecular G-quadruplexes, hereafter referred to as the [d(G4C2)]4 G-quadruplex dimer.In a proton-deuterium exchange experiment, the imino protons of G1 and G2 exchanged at a slower rate compared to G3 and G4, suggesting that dimerization occurs through the 5′end G-quartets (Figure S20).The [d(G4C2)]4 G-quadruplex dimer exhibited significantly higher thermal stability compared to the one in the presence of 15 NH4Cl alone, with no In a proton-deuterium exchange experiment, the imino protons of G1 and G2 exchanged at a slower rate compared to G3 and G4, suggesting that dimerization occurs through the 5 -end G-quartets (Figure S20).The [d(G 4 C 2 )] 4 G-quadruplex dimer exhibited significantly higher thermal stability compared to the one in the presence of 15 NH 4 Cl alone, with no unfolding observed, even at 95 • C (Figures S9 and S10). 1 H-15 N HSQC experiments conducted at each addition of KCl provided the exchange of 15 NH4 + with K + ions at individual binding sites within the G-(Figure 6).Combining the measured Dt values with the HSQC data revealed zation occurs before 15 NH4 + ions fully exchange with K + ions (Figure 7).This f cated the presence of an additional K + ion at the interface of two tetramolecu ruplex structures (Figure 7).Within a G-quadruplex unit, K + ions initially repl ions at the O3 binding site.Simultaneously, additional cross-peaks O5' and chemical shifts up-field of O5 and I appeared (Figure 6).These cross-peaks presence of 15 NH4 + ions within G-quadruplex species where the O3 binding site by a K + ion (Figure 7).Approximately 70% of 15 NH4 + ions at the O3 binding s placed upon the addition of 1.0 mM of KCl.At 2.0 mM of KCl, around 90% of ing sites and 70% of the I binding sites were occupied by K + ions.The exis quadruplexes with K + ions at the O3 and I binding sites and 15 NH4 + ions at the site was evident from the presence of an additional cross-peak in the 2D 1 H spectrum (O5").At 5.0 mM of KCl, approximately 50% of the G-quadruplexes h binding sites occupied by K + ions, while in other structures, 15 NH4 + ions still re O5 binding site or both the O5 and I binding sites.In the presence of 20 mM proximately 80% of the G-quadruplexes had all three binding sites occupied At 80 mM of KCl, almost complete replacement of 15 NH4 + by K + ions was de sistent with the observation of a single G-quadruplex species in the 1 H NMR + with K + ions at individual binding sites within the G-quadruplex (Figure 6).Combining the measured D t values with the HSQC data revealed that dimerization occurs before 15 NH 4 + ions fully exchange with K + ions (Figure 7).This further indicated the presence of an additional K + ion at the interface of two tetramolecular Gquadruplex structures (Figure 7).Within a G-quadruplex unit, K + ions initially replaced 15 NH 4 + ions at the O 3 binding site.Simultaneously, additional cross-peaks O 5 ' and I' with 1 H chemical shifts up-field of O 5 and I appeared (Figure 6).These cross-peaks indicate the presence of 15 NH 4 + ions within G-quadruplex species where the O 3 binding site is occupied by a K + ion (Figure 7).Approximately 70% of 15 NH 4 + ions at the O 3 binding site were replaced upon the addition of 1.0 mM of KCl.At 2.0 mM of KCl, around 90% of the O 3 binding sites and 70% of the I binding sites were occupied by K + ions.The existence of G-quadruplexes with K + ions at the O 3 and I binding sites and 15 NH 4 + ions at the O 5 binding site was evident from the presence of an additional cross-peak in the 2D 1 H-15 N HSQC spectrum (O 5 ").At 5.0 mM of KCl, approximately 50% of the G-quadruplexes had all three binding sites occupied by K + ions, while in other structures, 15 NH 4 + ions still resided at the O 5 binding site or both the O 5 and I binding sites.In the presence of 20 mM of KCl, approximately 80% of the G-quadruplexes had all three binding sites occupied by K + ions.At 80 mM of KCl, almost complete replacement of 15 NH 4 + by K + ions was detected, consistent with the observation of a single G-quadruplex species in the 1 H NMR spectrum.

Dimerization of [d(G4C2)]4 G-Quadruplex Structures Occurs through Stacking of 5-Membered Rings
Due to the high symmetry of the [d(G4C2)]4 G-quadruplex dimer in the presence of K + ions, it was not possible to differentiate between restraints that corresponded solely to the stacking interface between two tetramolecular G-quadruplexes.Therefore, the highresolution structure was calculated only for a monomeric unit (Table S3).The resulting structure, which satisfied all experimentally derived structural restraints, closely resembled the one observed in the presence of NH4 + ions (PDB ID 8C7A, Figure 3B).However, in contrast to the structure in the presence of NH4 + ions, the C6 and C5 residues exhibited partial overlap, as supported by the C5H6-C6H6 cross-peak in the NOESY spectrum (Figure S21).
To evaluate the geometry at the stacking interface between the two tetramolecular [d(G4C2)]4 G-quadruplexes, four rotamers with different modes of the G-quartet stacking interface (stacking through 5-membered rings, 5/6-membered rings, 6-membered rings, and partial 6-membered rings, Figure S22) were constructed and subjected to MD simulation.A 200 ns MD simulation demonstrated that all four rotamers converged to a similar geometry, with the interface G-quartets composed of G1 residues stacking through 5membered rings at a separation distance of 3.57 Å (Figures S23 and S24).Interestingly, the G-quartets at the interface displayed a smaller twist angle compared to the G-quartets composed of G1 and G2 residues (14.8° vs. 21.6°, Figure 3B).

