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The emergence of sequence-dependent structural motifs in stretched, torsionally constrained DNA

The double-helical structure of DNA results from canonical base pairing and stacking interactions. However, variations from steady-state conformations result from mechanical perturbations in cells. These different topologies have physiological relevance but their dependence on sequence remains unclear. Here, we use molecular dynamics simulations to show that sequence differences result in markedly different structural motifs upon physiological twisting and stretching. We simulated overextension on four different sequences of DNA ((AA)12, (AT)12, (GG)12 and (GC)12) with supercoiling densities within the physiological range. We found that DNA denatures in the majority of stretching simulations, surprisingly including those with overtwisted DNA. GC-rich sequences were observed to be more stable than AT-rich, with the specific response dependent on base pair ordering. Furthermore, we found that (AT)12 forms stable periodic structures with non-canonical hydrogen bonds in some regions and non-canonical stacking in others, whereas (GC)12 forms a stacking motif of four base pairs independent of supercoiling density. Our results demonstrate that 20-30% DNA extension is sufficient for breaking B-DNA around and significantly above cellular supercoiling, and that the DNA sequence is crucial for understanding structural changes under mechanical stress. Our findings have important implications for the activities of protein machinery interacting with DNA in all cells.


INTRODUCTION
In the cell, DNA is constantly under mechanical perturbation from a range of proteins as well as protein/nucleic acid based molecular machines. These perturbations are necessary for a wide range of DNA functions, including replication, repair, gene expression, and chromosomal packaging [1], [2]. Single-molecule force spectroscopy experiments have shown that DNA can be overstretched from 10% up to 70% beyond its relaxed contour length at a nearly constant force of around 65-70 pN [3], [4]. This force-derived plateau has been associated with a structural transition from the canonical B-DNA to the extended form called S-DNA [2] that has been observed to be dependent on a number of different factors. It was observed that AT-rich DNA, in particular poly-d(AT) fragments, favoured the extension to the S-form in contrast to GC-rich or poly-d(CG) [5. In terms of torsional stress, unwinding greatly reduces the force at which the B-S transition occurs and overwinding makes it harder to happen [6]. For significantly overtwisted DNA (with a supercoiled density σ>0.037), stretching DNA with magnetic tweezers showed the emergence of a Pauling-like DNA (P-DNA) structure, which was deduced to have the bases flipped outside and the two helical backbones grouped inside [7].
However, it is difficult to visualize experimentally the effect of stretching and twisting DNA at the base pair level, for example using the most advanced dynamic super-resolution fluorescence microscopy methods for DNA whose spatial localisation precision for pinpointing individual reporter dye molecules is at best a few tens of nm [8]- [10]. This level of precision is equivalent to the separation of ~100 base pairs (bp) and so struggles to generate information about the orientation or specific interactions of any given nucleotide. Structural transitions have been discerned through force and torque considerations but the structures themselves are not directly visible [11]. By contrast, computer simulation works at its best over short length scales, being able to provide highresolution atomic level precise descriptions of the different overstretched DNA states, allowing identification of specific structural motifs which may emerge. These detailed descriptions can be correlated with experimental data, often at higher length scales, to build a holistic understanding of the structural dynamics of DNA molecules.
Atomistic molecular dynamics (MD) initially described S-DNA as a ladder-like structure where Watson-Crick (WC) hydrogen bonds were mostly maintained and the base-base intra-strand stacking was preserved through a high inclination of the base-pairs with respect to the molecular axis or substituted by stacking between bases from opposite strands (i.e. inter-strand) [12]- [14].
Later, it was demonstrated that S-DNA consists of a full umbrella of conformations where the Sladder motif can coexist with short melting bubbles generated especially on AT-rich segments [15]- [21]. Similarly, computer simulations described in atomic detail (and confirmed) the structural appearance of the overstretched and overtwisted form of P-DNA [22].
The effect of torque on simulated linear DNA structures has been relatively underexplored in comparison. By imposing torsional constraints, simulations have shown that unwounded DNA has a greater predisposition to form melting bubbles compared to relaxed DNA, with this propensity being strongly dependent on sequence: denaturation was only observed on an (AT)3 segment in linear DNA [23] and prominently in AT-rich areas in undertwisted small DNA circles between 60-110 bp [24]. Modelling an infinite linear tract of DNA upon undertwisting showed that DNA partitions its perturbations such that there are regions of extreme disruption in coexistence with regions which remain relatively close to the canonical B-form DNA structure, and that this is sequence-dependent [25].
Atomistic MD is not the only means of simulating DNA. Although atomic simulations have the capacity for generating highly resolved structural details, they are computationally very demanding and so the extent of time sampling is usually limited. Coarse-grained models like oxDNA and 3SPN [26], [27], which describe a DNA molecule with significantly reduced degrees of freedom, are an alternative, powerful tool for describing the mechanism of overstretching and longer length and time scales with the caveat of sacrificing some level of spatial precision [28], [29]. Force-induced melting was initially described by oxDNA [28], and later the combination between denaturation bubbles and S-DNA was observed using a 3SPN-based potential [29].
However, atomistic MD is a very convenient means of interrogating precise base pair level structural motifs. Despite this, the combined effects of precisely imposed stretching and twisting perturbations together with the dependence on different DNA sequences has not been studied in depth to date. In our present work, we report a comprehensive suite of atomically precise molecular dynamics simulations in order to interrogate the structural impact of DNA overextension on topologically-constrained molecules within the range of normal supercoiling density observed in vivo (σ±0.068) [30], [31]. We used four different sequences (poly-d(A), poly-d(AT), poly-d(C), polyd(CG)) which cover a significant variety of known DNA flexibility [32]. Additionally, these sequences cover two binding motifs known to be biologically relevant: the TATA box [33] which is used for transcription factor binding, and the CGCG box which is known to be part of many signalling pathways in plants [34] and which can occur within CpG islands, regions of high CG density which are found in approximately 40% of mammalian gene promoter regions [35].
We focused on the early-stage overstretching regime (just up to the level of 40% beyond the relaxed contour length) as this is the upper known limit of mechanical distortion that can be achieved through protein-binding (for example, in the TATA-binding protein [36], and the recombinase enzyme RecA [37]) and thus enabled us to explore the most physiological regime.
We found that this level of overstretching was sufficient to disrupt the B-DNA form in spite of the different torsional constraints, and that melting bubble behaviour and non-canonical structure formation were found to be significantly dependent on sequence.

