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# Condensates in RNA repeat sequences are heterogeneously organized and exhibit reptation dynamics

## Abstract

Although it is known that RNA undergoes liquid–liquid phase separation, the interplay between the molecular driving forces and the emergent features of the condensates, such as their morphologies and dynamic properties, is not well understood. We introduce a coarse-grained model to simulate phase separation of trinucleotide repeat RNAs, which are implicated in neurological disorders. After establishing that the simulations reproduce key experimental findings, we show that once recruited inside the liquid droplets, the monomers transition from hairpin-like structures to extended states. Interactions between the monomers in the condensates result in the formation of an intricate and dense intermolecular network, which severely restrains the fluctuations and mobilities of the RNAs inside large droplets. In the largest densely packed high-viscosity droplets, the mobility of RNA chains is best characterized by reptation, reminiscent of the dynamics in polymer melts. Our work provides a microscopic framework for understanding liquid–liquid phase separation in RNA, which is not easily discernible in current experiments.

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## Data availability

All data are included in the paper and the Supplementary Information. The raw data are available on Zenodo at https://zenodo.org/record/5794441.90

## Code availability

The codes to perform simulations and analyses are available at GitHub (https://github.com/tienhungf91/RNA_llps).

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## Acknowledgements

We are indebted to A. D. Bowen at the Visualization Laboratory (Vislab), Texas Advanced Computing Center, for generating the videos. We are grateful to H. Maity, S. Myong, M. Mugnai, S. Sinha and R. Takaki for stimulating discussions and critical reading of the manuscript. This work was supported by National Science Foundation Grant (CHE 19-00093) and the Welch Foundation Grant (F-0019) through the Collie–Welch chair. We thank the Texas Advanced Computing Center for providing computational resources.

## Author information

Authors

### Contributions

H.T.N. and D.T. conceived and designed research, H.T.N. conducted research, H.T.N., N.H. and D.T. analysed the results and wrote the manuscript.

### Corresponding author

Correspondence to D. Thirumalai.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 Determination of the concentrations of the two coexisting phases.

Results are shown for (CAG)47. Time dependent changes in the concentrations in the aqueous phase is on the left and for the droplet is on the right. The plateau values near the end are used to calculate the concentrations at which the two phases coexist.

### Extended Data Fig. 2 Structures of isolated (CAG)n monomers.

a, Distribution of the end-to-end distance Ree and b, radius of gyration Rg of (CAG)n with n=47, 31 and 20. The vertical dash lines in a indicate mean values for self-avoiding random walk chains with the same n. Snapshots are for (CAG)47. Cytosine is in cyan, adenine is in red and guanine is in black. c, Bond–bond orientational correlation function cos θ (s) as a function of the sequence distance s. The periodicity, as indicated by the vertical lines, is unmistakable. The inset shows average inter-nucleotide distances R(s) vs. s. The dashed line shows R(s) for a self-avoiding polymer (R(s) s0.588). At large s, there is an abrupt drop in R(s) because the two ends strongly interact with each other, thus bringing them to proximity. d, Contact map for (CAG)47 shows that the majority of interactions occur along the anti-diagonal, indicating the formation of hairpin structures.

### Extended Data Fig. 3 Sequence of events in early droplet formation extracted from the simulation of (CAG)47.

Eleven RNA chains were chosen and coloured to see how individual chains form oligomers and grow to a single droplet. All other chains are in grey for clarity. Each panel has a label indicating the simulation time. (a) At the earliest times, all the eleven chains are monomers with no interactions between them. (b) Two chains merge to form a dimer. (c) The dimer captures another chain and becomes a trimer. There is another dimer that is formed around the same time. (d) The two oligomers further grow to a tetramer and trimer, respectively, by interacting with another chain. (e) The tetramer and trimer coalesce into a heptamer. There are still four other chains in the monomer form. (f) One of the remaining monomers joins the oligomer making it an octamer. (g) Two of the remaining monomers form a dimer. (h) It takes some time to the next event (~ 4 × 106τ from (g) to (h)). (i) The octamer eventually captures the last monomer and becomes a nonamer. (j) The nonamer and the dimer finally coalesce into an 11-mer. The sequence of events is complicated, and is different for different chains.

### Extended Data Fig. 4 Simulations for the scrambled sequence.

a, Comparison of fraction of RNA chains inside the droplets for (CAG)47 and the scrambled sequence at three different concentrations. Snapshots near the end of the simulations for the two sequences are shown. b, Droplet size evolution for the scrambled sequence (top) vs. (CAG)47 (bottom). Each horizontal line corresponds to a specific droplet in the system. The size is denoted by the colour (colour scale is on the right). c, Concentrations of the two phases for the scrambled sequence.

