We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist–stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist–stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

DNA carries important genetic information about the organism and has an indispensable role in biological functions. In general, DNA exhibits various mechanical elasticities in biological processes, which depend on the corresponding biological environments.1–7 DNA can also be used as biosensors, nanoparticles, and molecular handles owing to the elasticity, and this utilization has contributed considerably to the development of nanotechnology.8–11 Expectedly, the effect of biological environments on the elastic properties of DNA has attracted growing interest in recent years.12 

Many studies have contributed to the elasticities of double-stranded DNA (dsDNA) in various biological environments, including the salt concentrations,13–20 ionic environments,4,18,21–28 and pH values.27,29–32 For example, Garai et al. used all-atom molecular dynamics (MD) simulations to study the elastic properties of short dsDNA at different salt concentrations.17 The authors observed that the bending persistence length gradually decreases while the stretch modulus increases with the increase in salt concentration. The simulation evidence showed that the electrostatic repulsion on the dsDNA backbone is enhanced by greater salt concentration, which makes the dsDNA easier to bend but less likely to stretch within the moderate slat concentration ranges.15 The ionic environment also affects the DNA elastic properties obviously due to the polyanionic nature of DNA. For instance, Guilbaud et al. observed the variation in the bending persistence length of dsDNA in the presence of the monovalent and divalent metal ions, where the bending persistence length decreases with the increase in ion concentration due to the electrostatic effects.25 Recently, the magnetic tweezer (MT) experiment and all-atom MD simulation reported that the high-valent cations decrease the bending persistence length and stretch modulus of dsDNA, which is in contrast to those of dsRNA.26 For pH dependence of dsDNA elasticities, for example, Zhang et al. analyzed the bending persistence length of dsDNA with several pH values at a MT experiment by applying a force to the dsDNA and found that the bending persistence length increases with the buffer pH; therefore, dsDNA stability and rigidity also increase.31 Another experiment exhibited that the proton-driven dsDNA spring is extremely sensitive to high pH, and it suggested an important implications for the implementation of various biological functions and the recognition of nucleic acid molecules.33 We note that the above MD simulations and MT experiments were performed at room temperature, which ignore the effects of high and low temperatures on dsDNA elasticities.

Temperature is another crucial factor that affects dsDNA elasticities and extensively exists in biological processes and technical applications. A considerable number of experimental and simulation works have devoted to the temperature dependence of dsDNA elasticities in the last two decades.20,34–43 For example, an earlier MT experiment suggested that the bending persistence length decreases rapidly with increasing temperature where long dsDNA chains were used.35 Geggier et al. observed that the bending persistence length of dsDNA with 2686 base pairs (bp) becomes smaller and more flexible with the increase in temperature by measuring the j-factors and equilibrium distribution of topoisomers.37 Driessen et al. carried out a similar experiment and observed similar results that the bending persistence lengths decrease obviously with increasing temperature.42 Brunet et al. performed an experiment on 2000 bp dsDNA and observed that the bending persistence length only decreases within 4 nm when the temperatures increase from 23 to 52 K C, which suggested that the temperature dependence of bending persistence length is weaker.40 Moreover, MD simulation results provide a deeper understanding of the experimental results about the dsDNA elasticities, indicating that the entropy plays a remarkable role in dsDNA elasticity inside the base pair or even between successive base pairs.38 Monte Carlo (MC) and MD simulations based on various models indicated that the bending persistence length decreases with increasing temperatures.34,41,43 Kriegel et al. combined the MT measures with all-atom MD to investigate the temperature dependence of dsDNA helical twist angles, and good agreements were obtained.39 Recently, Zhang et al. performed a MT and all-atom MD combination study on the twist–diameter coupling for dsDNA, and the results showed that the twist–diameter coupling is a common driving force for temperature-induced dsDNA twist changes.20 Although a series of studies have focused on the temperature dependence of dsDNA bend elasticity, the temperature dependence of dsDNA twist elasticities, such as the twist persistence length and twist modulus, especially of the twist–stretch coupling, is still needed to explore.

