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Research Article

A new molecular mechanism of RNA circularization and the microRNA sponge formation

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Received 02 Jun 2020
Accepted 26 Oct 2020
Published online: 17 Nov 2020

Abstract

A new mechanism of RNA circularization driven by specific binding of miRNAs is described. We identified the 71 CUUCC pentanucleotide motifs distributed regularly throughout the entire molecule of CDR1as RNA that bind to 71 miRNAs through their seed sequence GGAAG. The sequential binding of miR-7 RNAs (71 molecules) brings both ends of CDR1as RNA (1 molecule) together and stimulate phosphodiester bond formation between nucleotides C1 and A1299 at the 5’ and 3’ end, respectively. The binding of miRNAs to CDR1as RNA results in the unique complex formation, which shows three specific structural domains: (i) two short helixes with an internal loop, (ii) the hinge, and (iii) the triple-helix. The proposed mechanism explains specific RNA circularization and its function as a miRNAs sponge. Furthermore, the existing wet experimental data on the interaction of CDR1as RNA with miR-7 fully supports our observation. Although miR-671 shows the same seed sequence as miR-7, it forms an almost perfect double helix with CDR1as RNA and induces the cleavage of CDR1as, but does not stimulate circularization. To check how common is the proposed mechanism among circular RNAs, we analyzed the most recent circAtlas database counting almost 1.1 million sequences. It turned out that there are a huge number of circRNAs, which showed miRNAs seed binding sequences distributed through the whole circRNA sequences and prove that circularization of linear transcript is miRNA dependent.

Communicated by Ramaswamy H. Sarma

Introduction

Circular RNAs (circRNAs) are a class of non-protein coding RNAs that form covalently closed circular structures with various biological functions (Memczak et al., 2013; Petkovic & Muller, 2015; Sanger et al., 1976). CircRNAs occur in all kingdoms of life, as well as in proto-life forms, as viroids, viroid-like satellite RNA, and viruses (Sanger et al., 1976). Varied abundance and resistance to degradation by nucleases immediately suggest various roles of circRNAs within the cell (Petkovic & Muller, 2015; Sanger et al., 1976).

The flagship of circRNAs is CDR1as RNA, antisense of mRNA of Homo sapiens cerebellar degeneration related protein 1 (CDR1). It occurs at a high level in the human and mouse brain, where it sequestrates miR-7, a regulator of several genes in the brain. There are a wealth of data showing that CDR1as RNA and miR-7 are required for normal brain function, and disruption of their interactions cause serious abnormalities (Hansen et al., 2011; 2013; Piwecka et al., 2017).

Many data show that the linear transcript becomes circular. It has been suggested that circularization is an effect of back-splicing of an exon, where its downstream 5′ splice joins the upstream 3′ splice site and produces circRNA (Petkovic & Muller, 2015). However, it was noticed that the back-splicing does not automatically imply the RNA circularization, because the junction of the two ends gives only local information about the structure of RNA, and generally is not enough to fulfill a circular RNA topology (Pervouchine, 2019). Because RNA circularization is not random, and the entropy associated with that process is negative, one can imply some regulator(s) of a ring formation (Petkovic & Muller, 2015).

The back-splicing mechanism, although being facilitated by complementary sequences and specific protein factors, is extremely inefficient in the cell. It is more than 100-fold less efficient than canonical splicing reaction. One should also notice that the most recent models of RNA circularization are based on Watson-Crick interactions of inverted elements (repeats) (Hansen et al., 2016; Yoshimoto et al., 2018). Despite various reports on biogenesis, biology, and properties of circRNAs, the mechanism of their formation is still exclusive (Ashwal-Fluss et al., 2014; Kristensen et al., 2019; Pervouchine, 2019; Starke et al., 2015; Welden & Stamm, 2019; Wilusz, 2018). Therefore, the detailed knowledge of RNA circularization effectors is highly desired, which will bring us closer to understand the pathway of the RNA circle formation, function, and regulation (Hansen et al., 2016).

Our work shows a new mechanism of circRNAs biosynthesis based on a plethora of experimental wet data and in silico results. In this respect, CDR1as RNA is a very appropriate subject to work with. A broad analysis of currently available experimental data concerning CDR1as RNA structure and function brough us closer to a deep understanding of the biosynthesis circRNA. There are many data which support our model: (a) a very high cellular level of circular CDR1as RNA in the cell is observed, (b) a high abundance of CDR1as RNA (much higher than linear isoform) clearly indicates a high efficiency of CDR1as production, which stays in contrast with a very low efficiency of back-splicing, (c) back-splicing occurs largely post-transcriptionally, and (d) co-transcriptional nature of CDR1as circularization has been shown (Zhang et al., 2016).

