Energy landscapes of homopolymeric RNAs revealed by deep unsupervised learning

Abstract

Conformational dynamics of RNA plays important roles in a variety of cellular functions such as transcriptional regulation, catalysis, scaffolding, and sensing. Recently, RNAs with low-complexity sequences have been shown to phase separate and form condensate phases similar to lowcomplexity protein domains. The affinity for phase separation and the material characteristics of RNA condensates are strongly dependent on sequence composition and patterning. We hypothesize that differences in the affinities for RNA phase separation can be uncovered by studying sequence-dependent conformational dynamics of single RNA chains. To this end, we have employed atomistic simulations and deep dimensionality reduction techniques to map temperature-dependent conformational free energy landscapes for 20 base-long homopolymeric RNA sequences: poly(U), poly(G), poly(C), and poly(A). The energy landscapes of homopolymeric RNAs reveal a plethora of metastable states with qualitatively different populations stemming from differences in base chemistry. Through detailed analysis of base, phosphate, and sugar interactions, we show that experimentally observed temperature-driven shifts in metastable state populations align with experiments on RNA phase transitions. Specifically, we find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability, mirroring the propensity of RNA to form condensates. To conclude, this work shows that at least for homopolymeric RNA sequences the single-chain conformational dynamics contains sufficient information for predicting and quantifying condensate forming affinities of RNAs. Thus, we anticipate that atomically detailed studies of temeprature -dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Graphical abstract

Significance

The conformational dynamics of RNA molecules plays crucial roles in a variety of cellular functions such as transcriptional regulation, sensing, and metabolism. Recent experiments have shown an innate ability of RNAs to undergo phase separation by forming liquid-like condensates which may be closely linked with numerous RNA functions. In this study, we have employed atomistic simulations and deep learning techniques to characterize conformational ensembles of 20 repeat long single homopolymer RNA chains: poly(G), poly(A), poly(C), and poly(U). Energy landscapes of RNA chains reveal numerous metastable conformations with populations that show strong dependence on base chemistry. Furthermore, we find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability seen in experiments on RNA phase separation. Thus, we anticipate that atomically detailed studies of temeprature-dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Introduction

RNAs play crucial roles in nearly every facet of cellular information processing, encompassing catalysis, metabolism, and transcriptional regulation (1,2,3,4,5). Despite their ability to fold into intricate 3D structures, RNAs often retain a notable degree of conformational flexibility. An emerging perspective on RNA functionality underscores the significance of dynamic conformational ensembles, which are precisely calibrated to detect environmental cues such as small molecules, ion atmosphere variations, and temperature fluctuations (6,7,8,9,10).

While homopolymeric RNA sequences appear straightforward in composition, their biological roles are remarkably varied and intricate. Homo-ribo-polynucleotide tracts like poly(G), poly(A), poly(C), and poly(U) serve diverse functions (11,12,13,14). For example, mRNA molecules’ elongated poly(A) tails enhance translation and bolster mRNA stability (15,16). Similarly, such tracts are found in various noncoding RNAs—like U tracts in long noncoding RNAs—executing distinct roles. Yet, our understanding of the exact molecular mechanisms underpinning these tracts’ functionalities is limited, largely due to an incomplete understanding of their structural and dynamic features.

Numerous RNAs display high affinity for multivalent interactions with proteins, which facilitate phase separation and formation of membraneless organelles such as stress granules and ribonucleoproteins bodies (17,18). Recent experiments have shown that homopolymeric RNAs can also phase separate homotypically without any protein partners (17,18,19). Notably, the thermodynamics of this pure RNA phase separation is inherently sequence dependent, with the following order of condensate stability: poly(G) > poly(A) > poly(C) > poly(U) (18). Computational work employing coarse-grained models for RNAs has found that conformational transitions between hairpin and extended forms do take place even within condensate droplets (20,21). To fully grasp RNA’s inherent tendency for self-assembly and condensate formation, however, a detailed atomistic characterization of the RNA conformational free energy landscape, encompassing an array of metastable structures, is needed.