Of course, there are other factors that affect the elasticity of dsDNA in biological environments. These factors include the dsDNA composition, such as its base composition and sequence order,2,10,44–48 and the dsDNA chain lengths.49–55 In the current work, we used a 35 bp B-type dsDNA as an example and adjusted the system temperature value over a wide range to examine the effects of temperatures on dsDNA elasticity. We use all-atom MD simulations to investigate the effects of temperature on dsDNA elasticity by analyzing elastic parameters, including the bending and twist persistence lengths, stretch and twist modulus, and the twist–stretch coupling. In Sec. II, the all-atom MD method and calculations of dsDNA elasticities are described. The results on the stretch, bend, and twist elasticities and twist–stretch coupling of dsDNA at various temperature values are then discussed in Sec. III. A summary is presented in Sec. IV.

We selected an initial B-type dsDNA with 35 bps (5′- CGACT CTACG GAAGG GCATC TCTCG GACTA CGCGC -3′), which has been reported in a previous experiment,56 as the example to examine its elasticity. The melting temperature of this sequence is 79.9 ± 0.6 C. The model dsDNA sequence is shown in Fig. 1(a). The UCSF Chimera 1.15 software application was used to build the DNA structure file.57 We attempted to adjust the simulation box size by many times and then chose a box with a size of 10 × 10 × 15 nm3 in all simulations, where the periodic boundary conditions were used in three directions to keep the DNA as free from boundary effects. The previous experiments and simulations indicated that the electrostatic interaction between two nucleic acids decreases obviously as the distances between the two nucleic acids increases.58–60 These findings suggest that the simulation box size used in the current simulation is large enough to treat the nucleic acid as an isolated one even under the periodic boundary conditions. Then, the 100 mM NaCl61 and TIP3P water molecule models62 were added at random initial positions in the box to simulate the physiological environment. Given that the nucleic acid carries electronegativity, we added 68 Na+ with the ion model by Joung and Cheatham63 to ensure that the system as a whole is electrically neutral.

FIG. 1.

(a) Representative diagram for the molecular structure of 35 bps dsDNA with the sequence of 5′- CGACT CTACG GAAGG GCATC TCTCG GACTA CGCGC -3′. (b) The root mean square deviation (RMSD) curve of 29 base fragments in dsDNA center with the time of molecular dynamics simulation at T = 290 and 310 K, respectively, where the black line represents the average of the relevant parameters every 2 ns, which reaches equilibrium after 100 ns.

FIG. 1.

(a) Representative diagram for the molecular structure of 35 bps dsDNA with the sequence of 5′- CGACT CTACG GAAGG GCATC TCTCG GACTA CGCGC -3′. (b) The root mean square deviation (RMSD) curve of 29 base fragments in dsDNA center with the time of molecular dynamics simulation at T = 290 and 310 K, respectively, where the black line represents the average of the relevant parameters every 2 ns, which reaches equilibrium after 100 ns.

Close modal

We pre-equilibrated the systems to ensure that the MD simulation was carried out in an isothermal and isobaric environment. The initial DNA structure is bound to change when added into the solution. Thus, we started by energy-minimizing the system so that the atoms are not too close together and to ensure the stability of the DNA structure. Then, a restrictive force needs to be applied to the DNA prior to NVT simulation so that the random movements of atoms in the DNA chain are limited. The system was then warmed up to a desired temperature T by the V-rescale scheme, where the temperatures are coupled by a velocity rescaling method with a random term.64,65 The application of a limiting force prevented damage to the DNA structure during the warming process. After the system is warmed up to temperature T, the system pressure was adjusted to 1 atm by NPT simulation. When these pre-equilibrium processes were finished, the restrictive force was removed, and then, the MD simulations were performed for 500 ns without the restrictive force. The processes are the standard simulation procedure using Gromacs 4.6 software with the Amber bsc1 force field.66–70 In the current simulations, we adjusted the temperature T from 280 to 320 K, with a step of 10 K. Our MD simulations with various temperatures are similar to those in the previous all-atom MD simulations, where the Amber force fields were used.20,38,39,43 We calculated the root mean square deviation (RMSD) for the systems to examine the validity of simulations. Two examples are shown in Fig. 1(b), where the temperature values were selected to be 290 and 310 K. The RMSD represents the degree of molecular structure change of DNA, which follows:

RMSD=1Ni=1Nδi2,
(1)

where δi is the displacement between the i-th atom at moment t and moment 0 with a step of time Δt = 2 ps. We took the average value per 2 ns and plotted the black line in the middle, as shown in Fig. 1(b). The results show that the black lines reach equilibrium after 100 ns. Thus, the trajectory data from 100 to 500 ns were used in the subsequent statistical analyses in all simulations. In all data analyses, 3 bps were removed from each of the first and last strands of dsDNA during the statistical processes,53 and only the central 29 bps were selected to analyze the global elastic properties of the dsDNA.

In the current simulation, we concentrated on the stretch, bend, and twist elasticities of dsDNA, as well as their coupling, which involve the elastic parameters of stretch and twist moduli and bending and twist persistence lengths. According to the elasticity theory, the stretch and twist moduli can be extracted from the twist–stretch elastic matrix K, an inverse of 2 × 2 covariance matrix.71 The twist–stretch elastic matrix K is MD-associated, which can be determined by12,51,61,71,72

K=KSSKSTKTSKTT=kBTL0V1=kBTL0ΔL2ΔLΔΦΔLΔΦΔΦ21,
(2)

where kB is the Boltzmann constant, T is the temperature, and L0 is an average contour length L. Here, ΔL represents the variance of the contour length L, and ΔΦ is the variance of the cumulative H-twist angle Φ as described in the previous work.61,ΔL2 and ΔΦ2 denote the mean square errors for L and Φ that originated from the thermal fluctuations with Gaussian distribution functions.54,71,73 Diagonal elements KSS and KTT correspond to the stretch and twist moduli, respectively, whereas elements KST is related to the twist–stretch coupling coefficient; KSS, KTT, and KST are also denoted as S, C, and G in the experiments, respectively.73–75 We noted that the stretch modulus, twist modulus, and the twist–stretch coupling are associated with the global contour length and twist angle.

The persistence length provides an alternative method to describe the dsDNA elasticity, as it is also experimentally accessible. According to the elasticity theory, the elastic modulus and persistence length have a simple relationship. For example, the twist elasticity can also be characterized by the twist persistence length lT related to the twist elastic energy,76 and the twist persistence length lT can be simply written as73,74

lT=KTTkBT,
(3)

where the KTT is the twist modulus from Eq. (2).

The bending persistence length lB was extensively used to characterize the bend elasticity of dsDNA. Based on the wormlike chain (WLC) approximation, the bending energy is quadratic to the bending angle, and then, the relationship between the bending angle and bending persistence length can be deduced.22 Considering the normalization constant, the bending persistence length lB of dsDNA are determined by22,26,47,50,77,78

lnp(θ,l)sinθ=lB2lθ2ln2πlBl.
(4)

Here, p(θ, l) is a probability distribution, where θ is the bending angle formed by a dsDNA spanning 10 bps44 and l is the constant representing the average 10 bp profile length. Equation (4) shows that −ln(p(θ, l)/sin θ) varies as a quadratic function of the curve, which can be used to fit MD simulation data to obtain lB. We notice that Eq. (4) is accurate in the case of long chains where the contour length is much larger than the bending persistence length. However, the all-atom MD simulations showed that the short dsDNAs with excluding about 6 bps at each helix end can also be described by the WLC model with a bending persistence length of about 50 nm, which have similar flexibilities with those long dsDNA chains.53 In the current simulations, we analyzed the trajectory data by excluding 6 bps from the helix ends to estimate the bending persistence length and other elastic parameters, following the previous all-atom MD simulations used short dsDNA chains.26,28,47