Here, we describe for the first time the precise mechanism of circRNA synthesis induced by specific binding of miR-7 to CDR1as RNA and formation of a triple helix, which stabilizes these interactions. The model perfectly explains the antagonistic role of miR-671 and miR-7 with the same seed sequence. miR-671 shows a higher degree of complementary and lack of capacity for triple-helix formation, which induces the cleavage with Ago (Pan et al., 2018). The new mechanism supports a high specificity of circular CDR1as RNA biosynthesis and function and fills a gap in understanding of RNA circularization phenomenon. This mechanism is also observed for other circRNAs, for example has-PHF2_0015.

Materials and methods

The nucleotide sequences of CDR1as RNA (antisense of mRNA of Homo sapiens cerebellar degeneration related protein 1, has_circ_05408) and CDR1 RNA (mRNA of Homo sapiens cerebellar degeneration related protein 1, NM_004065) were taken from circRNADB (Chen et al., 2016) and GenBank (Benson et al., 2013), respectively. miRNA sequences were from miRBASE (Kozomara & Griffiths-Jones, 2014). Analysis of CDR1as RNA sequence and a graphical representation of nucleotide occupancy position was done with the CLUSTAL multiple alignments by MUSCLE (Corpet, 1988) and WebLogo (https://weblogo.berkeley.edu/) (Crooks et al., 2004; Schneider & Stephens, 1990). The secondary structure of miRNAs was calculated with RNAfold from the Vienna Package (Gruber et al., 2008). The structures of complexes of miR-7 and miR-671 with various fragments of CDR1as were calculated with RNA Duplex (Lorenz et al., 2011) and RNAComposer (Antczak et al., 2016).

To search for other circRNAs with similar miRNA binding patterns to CDRas1, we analyzed currently known sequences of human circRNAs collected in CircAtlas (Wu et al., 2020). We extracted all seed sequences (nucleotides 2–6) at 5′ end of human miRNAs and matched them to unique sequences of circRNAs. Finally, we developed a custom python script to search for circRNAs that contain both at least 20 or 50 binding sites for at least one or more seeds, and miRNA seed binding site matching to the 5′ and 3′ ends of circRNA.

Results

Although there are many suggestions that the circularization of RNAs arise by back-splicing, it does not fully explain its specificity or selectivity (Kristensen et al., 2019; Pervouchine, 2019). To get a better insight into the mechanism of the process, first we modeled the secondary structure of antisense and sense CDR1 transcripts (Figure S1). As one can see, the predicted structure of both RNAs shows many double-stranded stable fragments at which microRNA binding sites (pentanucleotide CUUCC) are identified. In the most sites, they are hidden and are not available to pair with the miR-7 or miR-671 seed sequence. In such cases, sponging capacity, the most important function of circRNAs is excluded. Free energy for predicted secondary structure RNA shows ΔG −339.50 and −161.81 kcal/mol for CDR1 RNA and CDR1as RNA, respectively. Although the calculated CDR1as RNA structure is less stable than its sense counterpart, it is clear that direct binding miR-7 or miR-671 to circular CDR1as RNA is rather difficult or even impossible.

Figure 1. Primary structure of CDR1as RNA and miR-7. (a) Nucleotide sequence of CDR1as RNA (1299 nt) with marked 71 CUUCC sequences (yellow). Pentapyrimidine CUUCC sequence appears regularly from 26th to 70th CUUCC sequences and are variable at the 5’ end of CDR1as (nucleotides 1–480). (b) Nucleotide sequence of miR-7 (in blue) with GGAAG pentanucleotide ‘seed region’(underlined).

Looking for a precise mechanism of circular RNA formation, we carried out the in-deep nucleotide analysis of CDR1as RNA. We found 71 pentanucleotide CUUCC sequences (seed binding sites, SBS), which are distributed regularly throughout the entire molecule (Figure 1, Figures S2a,b). The multiple alignments and the nucleotide occupancy analysis of CDR1as RNA showed a very high SBS sequence conservation at all RNA positions (Figure S2b,c).

