Base-pair resolution analysis of the effect of supercoiling on DNA flexibility and recognition

In the cell, DNA is arranged into highly-organised and topologically-constrained (supercoiled) structures. It remains unclear how this supercoiling affects the detailed double-helical structure of DNA, largely because of limitations in spatial resolution of the available biophysical tools. Here, we overcome these limitations, by a combination of atomic force microscopy (AFM) and atomistic molecular dynamics (MD) simulations, to resolve structures of negatively-supercoiled DNA minicircles at base-pair resolution. We observe that negative superhelical stress induces local variation in the canonical B-form DNA structure by introducing kinks and defects that affect global minicircle structure and flexibility. We probe how these local and global conformational changes affect DNA interactions through the binding of triplex-forming oligonucleotides to DNA minicircles. We show that the energetics of triplex formation is governed by a delicate balance between electrostatics and bonding interactions. Our results provide mechanistic insight into how DNA supercoiling can affect molecular recognition.


Introduction
Native genomic DNA in prokaryotes is maintained under negative-superhelical stress, a state of torsion that tends to unwind the DNA double helix [1][2][3] . The DNA response to this torsional stress is described as supercoiling, in which a change in linking number (∆Lk) of the DNA is partitioned into twist (Tw) and writhe (Wr) [1][2][3][4] . In prokaryotes, genomic DNA is globally negatively supercoiled, with superhelical density s ≈ -0.06 5 . This supercoiling operates synergistically with nuclear-associated proteins to regulate bacterial gene expression 6 . In eukaryotes, supercoiling is implicated in the regulation of oncogenes such as c-Myc 7 .
It plays a fundamental role in the formation and stability of looped DNA structures 8 and DNA R-loops 9 , and influences the placement of RNA guide sequences by the CRISPR-Cas9 gene editing toolkit 10 . The supercoiling-induced structural changes that modulate these DNA functions present a challenge for traditional structural methods that can provide atomistic resolution, i.e., X-ray crystallography 11 and nuclear magnetic resonance (NMR) 12 , because of the diverse conformational landscape of supercoiled DNA 13 .
As part of its role in regulating transcription, replication, and chromosomal segregation 14 , supercoiling has been proposed to play a role in the specificity of DNA-binding ligands, including major-groove binders such as triplex-forming oligonucleotides (TFOs) 15,16 . TFOs target specific DNA sequences, forming a triplex of the single-stranded TFO and the target duplex DNA 17 . The target specificity of TFOs combined with their ability to suppress gene expression has driven their development as anti-cancer agents.
Here we combine high-resolution atomic force microscopy (AFM) with molecular dynamics (MD) simulations to reveal how supercoiling affects global and local DNA conformation, structure and dynamics in DNA minicircles of length 250-340 bp. These minicircles are small enough to be simulated at the atomistic level by MD 13,18 and to be visualized at high (double-helix) resolution by AFM experiments in solution [19][20][21] . Minicircles are also representative of looped DNA at plectoneme tips 22 and small extrachromosomal circular DNAs (eccDNAs), which have tissue-specific populations and sequence profiles in human cells [23][24][25] . The DNA minicircles in this study incorporate a TFO-binding sequence, to assess how the interplay of electrostatic and base-stacking energies determines the formation of triplex structures in supercoiled DNA.