We notice that different models have been developed to describe the elastic parameters of dsDNA at a short length scale in recent years. Along with the path of WLC, the twist WLC model79–83 was recently extended to the non-local twist WLC model by considering the couplings between distal sites. The non-local twist WLC model is able to account for the length-scale elasticities of nucleic acids, and the results showed that the bending and twist behaviors are soft at short length scales while stiff at long length scales.83,84 Alternatively, the DNA molecules can be described by the mesoscopic model to investigate three-dimensional structures at the base pair level.54,55,85–89 In the mesoscopic model, the Hamiltonian contains both the twist and bending angles between the adjacent bps, which are able to handle the short length-scale dsDNA chains and obtain the reasonable values of bending persistence lengths for short dsDNA chains.54,55

The elastic properties of dsDNA can be analyzed by the structural parameters because the accumulation of microstructural excursions leads to variations in the macroscopic elasticity of dsDNA. The structural parameters include a series of translation and rotation parameters to describe the chain conformations.12,90–93 Here, we only describe the corresponding structural parameters used in the current simulations. An intrinsic coordinate frame was constructed in the base pair where the xy plane is attached to the base pair and the z axis is along its normal direction to describe the translation and rotation parameters. Here, the z axis points to the 5′ end of the nucleic acid chain, whereas the x axis points to the major groove.91 The essential translation parameters are shift (Dx), slide (Dy), and rise (Dz), which denote the displacements between two adjacent base pairs along the x, y, and z directions, respectively.90 The translation parameters can be cumulative, exhibiting more obvious effects on the length scale, and presented in the grooved model to conveniently analyze the DNA conformations under various biological environments.23,26,28,94–98 Three rotation parameters, namely, roll ρ, tilt τ, and twist ω, were defined to describe the rotation properties of dsDNA belonging to the angles constructed between two adjacent base pairs along the x, y, and z directions, respectively.90–92 We focus on the helical rise hz and helical twist γ, which are projection parameters on the helical axis of the nucleic acid. Helical rise hz and helical twist γ are the variables that twist and stretch the dsDNA, which can be manipulated and measured in single-molecule experiments.93,99 During the analysis, these structural parameters of the dsDNA were obtained using the Curves+ program.97 

In the current work, we set the temperature T as 280, 290, 300, 310, and 320 K to investigate the temperature dependence of the elastic properties for dsDNA. In Subsection III A, we concentrated on temperature dependence of the stretch elasticity, which is described by the stretch modulus KSS (Figs. 2 and 3). The temperature dependence of bend elasticity was characterized by the bending persistence length lB (Figs. 4 and 5) in Subsection III B. The temperature dependence of twist elasticity was characterized by twist persistence length lT and twist modulus KTT (Figs. 6 and 7) in Subsection III C. Finally, we investigated the temperature dependence of twist–stretch coupling (Figs. 8 and 9) in Subsection III D.

FIG. 2.

The temperature dependence of stretch modulus KSS. (a) Probability distribution p(L) of contour length L at T = 290 and 310 K, respectively. (b) The function of stretch modulus KSS as a function of temperature T, and the line is a fitting result with a slope of −8.89 pN/K. The previous results are also inserted for convenient comparison.

FIG. 2.

The temperature dependence of stretch modulus KSS. (a) Probability distribution p(L) of contour length L at T = 290 and 310 K, respectively. (b) The function of stretch modulus KSS as a function of temperature T, and the line is a fitting result with a slope of −8.89 pN/K. The previous results are also inserted for convenient comparison.

Close modal
FIG. 3.

(a) The average contour length L0 as a function of temperature T, whereas the line is a fitting result with a slope of kl = 0.002 nm/K. (b) The mean square error for H-rise 1/Δhz2 as a function of temperature T. The line is a fitting result with a slope of kh = −5.37 Å−2/K.

FIG. 3.

(a) The average contour length L0 as a function of temperature T, whereas the line is a fitting result with a slope of kl = 0.002 nm/K. (b) The mean square error for H-rise 1/Δhz2 as a function of temperature T. The line is a fitting result with a slope of kh = −5.37 Å−2/K.

Close modal
FIG. 4.