Figure 2. The structure of the complex of CDR1as RNA with miR-7 and miR-671. (a) The binding of three miR-7s (n-1, n, n + 1) to CDR1as RNA shows three structural domains of the complex: (i) two short helixes (helixes 1 and 2) separated with internal loop, (ii) the hinge and (iii) the triple-helix. (b) The binding of miR-671 to CDR1as RNA does not show the hinge and the triple helix. (c) The detailed secondary structure of the complex of CDR1as RNA with three consecutive miR-7s. In addition to canonical Watson-Crick pairs, G = C and A-U pairs, there are non-standard base pairs U-•-U, U-•-C and A-•-A in the bulge and hinge. The Hoogsteen base pairs in the triplex are marked as -■-. (d) The tertiary structure of the fragment of the complex of CDR1as RNA with two consecutive miR-7s. (e) Ring-like CDR1as RNA complexed with 71 miR-7s. (a–e) CDR1as – black, miR-7 – blue, miR-671 – green, GGAAG – seed sequence of miR-7, CUUCC – yellow – the sequence of CDR1as RNA perfectly complementary to seed regions of miR-7 and miR-671.

Next, the sequence of miRNAs were analyzed (Kozomara & Griffiths-Jones, 2014). We found five miRNAs, particularly miR-7, miR-671, miR-3202, miR-4533, and miR-6828, out of 2813 currently known miRNAs (miRBase), that contain the conserved GGAAG seed sequence, at positions 2–6 of their 5’ end (Figure S3a) (Ambros, 2004; Bartel, 2004). The analysis of a putative secondary structure of these five miRNAs showed that only miR-7 does not show the propensity to form a secondary structure, but the others are prone to form a hairpin structure (Figure S3b). That observation suggests that CDR1as RNA, through its SBS, can form the short double helix with miR-7. Because of the identified seed sequence, similar RNA-RNA interactions with miR-671 are also possible.

Figure 3. The mechanism of miR-7 induced ligation of CDR1as RNA. (a) Binding of the 1st, 2nd, and 71st miR-7s to CDR1as RNA. The 1st miR-7 pairs with CDR1as RNA, and gets together of the 3’ end (nucleotide A1299) and the 5’ end (nucleotide C1) of CDR1as RNA and promotes their ligation. The triple helix is not found. (b) miR-671 does not show the capacity to get together of both ends of CDR1as RNA. (c) The structure of the CDR1as RNA ligation site triggered by miR-7 (1st), which directs the covalent binding of A1299 with C1. (d) The tertiary structure of the complex of CDR1as RNA and miR-7 showing the ligation site. (a–d) CDR1as – black, miR-7 – blue, miR-671 – green, GGAAG – seed sequence of miR-7, CUUCC – yellow – the sequence of CDR1as RNA perfectly complementary to seed regions of miR-7 and miR-671. For details see also Figures S4–S6.

An in-deep analysis of the distribution of seed sequence suggests that along CDR1as RNA circularization, sequential binding of miR-7s is favorably possible. That newly synthesized unstructured fragments of transcribed RNA are good targets for miR-7 RNA binding, much better than full-length transcript with a strong secondary structure. One should remember that both miR-7 and CDR1as RNA co-express to high levels in neuronal tissues, especially the cerebellum and midbrain (Choudhury et al., 2013; Kleaveland et al., 2018; Piwecka et al., 2017) and both RNAs colocalize in the nucleus (Castanotto et al., 2009, 2018; Liao et al., 2010). Furthermore, miR-7s bind to CDR1as RNA and form a polypurine-polypyrimidine duplex. The double stranded parts facilitate bending of the miR-7/CDR1as double helix, which is proceed as long as the last and the first nucleotides, at the 3′ and 5’end of CDR1as RNA, respectively, come to close proximity. Such arrangement stimulates phosphodiester bond formation. This model explains the prevalence of circular isoform of CDR1as transcript (Barrett et al., 2017; Hansen et al., 2011, 2013; Memczak et al., 2013). Detailed analysis of miRNA/CDR1as complex, showed that each of 71 fully conserved CUUCC motifs of CDR1as RNA, perfectly matches the GGAAG seed sequence of miR-7 and miR-671. Each short double helix is followed by 12- and 13-nt fragments of CDR1as RNA with a partial complementary to miR-7 and miR-671, respectively (Figures S4–S6). Interestingly, the 3′ end of miR-7 does not show a full complementarity to CDR1as RNA, but nucleotides at positions 18–23 of the 3′ end of miR-671, fully match the adjacent CUUCC seed binding site (Figures S4–S6).