Software simulation platforms
All simulations were set up with the Amber 17 suite of programs and performed using the CUDA implementation of Amber's pmemd program [38]. The initial 24 bp structures for four different linear DNA fragments were obtained using Amber's NAB utility [38] [39] with bsc0 [40] and bsc1 [41] corrections for backbone dihedrals.

Simulations in implicit solvent
The Generalized Born (GB) model [42], [43] was applied to define the solvent implicitly, together with an effectively infinite longrange electrostatic cut-off, the latest GBneck2 corrections and mbondi3 Born radii set for a better reproduction of molecular surfaces, salt bridges and solvation forces [44]. Systems were minimized using a combination of steepest descent and conjugate gradient methods. Simulations were run at constant temperature (300 K), maintained by the Langevin thermostat [45], using an effective salt concentration of 50 mM determined by the Debye−Huckel screening parameter. Integration time steps were set at 1 fs with the DNA structure written to disk every 1 ps.
To stretch DNA while maintaining torsional constraints, fixed harmonic traps with an effectively infinite associated constant of 500 kCal/Mol/Å 2 were applied to all atoms in the terminal base pairs (see Figure 1). DNA was stretched on a series of umbrella sampling trajectories, where one of the terminal base pairs was moved 1 Å from the centre of the molecule along the helical axis ( Figure 1). The final frame of the previous umbrella sampling window was used as the starting structure for the next stretching event (Figure 1). Through analysis of temperatures and potential energies, the system was found to be almost instantly equilibrated after the perturbation (see Figure S1) as the increment on each extension step falls within the range of end-to-end thermal fluctuations found in a piece of unconstrained DNA [46]. Every simulation window was 500 ps in width, using an overall stretch rate of 2 Å/ns. On a single umbrella sampling trajectory, each DNA molecule was extended by a total of 30 Å, resulting in an increase in contour length of approximately 39.6% and a total run time of 15 ns. Each of the four DNA sequences considered was modelled using nine different supercoiling densities spanning a range used in previous magnetic tweezers studies (σ values of: 0, ±0.017, ±0.034, ±0.051, and ±0.068), whose negative Step 1: an initial structure is obtained.
Step 2: a terminal base pair (highlighted red) is displaced from its starting position by 1 Å. Step 3; the structure is minimized with harmonic constraints at both ends (pink crosses).
Step 4: the system is subjected to a production run of 0.5 ns and the final frame is used as the input for the next round of stretching, minimizing and modelling. extremity is also comparable to that estimated for live bacteria [31]. This led to 540 ns of simulation time in total.