K + Ion between Interface G-Quartets Is Firmly Bound
To determine the preferential cation binding sites within the [d(G4C2)]4 G-quadruplex dimer, a G-quadruplex composed of two [d(G4C2)]4 G-quadruplexes was constructed, with K + ions absent at the binding site O3 and an additional K + ion positioned between the interface G-quartets comprised of G1 residues, denoted as OGG.Within a few picoseconds, it was observed that the K + ion initially located at the binding site I migrated to the binding site O3 (Figure 3B).This movement could be attributed to the strong electrostatic repulsion between the K + ion at the binding site I and the K + ions at the binding sites O5 and OGG, with a distance of approximately 7.3 Å between the K + ions at the binding sites I and OGG.] 4 G-quadruplex dimer in the presence of K + ions, it was not possible to differentiate between restraints that corresponded solely to the stacking interface between two tetramolecular G-quadruplexes.Therefore, the highresolution structure was calculated only for a monomeric unit (Table S3).The resulting structure, which satisfied all experimentally derived structural restraints, closely resembled the one observed in the presence of NH 4 + ions (PDB ID 8C7A, Figure 3B).However, in contrast to the structure in the presence of NH 4 + ions, the C6 and C5 residues exhibited partial overlap, as supported by the C5H6-C6H6 cross-peak in the NOESY spectrum (Figure S21).
To evaluate the geometry at the stacking interface between the two tetramolecular [d(G 4 C 2 )] 4 G-quadruplexes, four rotamers with different modes of the G-quartet stacking interface (stacking through 5-membered rings, 5/6-membered rings, 6-membered rings, and partial 6-membered rings, Figure S22) were constructed and subjected to MD simulation.A 200 ns MD simulation demonstrated that all four rotamers converged to a similar geometry, with the interface G-quartets composed of G1 residues stacking through 5-membered rings at a separation distance of 3.57 Å (Figures S23 and S24).Interestingly, the G-quartets at the interface displayed a smaller twist angle compared to the G-quartets composed of G1 and G2 residues (14.8 • vs. 21.6 • , Figure 3B).

K + Ion between Interface G-Quartets Is Firmly Bound
To determine the preferential cation binding sites within the [d(G 4 C 2 )] 4 G-quadruplex dimer, a G-quadruplex composed of two [d(G 4 C 2 )] 4 G-quadruplexes was constructed, with K + ions absent at the binding site O 3 and an additional K + ion positioned between the interface G-quartets comprised of G1 residues, denoted as O GG .Within a few picoseconds, it was observed that the K + ion initially located at the binding site I migrated to the binding site O 3 (Figure 3B).This movement could be attributed to the strong electrostatic repulsion between the K + ion at the binding site I and the K + ions at the binding sites O5 and O GG , with a distance of approximately 7.3 Å between the K + ions at the binding sites I and O GG .MD simulation of the [d(G 4 C 2 )] 4 G-quadruplex dimer confirmed that the K + ion at the binding site O GG remained firmly bound throughout the simulation.Thus, the occupancy of the binding site O GG by a K + ion is likely crucial for the dimerization of the tetramolecular G-quadruplexes.