To get more insight into specificity of RNA circularization, we calculated the free energy of the structures of the complexes of miR-7 and miR-671 with different fragments of CDR1as RNA. The calculated minimal free energies (MFEs) of these potential RNA-RNA complexes are shown in Table S1. The MFEs of RNA-RNA hybrids with miR-7 are similar and vary from −8.1 (26) to −22.6 (8) kcal/mol (the discrepancy range of MFEs is 14.5 kcal/mol) (see Table S1). Fragments with miR-671 show MFE in the range of −9.7 (54) to −41.9 (62) kcal/mol (Figure S7). A high discrepancy of MFE of miR-671 hybrids (32.2 kcal/mol) shows that some CDR1as RNA fragments, especially those with CUUCC motifs 67 and 39 of highest MFE, are preferentially paired with miR-671 (Figure S8). The average MFE for hybrids with miR-7 is 13.95 kcal/mol and is significantly lower than for all hybrids with miR-671 (20.6 kcal/mol) (Figures S4–S7). The differences in calculated stability of RNA-RNA complexes are a result of the lack of the complementarity of the 3′ end of miR-7 and of miR-671 with CDR1as RNA. The observed energy and the structure differences show functional consequences. The single miR-7 can form Watson-Crick base pairs with the CUUCC sequence, therefore, 1 molecule CDR1as RNA binds with 71 molecules of miR-7s and forms stable structure with total MFE of 990.9 kcal/mol (stabilising effect of triplex has not been taken into consideration) (Figure S9). On the other hand, the single miR-671 binds two consecutive CUUCC sequences and therefore, its loading capacity to CDR1as RNA is 2x lower. Thus, 36 miR-671 molecules match to CDR1as RNA when the first hybrid includes the 1st and 71st CUUCC sequences, and 35 of miR-671 molecules when 1st and 2nd CUUCC sequences are involved (Figures S4–S6). The total MFEs of these two alternative structures show 759.2 and 704.8 kcal/mol for 1 molecule of CDR1as with 36 molecules of miR671 and 1 molecule of CDR1as with 35 molecules of miR671, respectively (Figure S9).

A detailed analysis of the whole complex of CDR1as RNA with 71 molecules of miR-7s showed three specific structural domains, starting with (i) two short helixes with an internal loop. The first helix (helix 1) contains the seed sequence GGAAG, at positions 2–6 at 5´end of miR-7, which perfectly match the CUUCC sequence. The second helix (helix 2) follows the internal loop. The second domain is the hinge (ii). The triple helix, where the 3′ end of miR-7, binds to helix 1 through Hoogsteen hydrogen bonds, forms the third domain (iii) (Figure 2 and Figure S4). All these domains appear regularly and show sequential, one by one mode of binding of 71 miR-7 molecules to single CDR1as RNA (Figure 2 and Figure S4). That specific binding of the GGAAG seed sequence of miR-7 to complementary CUUCC fragment of CDR1as, triggers RNA-RNA complex formation and its bending, which brings together both ends of CDR1as RNA. The double-stranded RNA curvature has already been observed in the Shine-Dalgarno sequence of the 3′ end of 16S rRNA and the 5′ end of mRNA (Shine & Dalgarno, 1975). It is the necessary but insufficient requirement for RNA circularization. The most important and critical step in circularization is a double-stranded RNA formation of 1st miR-7 with the both ends of CDR1as RNA (Figure 3). So, the 3’ end (nucleotide A1299) and the 5′ end (nucleotide C1) of CDR1as RNA can be precisely ligated and subsequently form circle-like (ring) structure (Figure 2).

Thus, we showed for the first time that CDR1as RNA circularization depends on precise sequential binding of miR-7, which is stabilized by the triple helix formation. Such mode of miR-7 binding perfectly explains the function of CDR1as RNA as the sponge, where the ligand (miR-7) molecule binds to CDR1as RNA with a ratio of two orders of magnitude higher (71:1). It is not surprising, because in some tissues, both CDR1as RNA and miR-7 occur at a high level (Memczak et al., 2013). If so, it is clear that circularization depends on the availability of miR-7, which facilitates the triple-helix formation with CDR1as RNA. The triplex stabilizes the complex, induces nuclease resistance and excludes RISC formation, making the circular RNA very stable (Memczak et al., 2013). The protective function of RNA triplex with Hoogsteen bonds has already been observed for the higher-order structure at the lncRNA MALAT1 3′ terminus, which protects the transcript from degradation (Ageeli et al., 2018; Brown et al., 2016; Ruszkowska et al., 2018). Recently, it has been found that miRNAs can also form a triple helix with double-stranded purine-rich sequences of gene promoters and modify gene transcription (Paugh et al., 2016). All these observations support that CDR1as RNA functions as the sponge and scavenger of a freely available miR-7, prevents it from interacting with unspecific targets (Piwecka et al., 2017).