Trajectory analysis
Trajectories were analysed using cpptraj [47] to find canonical and non-canonical hydrogen bonds using distance and angle cut-offs of 3.5 Angstroms and 120° respectively. The esander routine was used to extract Van der Waals interactions between successive nucleotides to find canonical stacking interactions, and between a nucleotide and every non-neighbour nucleotide for the noncanonical stacking energies. Energy calculations here were all performed in implicit solvation with the same forcefield and salt conditions as were used during the simulation. For each base pair, hydrogen bonds and stacking energies were averaged for each stretch extent in each simulation and these values were used to describe the structural details of DNA stretching and to quantify the presence of melting bubbles (defined to be two or more sequential base pairs which have on average less than one canonical WC hydrogen bond present). Representative structures were then extracted using VMD [48] or Chimera [49]. Two base pairs at each end of the fragment were not considered in the trajectory analysis to avoid end-effects.

Simulations in explicit solvent
For ensuring accuracy, key structures from implicit solvent simulations were simulated for 5 ns in explicit solvent. The final frames of the following umbrella sampling windows were chosen as initial structures for the subsequent simulations: (AA)12 with a 2 nm stretch, (AT)12, (GG)12, and (GC)12 with a 2.5 nm stretch, all on σ = ±0.068. These initial structures were solvated by a box of TIP3P water [50], neutralized and surrounded by extra 200 mM NaCl [51], [52] Before production simulations the solvated and relaxed systems were equilibrated using a standard protocol [53].
Simulations were carried out with an electrostatic cut-off of 1.2 nm, in the NPT ensemble using the Langevin thermostat and the Berendsen barostat [54] and using a 0.5 fs integration time. The full 5 ns simulations were analysed for hydrogen bonding and VdW stacking interactions to assess conformational drift away from the implicit solvent simulation, and the final 1 ns of the simulation was used to create an average structure. Trajectory analysis was performed as for the implicit solvent simulations using the GB solvation model with the Debye-Huckel parameter set to simulate 200 mM salt concentration.