In this study, we have employed atomistic simulations and simulated tempering to sample temperature- dependent conformational states of 20-nucleotide single chains of poly(G), poly(A), poly(C), and poly(U) chains. We subsequently use the sampled backbone dihedral angles of RNA to map free energy landscapes, which characterize the main and metastable conformational states of RNA chains. To ascertain robustness of conformational landscapes and their features, we have carried out a careful comparison between different reduction techniques: principal-component analysis (PCA), time-lagged independent component analysis (TICA), and variational autoencoders (VAEs). Furthermore, we have explored how the free energy landscapes change with temperature, which sheds light on the ability of RNAs to sense thermal fluctuations via conformational transitions. Additionally, we delved into the microscopic interactions of RNA molecules, which underly distinct sequence-dependent conformational preferences of RNA chains. Finally, we find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability seen in experiments on RNA phase separation. We thus anticipate that atomically detailed studies of temeprature-dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Materials and methods

System preparation

The structures of a 20-base-long single-stranded poly(G), poly(A), poly(C), and poly(U) chains were generated by using X3DNA (22,23). Each chain is placed in a cubic box of 10 nm. After that, 25 mM ions (Na⁺ or Cl⁻) and water are added to fill the box. After preparing a solvated box containing single-stranded RNA and ions, the system was subject to energy minimization using a99SBdisp-ILDN (24) and TIP3P water (25) force field. All simulations have been run using the OpenMM 7.6 library (26). Following energy minimization steps, we ran 4 ns NVT simulations followed by a 4 ns NPT simulation at temperature of 300 K by using the Langevin Middle integrator (27) with an integration time step of 2 fs. We used OpenMM’s Monte Carlo barostat to maintain an average pressure of 1 bar in all systems. All simulations used periodic boundary conditions in all directions. Maintaining a NaCl concentration at 25 mM allowed us to explore the impact of base chemistry on RNA conformation and dynamics (28). Experiments have shown that higher salt concentration suppresses the ability of RNA to undergo phase transitions. Therefore, we mimic experiments (29) by choosing a low salt concentration of NaCl at 25 mM.

Simulated tempering

Because of RNA chains’ rugged free energy landscape, sampling conformational space of RNA often necessitates adopting enhanced sampling strategies (30,31,32). For sampling the conformational space of disordered biomolecules, various tempering techniques are typically employed, such as parallel tempering, Hamiltonian tempering, and simulated tempering (33). Simulated tempering (34,35,36,37) presents an attractive alternative allowing for simulations to be run on a single, fast GPU such as V100s or A100s.

In simulated tempering, attempts to change the temperature are made periodically among a ladder of discrete values, Ti (38). The probability for transition from Ti to Tj follows the Metropolis criterion. Weights for each temperature are selected using the Wang-Landau algorithm (39). Upon successful temperature transition, the system’s momentum is scaled by √Tj⁄Ti. An exponentially distributed 40-rung temperature ladder is employed with specific temperature ranges, 300–600 K for poly(G) and poly(A), 300–520 K for poly(C), and 270–500 K for poly(U), at an exchange attempt of 4 ps. A total production run simulation was performed over 7.5 μs for each chain. The average acceptance ratios for temperature transitions are as follows: poly(G), 28.3%; poly(A), 28.6%; poly(C), 43.7%; and poly(U), 32.02%.

To assess the convergence of our simulations, we carried out bootstrapping analysis using PCA (40), followed by a comparison of the landscape of the projections dPC1 and dPC2 (Figs. S1 and S2). Moreover, we conducted a cosine content analysis for each RNA’s first five PC components (37). Detailed information is provided in Figs. S1 and S2. Collectively, these analyses demonstrate the convergence of our simulations and the capture of all major conformational transitions.

Mapping conformational free energy landscapes of RNAs using torsional angles as features

Internal coordinates, and dihedral torsional angles in particular, have been shown to be good order parameters capable of clustering flexible protein and RNA chains into structurally distinct conformations when combined with dimensionality reduction techniques such as PCA (41,42,43). RNA has six backbone torsional angles: alpha, beta, gamma, delta, epsilon, and zeta. Additionally, to account for the conformation of the sugar component, the glycosidic torsional angle chi is also considered (44). All seven of these torsional angles are illustrated in Fig. 1. We apply sine and cosine transformations to each angle to transform dihedral angles from angular to a linear coordinate metric. In our 20-nucleotide RNA system, a total of 126 torsional angles exist. To reduce the dimensionality of our analysis, we leverage three distinct techniques: PCA, TICA, and VAEs. These techniques are applied to the sine- and cosine-transformed values of all 252 dihedral angles.

Figure 1.