Results
High-Resolution AFM and MD reveal conformational diversity in supercoiled DNA minicircles: Figure 1 shows the structure of negatively-supercoiled DNA minicircles as viewed by high-resolution AFM and simulated by atomistic MD. High-resolution AFM images recorded in aqueous solution show DNA minicircles, isolated with native levels of supercoiling, in a range of conformations with sufficient resolution to resolve the two oligonucleotide strands of the double helix. For the 251 bp minicircle, this allowed 3 determination of the linking number, Lk = 24 ± 1 from direct measurements of twist (24 ± 1 turns) and writhe (≤ 1). The measured twist corresponds to a helical repeat of 10.5 ± 0.5 bp, consistent with canonical B-form DNA 1 . For each conformation of the surface-bound minicircles found by AFM (Fig. 1a-d), it was possible to find MD-generated conformers with a close resemblance in global structure (Fig. 1e). The high planarity of the minicircles, determined in the simulations as less than 15% on average (Supp. Fig. 1), is advantageous to structural determination by AFM, because distortions resulting from surface immobilisation are minimal for planar molecules. Atomistic models of supercoiled DNA minicircles have been shown to be consistent with cryo-ET density maps 13 , which provide sufficient resolution to capture the overall shape of the minicircles, but not their helical structure. The variation in structures observed in  (Fig. 1f) demonstrating that dynamic behaviour can occur in these molecules on the order of minutes, even when tethered to a surface, also implying that the structural perturbation caused by immobilisation is small. Similar dynamics were observed in MD simulations of the 339 minicircle (ΔLk = -1) in a continuum representation of the solvent, albeit at a much faster (picosecond) rate ( Fig. 1g and Supp. Videos 1, 2).
Experimental measurements have shown that adsorption to a surface for AFM slows dynamics 26,27 and in silico, the absence of friction with water molecules accelerates conformational dynamics 13,28 . Negative supercoiling induces defects in DNA minicircles: AFM not only provides resolution sufficient to observe the DNA helical repeat, but most critically achieves this without the need for ensemble averaging.
This uniquely permits us to observe heterogeneous structural perturbations, e.g. individual DNA defects, 5 that occur due to superhelical stress imposed on the minicircle. By combining AFM and in silico measurements of DNA minicircle topoisomers with increasing levels of supercoiling (Fig. 2) we were able to observe the effect of negative supercoiling on the structure and mechanics of DNA with Ångström resolution. We observed no defects in the structure of the relaxed topoisomer, which maintains a B-form structure throughout the molecule. However, in negatively-supercoiled DNA, defects were observed both by AFM (Fig. 1 a-d, red triangles) and atomistic MD simulations (Fig. 2a, red triangles). We observed the onset of defects in negatively-supercoiled minicircles of ΔLk = -1 onwards (s ≈ -0.03); across all in silico topoisomers, seven out of the ten defects observed are denaturation bubbles, where two or more base pairs are flipped out of the duplex (Fig. 2a insets and Supp. Fig. 2). This results in flexible hinges that can accommodate a 180⁰ turn within a single helical turn, radically altering the range of conformations the DNA can adopt. We also observed type I kinks in topoisomers -1 and -3 (in which a single base pair presents a strong bend, breaking hydrogen bonds and stacking), and a type II kink within topoisomer -3 (in which hydrogen bonds of two consecutive base pairs are broken and bases are stacked on their 5´ neighbours) Direct comparison of the level of negative supercoiling required to induce the onset of structural transitions, including denaturation of unbent DNA (typically taken to be around s ≈ -0.04 30 ) with that of DNA minicircles is not straightforward, because the DNA supercoiling response is so exquisitely sequence-dependent. For longer sequences, the statistical likelihood that a sequence will contain an element that undergoes a specific stress-induced structural transition (e.g. Z-DNA formation or cruciform extrusion) is larger 31 , and these element suppress defect formation by absorbing superhelical stress 32 . Our minicircle sequences do not contain any such supercoiling responsive sequences. The 