RNA G-quadruplexes emerge from a compacted coil-like ensemble via multiple pathways

Abstract

RNA G-quadruplexes (rG4s) are emerging as vital structural elements involved in processes like gene regulation, translation, and genome stability. Found in untranslated regions of messenger RNAs (mRNAs), they influence translation efficiency and mRNA localization. Additionally, rG4s of long noncoding RNAs and telomeric RNA play roles in RNA processing and cellular aging. Despite their significance, the atomic-level folding mechanisms of rG4s remain poorly understood due to their complexity. We studied the folding of the r(GGGA)₃GGG and r(GGGUUA)₃GGG (TERRA) sequences into parallel-stranded rG4 using all-atom enhanced-sampling molecular dynamics simulations, applying well-tempered metadynamics coupled with solute tempering. The obtained folding pathways suggest that RNA initially adopts a compacted coil-like ensemble characterized by dynamic guanine stacking and pairing. The three-quartet rG4 gradually forms from this compacted coil ensemble via diverse routes involving strand rearrangements and guanine incorporations. While the folding mechanism is multipathway, various two-quartet rG4 structures appear to be a common transitory ensemble along most routes. Thus, the process seems more complex than previously predicted, as G-hairpins or G-triplexes do not act as distinct intermediates, even though some are occasionally sampled. We also discuss the challenges of applying enhanced sampling methodologies to such a multidimensional free-energy surface and address the force-field limitations.

Graphical Abstract

Graphical Abstract.

Introduction

Guanine quadruplexes (G4) are important noncanonical nucleic acid structures formed by both DNA and RNA molecules [1]. Guanine-rich sequences capable of G4 formation are found across all domains of life [2]. Whilst the list of biological roles of DNA G4s (dG4) has been expanding for more than two decades, the existence of RNA G4s (rG4) in vivo has been demonstrated rather recently [3, 4]. Similarly to dG4, rG4s have been suggested to play major regulatory roles in gene expression [5–9] and at maintaining genome integrity at telomeres [10–13]. As such, rG4s present a promising target for treating various diseases, including cancer. Besides their biological roles, G4s are also used as building blocks in nanomaterials or utilized in biosensing [14, 15].

G4s are composed of at least two stacked guanine quartets (Fig. 1). Each quartet is formed by four guanines, which are H-bonded in a cyclical fashion using their Watson–Crick and Hoogsteen edges for pairing [16]. In the middle of the quartet, there is a cavity, which upon quartet-quartet stacking, forms a channel that runs through the G4 stem and binds cations, stabilizing the G4 structure.

Figure 1.

rG4. (A) Sketch of a parallel-stranded rG4; backbone of the first, second, third, and fourth G-tract (G-column, G-strand) is colored in red, orange, yellow, and mauve, respectively. (B) Guanine quartet; sugar moieties are not shown for clarity. (C) Top and side views of a model r(GGGA)₃GGG rG4 structure; G-tracts are colored as in panel (A). (D) Top and side views of the TERRA (GGGUUA)₃GGG rG4. G-tracts are colored as in panel (A).

There are some interesting differences between dG4 and rG4. dG4 can adopt diverse topologies differing in how the backbone winds around the quartets, leading to variability of G-strand orientations (parallel or antiparallel) and loop types (propeller, lateral, diagonal, or V-shaped) [17, 18]. Different dG4 topologies are intimately interrelated with specific syn/anti patterns of the glycosidic angles in the G-strands. Importantly, riboguanosine adopts the syn conformation much less likely than deoxyriboguanosine. As a result, rG4s adopt basically exclusively the all-anti parallel-stranded topology with propeller loops (Fig. 1) [19].

The folding kinetics of various G4s has attracted considerable attention. Most of the effort has been paid to DNA sequences, mainly the human telomeric sequence d(GGGTTA)₃GGG and its variants, whereas rG4 folding has been understudied. The folding process (its kinetics, involved intermediates, and its dependence on sequence, starting state and environment) of G4s is not only an interesting physical-chemistry phenomena per se, but it may also affect the biochemical roles of G4-forming sequences [20–22].

In general, dG4 folding kinetics (i.e. reaching thermodynamic equilibrium in a specific folding experiment) may be very slow; folding times from minutes up to weeks have been reported for dG4 [20–25]. The long folding timescales observed in many dG4 experiments can be explained by so-called kinetic partitioning [26, 27], i.e. presence of two or multiple long-living states (deep free-energy basins) on the G4 free-energy landscape which are acting with respect to each other as off-pathway kinetic traps. It has been argued that the key long-living states are diverse dG4 folds with different syn-anti patterns in their G-tracts. These different syn-anti patterns are thus essential to understand the unique topological frustration of the dG4 free-energy landscape [27–31].

In this context, the rG4 folding landscape is quite different. It has been theorized [27, 32] and subsequently demonstrated [33] that rG4 folding is faster compared to its dG4 counterparts. The reason is riboguanosine's reluctance to adopt the syn conformation. This generally eliminates the competing long-living G4 folds with non-native syn-anti G conformation patterns from the free-energy landscape and increases the chance that upon mutual encounter the guanines will be oriented in a manner favorable for a successful rG4 formation [32]. Thus, the folding landscape of an rG4 is much less topologically rugged than that of dG4.