One should also notice that the complexes of miR-7 and miR-671 with different fragments of CDR1as RNA show significantly different tertiary structures, although observed Watson-Crick interactions are similar (Figures 2 and 3, Figures S4–S6). miR-671 binding in contrast to miR-7 is not able to bring both CDR1as RNA ends close to each other, which is required for RNA circularization (Figure 3). The binding sites for miR-671 showed almost full complementarity to CDR1as RNA (Figure 2), and therefore, miR-671 can mediate slicing of CDR1as RNA in an Ago2-slicer-dependent manner (Hansen et al., 2011). The formation of the triple helix is impossible, therefore, it becomes clear that upon miR-671 binding, CDR1as depletion will take place once miR-7 is released from the complex (Hansen et al., 2013).

To check the same mechanism in other circRNAs, we analyzed over 341 000 human circRNAs deposited in the recent CircAtlas database that contains almost 1.1 million entries (Wu et al., 2020). We found a huge number circRNAs rich in miRNA seed, binding repeated sequences. For example, there are 1476 and 46 human circRNAs containing at least 20 and 50 pentanucleotide repeats, respectively (Tables S2 and S3). Most of them have more than one set of single repeats. On the other hand, hsa-intergenic_009898, of 1465 nucleotide length, contains AUGGA, AAUGG, GGAAU, and AGGAA motifs repeated 135, 133, 116, and 109 times, respectively. Similar circRNAs, which have at least one pentanucleotide repeated at least 60 times can be found Table S4.

Furthermore, we analyzed repeated sequences within circRNAs and found that most of them occurred regularly. To show that mechanism of RNA circularization concerns not only brain, but also other tissues, we analyzed stomach-specific has-PHF2_0015. One can see AGGUG pentanucleotide motif repeated regularly 60 times within that circRNA (Figure S10a and S11a). Within has-PHF2_0015 RNA, we identified 110 fragments of 12 nucleotide length and two shorter of 10- and 6-nt) fragments of very similar sequence. 60 of them have at least one AGGUG sequence motif at 5′ end of the sequence (Figures S10 and S11). The other fragments have similar sequences in this position, with one substitution as: AGG(C)UG and AGG(U)UG (1 fragment), AGG(A)UG (14 fragments) or two substitutions, i.e. A(G)GGU(A)G and A(G)GG(A)UG (19 and 16 fragments, respectively). When the ends of RNA are in close proximity, 61st AGGUG binding site is created. The consensus sequence of these fragments is AGGUGCAGGUGU. The sequence AGGUG at its 3′ end perfectly matches CACCU seed sequence at positions 2–6 at the 5´end of miR-3622a-3p RNA (Figures S10b and S11b).

Furthermore, in addition to miR-3622a-3p, we found other miRNAs, as miR-1306-5p, miR-3622b-3p, and miR-6765-3p, that have also CACCU seed sequence, being perfectly complementary to AGGUG regularly repeated sequences within has-PHF2_0015 RNA (Figure S12). Although, the sequence similarity between these miRNAs, beyond the seed region is very low, the high similarity (86%) of miR-3622a-3p and miR-3622b-3p sequences is observed. Furthermore, the secondary structure analysis of these miRNAs showed that miR-1306-5p, miR-3622a-3p, miR-3622b-3p have no propensity to form a secondary structure (Figure S12). Only miR-6765-3p is prone to form the hairpin structure. One can notice that also in this case the seed sequence could easily bind AGGUG sequence of has-PHF2_0015 RNA.