(A) Zoomed-in view of the RNA’s backbone and uracil base. We labeled dihedral angles, which are used in featurization and dimensionality reduction of sampled conformational ensembles. (B) Schematic representation of the VAE, with the energy landscape plotted from reduced dimensions x and y of the dihedral angle from the latent space of the VAE. To see this figure in color, go online.

PCA

PCA is a widely used technique for reducing the dimensionality of appropriately featurized ensembles of biomolecules (45). PCA transforms the original feature space into a new set of orthogonal features called PCs, generated via linear combinations of the original features. The first PC captures the direction of maximum variance in the data. Subsequent PCs are orthogonal to the previous ones and capture decreasing variance. PCA involves calculating the covariance matrix of the original data and then finding its eigenvalues and eigenvectors. The eigenvectors represent the directions (PCs) along which the data vary the most, and the corresponding eigenvalues represent the magnitude of variance along those directions. A key limitation of PCA is that it assumes linear relationships between correlated features and may not capture more complex nonlinear relationships.

TICA

TICA introduces the concept of lag time, which determines the time span over which time correlations are examined (46,47). Based on a lag time, TICA identifies collective degrees of freedom that exhibit strong time correlations. After specifying a lag time, TICA focuses on identifying the data’s slowest and most persistent temporal patterns. Here “t1” represents the slowest reaction coordinates, while “t2” corresponds to the second slowest reaction coordinates. They are orthogonal in a scaled space. TICA offers several advantages over PCA in scenarios where temporal dynamics are important. Instead of just capturing variance, TICA emphasizes capturing time-dependent structures, making it more suitable for data sets with evolving patterns. With appropriate weighting, TICA can also be applied to data generated by replica exchange and simulated tempering where natural dynamics is not preserved.

VAE

While methods like PCA and TICA are limited to linear transformations, variational autoencoders (VAEs) leverage neural network architectures for capturing arbitrarily complex nonlinear relationships in the data (48). VAEs reduce the dimensionality of feature space by an encoder/decoder map. The encoder maps the input data to a lower-dimensional latent space, and the decoder reconstructs the input data from the latent representation. In VAEs, the encoder maps to mean and variance of a predefined distribution (usually a normal distribution). This enables the VAE to generate new data points, which have the same characteristics as training data, by sampling from this distribution. Here, the encoder generates a pair of mean and variance, which is used to construct x and y dimensions. The energy landscape is then built from x and y. Fig. 1 B illustrates a schematic diagram of this process. The architecture of our VAE is depicted in Fig. S3. The neural network used in VAE contains three hidden layers and ReLU activations in between them. We have employed the mean square loss for training.

Results

Learning conformational energy landscapes of poly(G), poly(A), poly(C), and poly(U) RNAs

Finding an optimal dimensionality reduction method for conformationally flexible macromolecules is not a trivial task because, generally, the intricate interdependence of structural features is poorly understood. Given the conformationally flexible nature of the RNA chain without a single unique fold, internal coordinates have an advantage over cartesian coordinates. Therefore, we have featurized the conformational ensembles of RNA into 252 sine and cosine values of all torsional angles (Fig. 1). Next, we compare three popular dimensional reduction techniques in the space of dihedral angles, including PCA, TICA, and VAEs.

All three techniques are trained on a combined data set of all dihedral angles of four different RNAs sampled at different temperatures using simulated tempering. Training on a combined data set allows machine learning techniques to 1) learn the intricate differences in conformations accompanying thermal folding/unfolding transitions of individual RNAs and 2) learn to discriminate between conformations of different RNAs at each temperature. After training on the combined dihedral angle data set, we then projected the learned collective variables on the original data, thereby obtaining energy landscapes for different RNAs at different temperatures.

All three methods successfully delineate major conformational differences between RNAs with different bases. When it comes to differences between structurally distinct conformations of the same RNA and across temperatures, we find that the VAE resolves these differences much better. In contrast, PCA and TICA generate less rugged landscapes, often lumping together structurally distinct conformations into single basins (Figs. 2, A–C, and S4–S6). For instance, when considering poly(A), the PCA group pseudoknot structure “D1” and stem structure “D5” are identical, while TICA and the VAE cluster these into separate states. The PCA and TICA groups have together distinct knot structures denoted as “D3,” “D4,” “D6,” and “D7” under one basin whereas the VAE clusters those states into separate basins (Fig. 3). This trend holds across the remaining bases and temperatures (Figs. S4–S6). In conclusion, although PCA, TICA, and VAEs succeeded in projecting landscapes for poly(G), poly(A), poly(C), and poly(U) separately, the VAE stands out as the superior option for delineating intricate conformational differences. This is attributed to the ability of neural networks to learn highly nonlinear relationships within feature space.