Discussion
Tetramolecular G-quadruplexes are considered the simplest structures of G-quadruplex nucleic acids, where all strands align parallel to each other, and guanine residues adopt an anti-conformation around the glycosidic torsion angle [2,52].Previous studies have suggested that both d(G 4 C 2 ) and r(G 4 C 2 ) can form such structures [53].The interaction of cations with G-quadruplexes plays a significant role in their final structure formation.In our research, we employed 15 NH 4 + ions as substitutes for biologically relevant K + ions and utilized NMR spectroscopy to investigate cation interactions with d(G 4 C 2 ).Our focus was on identifying any additional cation binding sites beyond the G-quartets and vacant cation binding sites, as they can impact the overall structural stability, cation dynamics, and the directionality of cation exchange through the central G-quadruplex cavity.The presence of 15 NH 4 + ions induced the formation of a parallel tetramolecular [d(G 4 C 2 )] 4 G-quadruplex with an all-syn G-quartet located at the 5 -end, and its high-resolution structure was determined using NMR.Previously, the formation of an all-syn G-quartet at the 5 -end has been observed only in the minor species of other tetramolecular G-quadruplexes, such as d(TG 3 T), d(TG 4 T), d(TG 5 T), and d(TG 8 T) [45,48].Additionally, the [d(G 4 C 2 )] 4 Gquadruplex structure is characterized by the presence of a C-quartet formed by C5 residues stacked over the neighboring G-quartet composed of G4 residues.Various structural motifs, including U-, A-, T-, and C-quartets, as well as base triads, enhance the thermodynamic stability and functional potential of G-quadruplexes, serving as recognition points for drugs or binding sites for biologically important molecules [54].
In the presence of 15 NH 4 + ions, the tetramolecular [d(G 4 C 2 )] 4 G-quadruplex demonstrated the presence of three cation binding sites with different binding affinities, as evidenced by their uneven occupancy.The O 5 binding site was fully occupied, while the other two sites (I and O 3 ) were only half populated by cations.Our findings revealed that the most populated binding site, O 5 , within the [d(G 4 C 2 )] 4 G-quadruplex is characterized by four syn-anti steps of guanine residues and is located between G-quartets with minimal discrepancy in the alignment of their negative charge centers, influencing the octahedral coordination geometries of cations.MD simulations indicated an additional binding site for ammonium ions in the cavity between the G-and C-quartets, composed of G4 and C5 residues.Stacking of the C-quartet to the G4-quartet is similar to the stacking of C-quartet to the G-quartet in the unimolecular G-quadruplex formed by the d[(G 4 C 2 ) 3 G 4 ] sequence [19].The C-quartet mediated by amino-O2 hydrogen bonds was also observed in a parallel G-quadruplex formed by the d(TG 3 CG 2 T) from the SV40 virus [55] and the tetramolecular d(TG 2 CG 2 C) G-quadruplex associated with Fragile X syndrome [56].This observation aligns with previous reports, where ion binding was observed not only between G-quartets but also to a C-quartet and between the G-quartet and loop residues [40,53,[57][58][59].
Cations within G-quadruplexes display dynamic behavior, moving between binding sites and the bulk solution [42,60].Previous studies have demonstrated that 15 NH 4 + ions exhibit faster motion within tetramolecular structures, predominantly parallel structures defined by an anti-orientation around the glycosidic bonds of all guanine residues within Gquartets, compared to monomolecular and bimolecular structures with parallel/antiparallel strand orientation and mixed anti/syn-conformations of guanine residues [42,46,60].Hence, we propose that the molecularity of the G-quadruplex plays a critical role in dictating the speed of cation movement through the central channel.Additionally, the movement of cations towards the bulk solution and along the central cation cavity of G-quadruplexes can also be influenced by loop residues [44,46].Consequently, the kinetics of cation motion appears to be closely associated with the structural rigidity of the G-quadruplex.However, the findings presented here, combining NMR data with molecular dynamics simulations, suggest that the rate of cation exchange is likely strongly influenced by the availability of vacant cation binding sites.The presence of unoccupied binding sites reduces the mutual repulsion between ions, which is the primary driving force behind cation movement through the central channel, in comparison to a scenario where all binding sites are occupied by cations.
The presence of an all-syn G-quartet composed of G1 residues in the central channel of the d(G 4 C 2 ) G-quadruplex structure results in its closure at the 5 -end for the exchange of cations such as 15 NH 4 + , while protons can still exchange between the interior and bulk solution.Consequently, the exchange of 15 NH 4 + ions within the G-quadruplex and the bulk solution takes place exclusively through the 3 -end of the structure.The observed asymmetrical movement of 15 NH 4 + ions within the [d(G 4 C 2 )] 4 G-quadruplex, attributed to the syn-anti step, is supported by a significantly different energy barrier for 15 NH 4 + ions to cross the outer G-quartets composed of G1 and G4 residues.In contrast, the major form of the tetramolecular [d(TG 4 T)] 4 G-quadruplex, which only exhibits anti-anti base stacking, results in essentially symmetrical 15 NH 4 + ion movement within the central channel, characterized by an average energy barrier of approximately 14 kcal/mol [61].
It is known that short oligonucleotide sequences with a single G-tract and lacking 5or 3 -end overhangs can form higher-order structures through the stacking of individual Gquadruplexes or interlocking of slipped G-rich strands from different G-quadruplexes [62][63][64][65].Studies on the oligonucleotide d(TG 4 T) have demonstrated that replacing T with U at the 5 -end promotes the dimerization of two tetramolecular G-quadruplex units in the presence of 15 NH 4 + and K + ions, but not Na + ions [60].Similar observations have been reported for the dimerization of the dimeric G-quadruplex formed by d(GCG 2 AG 4 AG 2 ) via tail-to-tail stacking [66].In our study, we showed that while 15 NH 4 + ions promoted the formation of tetramolecular G-quadruplexes, the presence of K + ions induced higher-ordered species where two tetramolecular [d(G 4 C 2 )] 4 G-quadruplexes stack.Titrating KCl into a solution of [d(G 4 C 2 )] 4 folded in the presence of 15 NH 4 Cl revealed that a single K + ion at the interface of two separate tetramolecular G-quadruplex structures is sufficient to initiate dimerization.Recent studies have also indicated that at 100 mM of KCl, d(G 4 C 2 ) n sequences with n equal to 1, 2, and 4 form supramolecular G-quadruplex assemblies, known as G-wires, extending beyond 80 nm in length [67].
Hexanucleotide repeat expansions of d(G 4 C 2 ) in the c9orf72 gene are the most common genetic cause of ALS and FTLD [68].Although the full extent and implications of G-quadruplex formation in this region are yet to be determined, it is known that the transcription of the c9orf72 gene is negatively regulated by d(G 4 C 2 ) n G-quadruplexes formed within the gene [20].It is speculated that the formation of r(G 4 C 2 ) n prevents protein-RNA interactions crucial for the pathomechanism leading to ALS and FTLD [69,70].Recent studies have also indicated that the stabilization of d(G 4 C 2 ) n quadruplexes by small molecules mitigates ALS/FTLD pathology both in vitro and in vivo [71,72].Our study highlighted that the formation of an all-syn G-quartet may exhibit different binding properties compared to an anti-quartet, which should be considered when designing small molecules as potential drugs.Additionally, we demonstrated that K + ions, which are abundant in the intracellular environment, significantly stabilized the [d(G 4 C 2 )] 4 G-quadruplex compared to other ions and induced its immediate dimerization.The formation of such higher-ordered structures mediated by cations in vivo could introduce additional structural features in the hexanucleotide repeat expansions of the c9orf72 gene and potentially impact genomic stability and the pathophysiology of ALS and FTLD.