Unfortunately, G4 folding is difficult to monitor at fine resolution using experimental methods. Techniques, such as optical/magnetic tweezers usually combined with fluorescence resonance energy transfer (FRET) [21, 30, 31, 34–43], circular dichroism (CD) [24, 25, 42, 44, 45], nuclear magnetic resonance (NMR) [22, 28, 33, 46, 47], or mass spectrometry [29, 48, 49] have been used to study the folding process, but none of them has sufficient temporal and spatial resolution to provide atomistic details. Indeed, most direct information about the folding has been obtained by time-resolved NMR [22, 28, 33, 46, 47, 50], and small-angle X-ray scattering (SAXS) [51]. Computer simulations have been used to complement the experiments by providing the atomistic aspect of the G4 folding [32, 38, 44, 52–75]. Standard (unbiased) all-atom explicit-solvent molecular dynamics (MD) simulations are the most accurate tool, but they are severely limited by the affordable time scale, reaching up to hundreds of microseconds, which is not enough to capture the entire G4 folding process [76]. Thus, standard MD simulations have been used to analyze properties of diverse types of structures that may participate in the G4 folding process and have indirectly suggested plausible mechanisms of the folding, including the kinetic partitioning [32, 52, 53, 55, 62, 63, 65–67, 71, 73]. Besides that, many atomistic simulation studies used diverse enhanced-sampling methods to probe the G4 folding [32, 38, 55, 58–61, 63, 65, 67–70, 72, 74, 75, 77, 78]. These methods are designed to investigate broader portions of the free-energy landscape. However, these approaches can also distort the folding mechanism, mainly due to excessive dimensionality reduction associated with the use of so-called collective variables (CVs) along which the sampling is enhanced (for a review see [27, 76]). Yet another approximate option is to use nonatomistic (coarse-grained, CG) methods [55, 57, 64, 79–82]. Accuracy of all simulation methods obviously depends on the quality of the potential energy function (the force field) describing the nucleic acid molecule [83].

All-atom MD simulations have also been used to study putative rG4 folding intermediates, namely hairpins formed by the sequence rGGGAGGG and telomeric repeat-containing RNA (TERRA) fragment rGGGUUAGGG [32]. Although these sequences are theoretically capable of forming G-hairpins, the simulations predicted that “G4-like” or “ideal” G-hairpins are unstable in the parallel orientation. Instead, a cross-like state was favored. However, unfolded, coiled and antiparallel hairpins were even more frequently populated. The key distinction between the “G4-like” and cross-like states lies in their pairing patterns (Supporting Fig. S1): in the “G4-like” state, all Gs are Hoogsteen-paired with their “correct” partners—matching those in a fully folded G4 structure. In contrast, the cross-like state represents an ensemble of structures where the strands are rotated relative to each other. This rotation results in Gs being paired in a less specific manner, with some Gs possibly remaining unpaired. The simulations have also suggested that parallel G-triplexes are likely rather unimportant intermediates due to their low structural stability. Instead, compact but rather unstructured coil-like states have been suggested as potential seeds from which the G4 fold can emerge. CG simulations investigating the rG4 folding suggested a multipathway process, with salient formation of stacked rGGG columns, devoid of any coil-like or cross-like structures [79], inconsistent with all-atom simulations of the hairpins [32]. The struggle to capture the rG4 folding by computational tools and the complexity of the rG4 free-energy landscape can be demonstrated by recent simulations using another CG model, in which the RNA chain folded into the native rG4 only when the native G:G base pairs were predefined manually [84].

We have recently reported all-atom folding simulations of d(GGGA)₃GGG dG4 using enhanced-sampling MD, combining replica-exchange approach with metadynamics [68]. The sequence used has the minimal loop length (one nucleotide) and thus folds just into a single dominant topology, the parallel-stranded all-anti dG4. The study highlighted the multipathway nature of the folding process devoid of distinct well-defined simple intermediates. The simulations suggested that the molecule first forms a loosely structurally defined compacted coil-like ensemble, from which the dG4 structure itself emerges through multiple small consecutive steps; the compacted coil-like state can be considered as equivalent to the molten-globule-like state inferred from the latest SAXS experiments [51]. At the same time, however, the simulations predicted that the folded dG4 does not correspond to the global minimum on the free-energy landscape [68]. This has been attributed to inaccuracy of the simulation force field, which does not capture the proper balance between the unfolded and folded ensembles; the correctly folded structure has nevertheless been reached with the help of the used CV and the associated biasing metadynamics potential.

In the present work we use the same method to probe the free energy landscapes of r(GGGA)₃GGG and r(GGGUUA)₃GGG (TERRA) rG4s. The results enable us to assess similarities and differences in the folding process of dG4 and rG4 and the effect of the loop length. The data suggest that the folding of parallel-stranded rG4 is in many aspects similar to the folding of dG4 with single-nucleotide loops; it may proceed via various intermediates, including cross-like triplexes, two-layered G-triplexes, and slip-stranded rG4s. It also seems that longer loops of TERRA increase the likelihood of folding routes sampling the triplex-like intermediates. Importantly, regardless of the rG4 sequence, all these intermediates are again emerging from the loosely defined compacted coil-like (molten-globule-like) ensemble, which thus serves as the key transitory ensemble of the folding process.

Materials and methods

Starting structures

The folding simulations were initiated from a fully extended r(GGGA)₃GGG and TERRA r(GGGUUA)₃GGG RNA strands, built by nucleic acid builder in the A-RNA conformation [85]. The RNA was described with OL3 all-atom force field [86–88] and solvated in explicit SPC/E [89] water under the presence of 0.15 M KCl salt excess [90]. The minimal distance between the extended RNA strand and the solvent box border was 25 Å.