Sequence and stretch dominate over twist for the emergence of melting bubbles
For gaining a general perspective of the degree of disruption of the B-DNA state among the whole set of simulations, we quantified the emergence of denaturation events. Figure 2 shows The strength of stacking interactions [55], [56] and three hydrogen bonds between C and G are the probable reasons for preventing  A) (AA)12 presents melting bubbles for undertwisted structures as early as 7% overstretching, while overtwisted constructs form bubbles prior to 15% extension. B) (AT)12 denatures in places almost immediately, for undertwisted structures at 2% overextension in the earliest case, while the last structure to form a melting bubble is overtwisted by σ=0.051 and maintains its B-DNA structure until around 13% extension. C) (GC)12 is considerably more stable with undertwisted structures forming melting bubbles only after 20% extension and DNA with σ=0.051 maintaining B-DNA hydrogen bonding up until 37% overstretching. Also C) (CC)12 is stable in the B-DNA form for all extensions and all σ and is therefore the most stable structure. Note that the minimum of bp involved in a single bubble are two and that the total number of bp can be originated from one long melted DNA stretch or several small denaturation events. For each sequence, the bubble size for σ=-0.068, σ=0, and σ=0.068 are plotted with dashed lines. dependence: the earliest onset of a melting bubble is at an extension of ~20% and occurs for σ=-0.051, while the last supercoiling density to create a melting bubble is σ=0.051 at an extension of ~38%, meaning that a changed supercoiling density allows the DNA to absorb twice as much extension before melting. This is in line with what could be expected -negative supercoiling tends to open the helix up and make it easier for base pairs to dissociate, whereas positive supercoiling is associated with packing the base pairs more tightly and constraining them in place. Significantly, there is only ever one melting bubble produced in the (GC)12 fragment, demonstrating that the perturbation is efficiently localized and grows in place rather than producing new bubbles (see further Results section).
However, in these physiologically relevant supercoiling regimes even positively supercoiled DNA can form melting bubbles in a sequence-and extension-dependent manner. Thus, in general terms, our simulations show that the formation of denaturation bubbles is dependent on applied torsion only in a moderate way, suggesting that at these extensions the overstretching strain dominated over the stress due to twist.
In terms of sequence content, these results confirm the long-standing view that AT-rich sequences are more fragile compared with GC-rich sequences, although they also point to a far more complex picture than had previously been envisioned due primarily to the importance of stacking forces. Indeed, beyond melting bubble formation, the generation of stable structural motifs is entirely sequence specific (see the following Results sections), with the behaviour of poly-d(A) and poly-d(C) strikingly different from that of poly-d(AT) and poly-d(CG), respectively, indicating that simple approximations of DNA behaviour based on AT/GC content are reliable for comparatively long DNA sequences only in situations such as DNA melting for PCR considerations and single-molecule buckling point determinations [57] analysis. Figure 3 shows the evolution of non-bonded interactions as the poly-d(A) sequence is stretched at the negative supercoiled density of -0.068. We found that canonical hydrogen bonds started to be significantly disrupted around a relative overextension of ~10%, with completely disrupted base pairs seen at 15% extension. Simultaneously, the disrupted WC hydrogen bonds begin to be substituted by non-canonical hydrogen bonds. At around an extension of 35%, non-canonical hydrogen bonds largely disappear from the central region of the DNA indicating a far more melted configuration, though they persist at one end, likely due to edge effects from the immobilized base pair. As the WC hydrogen bonds are lost and non-canonical ones formed, stacking interactions follow suit. Canonical stacking energies reduce while non-canonical stacking increases, as may be expected for a DNA molecule whose bases are hydrogen bonding with unusual partners.

The poly-d(A).poly-d(T) sequence generates flexible dual motifs which may function as shock absorbers
The structure extracted at the overstretch step of 24% (Figure 3) shows detail of the denatured conformation, indicating two separate but linked modes of structural adaptation to the applied mechanical perturbation. On one hand, the central region of the DNA fragment (between bases 11 and 14) contains a low number of non-canonical hydrogen bonds and stable noncanonical stacking interactions. This low hydrogen bonding area is highlighted in blue on Figure 2 and presents a region with a collapsed backbone and associated rotation of the bases themselves stacking/hydrogen bond interplay does not persist beyond an extension of 35%. This is well expected for the sequence with some of the weakest stacking interactions (see for example [55], [56]) as well as fewest number of WC hydrogen bonds: the structure simply does not have sufficient stability to form a new, lower-energy structure, and thus melts. For the trajectory containing this sequence at the highest level of overtwisting (σ=+0.068, see Supplementary Figure   S2) we also observe denaturation bubbles although to a lesser extent. The structure is more stable in the early stages of overstretching as is expected from previous work [58]. However, there are disruptions to the WC hydrogen bonding at ~10% strain, and at ~20% strain an isolated melting bubble briefly comes into existence. It lasts only a few more stretching events, however, before  increased extension a qualitatively P-DNA like state with exposed bases could be reached, albeit with a significantly greater helical pitch, and suggests an alternative pathway for exposing and manipulating short sequences of bases.