Figure 2.

Comparative conformational energy landscapes of RNAs generated by PCA, TICA, and VAEs. All three techniques are trained on a combined data set of all the dihedral angles of four RNAs across all temperatures. Poly(G) is denoted in black, poly(A) in blue, poly(C) in red, and poly(U) in green. Shown are the projections at a T of ∼300 K from (A) PCA, (B) TICA, and (C) VAE. To see this figure in color, go online.

Figure 3.

The projection of the reduced representation of dihedral angles of poly(A) is presented as (A) PCA as a function of pc1 and pc2, (B) TICA as a function of t1 and t2, and (C) VAE as a function of x and y. (D) Representative structures correspond to the different parts of the three landscapes shown in (A)–(C). To see this figure in color, go online.

Temperature dependence of RNA energy landscape reveals the base-specific nature of RNA unfolding

Temperature-induced unfolding is a natural way to characterize RNA folding thermodynamics (49). Experimental techniques such as temperature-controlled optical tweezers, isothermal titration calorimetry, or temperature jump experiments exploit temperature-induced conformational changes to investigate the thermodynamics and kinetics of RNA folding (50,51,52). The atomistic details of sequence-encoded conformational differences, however, remain inaccessible to most experiments. We have mapped the free energy landscape for poly(G), poly(A), poly(C), and poly(U) across a range of temperatures (Figs. 4 and S9–S12). Through projections of the reduced components of dihedral angles, we find the impact of RNA base chemistry on the temperature dependence of the conformational dynamics of RNA chains (Fig. 2, A–C). When comparing different dimensionality reduction techniques on their ability to discern structurally distinct conformations, the VAE emerges as a better tool for characterizing RNA’s free energy landscape. Specifically, we find multiple closely nested minima in free energy landscapes that are prominent at lower temperatures (Figs. 4 and 5). Interestingly, the energy landscapes of poly(G) and poly(A) exhibit a slightly more intricate nature than that of poly(C), while poly(U)’s landscape appears simpler than the other three (Fig. 5).

Figure 4.

Temperature-dependent energy landscapes generated from VAE- based projection of trajectories onto two main coordinates, x and y. (A–D) Guanine at temperatures 300, 384, 420, and 480 K. (E–H) Adenine at temperatures 300, 352, 384, and 420 K. (I–L) Cytosine at temperatures 300, 326, 350, and 381 K. (M–P) Uracil at temperatures 306, 326, 353, and 382 K. To see this figure in color, go online.

Figure 5.

Structural diversity seen in VAE-based free energy landscapes of RNA at a temperature of ∼300 K. (A) Poly(G) landscape, (B) poly(G)’s major structures, (C) poly(A) landscape, (D) poly(A)’s major structures, (E) poly(C) landscape, (F) poly(C)’s major structures, (G) poly(U) landscape, and (H) poly(U)’s major structures. To see this figure in color, go online.

As the temperature increases, RNA molecules access more conformations, accompanied by an expanded landscape with smoother features. After crossing folding temperature, all four RNAs adopt single global minima corresponding to fully unfolded chains. Melting temperatures are dictated by base chemistry, with poly(G) exhibiting thermal melting at the highest temperatures. Following poly(G) are poly(A), poly(C), and poly(U). We characterize structural diversity on the free energy landscapes and classify the structures into the the following types: 1) unfolded structures, 2) stem structures, 3) hairpin loops, 4) pseudoknot structures, and 5) knot structures (53).