To create the reference target rG4 structure for r(GGGA)₃GGG, we took the parallel-stranded dG4 structure (PDB ID: 2LEE [91]), mutated the cytosines in the single-nucleotide loops to adenines and converted the whole molecule into RNA; this procedure is justified as the sequence is known to form a parallel-stranded rG4 [19]. The molecule was then carefully equilibrated to assure that it adopts a proper rG4 structure which can be used for evaluation of the simulated structures by the ϵRMSD metric (see below) [92]. The reference structure for the TERRA sequence was created by taking the TERRA rG4 bimolecular structure (PDB ID: 2KBP [93]) and modeling the missing middle UUA loop, followed by relaxation of the rG4 in a standard MD simulation.

Simulation protocol

We used the replica-exchange solute-tempering simulation protocol (REST2) [94] coupled with well-tempered metadynamics [95] (thus called ST-metaD) to enhance the sampling. In total, we ran four ST-metaD simulations for the r(GGGA)₃GGG sequence, each with 16 replicas, and one ST-metaD simulation for the r(GGGUUA)₃GGG sequence with 32 replicas (Table 1). The replicas spanned the effective temperature ladder from ∼280 to ∼500 K, and the metadynamics bias potential was built in each replica. As a CV, we used the inter-tract ϵRMSD metric [68, 92], which describes the fit of guanine base positions and orientations with respect to the reference folded rG4 structure. In general, ϵRMSD is a metric tailored for a description of nucleobase interactions in nucleic acids. It is sensitive to changes in base-pairing and stacking and thus is suitable for monitoring of the G4 folding process. Inter-tract ϵRMSD is a modification that considers only ϵRMSD contribution between G-tracts, while ignoring stacking of guanines within a single G-tract to avoid an excessive promotion of intra-tract guanine stacking at the expense of inter-tract encounters (Supporting Fig. S2) [68, 92].

Table 1.

List of rG4 folding simulations

Simulation number	Replicas × simulation time (μs)	ΔGfold (kcal/mol)a	Number of folding events
r(GGGA)3GGG
a1	16 × 4.0	9.6	4
a2	16 × 4.0	15.6	3
a3	16 × 4.0	12.3	3
a4	16 × 2.0	-	1
r(GGGUUA)3GGG
uua1	32 × 4.0	18.5	5

^aSnaphots with ϵRMSD to the reference folded structures <0.7 were considered as part of the folded ensemble (see Supporting Figs S3 and S4) while the remaining snapshots were counted as the unfolded ensemble.

While we only used the reference replica (with an effective temperature of 298 K) to calculate ΔG_fold, we have monitored the development in the continuous (demuxed) trajectories to visualize the folding events. As folding events we consider portions of the continuous trajectories, so-called reactive trajectories, which bring the simulated molecule from a clearly unfolded state to a fully folded G4. In the reactive trajectories we monitor the development of simulated structure in detail to capture the folding pathway. Snaphots with ϵRMSD to the reference folded structures <0.7 were considered as part of the folded ensemble, while the remaining snapshots were counted as the unfolded ensemble. In addition to ϵRMSD, we also monitored K⁺ coordination number CN to guanine O6 atoms, measuring the instantaneous distance r_ij (in Å) between i^th K⁺ and j^th O6 atom, defined as CN_i = Σ_j [1 – (r_ij / 3.5)⁶] / [1 – (r_ij / 3.5)¹⁸].

Before the ST-metaD simulations, the systems were relaxed to avoid unfavorable contacts and voids. The structures were minimized and equilibrated in a series of steps with gradual decrease in position restraints. Then we performed a 500 ns long nVT simulation, from which we extracted 16 or 32 starting structures for the 16 or 32 replicas of the actual ST-metaD simulation to heterogenize the sampling (Table 1). We used the V-rescale thermostat to keep the temperature at 298 K [96]. We employed the SHAKE algorithm [97] together with the hydrogen-mass repartitioning [98], which allowed us to use a 4-fs integration time step. Simulations protocols are available in Supporting Information.

While the bias potential in ST-metaD simulations converges after ∼2–3 μs in our simulations, it is certainly not possible to obtain complete sampling of the folding landscape due to the very rich conformational space of the simulated molecules. Therefore, while the ST-metaD protocol combined with ϵRMSD is, to our knowledge, one of the most powerful methods to simulate G4 folding, it could only sample lower singles of folding events in the 16- and 32-replica simulations. One of the r(GGGA)₃GGG ST-metaD simulations we carried out sampled only a single folding event after 2 μs and predicted a very high ΔG_fold. Thus, we stopped that run. Detailed analyses of the individual continuous trajectories (ϵRMSD and travel through the replica space) are provided in the Supporting Information. Limitations of the ST-metaD method that we encountered in course of this study are discussed in the ‘Results and discussion’ section.

Finally, to complement the biased r(GGGA)₃GGG ST-metaD simulations, we have run a set of unbiased (standard) MD simulations starting from the same extended RNA conformation. These standard simulations were carried out in either 0.15 M KCl salt excess or net-neutralizing Li⁺. Otherwise, the simulation conditions were the same as those in reference replicas from ST-metaD simulations. We ran simulations with Li⁺, which does not stabilize G4s in general, to estimate the effect of the salt concentration on the dynamics of extended RNA strand. We performed four and two 10 μs-long independent replicates using KCl and Li⁺ ion conditions, respectively.

The Gromacs package (v. 2018.8 and 2021.4) [99] with PLUMED (v. 2.5.6 and 2.7.3) [100] was used to run the ST-metaD simulations, while AMBER20 [85] was used for the unbiased simulations.