The poly-d(AT).poly-d(AT) sequence generates stretch-resistant motifs stabilized by stacking and non-canonical hydrogen bonds
The poly-d(AT)·poly-d(AT) sequence showed a similar tendency to melt as the poly-d(A)·poly-d(T) under supercoiling density σ = -0.068 (see Figure 2), but the non-canonical interactions we found to be significantly more stable with applied extension (see Figure 4). As in the poly-d(A) fragment, non-canonical hydrogen bonds appear where canonical ones have broken, replacing the WC interactions entirely, and the stacking forces follow the same trend. At an extension of 17%, the DNA molecule forms a structure with a regular pattern of increasing and decreasing non-canonical hydrogen bonds, suggesting a new stable structural motif. Two distinct states are clearly seen in the structure. The first type of regions is 6 nucleotides long, it is stabilised by non-canonical hydrogen bonds (highlighted in red on Figure 4A) and it has a B-DNA like macrostructure although the bases are slightly flipped away from the helical axis. The second type of structural motif is shorter (~3 base pairs) and is dominated by stacking interactions, presenting low hydrogen bonding (highlighted in blue on Figure 4A). The bases on opposite strands tend to be interlinked, suggestive of a conformation similar to zip-DNA [59]. Our results suggest that this dual coexisting method of duplex stabilization is mechanically stronger than the previous structural motif emergent  Figure 4A can be generated singly also. Whether this is supercoiling-dependent is unclear, but it seems likely that it plays a role given that the motifs appear always in tandem in undertwisted fragments while the only single motif occurred in the overtwisted DNA (see Figure 4B).
Once again, in the overtwisted simulation, there are individual bases seen flipped outwards as a consequence of a collapsing backbone, once again demonstrating that a pathway to a bases-exposed conformation other than significant positive supercoiling exists early in the overstretching regime in AT rich DNA.

The poly-d(C).poly-d(G) sequence has a high resistance to mechanical perturbation due to strong canonical stacking and hydrogen bonding
The poly-d(C)·poly-d(G) is the most stable of all the sequences that we simulated here. All stretching simulations constrained at different σ maintain most of the canonical non-bonded interactions as seen in Figure 5 and Supplementary Figure S4. Base pairs adopt a steeply inclined configuration in a similar way as was previously described for S-DNA [2], [8], [10]. We observed an increase in the non-canonical stacking interactions as the DNA is being pulled due to the more prominent role of the diagonal interactions (or cross-stacking), although these changes are much less dramatic and cannot be related to any other configuration apart from S-DNA. Similar S-DNA like configurations were observed on over-winding DNA (see Supplementary Figure S4 and inset structures), though there is a smaller level of structural alteration as opposed to under-twisted DNA. This indicates the tighter packing of highly twisted bases is a substantial factor in regards to determining the level of structural stability. In summary, it seems here that the canonical stacking and the three WC hydrogen bonds are largely sufficient to stabilize this level of perturbation.

The poly-d(CG).poly-d(CG) construct forms mechanically stable four bp motifs which may accommodate significant overextension
We found that the behaviour of the poly-d(CG)·poly-d(CG) sequence was significantly different from that observed for the poly-d(C)·poly-d(G) sequence, in spite of the CG content being the same. The principal difference here is the presence of intra-strand stacking of RY and YR bases instead of YY and RR (Figure 6). At an extension of 14% we observed backbone collapse similar to that of the AT-rich sequence, with a resultant loss of around two of the canonical hydrogen bonds in favour of non-canonical bonds. As seen for other sequences, there is a corresponding increase in non-canonical stacking energy as canonical hydrogen bonds are lost. The structural details of This interaction seems to facilitate the formation of a four bp motif, which consist of two bases on one strand followed by two bases from the opposite strand and is similar to what have been described in previous studies [15], [36]. This quadrubase configuration is characterized by a high inclination of the bases almost perpendicular to their usual orientation and maintains the stacking order CGCG, which is maximally strong [55], [56]. The disruption here preserves the canonical structure in other parts of the fragment, and the novel conformation appears able to absorb significant additional perturbation, as it does not grow in size through the simulation.
For the overtwisted case (Supplementary Figure S5), the behaviour is qualitatively similar to that indicated in Figure 6 though with σ = 0.068 the structure is considerably more resilient to applied strain, with WC base pairing being lost and non-canonical interactions appearing after around 30% extension. As in Figure 6, the loss of WC hydrogen bonds and canonical VdW stacking correlates exactly with the rise in non-canonical hydrogen bonding and stacking. Once again, indicated in the inset in Supplementary Figure S5, the 4 base pair motif reminiscent of [15], [36] clearly develops and is stable to the end of the simulation.
That the 4 base pair motif is strongly conserved is an important, unexpected result. While in other sequences the produced motifs were similar (see Figure 3 and Supplementary Figure S2, and Figure 4 and Supplementary Figure S3) in this case the motif produced is identical in every respect. Four bases tilt such that they are almost aligned with the helical axis, and stack around the outside of a collapsed backbone. These motifs appear separate and stable on their own. Perfect replication of this motif in the over and undertwisted DNA suggests that there could be an important a biological role either in stabilizing the DNA or in exposing the base sequence for replication, regulation, or repair, especially in mammalian promoter sites with significant CpG islands [35] and plant cell signalling pathways making use of a CGCG box [34] The motif we observe could be a mechanism for recognition regulation in cell in either of these cases.