Interestingly, a tendency to form stem or hairpin loop structures emerges across all RNA sequences. Notably, poly(G) prefers well-ordered hairpin loops or stem structures, as illustrated in Fig. 5 B. Poly(A) leans toward forming these structures, albeit not to the extent of poly(G). On the other hand, poly(C) and poly(U) display the propensity for highly mobile stem structures Where some RNA regions adopt hairpin loop or stem structures, the remaining part exhibits a mobile unfolded state (Fig. 5, F–H). Pseudoknot structures are also observed, with poly(A) and poly(G) displaying a more pronounced inclination toward this configuration, particularly poly(A) (Fig. 5 D). Poly(G) and poly(A) display well-ordered structures, whereas poly(C) and poly(U) adopt structures featuring highly mobile segments. The tendency to assume well-ordered structures is as follows: poly(G) > poly(A) > poly(C) > poly(U). This hierarchy underscores the varying propensities of different RNA sequences to form organized configurations. Comprehensively understanding how RNA bases shape the free energy landscape necessitates more in-depth exploration of microscopic interactions, which include solvent and ion components.

Temperature-dependent profiles of hydrogen bonding, base stacking, and base pairing

To learn the microscopic details driving base-specific melting profiles and conformational landscapes of RNAs, we first turn to the detailed atomistic analysis of stacking and base-pairing interactions. Before that, it is intriguing to observe that the latent spaces generated by various unsupervised dimensionality reduction techniques exhibit similarities between poly(G) and poly(C), as well as between poly(A) and poly(U). It appears that poly(C) and poly(U) are milder counterparts of poly(G) and poly(A), respectively. Therefore, we have looked into the interactions between 1) bases, 2) base and phosphate groups, and 3) bases and sugars by plotting the radial distribution function for all four RNA chains: poly(G), poly(A), poly(C), and poly(U).

We find that poly(G) and poly(C) exhibit similar behaviors in the interaction between base and phosphate groups at two specific distances, approximately 4 and 7 Å, with poly(G) showing slightly more extensive interactions (Fig. S15 A). Conversely, poly(A) and poly(U) lack a pronounced peak at around 4 Å in this interaction (Fig. S15 B). Likewise, in the interaction between bases and sugars, poly(G) and poly(C) display similar behaviors, while poly(A) and poly(U) exhibit more pronounced interactions. Poly(U) displays sharp peaks at nearly 4 Å (Fig. S15, C and D). In the context of base-base interactions, as expected, poly(G) and poly(A) exhibit stronger interactions than poly(U) and poly(C) (Fig. S16). The absence of strong base-base interactions in poly(C) and poly(U) characterizes them as milder counterparts of poly(G) and poly(A).

We use the radius of gyration (Rg) as a function of temperature as a measure of RNA folding/unfolding transitions (Fig. 6 A). The Rg displays a sigmoidal shape indicative of two-state thermodynamics of folding. Consistent with temperature dependence of free energy landscapes, melting temperatures follow the poly(G) > poly(A) > poly(C) > poly(U) order. We break down the intramolecular RNA contacts into hydrogen-bonding and base-stacking groups. Hydrogen bonding includes contacts between basepairs and between phosphate and base, as well as between sugar and base. Stacking includes intra-RNA stacking interactions. We computed the average number of hydrogen bonds against temperature (Fig. 6 B), the average number of stacking interactions against temperature (Fig. 6 C), and the average number of basepairs against temperature (Fig. 6 D). While all three plots exhibit folding transitions with a sigmoid shape, they do not mirror each other precisely. This discrepancy underscores the pivotal role of specific interactions within each system.

Figure 6.

Quantifying microscopic drivers of RNA (un)folding as a function of temperature. Guanine is denoted in black, adenine in blue, cytosine in red, and uracil in green. (A) Average radius of gyration versus temperature. (B) Average number of hydrogen bonds versus temperature. (C) Stacking interactions versus temperature. (D) Average number of basepairs versus temperature. To see this figure in color, go online.

Poly(G) notably displays the highest count of hydrogen bonds and stacking interactions. Purines, such as guanine and adenine, can clearly engage in more stacking interactions compared to pyrimidines, such as cytosine and uracil (Fig. 6 C). The number of hydrogen bonds follows the poly(G) > poly(A) > poly(C) > poly(U) order (Figs. 6 B and S17), while the stacking interactions follows the poly(G) > poly(A) > poly(C) = poly(U) order. Interestingly, poly(A) can readily form basepairs (Fig. 6 D), a capability not present in the other bases.

To reveal sequence-specific forces driving the folding of RNA into different structures, we compute the Pearson correlation between the Rg and nonbonded interaction types and between hydrogen bonds and stacking interactions across temperatures.