1 or 2 bp size defects we observe in minicircles are smaller than those that have been probed in 2-5 kbp negatively-supercoiled plasmids (> 30 bp) 31 . However, coarse-grained simulations of 600 bp supercoiled linear DNA show the formation of small defects (2-3 bp) at plectonemic loops, with larger bubbles (up to 20 bp) observed when plectoneme formation is prohibited by an applied force 29 . We deduce from these observations that DNA bending promotes and localises supercoiling-induced defect formation. Bent DNA structures are ubiquitous in the genome; as well as forming ends of plectonemes 33 , bent DNA is vital to a number of recognition processes, including transcription regulation via DNA looping 34 , and DNA damage detection 35,36 .
Estimate of critical bend angle associated with defect formation: We determined the critical bending angle required to form a defect through curvature analysis for all in silico topoisomers (Fig. 2a, b) and for nativelysupercoiled DNA minicircles by high-resolution AFM (Fig. 2c). Kinks were observed by AFM as discontinuities in the helical repeat of DNA where the angle of the helix changes rapidly, or where the DNA appears thinner or disrupted (Fig. 2c). Defects in the MD were classified as disruptions to base stacking and complementary base pairing (Fig. 2a, insets). Figure 2d shows DNA minicircle bend angles classified as either B-form (black crosses) or defective DNA (red triangles), both for AFM (1 st column) and MD (all 6 other columns). We deduce that canonical B-form DNA can sustain an angle of up to ~75° through regions of high bending stress (critical angles of 76° and 74° for AFM and MD respectively -Supp. Fig. 2) without disruption to either base stacking or hydrogen bonding. For defective DNA, an average bend angle of 106 ± 15° was measured for AFM and 120 ± 32° for MD, almost double the bend angle measured for canonical DNA, of 69 ± 5° for AFM and 57± 9° (mean ± standard deviation). This maximum bend angle of 75°, implies that for a DNA bend (such as a plectoneme), to remain free of defects the loop must be more than 7-10 nm wide, which requires approximately 55 bp or five helical turns, showing remarkable similarity with coarse grained simulations 29 . Global compaction in DNA structure correlates with the formation of defects: To probe how the supercoiling-induced changes in DNA structure vary with the global conformation of DNA minicircles, we generated a range of relaxed and negatively-supercoiled topoisomers experimentally (Fig. 3a,b) for comparison with those generated in silico (Fig. 2). For each topoisomer we quantified the degree of molecular compaction observed by AFM (Fig. 3a) and determined the supercoiling as an average of all bands observed by gel electrophoresis (Fig. 3b). Aspect ratios were calculated for individual minicircles within images (Fig. 3a). While relaxed DNA minicircles appear predominantly as open rings, with high aspect ratio, increasing superhelical density increases the global compaction generating a range of heterogeneous structures containing defects (Fig. 3c,d). This global compaction from relaxed to maximally supercoiled structures is accompanied by a decrease in the aspect ratio of 35% by AFM (Fig. 3e) and 40% by MD (Fig. 2e).
As expected, as ΔLk decreases from 0 to -1, (σ ≈ 0 to -0.03) the DNA writhes and compacts. However, further negative-supercoiling of the helix to ΔLk ≈ -2 (σ ≈ -0.06) results in a counterintuitive decrease in compaction (Fig. 3e). This correlates with a smaller electrophoretic shift for -1 to -2 than for the other topoisomer transitions (Fig. 3b) and a smaller change in writhe in the MD simulations than for other transitions (ΔWr = -0.4 turns and -1.7 turns for the -1 to -2 and -2 to -3 transitions respectively). This anomalous behaviour correlates with the onset of defects observed by both AFM and MD. Defects relieve torsional stress and allow the DNA to partially relax, resulting in an increased number of open conformations (Fig. 3c). Comparing the writhe of a defect containing (-1.1 ± 0.1 turns) and defect free simulation (-1.7 ± 0.1 turns) of the ΔLk = -2 topoisomer shows that defects cause a reduction in writhe of 0.6 turns (conformers shown in Supp. Fig. 2). When further negative supercoiling is introduced, the DNA becomes increasingly writhed and compacted, as the superhelical stress can no longer be dissipated purely through the formation of defects.