Simulations in explicit solvent
In order to demonstrate that the structures extracted from the full-length implicit solvent routines were not an artefact associated with the approximation from the solvation model, 5 ns of explicitly solvated molecular dynamics was performed (see Materials and Methods), using as a starting structure the final frame of the appropriate implicit solvent umbrella sampling window. The structures chosen were (AA)12 with extension 25%, (AT)12 with extension 32% and (GC)12 with extension 32% as in these cases unexpected behaviour was observed in the implicit solvent simulations. In each case the two maximally torsionally stressed states were simulated (i.e. σ = ±0.068).
Supplementary Figure S7 shows the hydrogen bonding and stacking interactions for the 5 ns simulation of each structure. In general, the drift from the starting structure is very low indicating that the structures found in the implicit solvent simulation are a stable minimum energy state. The key features from the implicit solvent simulations of all structures remain in place. Specifically, the overtwisted AT rich structures continue to show melting bubbles, and the (AA)12 simulation maintains the dual stacking/hydrogen bonding states. (AT)12 retains the distinctive alternating motifs, indicating that the partitioning of perturbation between stacking and hydrogen bonding is energetically favourable in physiological conditions and is not an artefact of the solvation system used. As in the implicit case, the (GC)12 demonstrates a distinct edge between highly hydrogenbonded and less bonded regions, and indeed between regions of high and low stacking energy.
The remarkable correspondence between the implicitly and explicitly solvated systems is indicative both that the implicit solvation simulations are reliable but also that the transitions seen are available in the living cell, at normal physiological stresses and ionic strengths, and therefore these structures may play a role an important role in the expression of genes.