Poly(G) adopts well-organized stem or hairpin loop structures as a result of strong stacking interactions among its bases, supported by the formation of hydrogen bonds between the NH₂ and NH groups of the base and the phosphate groups (Fig. 7 C). The correlation between the Rg and stacking sharply decreases with increasing temperature, while the correlation between the Rg and hydrogen bonds remains relatively unaffected (Fig. 7, A and B). This observation implies that stacking interactions primarily govern the poly(G) dynamics rather than hydrogen bonds.

Figure 7.

Correlation of hydrogen-bonding patterns with conformational dynamics of RNA as a function of temperature. (A) Pearson correlation between radius of gyration and hydrogen bond count. (B) Correlation between radius of gyration and stacking interactions in RNA. (C) Illustration of the hairpin loop structure in poly(G), highlighting stacking interactions between bases and hydrogen bonds between bases and phosphate backbone on the right side. (D) The pseudoknot structure in poly(A) is represented with base pairing shown on the right side. (E) Depiction of the knot structure in poly(C), emphasizing the hydrogen bond between the base and phosphate backbone on the right side. To see this figure in color, go online.

Poly(A)’s ability to form basepairs (Fig. 7 C) leads to numerous base-paired stems, hairpin loops, and pseudoknot structures. This is distinct from poly(A), where well-ordered stacking interactions are predominant. Fig. 7 C highlights that poly(A) tends to form pseudoknot structures attributed to base-paired stems and NH₂ groups of parallel loop bases forming hydrogen bonds with stem phosphate groups. The correlation between the Rg and hydrogen bonds sharply increases with temperature, while the correlation between Rg and stacking interactions remains relatively stable (Fig. 7, A and B). This outcome emphasizes that hydrogen bonds primarily dictate the dynamics of poly(A) rather than stacking interactions. In poly(C), hydrogen bonds between the NH₂ of the base and phosphate groups emerge as the predominant interactions (Fig. 7 E), forming flexible, mobile stems, hairpin loops, or pseudoknot structures. Conversely, in poly(U), the absence of dominant interactions contributes to the highly mobile nature of its structure compared to the other three bases.

In sum, from atomistic analysis of nonbonded contacts, it is clear that chemical structures of the nitrogen base play a significant role in shaping its conformational preferences. This influence is exerted through interactions of the nitrogen base with itself, the phosphate group, and the ribose sugar.

Impact of temperature-dependent hydration and ionic condensation on RNA conformational dynamics

The conformationally extended RNA forms form an extensive network of hydrogen bonds and, due to high charge density, are screened significantly by the ionic environment. To discern the base-specific nature of RNA conformational preferences, it is necessary to dissect the role of ion and water-mediated interactions. We quantify the number of water molecules within 4 Å of RNA at various temperatures. As anticipated, with increasing temperature, RNA unfolds, coinciding with a rise in the average count of water molecules surrounding it (Fig. 8, A–C). Furthermore, we calculate correlations between the Rg and the number of water molecules surrounding RNA at different temperatures, as well as correlations between the number of water molecules and the number of hydrogen bonds at various temperatures.

Figure 8.

Quantifying the role of water on the conformational dynamics of RNAs. (A) Depiction of water expulsion as RNA folds into a knot structure. (B) Distribution of the amount of water within a 4 Å of RNA for all four RNAs at a T of ∼300 K. (C) Average amount of water within 4 Å across temperatures for all four RNAs. (D) Pearson correlation between radius of gyration and number of water molecules within 4 Å of RNA. (E) Correlation between the number of water molecules within 4 Å of RNA and the number of hydrogen bonds. To see this figure in color, go online.

The correlation between the Rg and the number of water molecules around RNA proves to be highly positive (as depicted in Fig. 8 D). This positive correlation points to entropy gain resulting from water-expulsion-driven RNA folding (Fig. 8 A).

The number of water molecules around RNA at T = 300 K is poly(A) < poly(G) < poly(C) < poly(U) (Fig. 8 B), whereas the Rg at T = 300 K is poly(G) < poly(A) < poly(C) < poly(U) (Fig. S13). This suggests that while poly(G) has the lowest Rg, poly(A) possesses the lowest count of water molecules around it. Additionally, the correlation between the Rg and the average number of water molecules is poly(A) > poly(G) > poly(C) > poly(U) (Fig. 8 D), and the correlation between water molecules around RNA and the number of hydrogen bonds is poly(A) << poly(G) = poly(U) = poly(C) (Fig. 8 E).