### Extended Data Fig. 5 Effect of non-canonical bps.

Simulations for an isolated (CAG)47 monomer where non-canonical bps are allowed (purple), compared with the original model where there are only WC bps (orange). Shown on the left are histograms of the end-to-end distance Ree (top) and radius of gyration Rg (bottom). An intramolecular contact map is shown on the right. Some representative snapshots from the simulations are shown at the bottom.

### Extended Data Fig. 6 Calibration of the bp interaction strength $${U}_{bp}^{o}$$.

a, Structural dependence of a small CAG repeat sequence (AGGCAGCAGCCAAAAGGCAGCAGCCA) on $${U}_{bp}^{o}$$. The sequence we chose to calibrate $${U}_{bp}^{o}$$ is almost identical to the X-ray structure (PDB 3NJ6) (ref. 3), except with the addition of an AAAA tetraloop and two terminal A nucleotides. The sequence adopts extended conformations for small $${U}_{bp}^{o}$$ ($${U}_{bp}^{o} < 4.5$$ kcal mol−1), and folds into hairpin conformations in the bp interaction range, $$4.5 < {U}_{bp}^{o} < 6.0$$ kcal mol−1. We set $${U}_{bp}^{o}=-5.0$$ kcal mol−1. b, Root mean squared deviation (RMSD) between the simulations and the X-ray crystal structure, shown for $${U}_{bp}^{o}=-5.0$$ kcal mol−1. The averaged value for RMSD is around 5 Å, which is reasonable given the coarse-grained nature of the model. c, Superposition of the simulated structure (yellow and grey beads) onto the X-ray structure for the lowest RMSD (around 1 Å).

### Extended Data Fig. 7 Condensate formation does not depend on the cooling rate.

Fraction of chains in droplets or existing as oligomers/monomers. The vertical dashed lines indicate when the temperature is lowered (from 100C to 20C). Snapshots from left to right correspond to, respectively, the end of 80C, the end of the cooling period and the final state of the simulation.

### Extended Data Fig. 8 Structures of isolated (CUG)n monomers.

Same as Extended Data Fig. 2, but for (CUG)n monomers. In addition to WC G-C base pairs, Wobble base pairs between G-U could also form. a, Distribution of the end-to-end distance Ree and b, radius of gyration Rg of (CUG)n with n=47, 31 and 20. The vertical dash lines in a indicate mean values for self-avoiding random walk chains with the same n. c, Bond–bond orientational correlation function cos θ (s) as a function of the sequence distance s. The inset shows average inter-nucleotide distances R(s) vs. s. The dashed line shows R(s) for a self-avoiding polymer (R(s) s0.588). At large s, there is an abrupt drop in R(s) because the two ends strongly interact with each other, thus bringing them to proximity. d, Contact map for (CUG)47 shows that the majority of interactions occur along the anti-diagonal, indicating the formation of hairpin structures.

### Extended Data Fig. 9 Dissociation of RNA droplets at 150 mM NaCl.

The simulations were started from the final configuration obtained in the droplet simulation of 200μM of (CAG)47 (left). The repulsive electrostatic interactions between RNA nucleotides (due to the incomplete neutralization of phosphate charges) lead to the disassembly of the droplets, leaving only monomers and small oligomers (right).

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–7.

### Supplementary Video 1

Dynamics of phase separation in (CAG)47 from monomers to condensates. The monomer RNA concentration is 200μM. At the initial time (τ = 0), the chains exist as monomers. At intermediate times, oligomers form, which subsequently fuse together resulting in large droplets as time progresses. See Figures 1a, 3a, and 5 for the corresponding trajectories. Note that some of the individual RNA chains may look less helical shape due to trajectory-smoothing needed for easier visualization. The movie shows both fusion as well as fission of the droplets.

### Supplementary Video 2

Growth and fusion of condensates. The movie shows two small clusters of RNA chains (green and magenta) fuse to form a droplet. In the process, the cluster in magenta is once partially dissolved but eventually coalesce with the other cluster (green).

### Supplementary Video 3

Jamming dynamics of two labelled RNA chains inside a droplet. The movie shows the late-stage dynamics in a simulation trajectory at 200μM (CAG)47 after the formation of a large droplet. For clarity, focus is on two RNA chains shown in yellow and red colours, whereas all other chains in the same droplet are shown as transparent blue chains. The motions of these RNA chains are highly restricted, resulting in reptation dynamics (Fig. 7c).

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Nguyen, H.T., Hori, N. & Thirumalai, D. Condensates in RNA repeat sequences are heterogeneously organized and exhibit reptation dynamics. Nat. Chem. (2022). https://doi.org/10.1038/s41557-022-00934-z

• Accepted:

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• DOI: https://doi.org/10.1038/s41557-022-00934-z

• ### Modeling condensate formation in silico

• Arunima Singh

Nature Methods (2022)