a, Schematic of the single-molecule TIRF set-up that was used for measuring Cas1–Cas2 binding to canonical or precursor prespacer DNA. b, FRET efficiency histograms of binding events observed for canonical and precursor prespacer DNAs with 3′-overhangs of various lengths. c, Dwell-time (Δτ) distributions and average binding time (τ off ) determination for canonical and precursor prespacer DNAs with 3′-overhangs of various lengths. d, Left, representative time trace from a binding assay in the absence of Cas1–Cas2. DNA was added at t = 5 s. Right, image of a field of view with Cy3 signals on the left and Cy5 signals on the right. The image was recorded 1 min after the addition of DNA. e, Schematics of precursor prespacer DNAs with different labelling positions. f, FRET efficiency histograms of individual precursor prespacer DNAs with different labelling positions bound to Cas1–Cas2. g, FRET distribution and fractions of precursor prespacer DNAs from a single-molecule competition assay using precursor prespacer DNAs with different labelling positions. Histograms were obtained by incubating equal concentrations of precursor prespacer DNAs. To track the stably bound population, the flow chamber was washed and the fluorescence signals of the remaining population were measured. h, Cumulative distribution of the arrival times for binding events and k on for precursor prespacer DNAs with different labelling positions. i, Dwell-time distributions and k off of binding events for precursor prespacer DNAs with distinct labelling positions. j, Cumulative probability of the arrival times for precursor prespacer DNAs with 3′-overhangs of various lengths. k, Schematics of precursor prespacer DNAs with 3′-overhangs of various lengths. Each DNA construct consists of a 23-bp central duplex and 5-nt 3′-overhangs at both ends, which are further extended with N number of single-stranded deoxythymidine (dT) nucleotides. Both strands were labelled with a Cy3 fluorophore at the 5′-end of the top strand and a Cy5 fluorophore at the 16th nucleotide (T) from the 5′-end. l, Cumulative distribution of the arrival times for binding events and k on for precursor prespacer substrates with 3′-overhangs of various lengths. m, Dwell-time distributions of binding events and k off for precursor prespacer DNAs with 3′-overhangs of various lengths. n, Survival probability of stably bound substrates with 3′-overhangs of various lengths. The solid lines represent single-exponential fits using maximum-likelihood estimation. o, Schematics of canonical and precursor prespacer DNAs with different labelling positions and 3′-overhang lengths for a single-molecule competition experiment. p, q, FRET distributions (p) and fractions (q) of each FRET population from single-molecule competition experiments for canonical and precursor prespacer DNAs with 3′-overhangs of various lengths. ‘Before washing’ includes both transient and stably bound molecules; ‘after washing’ includes only the stably bound molecules. r, EMSAs on various canonical and precursor prespacer DNA substrates with increasing amounts of wild-type Cas1–Cas2. The top and bottom strands were labelled at the 5′-end with Cy3 and Cy5, respectively. Cas1–Cas2-bound and unbound precursor prespacer DNAs are indicated on the right. For b, f, g, p, solid lines represent Gaussian fits; the centre of each peak corresponds to the predetermined position of each individual construct in g, p. For c, h–j, l, m, solid lines represents single-exponential fits (maximum-likelihood estimation) that were used to determine the binding frequency (k on ) (h, j, l) and dissociation rate (k off ) (c, i, m). For the cumulative probability of the arrival times for k on bar plots and dwell times for k off bar plots, data are mean ± 95% CI, obtained by bootstrap analysis of a single replicate with n ≥ 300 (h, j, l) or n ≥ 500 (c, i, m) individual molecules. For the FRET fractions, data are mean ± s.e.m. from three independent measurements (n = 3) with n ≥ 5,000 molecules for each measurement (g, q). Data are representative of three replicates with similar results (b, c, f, h–j, l–n, q). Source data