Supercoiling-induced conformational variability affects binding of triplex forming oligonucleotides:
The effect of supercoiling-induced structural variability on DNA binding interactions was investigated through the site-specific binding of a triplex forming oligonucleotide (TFO) to supercoiled DNA minicircles. The formation of triplex DNA occurs via Hoogsteen base-pairing between the (CT)16 triplex-forming oligonucleotide (TFO) and the double-stranded minicircle sequence (GA)12 38 . By AFM, we observe triplex formation as small, sub-nanometre protrusions from natively-supercoiled DNA minicircles (Fig. 4a). This was verified by AFM measurements on linearised DNA minicircles (Supp. Fig. 3). Strikingly, SPR experiments showed that the superhelical density of the minicircles has a minimal effect on the affinity of triplex formation, with binding constants (Kd) of the order of 10 pM across superhelical densities (ΔLk = 0 to -4.9, Supp. Fig. 4 and Supp. Table 1).
To understand the unexpected lack of sensitivity of triplex binding to supercoiling in minicircles, we

Conclusion
Using a combination of high-resolution AFM and atomistic MD simulations, we describe the structure, dynamics and recognition of negatively-supercoiled minicircle DNA, with double-helical resolution. We quantify the critical bend angle for canonical B-form DNA under superhelical stress as 75⁰, implying that a 11 DNA loop must be formed of at least 5 helical turns to be free of defects. These defects dominate DNA mechanics by contributing to the flexibility and conformational diversity of supercoiled DNA.
We observe that superhelical stress globally compacts DNA, resulting in a decreased aspect ratio, and radius of gyration. However, at superhelical densities close to the that of genomic DNA, we see an unexpected reduction in compaction. We attribute this reduction to the onset of supercoiling-induced kinks and defects, through which torsional stress can be dissipated. Beyond this point the trend to compaction continues, as the defects generated are not sufficient to absorb increased superhelical stress.
The conformational diversity of supercoiled DNA allows for structural perturbations that can accommodate the binding of external substrates as exemplified the formation of triplex DNA. The supercoiling dependence of triplex formation is governed by a balance of two competing energetic interactions. An increased electrostatic penalty is incurred in negatively-supercoiled DNA due to supercoiling-induced compaction, whilst additional hydrogen bonds are facilitated by DNA undertwisting. This balance in the energetics facilitates triplex formation across a range of superhelical densities.
We show remarkable synergy between atomistic simulations and experimental data; despite caveats in both, including a requirement for surface binding, and the use of empirical classical forcefields with sampling limitations imposed by finite computational resources. However, in combination these two biophysical tools enable us to determine the effect of supercoiling on local and global DNA structure and its wider influence on dynamics and recognition. Though we note that the bending stress for DNA minicircles is much higher than for longer DNA, such as plasmids, or eukaryotic topologically associated domains (TADs), the significant perturbation on the mechanics of the DNA enforced by the bending energy in minicircles of this size has particular relevance for the structure of tightly constrained DNA for example at plectoneme ends 22,39 , short DNA loops and in small eccDNAs. We believe that this data, taken in conjunction with studies of longer DNAs under superhelical stress, will provide a more complete study of DNA structure under stress and can be used to inform future studies on DNA nanotechnology, plectoneme 39 and topology prediction 22 . As well as improving our fundamental understanding of DNA mechanics, our findings have applications in bioengineering, given the proposed therapeutic potential of small circular DNAs and TFOs 40 and the required optimisation of DNA for diagnostics 41 and therapeutics 42 .

Generation and purification of small DNA circles
Small DNA circles (minicircles) of 339 and 251 bp were prepared using bacteriophage λ-Int site-specific recombination in vivo, based on a method previously described with some minor modifications 43 . In each case, a 16 bp triplex-binding site (for the triplex-forming oligo TFO1R: 5´[Bt] -CTC TCT CTC TCT CTC T (where Bt indicates biotin), the reverse of the sequence described previously 16 .
Plasmids containing the original minicircle sequences were provided by Lynn Zechiedrich (Baylor College, Houston, Texas). For the 251 bp circles we experienced low yields for the methods described above so most material was obtained from Twister Biotech (Houston, TX, USA); we also obtained larger quantities of 339 bp circles from this company.
The triplex-forming region were incorporated into the parent plasmids by site-directed mutagenesis using the QuikChange Site-Directed Mutagenesis Kit (Stratagene) following the manufacturer's protocol.
Plasmids were transformed into Escherichia coli LZ54 43 ; the 339 bp minicircles were prepared and isolated using three methods.
On a small scale (2 L), plasmid-containing strains were grown in LB medium, as described previously 43 except that BamHI (which linearises the large circular product that is catenated to the minicircle) was not used to release the minicircle; we found that treatment with BamHI did not increase the yield of the Fractions containing minicircle DNA were pooled, and concentrated by isopropanol precipitation, washing the precipitate with ethanol. Purification by gel filtration was repeated a few successive times in order to ensure complete removal of dimeric minicircle. The purified and concentrated minicircle DNA was resuspended in TE buffer.