To get better insight into the role of these miRNAs in the specificity of RNA circularization, we calculated the free energies of the structures of the complexes of these miRNAs with different fragments of has-PHF2_0015. The calculated minimal free energy (MFE) showed that miR-3622a-3p is the most prompt to bind all fragments of has-PHF2_0015, and what is the most interesting, it gets together of the 3’ end (nucleotide G1332), and the 5′ end (nucleotide G1) of has-PHF2_0015 RNA could facilitate its ligation (Figure S13)

A detailed analysis of the whole complex of has-PHF2_0015 RNA with miR-3622a-3p showed three specific structural domains similar to these observed for CDR1as RNA and miR-7. They are (i) short helixes separated with internal loop, (ii) the hinge, and (iii) the triple-helix (Figure S13a) All domains appear regularly and show sequential mode of binding of 112 miR-3622a-3p molecules to single has-PHF2_0015 RNA. The specific binding of the CACCU seed sequence of miR-3622a to complementary AGGUG fragment of has-PHF2_0015, triggers RNA-RNA complex formation and its bending, which brings together both ends of has-PHF2_0015 RNA. The most important and critical step in circularization is a double-stranded RNA formation of 1st miR-3622a-3p to the both ends of has-PHF2_0015 RNA (Figure S13b). So, the 3’ end (nucleotide G1332) and the 5′ end (nucleotide G1) of has-PHF2_0015 RNA can be precisely ligated and subsequently form circle-like (ring) structure.

Conclusions

In this paper we have showed that miR-7 facilitates circularization of CDR1as RNA and specific phosphodiester bond formation between two nucleotides: C1 and A1299. Furthermore, our model is supported by the following observations: (i) miR-7 and CDR1as co-expresse to a high level in neuronal tissues, especially the cerebellum and midbrain (Choudhury et al., 2013; Kleaveland et al., 2018; Piwecka et al., 2017), (ii) both RNAs co-localize in the nucleus (Castanotto et al., 2009, 2018; Liao et al., 2010), (iii) newly synthesized, unstructured CDR1as transcript is freely available for miR-7 binding (much better than full-length transcript with tight structure), (iv) miR-7 binding to CDR1as induces bending of CDR1as (Shine & Dalgarno, 1975) and is proceeded as long as the last nucleotide at the 3’end and the first nucleotide at the 5’end of CDR1as come to proximity, what facilitates the ligation reaction.

It is obvious that the specific ligation can happen only under ‘supervision’ of the complementary sequence, which precisely defines the ligation site. It is well-known that ligation of the blind ends of DNA or RNA is difficult, but the efficiency of sticky ends joining is efficient. The sequential binding of 70 molecules of miR-7 brings the 3’ end and 5’ end of CDR1as RNA to the proximity and then, the 71st molecule of miR-7 overlaps both ends of CDR1as RNA (form sticky ends) and stimulates A1299 – C1 phosphodiester bond formation.

The strong support for our model of RNA circularization, comes from transfer RNAs (Paugh et al., 2016). Since all tRNAs have the 3′ hydroxyl and the 5′ phosphate groups, one could suggest a possibility of circle formation. However, it is not the case. Although both tRNA ends are in close proximity, the ligation does not happen (Bruce & Uhlenbeck, 1978). It means that the proximity of RNA ends being a result of the perfectly paired stem in the case of tRNA (analogy to back-splicing) is not enough for ligation. It is reasonable to think that RNA circularization is very specific and it is the consequence of the inner propensity of RNA molecule to circularize (cis-factors) and their interactions with trans factors.

In the paper, we have described the new mechanism of CDR1as RNA circularization induced by miR-7. It explains clearly its function as a sponge. It provides precise structural requirements to explain the antagonistic role of miR-7 and miR-671, with the same seed sequence. The same mode of circularization, we found also for has-PHF2_0015, which binds miR-2622a-3p. The analysis of data from CircAtlas (Wu et al., 2020), clearly shows that the proposed mechanism of circularization is very common and confirms function of circular RNAs as a sponge. The proposed mechanism of RNA circularization with miRNAs is a general phenomenon.

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Disclosure statement

The authors declare no conflicts of interest with the contents of this article.

Author Contributions

Conceptualization, A.B., M.P., J.B.; Funding acquisition, A.B.; Investigation, A.B., M.P., and J.B; Methodology, A.B., M.Sz. and M.P.; Software, M.S. and T.W, M.P.; Supervision, A.B., S.J., and J.B.; Visualization, A.B., and M.P.; Writing – review & editing, A.B., M.Z.N.-B., M.Sz., S.J., and J.B.

Additional information

Funding

This research was funded by the Polish Ministry of Science and Higher Education under the KNOW program. Partial support by grants from the Polish National Science Centre is acknowledged by A.B. (2018/28/C/NZ1/00497), J.B. (2015/17/B/ST5/01467), M.P. and M.Sz. (2016/23/B/ST6/03931). Funding for open access was provided by SBAD of the Institute of Computing Science, Poznan University of Technology.

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