Results and discussion

We have performed four simulations of the RNA rG4 with the r(GGGA)₃GGG sequence, and one simulation of the TERRA rG4 r(GGGUUA)₃GGG, and observed eleven and five rG4 folding events, respectively (Table 1, Supporting Table S1, and Supporting Movies SM1–SM16). Most importantly, the simulations show that the folding proceeds via a loosely defined compacted coil-like ensemble for both sequences, from which rG4 gradually arises by following diverse micro-routes and intermediates. High ΔG_fold energies of both rG4s (Table 1) nevertheless indicate that the force field is unable to reproduce the rG4 thermodynamic stability correctly; the folding is achieved because it is boosted by the bias potential along the used CV.

Folding free energy

The simulations predict that the rG4 ΔG_fold energy is about +12.5 kcal/mol on average for r(GGGA)₃GGG and +18.5 kcal/mol for TERRA (Table 1; we estimate the error to be on the order of a few kcal/mol [68]), with the fully folded rG4 separated from the rest of the ensemble by a relatively low energy barrier (Fig. 2). The bias potential converged, and the replica space seems to be sampled sufficiently well (Fig. 2 and Supporting Fig. S5), but the folding events were rather rare. In comparison to the analogous dG4 with single-nucleotide loops studied before [68], the average rG4 ΔG_fold is lower than that of dG4 by ∼4.5 kcal/mol while the shape of the free-energy profile along the ϵRMSD CV is rather similar (Fig. 2). Thus, in both cases, as well as for the longer TERRA sequence, the global minimum ensemble is far from the folded G4, suggesting that the AMBER force field struggles to capture G4 thermodynamic stability in general.

Figure 2.

Folding free energy. (A) Bias convergence in the three rG4 folding simulations of r(GGGA)₃GGG (a1–a3), TERRA rG4 r(GGGUUA)₃GGG (uua1), and their comparison with DNA dG4 d(GGGA)₃GGG (aDNA) from a previous work [68]. (B) ΔG_fold along the ϵRMSD CV. Values are calculated using a bin width of 0.1.

The evident global force-field imbalance is most likely dominantly caused by the lack of polarization in pair-additive force fields [101]. This leads, for example, to well-documented large-scale inaccuracies in description of the ion–ion and ion–G-quartet interactions in the G-stems [102]. Treatment for these inaccuracies may come from the polarizable force fields, which have already been shown to improve the behavior of ions in the G-stems. However, the description of the loop regions is still suboptimal there [103–105]. Reparametrization of nonbonded interactions specifically designed for G4 structures is another possible approach that may improve the calculated free energy of G4 folding [59]. Besides the absence of polarization, we have also noticed several times that the propeller loops in atomistic simulations may be spuriously destabilized by the current force fields though no clear origin of such under-stabilization has so far been suggested [27, 32, 65, 71, 106].

In summary, although our folding free-energy estimation is clearly offset by a huge margin, the simulated folding pathways should still provide some valid insights into structural ensembles populated on the G4 folding landscape since the ST-metaD potential energy bias overcomes the force-field misbalance.

Multipathway folding of rG4s

From the four ST-metaD simulations of r(GGGA)₃GGG (cumulative time of 224 μs) and one ST-metaD simulation of TERRA (128 μs), we obtained eleven (Figs 3 and 4, Supporting Fig. S6, Supporting Table S1, and Supporting Movies SM1–SM11) and five (Fig. 5, Supporting Figs S7 and S8, Supporting Table S1, and Supporting Movies SM12–SM16) folding events, respectively. Although the pathways of the individual folding events were very diverse and each was unique (Figs 3–5, Supporting Fig. S7, and Supporting Movies SM1–SM16), we identified a few general features that were common among the simulations. Typically, the folding started by a compaction of the extended RNA chain by formation of H-bonds between two G-tracts [e.g. the first and last (fourth) G-tract (labeled as 1–4), or the second and third one (2–3)], although not necessarily leading to the correct native rG4-like pairing. Although the guanines within the individual G-tracts tended to be stacked, we commonly observed states with only two guanines stacked while the third one was then typically stacked on another G-tract or with the loop base(s). Notably, these structures with two G:G base pairs were not necessarily the ideal G4-like G-hairpins, but they often had the G-tracts rotated into the cross-like shape (Supporting Fig. S1). In the cross-like arrangement, the base pairing is looser compared to the Hoogsteen base pairing (with just one H-bond or a bifurcated H-bond between two Gs) as the bases are not coplanar. The initial pairing led to (or was followed by) a compaction of the chain into the coil-like arrangement. This intermediate state cannot be characterized by some structure-specific interactions, as it was structurally very diverse ensemble, containing parallel, cross-like, as well as antiparallel hairpins. The hairpins could be formed by pairing of two or three guanines either from neighboring G-tracts (i.e. G-tracts 1–2, 2–3, or 3–4) or between the first and last G-tract (1–4). The pairing and the whole compacted coil-like ensemble were very dynamic, so when a hairpin was formed, it could have unfolded later. Importantly, the initial inclusion of ions usually happened in this compacted coil-like state, thus preceding formation of quartets, and was dynamic, too (see below).

Figure 3.