(a) The relation between −ln(p(θ, l)/sin θ) as functions of the bending angle θ. The bending angle θ is formed by ten consecutive base pairs in 29 base segments of the dsDNA center at T = 290 and 310 K, respectively. (b) The function of bending persistence length lB as temperature T. The line is a fitting result with a slope of −0.29 nm/K. The previous results are also inserted for convenient comparison.

FIG. 4.

(a) The relation between −ln(p(θ, l)/sin θ) as functions of the bending angle θ. The bending angle θ is formed by ten consecutive base pairs in 29 base segments of the dsDNA center at T = 290 and 310 K, respectively. (b) The function of bending persistence length lB as temperature T. The line is a fitting result with a slope of −0.29 nm/K. The previous results are also inserted for convenient comparison.

Close modal
FIG. 5.

(a) The probability distribution p(θ, l) as functions of the bending angle θ, where the bending angle θ is formed by ten consecutive base pairs in 29 base segments of dsDNA center at T = 290 and 310 K, respectively. (b) The average bending angle ⟨θ⟩ as a function of temperature T. The line is a fitting result with a slope of kθ = 0.042π/180 K. (c) The ratios between the thermal fluctuation for the tilt and roll angles Δρ2/Δτ2 as a function of temperature T. The line is a fitting result with a slope of kρτ = −0.005/K.

FIG. 5.

(a) The probability distribution p(θ, l) as functions of the bending angle θ, where the bending angle θ is formed by ten consecutive base pairs in 29 base segments of dsDNA center at T = 290 and 310 K, respectively. (b) The average bending angle ⟨θ⟩ as a function of temperature T. The line is a fitting result with a slope of kθ = 0.042π/180 K. (c) The ratios between the thermal fluctuation for the tilt and roll angles Δρ2/Δτ2 as a function of temperature T. The line is a fitting result with a slope of kρτ = −0.005/K.

Close modal
FIG. 6.

The temperature dependence of twist modulus KTT. (a) Probability distribution p(γ) of H-twist γ at T = 290 and 310 K, respectively. (b) The twist modulus KTT as a function of temperature T, and the line is a fitting result with a slope of −1.68 pN⋅nm2/K. The previous results are also inserted for convenient comparison.

FIG. 6.

The temperature dependence of twist modulus KTT. (a) Probability distribution p(γ) of H-twist γ at T = 290 and 310 K, respectively. (b) The twist modulus KTT as a function of temperature T, and the line is a fitting result with a slope of −1.68 pN⋅nm2/K. The previous results are also inserted for convenient comparison.

Close modal
FIG. 7.

(a) The function of twist persistence length lT as a function of temperature T, and the line is a fitting result with a slope of −0.76 nm/K. The previous results are also inserted for convenient comparison. (b) The mean square error for H-twist 1/Δγ2 as a function of temperature T. The line is a fitting result with a slope of kγ = −0.02 × 1802/π2 K.

FIG. 7.

(a) The function of twist persistence length lT as a function of temperature T, and the line is a fitting result with a slope of −0.76 nm/K. The previous results are also inserted for convenient comparison. (b) The mean square error for H-twist 1/Δγ2 as a function of temperature T. The line is a fitting result with a slope of kγ = −0.02 × 1802/π2 K.

Close modal
FIG. 8.

(a) The correlations between the data about H-rise hz and H-twist γ. The line is a fitting with a positive slope of 0.015 × 180/π Å. (b) Comparison of twist–stretch coupling dL/dN between the current work and the previous studies T = 300 K. (c) The twist–stretch coupling dL/dN as a function of temperature T. The line is a fitting result with a slope of kln = 0.004 nm/turn K.

FIG. 8.

(a) The correlations between the data about H-rise hz and H-twist γ. The line is a fitting with a positive slope of 0.015 × 180/π Å. (b) Comparison of twist–stretch coupling dL/dN between the current work and the previous studies T = 300 K. (c) The twist–stretch coupling dL/dN as a function of temperature T. The line is a fitting result with a slope of kln = 0.004 nm/turn K.

Close modal
FIG. 9.