Sample Preparation
Oligonucleotide d(G 4 C 2 ) was synthesized on K&A Laborgeraete GbR DNA/RNA Synthesizer H-8 using standard phosphoramidite chemistry in DMT-off mode.Deprotection was performed with overnight incubation in 20% aqueous ammonia at 50 • C.Then, 2 M LiCl was added before heating samples at 90 • C for 10 min.Samples were purified and concentrated using an ultra-filtration device (Merck Millipore, Watford, UK) and an ultra-filtration membrane with a cut-off mass of 1 kDa (regenerated cellulose, Millipore).The samples were lyophilized overnight and diluted in 90% H 2 O and 10% 2 H 2 O to a final concentration of 2.0 mM per strand in the presence of 100 mM of 15 NH 4 Cl or 100 mM of 15 NH 4 Cl and 80 mM of KCl.Sample concentrations were determined by measuring absorbance at 260 nm using a Varian Cary 100 Bio UV-VIS spectrometer (Varian Inc., Palo Alto, CA, USA, Agilent Tecnologies, Santa Clara, CA, USA).The extinction coefficient was determined by the nearest-neighbor method.

Circular Dichroism Spectroscopy
All CD spectra were recorded on an Applied Photophysics Chirascan CD spectrometer (Leatherhead, UK) at 25 • C using a 0.1 or 1 mm-path-length quartz cell.The wavelength ranged from 220 to 320 nm.For CD spectra, an aliquot of the NMR sample was taken.Then, 100 mM 15 NH 4 Cl or 80 mM KCl and 100 mM 15 NH 4 Cl solutions were used for baseline correction.For CD melting experiments, 70 µM oligonucleotide solutions with 10 mM of Li-cacodylate buffer pH 6.0 and either 100 mM of NH 4 Cl or 100 mM of NH 4 Cl and 80 mM of KCl were used.A mixture of 10 mM of Li-cacodylate buffer and the respective salt concentrations were used as blank samples.Unfolding/folding processes were followed between 10 and 95 • C at a heating rate of 0.1 • C min −1 .CD spectra were acquired every 1 • C. Transition temperatures (T m ) were calculated as an average of T m , determined using the first derivative method at wavelengths of 260 and 300 nm.

UV Spectroscopy
UV melting experiments were performed on a Varian Cary 100 Bio UV-VIS spectrometer (Varian Inc., Agilent Tecnologies, Santa Clara, CA, USA) equipped with a thermoelectric temperature controller.Samples were prepared at 300, 100, 30, and 10 µM oligonucleotide concentrations in 10 mM of Li-cacodylate buffer, pH 6.0, 100 mM of NH 4 Cl, or 10 mM of Li-cacodylate buffer, pH 6.0, 100 mM of NH 4 Cl and 80 mM of KCl.Unfolding/folding processes were followed between 10 and 95 • C at a heating rate of 0.1 • C min −1 .Absorbance at 295 nm was measured every 0.5 • C.Then, 1, 2, 5, and 10 mm-path-length quartz cells were used for 300, 100, 30, and 10 µM samples, respectively.A combination of mineral oil and a fixed cuvette cap was used to prevent evaporation and sample loss due to high temperatures.A stream of nitrogen was applied throughout the measurements to prevent condensation at lower temperatures.Transition temperatures (T m ) were determined using the first derivative method.

NMR Spectroscopy
NMR experiments were performed on Agilent Technologies (USA) DD2 600 MHz and VNMRS 800 MHz NMR spectrometers at 25 • C (unless otherwise stated) using a tripleresonance cold probe.The 1D 1 H spectra were acquired with the use of DPFGSE solvent suppression.Diffusion coefficient measurements were performed by a spin-echo pulse sequence with PFG gradient strengths between 0.49 and 29.06 G cm −1 .The 2D NOESY spectra were acquired with mixing times ranging from 80 to 250 ms with the use of DPFGSE water suppression.Imino proton resonances were assigned through cross-peak analysis in the imino-imino and imino-aromatic regions of 2D NOESY spectra (Figure S4).The assignment of non-exchangeable aromatic and sugar proton resonances was accomplished by continuous sequential walks from G1 to C6 in the H8/H6-H1 , H8/H6-H2 /H2 , and H8/H6-H3 regions of 2D NOESY spectra (80, 150, and 250 ms mixing times) (Figure S5), complemented with 2D DQF-COSY, 2D TOCSY (20 and 80 ms mixing times), 2D ROESY (80 ms mixing time), and 2D 1 H-31 P COSY spectra (Figure S6), acquired on samples in 100% 2 H 2 O. Resonances of exchangeable protons were assigned using 2D NOESY recorded in 90% H 2 O and 10% 2 H 2 O.The number and location of 15 NH 4 + ion binding sites were determined using 2D 1 H-15 N HSQC, 2D NOESY, and 2D ROESY spectra.Assignment of well-resolved autocorrelation cross-peaks in the HSQC spectrum corresponding to bound 15 NH 4 + ions was established through NOE and ROE connectivity between 15 NH 4 + ion protons and neighboring imino protons of guanine residues.The movements of 15 NH 4 + ions and protons were followed by a series of 1 H-15 N NzExHSQC and 1 H-15 N HzExHSQC spectra with mixing times ranging from 13 ms to 3 s, and from 14 ms to 2 s, respectively.NMR spectra were processed and analyzed using VNMRJ 3.2 (Varian Inc.), Sparky (UCSF, San Francisco, CA, USA), and Mestrenova 9.1 software (Mestrelab Research, Santiago de Compostela, Spain).

