Quantifying complexity in DNA structures with high resolution Atomic Force Microscopy

Abstract

DNA topology is essential for regulating cellular processes and maintaining genome stability, yet it is challenging to quantify due to the size and complexity of topologically constrained DNA molecules. By combining high-resolution Atomic Force Microscopy (AFM) with a new high-throughput automated pipeline, we can quantify the length, conformation, and topology of individual complex DNA molecules with sub-molecular resolution. Our pipeline uses deep-learning methods to trace the backbone of individual DNA molecules and identify crossing points, efficiently determining which segment passes over which. We use this pipeline to determine the structure of stalled replication intermediates from Xenopus egg extracts, including theta structures and late replication products, and the topology of plasmids, knots and catenanes from the E. coli Xer recombination system. We use coarse-grained simulations to quantify the effect of surface immobilisation on twist-writhe partitioning. Our pipeline opens avenues for understanding how fundamental biological processes are regulated by DNA topology.

Fig. 1. Determining the topology of individual DNA molecules using AFM.

a 4-node DNA catenane visualised using AFM with helical structure visible (of N = 1010 total DNA plasmid, knot and catenane molecules imaged). Scale bar: 20 nm. Colour bar: −2 to 6 nm. b Schematic of the right-handed 4-node catenane in a with crossing orders determined by eye. c Schematic of the expected crossing height profiles of over-(lime green) and under-passing (hot pink) DNA duplexes at a crossing. d tilted 3D height profiles of each catenane crossing, schematics of each crossing in 3D, and manual line profiles of each crossing (numbered as in a). The large circle is coloured blue and small purple. The crossing order of each crossing is determined visually and agrees with the known topology of the catenane. e Automated tracing and topological determination of DNA structures from AFM images, for: i, relaxed (N = 67) and; ii, supercoiled plasmid (2260 bp) (N = 78); iii, 5-node twist knot produced from pDIR (2260 bp) (N = 108) and; iv, catenated (1253 bp, 398 bp) plasmids produced from p4CAT (N = 604). Automated traces (blue) show under-passing (hot pink) and over-passing (lime) segments at crossings. Scale bar: 50 nm. Height scale: −2 to 6 nm. Source data is provided as a Source Data file.

Fig. 2. Automated tracing and topological determination for complex DNA molecules from AFM images.

Pre-processed AFM images are masked to identify molecules (of N = 1010 total DNA plasmid, knot and catenane molecules imaged) using (a) classical image processing and b deep learning methods (U-Net masking). c An enhanced skeletonisation method, using height-biasing, reduces binary masks to single pixel traces along the centre of the molecule, and d locates the central point or node of the crossings (black), minimising misalignment of emanating branches. e Emanating branches (purple, pink, blue and dark green) are paired based on their propagating vectors and a height trace spanning the crossing segment (light green and pink) is obtained. Arrows show the propagation direction of the segments. f The full-width half-maximum (FWHM) of each crossing is used to determine the crossing order of the segments, with the maximal FWHM designated as over-passing. The over-passing segment can be seen in green while the under-passing segment can be seen in pink. Dotted lines illustrate their FWHM measurements. g, h Branch pairing at each node enables separation of entangled molecules, shown here in magenta and cyan. i Under- and over-passing crossing classifications allow for topological classification which is output in Rolfsen knot notation format, where 4²₁ correctly denotes the 4-node DNA catenane formed of two circular molecules that cross one another a minimum of four times. Scale bar: a–c: 50 nm, d, e: 10 nm, g–i: 50 nm. Height scale (c): −2 to 6 nm. N = 1 repeat for this image. Source data are provided as a Source Data file.

Fig. 3. Automated determination of DNA replication intermediates stalled using either the Lac Repressor protein or the Tus-Ter Complex, at 40 and 80 minute timepoints.

a Bulk DNA replication reaction products visualised on agarose gel. 4402 bp plasmid with 48 LacO sites (pJD97), or 3574 bp plasmid with 24 Tus sites (pUCattB-Ter24) are used as indicated. LacI or Tus proteins are added as indicated before initiation of the DNA replication reaction, which is then terminated after 10, 20, 40, 80 and 120 min. DNA samples are separated on agarose gel and nascent DNA is visualised by autoradiography. Replication products stalled at 40 and 80 minutes were imaged by AFM, with stalling performed using the (b) lac repressor protein (L40 N = 51, L80 N = 54) on a 4402 bp plasmid, and c Tus-Ter complex (T40 N = 20, T80 N = 18) on a 3574 bp plasmid. AFM micrographs of (d) stalled forks with i single-stranded DNA at the start of the fork, ii, including a high-resolution image of ssDNA gap. iii, a reversed replication fork, iv, including a high-resolution image of the reversed fork. Scale bars for ii and iv are 20 and 25 nm, respectively. Automated measurement of unreplicated DNA contour length, (e) 313 ± 156 nm, (L40, N = 12) and 218 ± 153 nm, (L80, N = 12), total contour length of lac repressor stalled DNA, (f) 2400 ± 168 nm, (L40, N = 51), 2500 ± 219 nm, (L80, N = 54) and Tus-Ter treated DNA (bimodal distribution) (g) 2240 ± 77 nm and 1170 ± 8 nm, (T40, N = 20), 1110 ± 90 nm and 2200 ± 83 nm (T80, N = 18). All singular values are mean ± SD, and bimodal values are calculated using a Gaussian mixture model with two components. Remaining scale bars: 100 nm. Height scale: −2 to 4 nm. Source data are provided as a Source Data file.

