## 3 Results
### Homooligomerization of kUrds  
A new class of Urd variants bearing the KT-15 motif was designated as kink-turn unit ribozyme dimer (abbreviated as kUrd, Figure 1). To optimize kUrd linkers, we compared three linker elements, each of which had the KT-15 motif flanked by a pair of duplexes with 15 bp/10 bp, 15 bp/9 bp, or 14 bp/9 bp (Figure 2A). The three distinct kUrd linkers were used to connect two RzM monomers (RzM-1 and RzM-1\({}^{\prime}\)) in a tail-to-tail manner, yielding three **1-K-1\({}^{\prime}\)** RNAs (Figure 2A and Figure S2). The three **1-K-1\({}^{\prime}\)** were designed to homotrimize to form closed trimers (Figure 1). For each **1-K-1\({}^{\prime}\)**, we prepared **1x-K-1\({}^{\prime}\)** and **1-K-1\({}^{\prime}\)** to eliminate assembly ability of the RzM on one side by introducing a UUCG tetraloop [44,45] into the L2 element (where **x** designates L2 UUCG, see Figures S1D and S3). We also prepared **1x-K-1\({}^{\prime}\)** mutant for each **1-K-1\({}^{\prime}\)** to eliminate assembly ability of RzMs on both sides (Figure S3). We analyzed three **1-K-1\({}^{\prime}\)** kUrds with distinct pairs of helices by electrophoretic mobility shift assay (EMSA) to characterize their assembly properties. Each **1-K-1\({}^{\prime}\)** kUrd was composed of two RNA strands (\(\alpha\)- and \(\beta\)-RNA chains) (Figures S2B and S3, Table S1). Preliminary experiment showed that the two RNA strands assembled efficiently to form the kUrd monomer (Figure S4). We first labeled the 3\({}^{\prime}\)-end of the \(\beta\)-chain RNA with the BODIPY fluorophore [32] to visualize kUrd and its assembly in native gels in the presence of 10 mM Mg\({}^{2+}\) (Figure S5A), 15 mM Mg\({}^{2+}\) (Figure 2B) and 20 mM Mg\({}^{2+}\) (Figure 2C). BODIPY-labeled \(\beta\)-chain RNA of **1x-K-1x\({}^{\prime}\)**, which can also be used as \(\beta\)-chain RNA of **1-K-1x\({}^{\prime}\)**, showed broad and multiple bands (lanes 1, 5 and 9 in Figure 2B,C). The \(\beta\)-chain RNA, however, showed a sharp and retarded band in the presence of an equimolar amount of the partner \(\alpha\)-chain RNA (lanes 2, 6 and 10 in Figure 2B,C), indicating assembly of the \(\alpha\)- and \(\beta\)-chains RNAs to form a structured kUrd **1x-K-1x\({}^{\prime}\)** monomer. Introduction of two L2-UUCG loops into both of the RzMs in kUrd afforded **1x-K-1x\({}^{\prime}\)** to selectively form a monomeric state (lanes 2, 6 and 10 in Figure 2B,C). We then confirmed the assembly state of **1-K-1\({}^{\prime}\)** and its mutants by preparing a solution containing equal amounts of four kUrds (**1x-K-1x\({}^{\prime}\)**, 1x-K-1\({}^{\prime}\)**, 1-K-1x\({}^{\prime}\)** and 1-K-1\({}^{\prime}\)**), prepared by mixing two \(\alpha\)-chain RNAs and two \(\beta\)-chain RNAs in a single tube (lanes 3, 7 and 11 in Figure 2B,C). BODIPY-labeled \(\beta\)-chain RNAs for **1x-K-1x\({}^{\prime}\)** and **1-K-1x\({}^{\prime}\)** selectively visualized kUrd monomer (**1x-K-1x\({}^{\prime}\)**), kUrd dimer (**1x-K-1\({}^{\prime}\)**:1-K-1x\({}^{\prime}\)**) and kUrd open trimer (**1x-K-1\({}^{\prime}\)**:1-K-1\({}^{\prime}\)**:1-K-1x\({}^{\prime}\)**). In addition, to kUrd monomers, two new bands with lower mobilities were observed (lanes 3, 7 and 11 in Figure 2B,C), which were expected to be a kUrd dimer consisting mainly of **1x-K-1\({}^{\prime}\)**:1-K-1x\({}^{\prime}\)** and a kUrd open trimer consisting mainly of **1x-K-1\({}^{\prime}\)**:1-K-1\({}^{\prime}\)**:1-K-1x\({}^{\prime}\)**. We then analyzed the solution containing only **1-K-1\({}^{\prime}\)** (lanes 4, 8 and 12 in Figure 2B,C), which was expected to form homooligomers, including a closed form homotrim. The dominant band was retained in the gel slot, suggesting the formation of high-molecular weight oligomers. Two new bands, which were not seen in lanes 3, 7 and 11, were also observed. The lower mobility band would correspond to the desired closed trimer containing six ribozyme units (lanes 4, 8 and 12 in Figure 2B,C).