Development of key structural features in the 11 folding events, i.e. the reactive trajectories, of the r(GGGA)₃GGG sequence. The respective simulation runs and continuous trajectories are indicated on the y-axis (see Supporting Table S1). Irrelevant trajectory portions (not considered as part of the folding event) are omitted in the graphs. The four top-most stripes in each graph monitor stacking of the G-tracts; the green color means that all three guanines are stacked. The next four stripes monitor mutual orientations of the neighboring G-tracts (see the detailed legend to the figure in the top right). The following five stripes indicate formation of the individual rG4 layers (triads or quartets) and cation coordination between them. When all the stripes are colored as in the left column of the legend, the rG4 is fully formed. The last stripe shows the overall radius of gyration (Rg); note that Rg does not appear to be a good descriptor of the folding (see also below). Representative examples of mutual orientation of two G-tracts are shown in the bottom left corner. Actual structures from seven folding events are shown in Fig. 4. Verbal description and movies of the events (Supporting Movies SM1–SM11) are provided in Supporting Information while the development of complete trajectories is shown in Supporting Supporting Fig. S6. Equivalent analysis for the TERRA sequence is presented in Supporting Figs S7 and S8.

Figure 4.

Example of seven r(GGGA)₃GGG rG4 folding pathways with various intermediates and one unproductive pathway with misfolded rG4 (bottom line). The reactive trajectory numbering corresponds to that in Fig. 3 and Supporting Table S1. The intermediates shown are snapshots representing broad ensembles of similar structures. All folding events are also visualized in Supporting Movies SM1–SM11.

Figure 5.

Five TERRA rG4 folding pathways with various intermediates. The reactive trajectory numbering corresponds to that in Supporting Fig. S7 and Supporting Table S1. The intermediates shown are snapshots representing broad ensembles of similar structures. The events are also visualized in Supporting Movies SM12–SM16.

As a side note, in 40 μs of unbiased MD simulations starting from the extended RNA strand in KCl, ran independently from the ST-metaD simulations, we achieved only two transient formations of the cross-like hairpins and slip-stranded parallel hairpins (Supporting Fig. S9; see Supporting Results for detailed information). It is essentially the same result as obtained for a short single-nucleotide-loop and the longer TERRA hairpin-forming sequences in an earlier MD simulation study [32]. The ST-metaD and unbiased MD simulations follow the same very early folding pathway (before the compacted coil-like ensemble is reached) but no further progress is then seen in the unbiased simulations confirming the essential role of the used enhanced sampling protocol.

After reaching the compacted coil-like state, the rG4 gradually grew from it via numerous incremental rearrangements. We usually observed the formation of two-quartet rG4 intermediate ensembles, which could be slip-stranded, i.e. with vertically shifted G-tracts. In r(GGGA)₃GGG (Figs 3 and 4), we did not detect any formation of states that would contain just one quartet. Complete fully folded three-quartet rG4 then emerged by incorporation (zipping) of the missing guanines into the two-quartet intermediate and strand-slippage to achieve the correct pairing, if necessary. Interestingly, three-layered G-triplex with the fourth G-tract in the cross-like orientation to it was observed in two simulations, but it did not lead directly to fully folded rG4 formation.

For the TERRA sequence (Fig. 5 and Supporting Fig. S7), all observed folding pathways passed via G-triplex-like intermediates. However, it was not a single G-triplex structure. The structures had two or three G-triads, and various combinations of strands were involved. Even all four strands could form the G-triplex when one of its columns was mixed from Gs of two strands. These triplex intermediates were often stabilized by interaction of the triplex stem with loop uracils. Nevertheless, the triplexes never converted directly into the fully folded rG4. Instead, all folding events finally proceeded via a two-layered rG4 intermediate, usually with slipped strands.

Analysis of cation binding showed that incorporation of cations into the growing G4 did not require some specific structure but occurred rather randomly during the compacted coil-like ensemble stage, as already stated above. As the compacted coil was getting structured, the coordination number of the bound cations was increasing, thus possibly helping to structure the intermediates (Fig. 6 and Supporting Figs S10 and S11). For the formation of two- or three-quartet G4, a bound cation was already required.

Figure 6.

Cation coordination in simulations of the r(GGGA)₃GGG sequence. (A) Cation coordination to guanine O6 atoms plotted with respect to ϵRMSD to the native folded structure. (B) Cation coordination to O6 atoms of guanines plotted with respect to the Rg. Rg was calculated for the whole RNA molecule. Frames from reference replicas of simulations a1–a4 (cf. Supporting Table S1) were used to make both plots. For plotting, 50 bins were used for each axis. Cation coordination in the TERRA simulation follows qualitatively the same trend (Supporting Fig. S11).

Interestingly, although the simulated rG4s typically adopt the expected parallel all-anti topology, in one r(GGGA)₃GGG folding simulation we detected formation of a misfolded two-layered rG4, which had an antiparallel G-tract with all guanines in the syn conformation (this would correspond to 3 + 1 hybrid topology; Fig. 4, bottom line). The true extent of this phenomenon cannot be evaluated from the current simulations reliably because the ϵRMSD CV drives the RNA towards the all-anti parallel-stranded G4, i.e. the simulations are rather biased against the syn orientation of Gs in the later stages of the folding pathways. However, the simulations show that the syn G conformation is not prohibited and its occurrence in some of the misfolded rG4s indicates that structures with syn G orientation may be transiently populated during the folding attempts. It also indicates that folding of structures of rare rG4s with syn-oriented guanines [107, 108] may arise by the same folding mechanism as the “common” all-anti rG4s.

