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 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.
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File name | Size | Description |
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Fig1.txt
MD5md5:007b052df5ee0d522981bb9aeb97e2bf
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158 Bytes | RNA fold in dot-bracket format (figure 1) |
Fig2a.csv
MD5md5:94c2b5d2fb61ba560952a337936dd242
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263 Bytes | Average Ladder Distance as a function of the number of nucleotides (figure 2a) |
Fig2a_inset.csv
MD5md5:6a0962d78f99095645c14fdb614a8998
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247 Bytes | estimation of rho exponent from ALD scaling (inset figure 2a) |
Fig2b_13500.csv
MD5md5:9277b79cfaf7fd1b4496f3cd14f82022
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19.7 KiB | probability distribution of scaled path length for N=13500 (figure 2b) |
Fig2b_100.csv
MD5md5:7f46988719f703e4a1d00fe8066b0613
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622 Bytes | probability distribution of scaled path length for N=100 (figure 2b) |
Fig2b_200.csv
MD5md5:71f3e2553b62282347d2d37a17cfb89a
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1.2 KiB | probability distribution of scaled path length for N=200 (figure 2b) |
Fig2b_300.csv
MD5md5:854ff009a773569d26a0086bccbd9e60
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1.6 KiB | probability distribution of scaled path length for N=300 (figure 2b) |
Fig2b_500.csv
MD5md5:a0fd06077aed5e1eb2ca9aeda485a171
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2.4 KiB | probability distribution of scaled path length for N=500 (figure 2b) |
Fig2b_800.csv
MD5md5:c1453fb849828fad53415689363772c0
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3.4 KiB | probability distribution of scaled path length for N=800 (figure 2b) |
Fig2b_1200.csv
MD5md5:a0a87bb6d59183e0ce1c3ca16f08478e
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4.2 KiB | probability distribution of scaled path length for N=1200 (figure 2b) |
Fig2b_1800.csv
MD5md5:60d38be21cfeecacd4183c28ee063389
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5.4 KiB | probability distribution of scaled path length for N=1800 (figure 2b) |
Fig2b_2700.csv
MD5md5:38e19b3f130d5b53c0b446a818372198
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7.3 KiB | probability distribution of scaled path length for N=2700 (figure 2b) |
Fig2b_4000.csv
MD5md5:74e7d3d81c6c788064cffc0f6fb3259c
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9.6 KiB | probability distribution of scaled path length for N=4000 (figure 2b) |
Fig2b_6000.csv
MD5md5:3579330948e594b05288cf24f720c11b
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12.2 KiB | probability distribution of scaled path length for N=6000 (figure 2b) |
Fig2b_9000.csv
MD5md5:920ac2bb6d76620bfc5f23a7b348fc31
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16.5 KiB | probability distribution of scaled path length for N=9000 (figure 2b) |
Fig2b_inset.csv
MD5md5:8b9721e4a0b55db18e1944c9ed86f997
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460 Bytes | Estimation of exponents rho_theta and rho_t from scaled path length distributions, (figure 2b,inset) |
Fig2c.csv
MD5md5:18c8f10266e7184ba31d6df547d2b9d0
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263 Bytes | branch length as a function of the number of nucleotides (figure 2c) |
Fig2c_inset.csv
MD5md5:5f55152e6dd96a820cbd1078d8a65a7a
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249 Bytes | estimation of epsilon exponent from branch weight scaling (figure 2c, inset) |
Fig2d_100.csv
MD5md5:98b2591fb647693eb243dd8adc447b1e
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173 Bytes | probability distribution of branch weights for N=100 (figure 2d) |
Fig2d_200.csv
MD5md5:bc9b21b532c92ae2e2d0199039bc8102
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368 Bytes | probability distribution of branch weights for N=200 (figure 2d) |
Fig2d_300.csv
MD5md5:a82e9bab7f87d37785a5d0e8a041ef9a
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567 Bytes | probability distribution of branch weights for N=300 (figure 2d) |
Fig2d_500.csv
MD5md5:cd23bebd8e71282e570713a5294aa601
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1001 Bytes | probability distribution of branch weights for N=500 (figure 2d) |
Fig2d_800.csv
MD5md5:51a0b88701ebb6356159e9159cf8bb7a
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1.6 KiB | probability distribution of branch weights for N=800 (figure 2d) |
Fig2d_1200.csv
MD5md5:e2a62c0982ed8b3d6ce4b4cbe7aa2d75
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2.5 KiB | probability distribution of branch weights for N=1200 (figure 2d) |
Fig2d_1800.csv
MD5md5:feea63ae033f26aabb977e4172ed0686
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4.0 KiB | probability distribution of branch weights for N=1800 (figure 2d) |
Fig2d_2700.csv
MD5md5:ed3082b3ec4faf84f01afb3c5a830311
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6.1 KiB | probability distribution of branch weights for N=2700 (figure 2d) |
Fig2d_4000.csv
MD5md5:27b945836d6ae7afe548f5a912c15577
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9.3 KiB | probability distribution of branch weights for N=4000 (figure 2d) |
Fig2d_6000.csv
MD5md5:b3465edfc2f1c74e3641ad4e2f9d67b7
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14.0 KiB | probability distribution of branch weights for N=6000 (figure 2d) |
Fig2d_9000.csv
MD5md5:7938c2a6a9bd0259f6abb1419b8f69b7
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21.6 KiB | probability distribution of branch weights for N=9000 (figure 2d) |
Fig2d_13500.csv
MD5md5:9f76ae73cde084f6780dd0aebef177ce
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33.1 KiB | probability distribution of branch weights for N=13500 (figure 2d) |
Fig2d_inset.csv
MD5md5:6d626b26491fc8d407db79209ae33583
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270 Bytes | estimation of epsilon exponent from branch weight distributions (figure 2d, inset) |
Fig3.csv
MD5md5:7ede661cfaa595056d8b5b4eb5dc63c0
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987 Bytes | convergence of scaling exponents with N |
Fig4.csv
MD5md5:0c30b8f99d19b0b5695e5d7533a7dbcf
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161 Bytes | comparison of scaling exponents with notable ones from polymer theory |
2023.91 (version v1) [This version] | Jun 08, 2023 | DOI10.24435/materialscloud:js-fx |