1 H-15 N NzExHSQC Data Analysis
Volumes of autocorrelation and cross-peaks in 1 H-15 N NzExHSQC spectra were integrated using VNMRJ 3.2 (Varian Inc.) software.The volume of autocorrelation peak O 5 at a mixing time of 13 ms was set to 100, and all other integrals were normalized to this value.Exchange rates were determined using iterative least-squares fitting, performed in Origin 8.1 (OriginLab, Northampton, MA, USA).The decrease of intensity of the autocorrelation peaks B, O 5 , I, and O 3 , as a function of the mixing time (τ m ), is a result of ion movement from the original binding site as well as the spin-lattice relaxation (T 1 ), and is best described by the bi-exponential function [44,46]: where A 1 and A 2 are scaling factors and r 1 is a rate constant.Estimated T 1 relaxation times of autocorrelation peaks B and I were used in the analysis of cross-peak volumes as a function of the mixing time, corresponding to 15 NH 4 + ions exchanging with the bulk solution and ions moving within the [d(G 4 C 2 )] 4 G-quadruplex, respectively.Cross-peak volumes as a function of the mixing time were fitted to the following equation [44,46]: where A is a scaling factor and k is the exchange rate.

NMR Restraints and Structure Calculations
NOE distance restraints for exchangeable and non-exchangeable protons were obtained from 2D NOESY spectra with a mixing time of 150 ms, recorded at 25 • C in 90% H 2 O, 10% 2 H 2 O, and 100% 2 H 2 O, respectively.Due to severe overlap of cytosine H5-H6 cross-peaks, the average volume of the H1 -H2 cross-peak was used as a distance reference of 2.20 Å [73].NOE interactions were classified as strong (1.8-3.6 Å), medium (2.6-5.0Å), and weak (3.5-6.5 Å).The torsion angle, χ, was restrained between 30 and 90 • for residues in syn-orientation and between 200 and 280 • for residues in anti-orientation.Due to the symmetric nature of G-quadruplexes formed by d(G 4 C 2 ) in the presence of 15 NH 4 + or K + ions, NOE connectivity of only one strand was observed in NOESY spectra.In order to calculate high-resolution structures of G-quadruplexes adopted by d(G 4 C 2 ), all NMR-derived restraints were multiplied four times and assigned to chains A, B, C, and D. Structure calculations were performed with AMBER 14 software using the parmbsc0 force field [74], with parmχOL4 [75] and parmε/ζOL1 [76] modifications.The initial extended structure was obtained using the leap module of AMBER 14.Then, 1000 structures were calculated in 160 ps NMR-restrained simulated annealing (SA) simulations using the generalized Born-implicit model.The cut-off for non-bonded interactions was 999 Å, and the SHAKE algorithm for hydrogen atoms with tolerance of 0.0005 Å was used.Random velocities were used for each SA simulation.In the first 20 ps of simulation, the temperature was increased from 300 to 1000 K.In the next 20 ps, the temperature was kept constant at 1000 K.Then, molecules were gradually cooled, first to 500 K in the next 50 ps of SA, and then to 100 K in the next 30 ps of SA.In the last 40 ps of SA, the temperature was scaled to 0 K.This long cooling process was used to prevent stacking of cytosines in grooves of the G-quadruplex core.Force constants for hydrogen bond restraints and NOE-derived distance restraints were 20 kcal mol −1 Å −2 , while 200 kcal mol −1 rad −2 was used for the torsion angle χ, and 20 kcal mol −1 rad −2 for torsion angles ε and β.No planarity restraints for G-quartets were used during structure calculation.Structures were energy-minimized with a maximum of 20,000 steps, and 10 structures were selected based on the smallest number of restraint violations and the lowest energy.UCSF Chimerasoftware version 1.17.1 was used for visualization and preparation of figures [77].Atomic coordinates and the list of chemical shifts for [d(G 4 C 2 )] 4 : 15 NH 4 have been deposited in the Protein Data Bank under accession numbers PDB ID 8C7B and BMRB ID 30743.Atomic coordinates and the list of chemical shifts for [d(G 4 C 2 )] 4 :K + have been deposited in the Protein Data Bank under accession numbers PDB ID 8C7A and BMRB ID 30914.

