## 3 Results
### Trans-Splicing Reaction Promoted by kUrd Oligomer Formation  
The intron form of \(\Delta\)P5 core ribozyme module can perform the self-splicing reaction to yield ligated exons in the presence of the P5 abc activator module (Figure 7A) [18]. The pair of \(\Delta\)P5 core ribozyme modules in each kUrd were composed of \(\alpha\)- and \(\beta\)-chain RNAs. In the intron form of wild-type \(\Delta\)P5 core ribozyme module on one side of kUrd, 5\({}^{\prime}\) and 3\({}^{\prime}\) exons were provided by \(\alpha\)- and \(\beta\)-chain RNAs, respectively (Figure S10A). In the intron form of the M1 type \(\Delta\)P5 core ribozyme module on the opposite side of kUrd, 5\({}^{\prime}\) and 3\({}^{\prime}\) exons were provided by \(\beta\)- and \(\alpha\)-chain RNAs, respectively (Figure S6B). The organization of \(\alpha\)- and \(\beta\)-chain RNAs in the intron form of the \(\Delta\)P5 core ribozyme modules would conduct _trans_-splicing reaction joining 5\({}^{\prime}\) and 3\({}^{\prime}\) exons, which were provided by two separate RNA chains, to produce a mature exon sequence (Figure S10A,B) [31,48]. _Trans_-splicing promoted by group I ribozyme has been recognized as a promising strategy to repair mRNAs of disease-related genes bearing undesirable mutations [48, 49, 50]. Therefore, we examined _trans_-splicing reaction catalyzed by a kUrd in triblock copolymers (**3-K-2'-2-K-4'-4-K-3'**) including the closed trimer. Figure 7: _Trans_-splicing reaction by the ribozyme unit 2 formed in the closed kUrd heterotrimer. (**A**) Parent _cis_-splicing reaction of the bimolecular group I ribozyme. 5\({}^{\prime}\) and 3\({}^{\prime}\) exons were both provided by the unimolecular \(\Delta\)P5 ribozyme RNA, the activity of which is repressed in the absence of the P5 abc RNA. Splicing reaction produced Spinach RNA as the ligated exons. Spinach RNA captured DFHBI and induced its fluorescence. (**B**) Closed kUrd trimers and their partial dimers used for analysis of the _trans_-splicing reaction. (**C**) Time-dependent increases in fluorescence of Spinach RNA–DFHBI complex. Splicing reactions were carried out at 37 \({}^{\circ}\)C.  
We installed 5\({}^{\prime}\) and 3\({}^{\prime}\) exon sequences and their recognition elements into the \(\alpha\)- and \(\beta\)- chain RNAs of **2-K-4\({}^{\prime}\)** kUrd, respectively (Figure S10C and Table S2). Exon sequences were appended to the ribozyme module consisting of the wild-type \(\Delta\)P5 ribozyme module activated by the P5 abc module provided by **3-K-2\({}^{\prime}\)** kUrd through the **2:2\({}^{\prime}\)** interface (Figure 7B and Figure S10C). We used a shortened derivative of the Spinach RNA aptamer as a ligated exon sequence dissected in precursor form (Figure 7A) [51]. Spinach RNA is an RNA receptor for DFHBI and its fluorescence is induced by restricting the molecular motion of DFHBI in the complex form [52]. The progression of _trans_-splicing reaction can be monitored in the presence of DFHBI [51; 53]. To evaluate the effects of kUrd oligomer formation on the _trans_-splicing reaction, we prepared a set of kUrd variants some of which possessed 5\({}^{\prime}\) and 3\({}^{\prime}\) exon sequences (Figure 7B and Figure S10, see also Table S2). A trio of kUrds **(3-K-2\({}^{\prime}\)2-K-4\({}^{\prime}\)4-K-3\({}^{\prime}\))** to form a triblock oligomer (**trimer-1**) exhibited an increase in emission (green plot in Figure 7C). We also examined two sets of triblock oligomers (**trimer-2** and **trimer-3**) in which the 5\({}^{\prime}\) exon and 3\({}^{\prime}\) exon were installed to incorrect RNA chains and the two exons were unable to meet in one \(\Delta\)P5 ribozyme unit. The two sets of kUrds showed no increase in fluorescence from Spinach RNA complexed with DFHBI (purple plot and blue plot in Figure 7C). These data indicated that the correct assignments of 5\({}^{\prime}\) and 3\({}^{\prime}\) exons in six RNA chains are crucial in the oligomeric state of kUrds.