a, Schematic of SpCas9 REC3 with FRET dyes at positions S701C and S960C, with HNH domain omitted for clarity. Inactive to active structures represent REC3 in the sgRNA-bound (PDB accession number 4ZT0) to dsDNA-bound (PDB accession number 5F9R) forms, respectively. b, c, smFRET histograms showing HNH conformational activation with black curves representing a fit to multiple Gaussian peaks for (b) WT SpCas9 REC3 and (c) SpCas9-HF1 REC3 bound to perfect and PAM-distal mismatched targets. The purple peak denotes the sgRNA-only bound state, while the red and green peaks represent two states of REC3 with conformational flexibility upon binding to DNA substrates. d, REC3 in vitro complementation assay with SpCas9∆REC3 by measuring cleavage rate constants. e, On-target DNA binding assay in the presence or absence of the REC3 domain; mean and s.d. are shown. f, REC3 in vitro complementation assay with SpCas9∆REC3 by measuring HNH activation with (ratio) A values. g, (Ratio) A data with SpCas9 REC2 and SpCas9 HNH showing reciprocal FRET states with the indicated substrates. For d–g, mean and s.d. are shown; n = 3 independent experiments (overlaid as white circles in d, f, and g). h, Schematic of SpCas9∆REC3 REC2 with FRET dyes at positions E60C and D273C, with the REC3 domain added in trans. Inactive to active structures represent REC2 in the sgRNA-bound (PDB accession number 4ZT0) to dsDNA-bound (PDB accession number 5F9R) forms, respectively. i, smFRET histograms measuring REC2 conformational states with SpCas9∆REC3 REC2 in the absence and presence of the REC3 domain when bound to an on-target substrate. Source data