DNA minicircle sequences:
AttR sequence is highlighted in blue, and triplex forming sequence in green.

Preparation and analysis of different topological species of minicircles
To generate negatively-supercoiled species, the 339 bp minicircle was first nicked at a single site using Nb.BbvCI (New England Biolabs) at 37°C. After incubation at 80°C for 20 min to inactivate the endonuclease, nicked DNA was purified and isolated using the QIAGEN miniprep kit. Then, 15 µg of the purified nicked minicircle was incubated with T4 ligase (New England Biolabs) and ligase buffer containing 25 µg mL -1 BSA, in the presence of different quantities of ethidium bromide (EtBr) in a total reaction volume of 3 mL, at room temperature overnight. This was followed by successive purification and isolation of pure Plasmid pBR322 was supplied by Inspiralis Ltd (Norwich, UK) and analysed by electrophoresis through 1 % agarose gels in TAE buffer at 80 V for ~2 h. Gels were stained with EtBr and analysed using a Molecular Dynamics STORM 840 imaging system with quantitation using ImageQuant.

S1 nuclease digestions
To determine whether triplex formation between TFO1R and minicircle DNA had occurred, samples were probed with S1 nuclease. To prepare the triplex complex, an excess of TFO1R (2.5 µM) was incubated with the minicircle/plasmid (150 nM) in 100 mM calcium acetate pH 4.8, in a total volume of 20 µL at room temperature for 30 min. (In control experiments reactions were also carried out in TF buffer: 50 mM sodium acetate pH 5.0, 50 mM NaCl, 50 mM MgCl2.) Aliquots (5 µL) were taken and S1 nuclease (0 to 1000 U; Thermo Fisher Scientific) was then added and the incubation continued in S1 nuclease buffer ( adsorbed for 30 minutes followed by four washes in the same buffer to remove any unbound DNA minicircles. Ni 2+ immobilisation was used to obtain the data shown in Figures 1 and 2 and PLL for the data shown in Figure 3.

Triplex formation:
For experiments with TFO, DNA minicircles were incubated in an Eppendorf with a ten-fold excess of TFO in 50 mM NaOAc buffer at pH 5.3, prior to adsorption onto the mica substrate using the PLL method, as above. To verify the location of the TFO on the DNA sequence (Supp. Fig. 2), the minicircles were first linearised by cutting with NdeI.

AFM imaging:
All AFM measurements were performed in liquid. All experiments except Fig. 1f 19 . FastScan D (Bruker) cantilevers were actuated photothermally in tapping mode at amplitudes of 1-2 nm. Imaging was carried out at line rates of 3 Hz, over scan sizes of 50 nm with a setpoint ~80 % of the free amplitude, which correlates to a peak force of ≤100 pN 19 .