Molecular Dynamics Simulation
Initially, three ammonium or potassium ions were placed between the O 5 , I, or O 3 binding sites, respectively.Three additional models were built, in which the ammonium ion was absent in the O 5 , I, or O 3 binding sites.The [d(G 4 C 2 )] 4 G-quadruplex dimer models were built based on the last snapshots of the MD simulation of the monomer.The dimeric model of the [d(G 4 C 2 )] 4 G-quadruplex in the presence of potassium ions was built based on the stacking of the G-quartet composed of G1 residues.Four different models were generated by manual rotation of one subunit along the axis, defined by the center of the Gquartet to produce four different types of dimer-stacked interfaces, i.e., partial 6-membered rings, 6-membered rings, 5/6-membered rings, and 5-membered rings (Figure S19), as observed in crystallographic structures [78].A K + ion was manually positioned between the dimer interfaces.The G-quadruplexes were then placed in a truncated octahedral (for monomers) or cubic (for dimers) box of TIP3P water molecules, with the box border at least 10 Å away from any atoms of the G-quadruplex.Extra ammonium or potassium ions were added to neutralize the negative charges of the G-quadruplex.After the models were built, the ion positions were randomized using CPPTRAJ [79] by swapping random water and ion positions, such that no ion was closer than 4 Å to another and all ions were greater than 6 Å away from the DNA, to avoid any biasing created by the initial placement of the ions.
The force field for MD simulation was the same as the SA simulation.The simulations were performed with the CUDA version of the pmemd module of AMBER 14 [80][81][82][83].Before the MD simulation, the systems were subjected to a series of minimizations and equilibration.The equilibration protocol started with 500 steps of steepest descent minimization, followed by 500 steps of conjugate gradient minimization with 25 kcal mol −1 Å −2 position restraints on DNA atoms.Then, the system was heated from 0 to 300 K during 100 ps, with position restraints of 25 kcal mol −1 Å −2 on the G-quadruplex.Afterwards, the system underwent minimization with 5 kcal mol −1 Å −2 restraints on DNA atoms using 500 steps of the steepest descent method, followed by 500 steps of the conjugate gradient.Then, the system was equilibrated during 50 ps at a constant temperature of 300 K and pressure of 1 atm with 5 kcal mol −1 Å −2 position restraints on DNA atoms.An analogous series of alternating minimizations and equilibrations was performed, consecutively using decreasing position restraints of 4, 3, 2, and 1 kcal mol −1 Å −2 .Finally, an equilibration using position restraints of 0.5 kcal mol −1 Å −2 and starting velocities from the previous equilibration, followed by a short 50 ps molecular dynamics, took place without any restraints.Pressure coupling used during equilibration was set to 0.2, and coupling during the last molecular dynamics phase was set to 5.
The production simulation was carried out at a constant pressure of 1 atm, and a constant temperature of 300 K, maintained using Langevin dynamics with a collision frequency of 2.0, respectively.Periodic boundary conditions were used, and electrostatic interactions were calculated by the particle mesh Ewald method [84,85], with the nonbonded cut-off set to 9 Å.The SHAKE algorithm [86] was applied to bonds involving hydrogens, and a 2 fs integration step was used.The production run was continuously carried out for 200 ns, and the snapshots were written at every 1 ps.Trajectories were analyzed using the CPPTRAJ module of AMBER.

Figure 1 .
Figure 1.Imino and aromatic regions of the 1 H NMR spectrum of d(G4C2 presence (B) of 100 mM of 15 NH4Cl.Spectra were recorded in 90% H2O 6.0, on a 600 MHz NMR spectrometer.The oligonucleotide concentrati The doublet signal (J = 74 Hz) denoted with asterisks corresponds to binding site O5 within the G-quadruplex.

Figure 1 .
Figure 1.Imino and aromatic regions of the 1 H NMR spectrum of d(G 4 C 2 ) in the absence (A) and the presence (B) of 100 mM of 15 NH 4 Cl.Spectra were recorded in 90% H 2 O and 10% 2 H 2 O at 25 • C, pH 6.0, on a 600 MHz NMR spectrometer.The oligonucleotide concentration was 2.0 mM per strand.The doublet signal (J = 74 Hz) denoted with asterisks corresponds to ammonium ions bound to binding site O 5 within the G-quadruplex.Upon addition of 100 mM of 15 NH 4 Cl, the formation of G-quadruplexes was initiated, and a fully folded state was achieved after three weeks (Figures 1B, S1 and S2).Four distinct signals of imino protons from guanine residues indicated that all guanines in d(G 4 C 2 ) were involved in Hoogsteen-type hydrogen bonds.No signals suggesting the formation of hemi-protonated C + -C base pairs were observed, even at pH 4.5 and 5 • C (FigureS3).The NMR data obtained from various 2D NMR experiments (FiguresS4-S6) consistently supported the formation of a parallel tetramolecular G-quadruplex with a C 4 symmetry axis and four G-quartets (Figure2A), with G1 having a synand G2-G4 an anticonformation of their glycosidic torsion angle (FigureS7).The size and strand orientation of the G-quadruplex structure were supported by the translation diffusion coefficient (D t ) of 1.41 ± 0.05 × 10 −6 cm 2 s −1 and the CD spectrum (FigureS8).In the presence of 100 mM 15 NH 4 Cl, [d(G 4 C 2 )] 4 also exhibits a remarkable thermodynamic stability, with unfolding occurring only at 83 • C (FiguresS9 and S10). ).

Figure 2 .
Figure 2. (A) Folding topology and cation binding sites within G-quadruplex adopted by d(G4C2) in the presence of 15 NH4 + ions, with the three ion binding sites shown.Syn-and anti-conformations of guanines are represented with grey and white rectangles, respectively.The arrows represent the observed movements between cation binding sites, with apparent rate constants depicted next to them.(B) Imino-aromatic region of the NOESY spectrum (left), showing cross-peaks between bound 15 NH4 + ions and nearby imino protons, and the 2D 1 H-15 N HSQC spectrum (right) exhibiting crosspeaks corresponding to 15 NH4 + ions in different chemical environments within [d(G4C2)]4.The vertical and horizontal dashed lines connect resonances of guanine imino and 15 NH4 + ion protons.(C) The 2D 1 H-15 N NzExHSQC spectrum at a mixing time (τm) of 1.1 s (left) and the 2D 1 H-15 N HzExHSQC spectrum at a mixing time (τm) of 40 ms (right).Annotations of autocorrelation and exchange cross-peaks are shown next to the cross-peaks.