These observations indicate that poly(A) needs to repel a substantial number of water molecules in order to adopt folded conformations. Conversely, poly(G) folds with less water repulsion, implying that the folding of poly(G) is driven by a stronger energetic component. These correlations remain stable with increasing temperature in contrast to the other three, underscoring that water’s influence on poly(G) is comparatively limited due to its dynamics being driven by stacking interactions.

For the other three sequences, poly(A), poly(U), and poly(C), these two correlations exhibit a steep decline with rising temperature (Fig. 8, D and E), emphasizing the significant influence of water on their conformational behavior. Finally, when examining the ionic environment around RNA chains, we find a negative correlation between the Rg and the number of ions, implying that as RNA folds, an increasing number of cations gather around to counteract the repulsive force generated by the negatively charged backbone of RNA (Fig. S14, A–C). Simultaneously, as the temperature rises, the number of ions around RNA increases due to greater exposure (Fig. S14 B).

Discussion

The conformational dynamics of RNA and its affinity to engage in multivalent interactions underlies the ability of RNA to form biomolecular condensates (20,21,29,54,55,56,57). In this work, we have employed simulated tempering and deep generative learning to map the energy landscapes of homopolymeric RNAs across a range of temperatures. Simulations and energy landscapes show a wide range of conformations from fully folded to unfolded. We employed VAE in the space of torsion angles, which we demonstrate to be superior in its ability to cluster structurally distinct conformations of RNAs into distinct basins on the free energy landscapes. Analysis of conformational ensembles of poly(G), poly(A), poly(C), and poly(U) at different temperatures reveals numerous insights into base-specific interactions that lead to distinct structural preferences for different sequences. We find that RNA tends to form stems, hairpin loops, or pseudoknot structures regardless of the base and the thermal melting trends as follows: poly(G) > poly(A) > poly(C) > poly(U). Additionally, we have found that the temperature dependence of radii of gyration, number of hydrogen bonds, and stacking interactions follow the same trend. Experiments using small-angle X-ray scattering also align with our findings, indicating that the Rg of poly(U) tracts is higher than that of poly(A) (28).

We find that stacking interactions are the predominant drivers for poly(G) for adopting well-organized stem or hairpin loop structures (11,58). Poly(A) conformational preferences, on the other hand, appear to be shaped to a great extent by hydrogen bonds driving the formation of stem and pseudoknot structures, a feature that has been noted in the past (11). In poly(C), hydrogen bonds between the NH₂ of the base and phosphate groups emerge as the predominant interactions, driving the formation of flexible, mobile stems, hairpin loops, or pseudoknot structures. In contrast, in poly(U), the absence of dominant interactions contributes to the highly mobile nature of conformations compared to the other three bases. The inability of poly(U) to form cross-links also aligns with recent experiments from the Banerjee group illustrating that the presence of multivalent ions like spermine or Mg²⁺ is essential for poly(U) to undergo phase separation (17,18), which facilitate intermolecular connections through chelation.

A recent study by Jain revealed that RNA’s propensity to undergo multivalent base pairing can induce gelation without proteins. This phenomenon was observed in CAG, CUG, and GGGGCC repeats (20,59,60). Nonetheless, the phase separation by poly(G), poly(A), poly(C), and poly(U) shows that sequence-specific base pairing is not necessary for phase separation (18). RNA folding is inevitably accompanied by the expulsion of hydration layers from RNA (61). We find distinct signatures of water hydrogen bonding, which contribute to the folding profiles of RNA. Hydrogen bonding and hydration significantly constrain the dynamics of poly(A), poly(U), and poly(C). In contrast, water dynamics appears to be less important for poly(G) dynamics compared to stacking interactions. Notably, poly(A) has to repel more water before folding than poly(G).

In conclusion, our study of energy landscapes of homopolymeric RNA provides fresh insights into conformational preferences of RNA behavior including detailed mechanistic explanations of base-specific and water-mediated interactions underlying such preferences. We find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability seen in experiments on RNA phase separation. Thus, we anticipate that atomically detailed studies of temeprature-dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Data and code availability

All data are available in the manuscript and supporting material.

Author contributions

Conceptualization, V.R. and D.A.P.; analysis, V.R.; methodology, V.R.; writing, V.R. and D.A.P.

Editor: Jianhan Chen.