DISCUSSION
In this study we have run an extensive set of molecular dynamics simulations deforming DNA within the biological regime of stretching and torsional forces for four different sequences in order to investigate the structural effects of the different type of perturbations and their sequencedependence.
Our simulations focus on the early-stage of the overstretching reaction (just up 40% of extension), comparable to the range of DNA extension resulting from the activities of DNA-binding proteins, such as TBP and RecA [37]. Likewise, torsional constraints correspond to supercoiled densities between -0.068 and 0.068, which are the values observed in vivo either for prokaryotes [31] or eukaryotes [30]. In general terms, we observe that this level of mechanical stress disrupts  [15], [23], [24], [36], although striking differences are found whether sequences contain RY and YR intra-strand stacking or YY and RR. Poly-d(C) appears to be significantly more resistant than the other G-rich sequence, polyd(CG), because the former is the sole sequence that do not form melting bubbles for any supercoiling density, and the latter presents denaturation for all torsional constraints. An important point to note is that poly-d(CG) is the sequence that shows the highest sensitivity to changes of DNA twist, according to the wide range of observed extensions at which DNA starts to melt, being the first one at 20% for σ = -0.051 and the latest at almost 40% for σ = 0.051. In contrast, for the two sequences with 100% AT content, the structure of the double helix is broken for all supercoiling densities at extensions as low as 15%, although the stability of the resultant conformation is notably different. Figure 7 summarizes the key structural motifs emerged as a result of the applied mechanical stress. At first glance, we can differentiate between GC rich sequences, which develop a ladder-like geometry that can be classified under the umbrella of S-DNA, and AT rich sequences, that present more apparent bubbles with bases flipped away. Nevertheless, DNA molecules with an alternating RY and YR sequence pattern produce alternative stable structural motifs due to the higher stability of non-canonical stacking interactions. Since both RY/YR sequences studied here have biological importance in promotion and regulation of genes (the TATA box [36], CGCG box [34], and CpG islands [35]) it is likely that the specific motifs we found have biological roles.
Specifically, both the TATA and CGCG boxes require recognition from an associated transcription factor, while the CpG islands are found in around 40% of promoter and exonic regions of mammalian genes. Mechanically stable structural motifs give a potential mechanism by which these regions may be activated or deactivated without significantly disrupting the local genome.
(AT)12 and (AA)12 polymers distort the helicoidal DNA shape with two alternating sequence motifs. The first one maintains a certain appearance to B-DNA although bases are slightly opened towards the major groove and stabilized by non-canonical hydrogen bonds. The second one makes a clear melting bubble by barely having hydrogen bonds, although we did observe some non-canonical stacking interactions. The different degree of strength in stacking forces seems to be the cause of poly-d(AT) higher resilience compared to poly-d(A).
A strong inclination of bp in respect to the molecular axis is what characterizes the S-like configuration of the two sequences with high CG content, although the conformations are somewhat different. While poly-d(C) has a regular structure and keeps most of the canonical nonbonded interactions, poly-d(GC) presents a non-canonical 4-base stacking motif at expense of breaking some of the canonical ones.
The different types of overstretched structures obtained thanks to the use of implicitly solvated simulations were subjected to additional molecular dynamics modelling with an explicit representation of the solvent without observing any significant change. In addition, these observed structures are remarkably similar to the ones observed in previous studies [16], [17], [19], [36] confirming the improvement on the implicit description of solvent [43], [44], [60].
Our simulations show that the overstretching behaviour not only depend on AT and GC content, but also on the nature of the different type of base pair step. Thus, extrapolating these results, we think that oversimplified models base only on AT/GC ratio for describing the DNA tendency to flex beyond the canonical B-form might only be valid for a rough and ambiguous picture. For understanding molecular machines and the biomechanical function of promoter regions such as the TATA and CGCG boxes and CpG islands, it is vital to capture the behaviour of individual sequences.

CONCLUSIONS
The 'physics of life' is characterized by complex and emergent features with typically substantive heterogeneity of molecular components in a system. The challenges of cutting through such heterogeneity, for example as exhibited in the dynamic structural states of DNA, can be best overcome by studying one molecule at a time [61], now feasible with studies in vitro, in live cells and in computational simulations [62]. In this study, we have focused on a computational strategy involving molecular dynamics simulations on four distinctly different constructs of DNA in order to investigate the effect of sequence on the emergence of structural motifs in response to physiological levels of mechanical twist and stretch. We find evidence that sequence differences contribute significantly to the emergence, or not, of mechanically stable motifs. The presence of such motifs may potentially aid in recognition and transcription [63]. For each different sequence simulated even positively supercoiled DNA was found to form melting bubbles at the early stages of overstretching, indicating that, in the physiological regime of mechanical perturbation we use here, stretch is the dominant perturbation. We also find evidence that specific structural transitions occur in short ~5 bp regions, possible even in the absence of any topoisomerase activity. Our findings reinforce the importance of sequence to DNA topology, of particular relevance to sequence differences in gene promoter regions, in which mechanical perturbations have crucial roles. Figure S1: Total, potential, and kinetic energies over a full stretching simulation of of poly-d(A)·poly-d(T) with σ=-0.064 stretched by 3 nm over 15 ns, with a sudden stretch of 0.1 nm every 500 ps. The energies rapidly return to an equilibrium level after the stretching event, demonstrating that the energy minimisation procedure has equilibrated the system effectively.