(a) The temperature dependence of twist–stretch coupling coefficient −KST. (b) The twist–stretch coupling KSTKSS2π as a function of temperature T. The line is a fitting with a slope of kts = 0.006 nm/turn K. (c) The standard errors for contour length L and the cumulative H-twist angle Φ, 1/σLσΦ, as function of temperature T. The line is a fitting result with a slope of kσ = −0.177 × 180/π(nm K)−1. (d) The Pearson correlation coefficient ρ as function of temperature T. The line is a fitting result with a slope of kρ = 0.002/K.

FIG. 9.

(a) The temperature dependence of twist–stretch coupling coefficient −KST. (b) The twist–stretch coupling KSTKSS2π as a function of temperature T. The line is a fitting with a slope of kts = 0.006 nm/turn K. (c) The standard errors for contour length L and the cumulative H-twist angle Φ, 1/σLσΦ, as function of temperature T. The line is a fitting result with a slope of kσ = −0.177 × 180/π(nm K)−1. (d) The Pearson correlation coefficient ρ as function of temperature T. The line is a fitting result with a slope of kρ = 0.002/K.

Close modal

We considered the temperature dependence of stretch modulus KSS, as shown in Fig. 2. Two typical probability distributions of contour lengths p(L) are shown in Fig. 2(a), indicating that the dsDNA has a distinct KSS at various T. Our observations about p(L) agree with the fact that contour length L fluctuates with the Gaussian distribution in the WLC model.50,78 By inversing the covariance matrix according to Eq. (2), we can arrive at

KSS=kBTL011ρLΦ21σL2,
(5)

where ρ is the Pearson coefficient between contour length L and cumulative H-twist angle Φ, and σL is the standard error of contour length L. According to Eq. (5), we obtained KSS, as shown in Fig. 2(b), where the available data were also inserted for comparison. In particular, we obtained KSS = 1398.5 ± 25.2 pN at T = 300 K, which enabled us to compare with the available data. Bao et al. observed that KSS = 1441 pN at T = 298 K for 40 bp dsDNA with 1M NaCl,61 whereas Marin-Gonzalez observed KSS = 1280 ± 70 pN at T = 300 K for 16 bp dsDNA with 150 mM NaCl.100 Our observations are in good agreement with the results from these two all-atom MD simulations. The current results about KSS also agree with the available data from an optical tweezer experiment, where the stretch modulus have about 1256 ± 217 pN at room temperature and various salt concentrations.13 However, the available experimental data99,101,102 showed that the dsDNA has a range about 1000–1760 pN, which is also inserted in Fig. 2(b) (more data are provided in Table S1 of supplementary material). The discrepancy between the current results and previous results are due to the various dsDNA chain length and salt solution concentrations used in the various systems. Then, we predicted the temperature dependence of KSS as shown in Fig. 2(b). The stretch modulus KSS decreased from 1537.0 ± 25.4 pN to 1169.1 ± 23.8 pN as T increased from 280 to 320 K. The linear fitting showed a linear relationship between KSS and T with a slope of −8.89 pN/K. Here, our data clearly demonstrated that the stretch modulus KSS strongly depends on temperature T with a linear relationship when the other parameters were constant.

We tried to explain the temperature dependence of KSS by analyzing the structural parameters as shown in Fig. 3. According to Eq. (5), the temperature dependence of the stretch modulus is related to several parts: the Pearson correlation coefficient ρ, the average contour length L0 and its standard error σL, and the temperature T. The Pearson correlation coefficient ρ was ∼0.11–0.18 (see Pearson coefficient in Table S2 of supplementary material) as T varies from 280 to 320 K; therefore, the factor of 1ρLΦ2 can be ignored. Then, we considered the average contour length L0 at various T, as shown in Fig. 3(a). The average contour length L0 has a very slight upward trend in the slope of kl = 0.002 nm/K. Indeed, the average contour length increased by ΔL0 = 0.083 nm when ΔT = 40 K. However, within the errors, the average contour length can be regarded as a constant value of L0 = 9.364 nm within the tested temperature range. A recent MD simulation predicted that the temperature dependence of dsDNA length is very weak because the length increase with temperature is absorbed by expanding the helix radius.43 This simulation confirms our observation on the average contour length. The constant L0 suggests that contour lengths are not attributed to the temperature-induced variations in the stretch modulus KSS. We plotted the 1/Δhz2 as a function of T as shown in Fig. 3(b), where Δhz2 denotes the mean square error for Helical rise hz and σL2=n2Δhz2. Here, n = 29 is the cumulative times. However, 1/Δhz2 decreases with T in a linear relationship with a slope of kh = −5.37 Å−2/K. This result suggests that the temperature dependence of stretch modulus KSS originates from the thermal fluctuation for the contour length.

