a, Schematic of intramolecular transposition. If the 3′ OH nucleophiles attack the strand on which they are located, the products are two deletion circles (top), but if they attack the opposite strand, a single inversion circle product is generated (bottom). Staggered attack on the target DNA backbone yields single-stranded gaps in the products, represented as five short vertical lines. b, Inverse PCR reaction to amplify inversion circles from purified intramolecular transposition product as in Fig. 5d, third lane. The band indicated with an arrow was excised, cloned and sequenced, yielding sites at which intramolecular transposition occurred to yield inversion circles, indicated in the map of the excised 12/23RSS central fragment (below). Half arrows indicate approximate locations of PCR primers. The location of deletion circle joints detected by sequencing are not indicated. c, Schematic of intermolecular in vitro transposition assay. An RSS-flanked Tet gene is mobilized from a linear donor by RAG-mediated DNA cleavage and can transpose into a target plasmid, which is detected after bacterial transformation by the appearance of colonies on Kan/Tet/Str (KTS) plates (streptomycin (str) is not relevant in this assay). d, In vitro DNA cleavage and intramolecular transposition by position 848-mutant cRAG1 (with RAG2(1–383)). Increased transposition compared to wild-type cRAG1 is revealed by diminished intensity of the double cleavage band and increased intensity of the slow-migrating intramolecular inversion circle transposition product band (red arrow). The intensity of the inversion circle band underestimates the efficiency of transposition because deletion circle transposition products—which are of heterogeneous size, and hence not visible as a discrete band—are also produced18. e, Quantification of intramolecular transposition efficiency from three independent experiments as in d, measured by ratio of double cleavage band to 23RSS cleavage band (the latter serving as an internal control for the total amount of cleavage). The ratio decreases as intramolecular transposition increases in efficiency, consuming the double cleavage band. Mean, with data range indicated by box. Two tailed t-test; P values are indicated. f, Distribution of transposition target site duplication lengths determined by sequencing of plasmid transposition products or from high-throughput sequencing of plasmid-to-genome transposition products (Extended Data Fig. 9d), as indicated above the bars. The RAG1 protein used is indicated below the bars. In vitro reactions as in Fig. 5e using RAG2(1–383); in vivo plasmid target reactions as in Fig. 5g using RAG2(1–350); genome transposition products generated using RAG2(1–350). In a small fraction of plasmids, sequencing revealed deletions at the site of insertion of the RSSs (red; deletion). g, In vitro cleavage and intramolecular transposition reactions using RAG2(1–352) and RAG2(1–383) (as indicated above the lanes) and wild-type or mutant cRAG1 (as indicated below the lanes). Transposition is readily detected with both forms of RAG2 and is increased by the RAG1(R848M) mutation. h, In vitro intermolecular transposition assays using RAG2(1–383) and RAG2(1–352) and wild-type or mutant cRAG1 (as indicated below the lanes). Deleting the RAG2 acidic hinge does not increase the efficiency of intermolecular transposition in vitro.