Domen Vaupotič^1*, Angelo Rosa^2*, Luca Tubiana^3,4*, Anže Božič^1*

1 Department of Theoretical Physics, Jozef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia

2 Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Bonomea 265, 34136 Trieste, Italy

3 Department of Physics, University of Trento, via Sommarive 14, 38123 Trento, Italy

4 INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, via Sommarive 14, 38123 Trento, Italy

* Corresponding authors emails: domenvaupotic@gmail.com, anrosa@sissa.it, Luca.tubiana@unitn.it, Anze.Bozic@ijs.si

DOI10.24435/materialscloud:js-fx [version v1]

Publication date: Jun 08, 2023

How to cite this record

Domen Vaupotič, Angelo Rosa, Luca Tubiana, Anže Božič, Scaling properties of RNA as a randomly branching polymer, Materials Cloud Archive 2023.91 (2023), doi: 10.24435/materialscloud:js-fx.

Description

Formation of base pairs between the nucleotides of a ribonucleic acid (RNA) sequence gives rise to a complex and often highly branched RNA structure. While numerous studies have demonstrated the functional importance of the high degree of RNA branching—for instance, for its spatial compactness or interaction with other biological macromolecules—RNA branching topology remains largely unexplored. Here, we use the theory of randomly branching polymers to explore the scaling properties of RNAs by mapping their secondary structures onto planar tree graphs. Focusing on random RNA sequences of varying lengths, we determine the two scaling exponents related to their topology of branching. Our results indicate that ensembles of RNA secondary structures are characterized by annealed random branching and scale similarly to self-avoiding trees in three dimensions. We further show that the obtained scaling exponents are robust upon changes in nucleotide composition, tree topology, and folding energy parameters. Finally, in order to apply the theory of branching polymers to biological RNAs, whose length cannot be arbitrarily varied, we demonstrate how both scaling exponents can be obtained from distributions of the related topological quantities of individual RNA molecules with fixed length. In this way, we establish a framework to study the branching properties of RNA and compare them to other known classes of branched polymers. By understanding the scaling properties of RNA related to its branching structure, we aim to improve our understanding of the underlying principles and open up the possibility to design RNA sequences with desired topological properties.