AFM image processing:
AFM images were processed using a user-designed Python script (pygwytracing.py) which utilises the Gwyddion 'pygwy' module 37 for automated image correction, DNA molecule identification and morphological analysis. The algorithm searches recursively for files within a user-defined directory. This search also excludes any files of the format '_cs' which are cropped files exported by the Nanoscope Analysis software (Bruker, CA, USA). AFM images are loaded using gwyddion functions and topography data is automatically selected using the choosechannels function. The pixel size and dimensions of each image are determined using the imagedetails function, which allows all inputs to be specified in real, i.e. nanometre values, in place of pixel values. This is especially important for datasets with changing resolution.
Basic image processing is performed in the function editfile which uses the functions: 'align rows' to remove offsets between scan lines; 'level' to remove sample tilt as a first order polynomial; 'flatten base' which uses a combination of facet and polynomial levelling with automated masking; and 'zeromean' which sets the mean value of the image, i.e. the background, to zero. A gaussian filter (s = 1.5) of 3.5 pixels (1-2 nm) was applied to remove pixel errors and high frequency noise.
Single DNA molecules are identified in images using a modified extension of Gwyddion's automated masking protocols, in which masks are used to define the positions of individual features (grains) on the imaged surface. The grains within a flattened AFM image are identified using the 'mask_outliers' function, which masks data points with height values that deviate from the mean by more than 1s (with 3s corresponding to a standard gaussian). Grains which touch the edge of the image (i.e. are incomplete) are removed using the 'grains_remove_touching_border' function and grains which are smaller than 200 nm 2 are removed using the 'grains_remove_by_size' function. Erroneous grains are removed using the removelargeobjects and removesmallobjects functions, which themselves use the function find_median_pixel_area to determine the size range of objects to remove. The 'grains_remove_by_size' function is then called again to remove grains which fall outside 50 % -150 % of the median grain area determined in the previous step.
Grain statistics are then calculated for each image using the grainanalysis function which utilises the 'grains_get_values' function to obtain a number of statistical properties which are saved using the saveindividualstats function as '.json' and '.txt' files for later use in a subdirectory 'GrainStatistics' in the specified path. In addition, each grain's values are appended to an array [appended_data], to statistically analyse the morphologies of DNA molecules from all images for a given experiment (presumed to be within a single directory). This array is converted to a pandas dataframe 45 using the getdataforallfiles function and saved out using the savestats function as '.json' and '.txt' files with the name of the directory in the original path.
Individual grains (i.e. isolated molecules) are cropped out using the function bbox, which uses the grain centre x and y positions obtained in the grainanalysis function to duplicate the original image and crop it to a predefined size (here 80 nm) around the centre of the grain. These images are then labelled with the grain ID and saved out as tiff files in a subdirectory 'Cropped' in the specified path.
To allow for further processing in python, there is an option to obtain the image or mask as a numpy array 46 , using the function exportasnparray. The processed image, and a copy with the mask overlaid are saved out using the savefiles function to a subdirectory 'Processed' in the specified path.
Statistical analysis and plotting is performed using the statsplotting script. This script uses the importfromjson function to import the JSON format file exported by pygwytracing and calculates various statistical parameters for all grain quantities, e.g. length, width and saves these out as a new JSON file using the savestats function. Both KDE plots and histograms are generated for any of the grain quantities using the matplotlib 47 and seaborn 48 libraries within the functions plotkde, plotcolumns and plothist.

Determination of minicircle bend angles by AFM:
To determine the bend angles for DNA minicircles by AFM, images were imported into Gwyddion, and basic processing was carried out as described above in the editfile script for basic flattening. Bend angles were then measured using Gwyddion's measurement tool.

Determination of triplex binding by AFM:
To verify that the small protrusions observed on DNA in the presence of the triplex forming oligonucleotide (TFO) at low pH were triplexes the site of the protrusions was determined. The 339 bp minicircles were linearised at the NdeI site and imaged by AFM as described above. Processed images were traced by hand in IMOD 2849 (University of Colorado, CO, USA) to determine the position of the protrusion along the DNA (Supp. Fig. 2). The tracing data was analysed using the TFOlength script. The mean and standard deviation for each length measurement (full minicircle, triplex, and triplex flanking lengths) were calculated using built in functions, and the data for each plotted as a histogram.

18
The length of the minicircle was determined as 109 ± 4 nm, with the triplex measured as 37 ± 2 nm, 34% of the length of the minicircle. The distance between the TFO site and the restriction site is 127 bp, which is 37 % of the length of the minicircle, and in good agreement with the AFM measurements. The length of the triplex as measured by AFM is 6 ± 2 nm. Errors quoted are standard deviations.