Key role of the compacted coil-like ensemble in the folding process

Our findings offer the following picture of the rG4 folding. At the atomistic level, it is a gradual, multipathway growth of the G4 from the compacted coil-like ensemble via numerous diverse individual routes avoiding sharply structured intermediates equivalent to cut-outs from the structure of the final rG4 (i.e. G4-like intermediates; Fig. 7, and Supporting Figs S6 and S8). As noted above, the results may be obviously limited by the accuracy of the atomistic force field and the used CV. However, the inter-tract ϵRMSD CV should not prevent formation of rG4-like hairpin and triplex intermediates; in fact, it may even facilitate their formation. Obviously, due to the use of both replica-exchange and metadynamics enhanced sampling methods, the present simulations cannot provide any insights into the kinetics (duration) of the individual folding attempts and pathways. However, they should be capable of providing insights into the structural ensembles that are involved in the process. The suggested folding mechanism is consistent with the one predicted for the analogous DNA sequence [68]. The structuring mechanism is also remarkably similar to the one theorized based on the simulation behavior of RNA G-hairpins and their preference of adopting the cross-like arrangement over the ideal G4-like parallel-stranded one [32].

Figure 7.

Generalized rG4 folding mechanism as suggested by all-atom simulations in the present work and previous CG simulations [79]. The rectangles are guanines, the empty circles are loops, and the K⁺ cations are shown as blue spheres. The CG model proposes a multipathway folding mechanism involving a few well-defined G-hairpin-based intermediates but does not specify when cations interact with the RNA. In contrast, the all-atom simulations reveal numerous atomistic pathways originating from a compact, unstructured coil-like ensemble, without the presence of well-ordered intermediates. Folding progresses incrementally, with structuring occurring within the compact coil-like state. During this process, cations are incorporated, and various two-quartet rG4 configurations emerge as important components of the late-stage folding transitory ensemble. Thus, while both models propose “multipathway” folding, their interpretations of the term differ significantly.

On the other hand, a recent CG simulation study of TERRA, the single-nucleotide-loop r(GGGU)₃GGG, and several other sequences suggested a different folding process [79]. The authors initially observed formation of three-layered parallel G-hairpins and either two of these combined to form the rG4 directly, or a three-layered G-triplex occurred and then the rG4 was formed by attachment of the fourth strand (Fig. 7). Thus, formation of columns of three stacked guanines was a hallmark of the CG model. In our all-atom simulations, guanines tended to stack together, too, but structures with just two stacked guanines in a tract were more prominent, leading to the gradual formation of two-quartet rG4s intermediates. Such structures were absent in the CG-based model. Thus, although both atomistic and CG simulations studies indicate a multipathway rG4 folding process, the nature of these pathways differs markedly between the two approaches (Fig. 7). The CG model proposes a few routes with salient straightforward rG4-like intermediates, while the atomistic model suggests a multipathway process with numerous individual atomistic folding routes, starting from a compacted coil-like ensemble, largely avoiding well-defined rG4-like intermediates. The compacted coil-like state can perhaps be likened to the molten globule state in protein folding, with the stacked G-tracts resembling simple secondary structure elements.

One reason for the difference is the nature of the CG model, which reduces nucleotide into three beads and does not include the explicit solvent with cations. This obviously leads to a less precise description of the interactions between nucleotides. It decreases the number of possible interactions and simplifies and smoothens the free-energy landscape, possibly pushing the system into regions that are structurally idealized. In other words, the CG model is unlikely to populate the compacted coil-like ensemble. Our all-atom simulations, on the other hand, are affected by the used CV (inter-tract ϵRMSD), and one might argue that it likely pushes the guanines together to form the compacted coil and might also promote formation of the two-quartet rG4 intermediate ensembles. We have tested alternative (and simpler) CVs, namely the number of native H-bonds and the K⁺-coordination number, which in our opinion would have had a smaller impact on the folding pathways. However, simulations using these CVs resulted neither in productive folding nor into structures at least remotely resembling partially folded rG4 (data not shown), justifying the use of the inter-tract ϵRMSD metric.

Clearly, without coarse-graining or enhanced-sampling with CV-based dimensionality reduction in all-atom MD simulations, spontaneous rG4 folding would be infeasible within the currently affordable simulation time scales. Each approach has limitations, and considering the potential impact of the methodological differences, it is possible that the actual folding mechanism may incorporate elements from both the CG model and the atomistic model presented here. We nevertheless think that the picture provided by the all-atom simulations is the one closer to reality. Although the G4 molecules with their quartets and bound ions are quite specific biomolecular structures, the G-rich nucleic acid chains should not fundamentally differ from the other biomolecular chains in their tendency to form compacted coil-like ensembles. The possible role of hidden (invisible) coil-like ensembles in G4 folding processes has been noted also in some experimental studies [28, 47]. Notably, a time-resolved NMR study of the TERRA sequence (with some flanking nucleotides not included in our study) suggests that there is an initial collapse of the RNA strand at the start of the folding process, which indirectly supports the presence of the compacted coil-like ensemble [33]. Furthermore, a recent time-resolved SAXS study of the human telomeric dG4 forming sequence suggests formation of a molten-globule-like state, containing dynamic transient hairpins, in the early stages of the folding process [51]. This matches well with the formation and description of the compacted coil-like ensemble in the MD simulations reported here. Considering the resolution limits of the SAXS experiments and major approximations of the MD simulation technique used here, we suggest that both studies may in fact report a similar phenomenon.

