Publication date: Jun 08, 2023
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 selfavoiding 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.
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File name  Size  Description 

Fig1.txt
MD5md5:007b052df5ee0d522981bb9aeb97e2bf

158 Bytes  RNA fold in dotbracket 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 
2023.91 (version v1) [This version]  Jun 08, 2023  DOI10.24435/materialscloud:jsfx 