Set up of the structures for supercoiled 339 bp DNA minicircles
Linear starting DNA molecules with the same 339 bp sequence as above were built using the NAB module implemented in AmberTools12 50 . DNA planar circles corresponding to six topoisomers (∆Lk = -6, -3, -2, -1, 0, 1) with/without the 16 bp triplex-forming oligomer were then constructed using an in-house programme. The AMBER99 forcefield 51 with different corrections for backbone dihedral angles including the parmBSC0 for α and γ 52 , the parmOL4 for χ (glycosidic bond) 53

Simulations of 339bp minicircles in explicit solvent
To select the starting structure for explicitly solvated simulations, we performed clustering analysis using the average linkage algorithm within PTRAJ for the implicitly solvated DNA trajectories. Representative structures of the most populated clusters then were chosen and solvated in TIP3P rectangular boxes with a 6 nm buffer, 339 Ca 2+ counterions 58 to balance the DNA charge and additional Ca 2+ /2Cl -ion pairs 59 corresponding to a 100 mM. Two replicas of the -2 and -3 topoisomers were subjected to 100ns explicitly solvated MD simulations, starting from the two most representative structures. Single 100ns MD simulations were performed for topoisomers -6, -1, 0 and +1. Solvated MD runs were performed using the GROMACS 4.5 program 60 with standard MD protocols 56 at 308 K and, afterwards, were carefully visualised to ensure that rotation of the solute was not significant compared to the size of the simulation box over the timescale of the MD. Only the last 30 ns sampled every 10 ps were used for the subsequent analysis.
VMD 61 and Chimera 62 were used to depict representative structures, to measure the longest distance across plectonemic loops and to detect defective DNA through visual inspection. DNA defects were confirmed through energetic analysis of stacking and hydrogen bonds at the relevant base steps using GROMACS 4.5. Hydrogen bonds were determined using 3.5 Å and 140⁰ as a distance and angle cutoff, respectively, as in Figure 4d.
Additional simulations for ∆Lk =-6, -2 and 0 topoisomers were performed using BSC1 forcefield corrections 63 for DNA backbone dihedral angles instead of parmOL4. Simulations were started using same initial structures and were run with equivalent solvent conditions in TIP3P rectangular boxes with a 3 nm buffer for 100 ns using CUDA version of AMBER16 63 . Again, trajectories were carefully visualised to ensure that rotation of the solute was not significant compared to the size of the simulation box over the timescale of the MD 64 . Only the last 30 ns and a snapshot every 10 ps were used for the subsequent analysis, which are presented in Supp. Fig. 4

Simulations of linear DNA in explicit solvent
A 36-mer fragment containing the triplex-binding site (TBS) was extracted from the 339 bp minicircle to compare binding energies of this site on unconstrained linear DNA or on supercoiled minicircles. The TBS was placed in the middle to avoid end-effects 65 . The linear starting structure was solvated explicitly for running MD simulations and was set up, minimized, and equilibrated following the protocols described previously.

Simulations of 260 bp minicircles
The structure used for mirroring the high-resolution AFM image of a 251 bp minicircle on Figure 1a was extracted from a simulation previously run for the -1 topoisomer of a 260 bp minicircle 56 . The slightly longer sequence of 260 bp was constructed based on the experimental sequence of 251 bp studied here.