Materials Cloud sections using this data

Files

File name	Size	Description
Fig1.txt MD5md5:007b052df5ee0d522981bb9aeb97e2bf	158 Bytes	RNA fold in dot-bracket format (figure 1)
Fig2a.csv MD5md5:94c2b5d2fb61ba560952a337936dd242	263 Bytes	Average Ladder Distance as a function of the number of nucleotides (figure 2a)
Fig2a_inset.csv MD5md5:6a0962d78f99095645c14fdb614a8998	247 Bytes	estimation of rho exponent from ALD scaling (inset figure 2a)
Fig2b_13500.csv MD5md5:9277b79cfaf7fd1b4496f3cd14f82022	19.7 KiB	probability distribution of scaled path length for N=13500 (figure 2b)
Fig2b_100.csv MD5md5:7f46988719f703e4a1d00fe8066b0613	622 Bytes	probability distribution of scaled path length for N=100 (figure 2b)
Fig2b_200.csv MD5md5:71f3e2553b62282347d2d37a17cfb89a	1.2 KiB	probability distribution of scaled path length for N=200 (figure 2b)
Fig2b_300.csv MD5md5:854ff009a773569d26a0086bccbd9e60	1.6 KiB	probability distribution of scaled path length for N=300 (figure 2b)
Fig2b_500.csv MD5md5:a0fd06077aed5e1eb2ca9aeda485a171	2.4 KiB	probability distribution of scaled path length for N=500 (figure 2b)
Fig2b_800.csv MD5md5:c1453fb849828fad53415689363772c0	3.4 KiB	probability distribution of scaled path length for N=800 (figure 2b)
Fig2b_1200.csv MD5md5:a0a87bb6d59183e0ce1c3ca16f08478e	4.2 KiB	probability distribution of scaled path length for N=1200 (figure 2b)
Fig2b_1800.csv MD5md5:60d38be21cfeecacd4183c28ee063389	5.4 KiB	probability distribution of scaled path length for N=1800 (figure 2b)
Fig2b_2700.csv MD5md5:38e19b3f130d5b53c0b446a818372198	7.3 KiB	probability distribution of scaled path length for N=2700 (figure 2b)
Fig2b_4000.csv MD5md5:74e7d3d81c6c788064cffc0f6fb3259c	9.6 KiB	probability distribution of scaled path length for N=4000 (figure 2b)
Fig2b_6000.csv MD5md5:3579330948e594b05288cf24f720c11b	12.2 KiB	probability distribution of scaled path length for N=6000 (figure 2b)
Fig2b_9000.csv MD5md5:920ac2bb6d76620bfc5f23a7b348fc31	16.5 KiB	probability distribution of scaled path length for N=9000 (figure 2b)
Fig2b_inset.csv MD5md5:8b9721e4a0b55db18e1944c9ed86f997	460 Bytes	Estimation of exponents rho_theta and rho_t from scaled path length distributions, (figure 2b,inset)
Fig2c.csv MD5md5:18c8f10266e7184ba31d6df547d2b9d0	263 Bytes	branch length as a function of the number of nucleotides (figure 2c)
Fig2c_inset.csv MD5md5:5f55152e6dd96a820cbd1078d8a65a7a	249 Bytes	estimation of epsilon exponent from branch weight scaling (figure 2c, inset)
Fig2d_100.csv MD5md5:98b2591fb647693eb243dd8adc447b1e	173 Bytes	probability distribution of branch weights for N=100 (figure 2d)
Fig2d_200.csv MD5md5:bc9b21b532c92ae2e2d0199039bc8102	368 Bytes	probability distribution of branch weights for N=200 (figure 2d)
Fig2d_300.csv MD5md5:a82e9bab7f87d37785a5d0e8a041ef9a	567 Bytes	probability distribution of branch weights for N=300 (figure 2d)
Fig2d_500.csv MD5md5:cd23bebd8e71282e570713a5294aa601	1001 Bytes	probability distribution of branch weights for N=500 (figure 2d)
Fig2d_800.csv MD5md5:51a0b88701ebb6356159e9159cf8bb7a	1.6 KiB	probability distribution of branch weights for N=800 (figure 2d)
Fig2d_1200.csv MD5md5:e2a62c0982ed8b3d6ce4b4cbe7aa2d75	2.5 KiB	probability distribution of branch weights for N=1200 (figure 2d)
Fig2d_1800.csv MD5md5:feea63ae033f26aabb977e4172ed0686	4.0 KiB	probability distribution of branch weights for N=1800 (figure 2d)
Fig2d_2700.csv MD5md5:ed3082b3ec4faf84f01afb3c5a830311	6.1 KiB	probability distribution of branch weights for N=2700 (figure 2d)
Fig2d_4000.csv MD5md5:27b945836d6ae7afe548f5a912c15577	9.3 KiB	probability distribution of branch weights for N=4000 (figure 2d)
Fig2d_6000.csv MD5md5:b3465edfc2f1c74e3641ad4e2f9d67b7	14.0 KiB	probability distribution of branch weights for N=6000 (figure 2d)
Fig2d_9000.csv MD5md5:7938c2a6a9bd0259f6abb1419b8f69b7	21.6 KiB	probability distribution of branch weights for N=9000 (figure 2d)
Fig2d_13500.csv MD5md5:9f76ae73cde084f6780dd0aebef177ce	33.1 KiB	probability distribution of branch weights for N=13500 (figure 2d)
Fig2d_inset.csv MD5md5:6d626b26491fc8d407db79209ae33583	270 Bytes	estimation of epsilon exponent from branch weight distributions (figure 2d, inset)
Fig3.csv MD5md5:7ede661cfaa595056d8b5b4eb5dc63c0	987 Bytes	convergence of scaling exponents with N
Fig4.csv MD5md5:0c30b8f99d19b0b5695e5d7533a7dbcf	161 Bytes	comparison of scaling exponents with notable ones from polymer theory

License

Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

External references

Keywords

RNA polymer physics statistical mechanics scaling