Figure 2 .
Figure 2. (A) Folding topology and cation binding sites within G-quadruplex adopted by d(G 4 C 2 ) in the presence of 15 NH 4 + ions, with the three ion binding sites shown.Synand anti-conformations of guanines are represented with grey and white rectangles, respectively.The arrows represent the observed movements between cation binding sites, with apparent rate constants depicted next to them.(B) Imino-aromatic region of the NOESY spectrum (left), showing cross-peaks between bound 15 NH 4 + ions and nearby imino protons, and the 2D 1 H-15 N HSQC spectrum (right) exhibiting cross-peaks corresponding to 15 NH 4 + ions in different chemical environments within [d(G 4 C 2 )] 4 .The vertical and horizontal dashed lines connect resonances of guanine imino and 15 NH 4 + ion protons.(C) The 2D 1 H-15 N NzExHSQC spectrum at a mixing time (τ m ) of 1.1 s (left) and the 2D 1 H-15 N HzExHSQC spectrum at a mixing time (τ m ) of 40 ms (right).Annotations of autocorrelation and exchange cross-peaks are shown next to the cross-peaks.

2. 3 .
C5 Residues Form a Well-Defined C-Quartet within [d(G 4 C 2 )] 4 G-Quadruplex A set of G-quadruplex structures formed by the d(G 4 C 2 ) sequence in the presence of 15 NH 4

Figure 3 .
Figure 3. (A) Lowest energy structure of the [d(G4C2)]4 G-quadruplex in the presence of 15 NH4 + ions (PDB ID 8C7B) and (B) of the dimeric form of the [d(G4C2)]4 G-quadruplex in the presence of K + ions (PDB ID 8C7A).Residues G1, G2, G3, G4, C5, and C6 are shown in magenta, blue, green, violet, orange, and red, respectively.Cations within both structures are shown.Ion binding sites in (A) and (B) are marked with O5, I, O3, and OGC.OGC is the binding site between G4 and C5 residues.In (B)

Figure 3 .
Figure 3. (A) Lowest energy structure of the [d(G 4 C 2 )] 4 G-quadruplex in the presence of 15 NH 4 + ions (PDB ID 8C7B) and (B) of the dimeric form of the [d(G 4 C 2 )] 4 G-quadruplex in the presence of K + ions (PDB ID 8C7A).Residues G1, G2, G3, G4, C5, and C6 are shown in magenta, blue, green, violet, orange, and red, respectively.Cations within both structures are shown.Ion binding sites in (A) and (B) are marked with O 5 , I, O 3 , and O GC .O GC is the binding site between G4 and C5 residues.In (B) an additional binding site, O GG , is present.It is located between G1 and G1 residues, formed by 5 stacking of two [d(G 4 C 2 )] 4 G-quadruplexes.Stacking of G-quartets and G-quartets and cytosines are shown.

Figure 4 .
Figure 4.The projection of the center of a G-quartet composed of G4 residues (marked as G4 tet) to the adjacent G-quartet composed of G3 residues (marked as G3-quartet) within [d(G4C the presence of 15 NH4 + ions.Due to clarity, the 15 NH4 + ion between G-quartets is not present.T

Figure 4 .
Figure 4.The projection of the center of a G-quartet composed of G4 residues (marked as G4-quartet) to the adjacent G-quartet composed of G3 residues (marked as G3-quartet) within [d(G 4 C 2 )] 4 in the presence of 15 NH 4 + ions.Due to clarity, the 15 NH 4 + ion between G-quartets is not present.The O6 atoms of the G-quartets are shown as red sphere models, and centers of the G-quartets are shown in blue.d is the distance between the centers of two adjacent G-quartets.

2. 5 .
Free-Energy Barriers of 15 NH 4 + Ion Movement Confirm Asymmetry between Binding Sites NMR experiments revealed that the exchange of 15 NH 4 + ions from the central channel of the [d(G 4 C 2 )] 4 G-quadruplex with the bulk solution occurs through the 3 -end.To investigate the free-energy profiles of NH 4

Figure 5 .
Figure 5. (A) Free-energy profile for NH 4 + ion movements through G-quartets of [d(G 4 C 2 )] 4 Gquadruplex and the pulling direction of 15 NH 4 + ions, as well as (B) the representation of the reaction coordinate.G-quartets composed of G1, G2, G3, and G4 residues are marked as G1-, G2-, G3-, and G4-quartets, respectively.2.6.[d(G 4 C 2 )] 4 G-Quadruplex Dimerizes into Higher-Order Structures in the Presence of K + Ions Upon gradual titration of KCl into a solution of [d(G 4 C 2 )] 4 G-quadruplex, folded in the presence of 15 NH 4 Cl alone, the imino region of 1 H NMR spectra exhibited additional signals, indicating the presence of various G-quadruplexes in the solution (Figure6).At 80 mM of KCl, a single G-quadruplex species was observed again, albeit different from the initial one.NMR and CD data revealed the formation of a parallel tetramolecular G-quadruplex with a C 4 symmetry axis, with the G1 residue in the syn-conformation (FiguresS16-S19).Furthermore, the D t value gradually decreased upon the addition of KCl, reaching 1.19 ± 0.05 × 10 −6 cm 2 s −1 at 80 mM of KCl, indicating the dimerization of two tetramolecular G-quadruplexes, hereafter referred to as the [d(G 4 C 2 )] 4 G-quadruplex dimer.In a proton-deuterium exchange experiment, the imino protons of G1 and G2 exchanged at a slower rate compared to G3 and G4, suggesting that dimerization occurs through the 5 -end G-quartets (FigureS20).The [d(G 4 C 2 )] 4 G-quadruplex dimer exhibited significantly higher thermal stability compared to the one in the presence of 15 NH 4 Cl alone, with no unfolding observed, even at 95 • C (FiguresS9 and S10).