Global shape and other geometrical analysis of simulations
The radius of gyration was determined using the AMBER program PTRAJ (40). Other geometrical descriptions of the global shape, such as writhe and bend, were performed using WrLINE molecular contour 66   20

Energy calculations of triplex DNA formation
To obtain theoretical insight into the thermodynamics driving triplex binding, we used the MD trajectories to estimate the global (e.g. electrostatics) and local (e.g. base-pair stacking and hydrogen bonding) contributions to the overall binding energy. The global electrostatic contribution for configurational energy ( 454 ) was evaluated using the AMBER program MMPBSA 67 . To compare between the different topoisomers, the individual components were referred to the relaxed DNA-naked topoisomer (∆ 4547; : = 4547 − 4547;: ) as it is shown in Figure 4c.
We also analysed the interaction energy between nucleotides in the triplex binding site, considering inplane base interactions and nearest neighbours only (e.g. 9 bases in total). All interaction energies were calculated using the GROMACS 4.5 program. The two components of the binding energy were calculated at the TBS for each topoisomer by discarding the effect of the unbound 3 rd strand ( ;*<= = >?@ − ABC ).
Values for the different topoisomers were referenced to the linear fragment (∆ ;*<=; D = ;*<= − ;*<=;D ), as shown in Figure 4d. The local interaction energy terms (Lennard-Jones and electrostatic interactions) between in plane nucleotides were used as an estimate of the Hoogsteen hydrogen bonding at the triplex binding site (TBS) (Fig. 4d, yellow bars), while the interaction energies between bases in the planes above and below were used as an estimation of base-stacking, hydrogen bonding and non-bonded backbone interactions (4d, blue bars). The presence of these hydrogen bonds was confirmed by visual inspection in VMD (Fig. 4b).
Surface plasmon resonance (SPR) SPR measurements were recorded at either 25°C or 35°C using a Biacore T200 system (GE Healthcare).
All experiments were performed using an SA Series S Sensor Chip (GE Healthcare), which has four flow cells each containing streptavidin pre-immobilised to a carboxymethylated dextran matrix. For immobilisation, a standard immobilisation protocol was used with a running buffer of HSB-EP+ buffer (10 mM HEPES pH 7.4, 150 mM NaCl, 3 mM EDTA, 0.05% [v/v] surfactant P20). The chip surface was first washed using three injections of 1.0 M NaCl, 50 mM NaOH for 60 s, each followed by buffer for 60 s (all at 10 μL/min). The 5´-biotinylated triplex-forming oligonucleotide (TFO1R, 30-60 nM) was then immobilised onto two of the flow cells (FC2 and FC4) and a response of approximately 250 Response Units (RU) was aimed for. The remaining two flow cells (FC1 and FC3) were kept free of ligand and were used as reference cells.
Experiments were carried out using conditions that were modified from those reported previously with plasmid pNO1 16 , optimised for the 339 minicircle. Using these optimised conditions (TFO1R [250 RU immobilised], flow rate 2 µL min -1 , 100 mM calcium acetate pH 4.8, 25°C, injection time 600 s; regeneration: 1 M NaCl, 5 mM NaOH, 60 s, 30µL min -1 ) a range of differently supercoiled samples at 50 nM of 339 nr (∆Lk -4.9 to +1) as well as relaxed, nicked, linear, and samples containing no triplex-forming sequences were injected and the binding monitored.
The kinetics of the binding between the small-circle DNA substrate and the TFO1R ligand were then measured using a multi-cycle kinetics approach using the same optimised conditions but with 221 RU of TFO1R immobilised. For the kinetic experiments, 339 bp minicircles (∆Lk -4.9, -2.8, linear and relaxed) were injected over flow cells 1 and 2 for 600 s at a range of concentrations (2.5, 5, 10, 20, 30 and 40 nM) and a buffer-only control. A buffer only solution was then flowed for 1 h so that the dissociation could be more accurately recorded. The SA chip was regenerated after each injection of DNA using 1 M NaCl, 5 mM NaOH. The experiment was carried out at 35°C with a flow rate of 2 µLmin -1 using 100 mM calcium acetate pH 4.8 as the running buffer. The inclusion of buffer-only controls enabled the use of double referencing, whereby, for each analyte measurement, in addition to subtracting the response in the reference flow cells from the response in the test flow cells, a further buffer-only subtraction was made to correct for the bulk refractive index changes or machine effects 68 . The data were analysed using the Biacore T200 Evaluation software version 2.0 using the kinetics fit assuming a 1:1 binding model.