Fig. 4. Automated topological determination of twist and torus-type 5-node knots.

a Diagram of knots that can be created by the cer ligation reaction. See Supplementary Fig. 2 for proposed knotting mechanism (b), 1D gel electrophoresis of the knots shown in a. c, d, e AFM micrographs of unknot (N = 145), 5-node twist (N = 108), 5-node torus (N = 89) with crossings labelled 1–5 showing the order in which to trace the molecule starting from 1–5 with f–h corresponding automated traces (N = 81, N = 18, N = 6, respectively) showing under-passing (hot pink) and over-passing (lime) segments at crossings. All crossing signs are negative in f and g, and positive in h. Schematics (i–k) of the unknot (c) and 5-node knot isolated from pDIR (d) and the 5-node knot isolated from pINV (e) (all 2260 bp). Automated traces of micrographs (f–h) are coloured to show the crossing order determined from the ratios of the FWHM. The numbers at each crossing are the crossing order reliabilities for each crossing. Scale bars: 50 nm. Colour Bar: −2 to 6 nm. Source data are provided as a Source Data file.

Fig. 5. Variability in catenane conformation is driven by topological state.

Conformation classifications of individual molecules from the AFM image are separated into (a) open (N = 136) (b) taut (N = 57) (c) clustered (N = 117) d and bow-tie (N = 73). Each molecule i, is identified using classification rules determined by Supplementary Table 2. ii shows representative schematics of each class of the catenane and iii, representative pseudo-AFM data from coarse-grained simulations. Conformational classification of molecules is performed on catenated species in (e), nicked (automated, N = 197, manual N = 217) and f, supercoiled (Automated, N = 116, Manual, N = 166) forms using automated (pink) and manual (green) classification. Scale bars: 50 nm. Height scale: −2 to 6 nm. Source data is provided as a Source Data file.

Fig. 6. Surface immobilisation drives conformational changes, however, topological species can still be separated by their linking number difference.

Coarse-grained molecular dynamics simulations of catenanes in (a) supercoiled with dihedral angle ${\phi }_0^{*}$ = 0 (b) supercoiled with adjusted dihedral angle and c nicked with adjusted dihedral angle in i, initial; ii, equilibrated; iii, adsorbed states and; iv, worm-like representations with crossings between the catenated molecules highlighted. Note that for the remaining sub-figures, both “nicked” and “supercoiled” correspond to simulations with adjusted dihedral angle. d Frequency of crossings between the same molecule of DNA within adsorbed catenanes for nicked and supercoiled molecules show a reduction in the number of crossings for supercoiled molecules. e Separation of crossings that occur between the two molecules within the catenane for nicked and supercoiled species. f Writhe and g, twist of the large circle for nicked and supercoiled species in equilibrated and adsorbed conformations. N = 100 Nicked equilibrated, N = 91, Nicked adsorption. N = 100 Supercoiled equilibration, N = 85 Supercoiled adsorption. Summary statistics (min, Q1, Q2, Q3, max, mean) for writhe: Nicked equilibrated (0.56, 0.82, 0.875, 0.94, 1.24, 0.874); Nicked adsorption (−0.9, 0.077, 0.99, 1.03, 1.18, 0.727); Supercoiled equilibrated (−3.27, −2.955, −2.755, −2.125, −1.18, −2.589); Supercoiled adsorption (−1.14, 0, 0.065, 0.94, 1.12, 0.306). For twist: Nicked equilibrated (−0.78, 0.057, 0.13, 0.185, 0.42, 0.107); Nicked adsorption (−1.12, −0.045, −0.010, 0.025, 0.19, −0.025); Supercoiled equilibrated (−1.65, −1.22, −1.065, −0.948, −0.68, −1.082); Supercoiled adsorption (−5, −4.05, −4, −3.95, −2.96, −3.937). h, PCA scores plot showing separation of nicked (green for equilibrated, orange for adsorbed) and supercoiled (blue for equilibrated, pink for adsorbed) species on one axis (PC1) and equilibrated and absorbed conformations on the other (PC2). i, PCA loadings for PC1 and PC2. Source data are provided as a Source Data file.