Figure 6 .
Figure 6.Imino regions of 1 H NMR and corresponding 1 H-15 N HSQC spectra of [d(G4C pH 6.0, in 10% 2 H2O in the presence of 100 mM of 15 NH4Cl and gradual addition of KC nucleotide concentration was 2.0 mM per strand.Assignments of imino resonances at t and end of titration are indicated above the signals.Annotations of cross-peaks are s the peaks.

Figure 6 .
Figure 6.Imino regions of 1 H NMR and corresponding 1 H-15 N HSQC spectra of [d(G 4 C 2 )] 4 at 25 • C, pH 6.0, in 10% 2 H 2 O in the presence of 100 mM of 15 NH 4 Cl and gradual addition of KCl.The oligonucleotide concentration was 2.0 mM per strand.Assignments of imino resonances at the beginning and end of titration are indicated above the signals.Annotations of cross-peaks are shown next to the peaks.1 H-15 N HSQC experiments conducted at each addition of KCl provided insight into the exchange of 15 NH 4+ with K + ions at individual binding sites within the G-quadruplex (Figure6).Combining the measured D t values with the HSQC data revealed that dimerization occurs before 15 NH 4 + ions fully exchange with K + ions (Figure7).This further indicated the presence of an additional K + ion at the interface of two tetramolecular Gquadruplex structures (Figure7).Within a G-quadruplex unit, K + ions initially replaced 15 NH 4 + ions at the O 3 binding site.Simultaneously, additional cross-peaks O 5 ' and I' with 1 H chemical shifts up-field of O 5 and I appeared (Figure6).These cross-peaks indicate the presence of 15 NH 4 + ions within G-quadruplex species where the O 3 binding site is occupied by a K + ion (Figure7).Approximately 70% of 15 NH 4 + ions at the O 3 binding site were replaced upon the addition of 1.0 mM of KCl.At 2.0 mM of KCl, around 90% of the O 3 binding sites and 70% of the I binding sites were occupied by K + ions.The existence of G-quadruplexes with K + ions at the O 3 and I binding sites and 15 NH 4 + ions at the O 5 binding site was evident from the presence of an additional cross-peak in the 2D 1 H-15 N HSQC spectrum (O 5 ").At 5.0 mM of KCl, approximately 50% of the G-quadruplexes had all three binding sites occupied by K + ions, while in other structures, 15 NH 4 + ions still resided at the O 5 binding site or both the O 5 and I binding sites.In the presence of 20 mM of KCl, approximately 80% of the G-quadruplexes had all three binding sites occupied by K + ions.At 80 mM of KCl, almost complete replacement of 15 NH 4 + by K + ions was detected, consistent with the observation of a single G-quadruplex species in the 1 H NMR spectrum.

Figure 7 .
Figure 7. Gradual exchange of 15 NH4 + by K + ions and the formation of dimeric species as the concentration of K + ions is increased from 0 to 80 mM.

Figure 7 .
Figure 7. Gradual exchange of 15 NH 4 + by K + ions and the formation of dimeric species as the concentration of K + ions is increased from 0 to 80 mM.2.7.Dimerization of [d(G 4 C 2 )] 4 G-Quadruplex Structures Occurs through Stacking of 5-Membered Rings Due to the high symmetry of the [d(G 4 C 2 )] 4 G-quadruplex dimer in the presence of K + ions, it was not possible to differentiate between restraints that corresponded solely to the stacking interface between two tetramolecular G-quadruplexes.Therefore, the highresolution structure was calculated only for a monomeric unit (TableS3).The resulting structure, which satisfied all experimentally derived structural restraints, closely resembled the one observed in the presence of NH 4 + ions (PDB ID 8C7A, Figure3B).However, in contrast to the structure in the presence of NH 4 + ions, the C6 and C5 residues exhibited partial overlap, as supported by the C5H6-C6H6 cross-peak in the NOESY spectrum (FigureS21).To evaluate the geometry at the stacking interface between the two tetramolecular [d(G 4 C 2 )] 4 G-quadruplexes, four rotamers with different modes of the G-quartet stacking interface (stacking through 5-membered rings, 5/6-membered rings, 6-membered rings, and partial 6-membered rings, FigureS22) were constructed and subjected to MD simulation.A 200 ns MD simulation demonstrated that all four rotamers converged to a similar geometry, with the interface G-quartets composed of G1 residues stacking through 5-membered rings at a separation distance of 3.57 Å (FiguresS23 and S24).Interestingly, the G-quartets at the interface displayed a smaller twist angle compared to the G-quartets composed of G1 and G2 residues (14.8 • vs. 21.6 • , Figure3B).