Finally, it should also be noted that the rG4 folding depends on the initial RNA conformation, because the shape of the strand can vary under different conditions. For instance, due to entropic considerations, the molecule is unlikely to be fully extended, unless externally constrained (e.g. tethered). Various pre-folded structures already featuring G4-like G:G base pairing even in the absence of K⁺ have been described by NMR for several DNA sequences [109, 110]. Partial prefolding was also suggested for the TERRA rG4 [33]. Therefore, adapting the computational protocol to use an alternative starting structure might be desirable when investigating the folding of a specific G4 under specific conditions. In our case, however, the use of an extended RNA strand is justified, as it collapses into a compacted coil-like state—an ensemble supported by experimental studies. Thus, despite starting from a rather unrealistic extended form, our MD simulations evolve towards plausible conformations and do not seem to be critically affected by the starting structure.

Unfolding pathways

Nearly all transitions in the direction of unfolding that we observed in our simulations were only partial unfolding events. Those typically were unzipping of a base from the G-stem or strand slippages. We evidenced only one full unfolding event in one of the r(GGGA)₃GGG simulations. It began with a base unzipping, leading to a two-layered G4. Then it proceeded via a deformed G-triplex and cross-like triplex into a cross-hairpin and ultimately ended up as a compacted coil (Supporting Fig. S12). Similar initial rG4 unfolding movements (unzipping a guanine or strand slippage) were reported in earlier MD simulation studies [52, 69]. Thus, it seems that the unfolding pathways are a reversal of the folding process towards the compacted coil ensemble. It makes sense under the rather equilibrium conditions during the MD simulations, where the principle of microscopic reversibility should apply. The lack of major unfolding transitions also reflects the limitations of the ST-metaD protocol for the G4 system discussed below.

RNA compacted coil-like ensemble is looser than that of DNA

Rg is sometimes used, in experimental as well as simulation studies, as a measure for determining whether G4 is folded or not. Small Rg values are implicitly assumed to indicate a folded state. However, Rg of the compacted coil ensemble is smaller than that of the fully folded rG4 (calculated for the whole molecule; Supporting Fig. S13), suggesting that Rg cannot reliably discriminate between fully unfolded but compacted, partially unfolded and fully folded rG4 states. We have demonstrated this before also for dG4 [64, 68]. Interestingly, comparison of the values with our previous study on dG4 [68] reveals that while Rg of folded rG4 is comparable to dG4, Rg of the coil-like ensemble formed by DNA is smaller, suggesting the DNA ensemble is more compact than the RNA one.

Limitation of the ST-metaD method with inter-tract ϵRMSD CV

ST-metaD simulations represent a high-end enhanced-sampling technique capable of overcoming free-energy barriers even in rather large systems, which was not computationally feasible until recently. A limitation that arises naturally from the metaD technique is its inability to accelerate sampling in directions orthogonal to the CV used. Identifying a single CV or a set of CVs that effectively capture the reaction coordinate (or mechanism) across a multidimensional free-energy space is often challenging. There is always a risk that important transitions may remain obscured by the chosen CVs. In cases where the conformational space is inherently highly multidimensional with many slow degrees of freedom, achieving a reliable dimensionality reduction may even be fundamentally impossible. We have previously suggested that, even though ϵRMSD is one of the best-known CVs, especially the dG4 folding landscapes are so intrinsically multidimensional that their description is principally irreducible to one or few CVs, no matter how carefully chosen they are [27, 76]. Therefore, we employed the replica-exchange solute tempering (ST) to help overcome enthalpic barriers and to somewhat alleviate the main drawback of metaD. However, the capabilities of the replica-exchange protocols to enhance sampling are also not unlimited [111, 112].

Notably, another recently introduced approach for improving sampling along CVs is the On-the-fly Probability Enhanced Sampling method (OPES) [113]. It modifies the way CV is influenced by focusing on reconstructing the probability distribution rather than building a bias potential as done in metaD [113]. Instead of depositing Gaussians to incrementally adjust the bias, OPES uses an on-the-fly kernel density estimate of the probability distribution to define the bias and has been suggested as a faster alternative to metaD for multidimensional free-energy surfaces where it is difficult to choose CVs [113]. OPES has recently been used to explore the folding and conformational transitions between several dG4 topologies of the DNA human telomeric sequence [60]. Although OPES can also be combined with parallel tempering methods [60, 114], detailed testing involving transitions in complex systems is required to confirm its benefits over the pure metaD approach, particularly when combined with parallel tempering methods.

Even though the combined ST-metaD method sounds robust, we have encountered a rather undesired behavior in our simulations, which clearly illustrates limits of the enhanced sampling simulations. Extending the simulations beyond 2 μs did not necessarily yield more folding events as most folding events occurred in the early simulation stages (Fig. 3, Supporting Fig. S8, and Supporting Table S1). We think that this simulation development likely stems from a stronger drive toward the folded state that is applied at the simulation start in conjunction with a suboptimal CV. In the later simulation stages after the rG4s was formed, we typically observed only reversible unzipping of one or more guanines from the rG4 and only in one case the rG4 unfolded completely. Once the bias starts reaching convergence in the second half of the simulations, the sampling of folding events becomes less efficient, i.e. the expected frequent reversible rG4 unfolding and refolding events did not happen. We admit that this limited structural sampling indeed may cast some doubts on the calculated rG4 ΔG_fold values, even though the bias was technically converged (Fig. 2). Previously reported simulations on dG4 [68] suffered from the same issue, so the relative comparison of the rG4 an dG4 ΔG_fold values could still be qualitatively correct. We also assume that the observed folding pathways are qualitatively representative from the structural point of view (Figs 4 and 5), considering the limitations that have already been discussed throughout the paper. Nevertheless, our observation is a reminder of the limitations that may be present even when using sophisticated enhanced-sampling methods like ST-metaD and which may not always be acknowledged in the literature. In fact, this issue might in principle be similar to the tradeoff between the convergence speed, number of folding events and the extent of exploration of the free-energy landscape caused by the bias deposition and suboptimal selection of CVs as described for the OPES method [115]. Yet, even with this sampling issue, ST-metaD is likely one of the best MD simulation techniques suited for studying the G4 folding problem at all-atom resolution available to date, and we still suggest that the simulations realistically reflect important features of the folding landscape [116]. Its use was essential in the present study, given the long folding times of rG4s; for example, the TERRA rG4 folding rate was estimated to be ∼1.45 min⁻¹ [33]. We would like to point out that no such problems were detected in our recent ST-metaD simulations of simple RNA stem-loop hairpins [112, 117]. We plan to explore this issue in greater detail in future work.

