Comparison between existing pairwise-destructive proximity measurements and auto-cycling proximity recording (APR). a In pairwise-destructive methods (e.g., proximity ligation), a particular target-bound probe generates a proximity record with only one neighbor that it becomes permanently attached to. This in turn yields only limited proximity information for a particular multitarget structure, necessarily resulting in incomplete reconstruction of its target arrangement. b With APR, proximity records are generated autonomously and continuously by transient pairing of any nearby probes, without destroying or depleting them. Not only are multiple copies of a record generated for a particular pair of probes, improving signal, but each probe can also produce proximity records with every neighbor, potentially allowing for complete reconstruction

Auto-cycling proximity recording (APR) mechanisms. a The APR cycle creates molecular records of proximity from pairs of hairpin probes. Probe-specific primers are (step i in a) extended to Half-records and (ii) reversibly displaced, (iii) bind palindromic domains of nearby Half-records, and (iv) are extended on each other to create and release Full-records, regenerating the probes. See text for detailed description. b Copy-and-release hairpin (CRH) detail, depicting primer binding domain b explicitly but labeling the entire copied template simply as t. Shown is the mechanism of (state i in b) initial primer binding, (ii) extension, and (iii) random walk of the strand displacement branch. For this combination of primer bulge l _T and Spacer9 stopper shown, the hairpin template strand t−b is computationally predicted to pair predominantly with the hairpin stem complement (iii, plot). See also Supplementary Fig. . c A more rapidly cycling hairpin does not utilize bulge l _T or domain b, but instead uses a phosphorothioate (PS) bond before the final primer (a) nucleotide, in conjunction with synthetic nucleotide pair iso-dC/iso-dG as a stopper. See Supplementary Fig.  for sequences and Supplementary Note  for other considerations

Proof-of-principle experiments. a Generation of Full-records requires the colocalization of probes, here by biotinylated hairpin loops bound to streptavidin, whereas isolated probes can always generate Half-records. Cropped denaturing PAGE gel depicting 10 μl reactions (40 min at 37 °C) with biotin–streptavidin association and 4:1 overall probe/streptavidin stoichiometry (inset), 8 and 22 nt barcodes (19 and 33 nt stem lengths copied), 10:1 initial primer/probe, and 40 nM total probe concentration. A single primer sequence was used and no secondary amplification was performed. b Auto-cycling is demonstrated by quantification of Cy5-labeled probes on cropped denaturing PAGE gels. Rapidly cycling probes with Iso-dC/dG stoppers and phosphorothioate primers were used, with probes at 0.1 nM and primers at 1000-fold excess to probes in each time series. Quantification of Full-records yields the plot. Half-records are difficult to detect because of low probe concentration. See probe details and sequences for a, b in Supplementary Fig.  and full gels in Supplementary Fig. . c An example of a single probe (with Barcode i) making multiple partnerships (with Barcodes ), read with Illumina MiSeq next-generation sequencing. Here, probes encoded a universal primer sequence and unique barcodes (in place of spacer s of Fig. ), and were held in tetramers by streptavidin. Primer sequences cropped for clarity. See Supplementary Fig.  for the unique-barcode APR cycle, probe details, and sequencing methods

Probe reach. a To characterize reach, relative probe positioning was controlled precisely. Probes were attached to 2D, rectangular, twist-corrected DNA origami structures measuring ~70 by 100 nm (origami shown with all possible Fig. 4 probe positions, as well as equivalent cartoon with 4 probes; see Supplementary Fig.  for origami design, Supplementary Table  for staple sequences, and Supplementary Fig.  for precise probe positions). After assembly, origami were deposited randomly on mica surfaces in the presence of 12.5 mM Mg²⁺ for firm adhesion, a condition we find protects origami from degradation by polymerase (see Supplementary Note ). Each probe was a direct extension of two origami staples (inset i) or covalent attachment to an intermediary oligonucleotide (inset ii; azide on probe loop covalently attached to alkyne on l _3T−d intermediary via DIBO-based click chemistry and gel-purified). Separation distances were measured between origami attachment points. Records were collected from the supernatant without disturbing the underlying origami, and PCR-amplified with, for example, and primers. b The maximum reach across which a probe pair can make a Full-record is determined by the cumulative lengths of their components, including double-stranded probe components and single-stranded Half-record components. These are shown as rigid and flexible, respectively, corresponding to their persistence lengths of ~50 nm and ~2 nm. Numbers indicate lengths in nucleotides. c Otherwise identical probes with spacer lengths of 0 or 12 nt (attached by staple extension), or 18 nt (covalently attached), were held in pairs separated by 6 to 48 nm in 6 nm increments (red positions in a), recorded (1 h at room temperature, 100 nM primers), and log-phase PCR-amplified (20 cycles, 500 nM primers) to gel-detectable levels. Denaturing PAGE band quantification was normalized to a constant reference pair for each well. Data for a given probe pair type were fit by least squares recursion to a simple sigmoidal curve c ₁/(1+Exp[c ₂(dist−c ₃)]), where dist represents separation distance and c ₁ through c ₃ were fit, and normalized to a maximum rate of 1. See probe sequences in Supplementary Table 

Complex geometry interrogation. a The same rectangular origami base used in Fig.  was adapted to hold three probes, of 18 nt spacer design, at 30 nm spacing (see Supplementary Fig. ). In the same conditions as in Fig. , probes were first placed in a triangular arrangement and recording was carried out. The sample was split, records PCR-amplified with separate pairs of probe primers (and reference primers), and products separated by gel electrophoresis and quantified (green plot profiles, marked (+) when judged to qualify for the proximity list). As expected, all three probe pairs yielded records, suggesting a triangular shape in reconstruction. b When those same probes were attached in a line, with P1 and P2 out of reach from one another, only two record types were amplified. This suggests a relatively linear arrangement. c More complex, 7-probe geometries were also interrogated, this time with 24 nm hexagonal grid spacing and 12 nt spacer probes. The full set of 21 primer pair amplifications yielded the gel shown, with 12 pairs in proximity. Computational reconstruction yielded the same hexagonal pattern. Insets show positional precision of any single point, with respect to others shown, as shaded region that satisfies this gel. Inset (i) shows the precision for computed hex pattern, while inset (ii) shows the precision for a random pattern that also satisfies gel result. d When center probe P7 was moved outside the hexagon, APR yielded the 8 expected proximities and correct reconstruction. e Similarly, when P1 was moved, the 11 expected proximities and correct reconstruction resulted. Throughout, computational reconstruction images were reflected and rotated, but not distorted, for best comparison to the programmed structure diagrams. See probe sequences in Supplementary Table  and full gels in Supplementary Fig. . All reference bands in the figure correspond to lengths indicated in b

State change. The same origami probe triangle was used as in Fig. , but probe P3 could be deactivated. (see Supplementary Fig.  for precise probe positions.) PCR amplification and denaturing PAGE of recording from active probe (i), after intermediate wash (ii), from deactivated probe (iii), after second intermediate wash (iv), and from reactivated probe (v). The intermediate wash results demonstrate that there were no leftover records. A single set of origami was used for all steps and resampled. Origami and PAGE otherwise treated as in Fig. . See probe sequences in Supplementary Table  and full gels in Supplementary Fig.