Conclusions

rG4s have been recently identified as structural species likely involved in a variety of biological processes. Despite its importance, the folding mechanism of rG4s has not yet been fully understood at the atomistic level of description. In this work, we successfully folded the r(GGGA)₃GGG and r(GGGUUA)₃GGG (TERRA) sequences into the parallel-stranded rG4 using all-atom MD simulations (Supporting Movies S1–S16). To achieve this goal, we employed the well-tempered metadynamics method coupled with solute tempering (ST-metaD), which enabled us to overcome the sampling limitations of standard unbiased MD simulations without the necessity to employ CG models. Our results suggest that the rG4-forming strand forms a compacted coil-like ensemble, in which consecutive guanines tend to stack to each other (Fig. 3 and Supporting Fig. S7). This ensemble is very dynamic. The arising columns of two or more stacked guanines interact together and form various intermediate subensembles, such as cross-like triplexes, two-layered G-triplexes, and most importantly two-quartet rG4s (Figs 4 and 5, and Supporting Figs S6 and S8). The compacted coil-like ensemble may thus functionally resemble the molten-globule state in protein folding. The monovalent ions extensively interact with the RNA (or DNA [68]) chain already at this stage, which may facilitate its further structuring. Finally, the full three-quartet rG4 emerges from this transitory ensemble by step-by-step rearrangements involving incorporation of additional guanines, G-tract rotations, strand slippage movements and possibly some other transitions. Compared to r(GGGA)3GGG, TERRA—with its longer three-nucleotide loops—shows a preference for folding pathways that proceed via triplex-like intermediates; however, these intermediates do not directly convert into the fully folded rG4 structure. We thus demonstrate that the rG4 folding process is inherently multipathway. However, by “multipathway” folding we mean a process where the final rG4 fold emerges from the compacted coil-like ensemble via numerous very diverse individual routes, and not a process that involves a few sharply defined intermediates possessing already the native Hoogsteen base pairing (Fig. 7). The difference between the two diverse but at the same time complementary interpretations of the term “multipathway G4 folding” is discussed in the paper.

As noted in the Introduction, earlier studies have attributed the long folding times of many DNA quadruplexes to kinetic partitioning [21, 27, 28]. This phenomenon arises from the presence of multiple deep free-energy basins (long-lived folds, probably diverse quadruplexes) on the energy landscape, which compete with each other. Our simulations show that while RNA can form off-pathway misfolded nonparallel rG4s to certain extent, their stability is rather low. This reluctance of RNA to form G4s other than all-anti parallel-stranded ones largely eliminates the kinetic partitioning and highlights the key difference from dG4 folding landscapes [27, 33, 76].

While the simulations have provided mechanistic insights into the process of rG4 folding, they have also disclosed a severe force field imbalance. The calculated rG4 folding free energy is ∼+12.5 kcal/mol and +18.5 kcal/mol for the r(GGGA)₃GGG and TERRA sequences, respectively, which is in striking disagreement with experiments. We assume that the prime reason for this discrepancy is the lack of polarization in the simulation force field leading to an imbalance between the folded and unfolded ensembles. We nevertheless suggest that the basic structural aspects of the atomistically visualized folding events are relevant.

Although the composed ST-metaD enhanced sampling method has helped us to successfully overcome the high free-energy difference and positive free energy of the folded state (as predicted by the force field), we have faced issues intrinsic to the enhanced sampling technique itself and its use on a highly multidimensional free-energy surface. The ST-metaD trajectories experienced most of the folding events shortly after the simulation start, when the bias towards the target native rG4 was the strongest. In later stages, the simulations became rather unproductive. This observation thus reminds us of limitations to consider and bear in mind when running enhanced sampling simulations of complex systems, which, in our opinion, are not always adequately acknowledged in the literature.

In summary, using enhanced-sampling all-atom MD simulations we have folded two different parallel-stranded rG4s from an extended RNA chain, tracking down altogether sixteen individual folding events in the continuous ST-metaD trajectories. Based on the simulations we suggest that rG4 folding is a multipathway process in which a compacted coil-like (or molten-globule-like [51]) ensemble plays a key role, forming a starting stage for the individual molecules to launch their folding attempts and structural transitions.

Supplementary data

Supplementary data is available at NAR online.

Conflict of interest

None declared.

Funding

This work has been funded by the Czech Science Foundation grant number 23-05639S. Funding to pay the Open Access publication charges for this article was provided by Czech Science Foundation grant number 23-05639S.

Data availability

Starting structures, reference structures, simulation protocols, and Supporting Movies are available at Github (github.com/ppokor/G4_folding_RNA), plumed input files are deposited in plumed-nest (plumed-nest.org/eggs/25/001/) and simulation trajectories (reference replicas, reactive trajectories) and the calculated bias files are available on Zenodo (10.5281/zenodo.15227933).