We considered the temperature dependence of bending persistence length lB for dsDNA. We fitted the simulation data by Eq. (4) to obtain the bending persistence length lB as shown in Fig. 4. Two typical examples are shown in Fig. 4(a), where the −ln(p(θ, l)/sin θ) as functions of bending angle θ are quadratic curves at T = 290 and 310 K, respectively, and the bending angle θ are formed by ten consecutive base pairs in 29 base segments of the dsDNA center. We obtained the bending persistence length lB = 57.40 ± 0.16 nm at T = 290 K and lB = 52.28 ± 0.14 nm at T = 310 K. Here, our results about the bending persistence lengths agree with those obtained in the previous all-atom MD simulations where the short dsDNAs were used.22,26 In the experiments, the dsDNAs have the bending persistence lengths of about 45–50 nm, in which the long chains are usually employed.103–105 Actually, the dsDNA cyclization experiments have indicated that the short dsDNAs have high bending flexibilities,106,107 which are different from the WLC predictions.36,88 The high flexibilities of short dsDNA chains were also observed in the small-angle x-ray scattering experiments56,108 and the atomic force microscopy experiment.49 The deviation between the WLC prediction and experiments on short chains may result from the model used and the different conditions in the experiments and simulations. The fitting results also hint that the dsDNA chain becomes more flexible in the solution with higher T. We investigated the effects of T on bending persistence length lB over a range of 280–320 K to observe this dependence more carefully. In particular, we plotted the bending persistence length lB as a function of T with a step of 10 K as shown in Fig. 4(b). Then, we observed a linear relationship between the bending persistence length lB and temperature T with the slope of −0.29 nm/K. The existing experimental data (see more data in Table S1 of supplementary material) are also inserted in Fig. 4(b) for convenient comparison, which confirmed our observations that the bending persistence length lB decreases as T increases.37,40,42 For examples, Brunet et al. observed a linear dependence of the bending persistence length lB on temperatures T, where ΔlB ≈ 4 nm was obtained at ΔT = 29 K.40 A similar dependence was also observed in the experimental results from Geggier et al., but the bending persistence lengths lB are smaller at the same temperature.37 However, this dependence is much weaker than those observed in another experimental results from Driessen et al.42 Brunet et al. explained that the bias induced by detector time-averaging blurring were neglected in those observations from Driessen et al., which led to the larger ΔlB (≈22 nm) with ΔT = 29 K. Our observations on the temperature dependences of bending persistence lengths lB confirmed those experimental results from Brunet et al.40 and Geggier et al.37 

We used the structural parameters involving the bend elasticity to understand the microscope mechanism about the temperature dependences of lB shown in Fig. 4. Two typical examples for the probability distribution of the bending angle θ at T = 290 and 310 K are shown in Fig. 5(a) according to Eq. (4). Clearly, this distribution is not a Gaussian distribution because the bending angle is not an independent variable, which is related to the tilt and roll angles.80,109 The results show that the maximum in the corresponding curve gradually shifts to the left, that is the most probable distributions for the bending angles θm are equal to 12.0 and 13.5π/180 at T = 290 and 310 K, respectively, as shown in Fig. 5(a). The smaller bending angle reflects the stronger dsDNA rigidity, which can help us make initial estimations on the chain rigidity. We obtained the average bending angles ⟨θ⟩ over the range of T = 280–320 K as shown in Fig. 5(b). The results indicate that the average bending angle ⟨θ⟩ has a linear relationship with temperature T in the slope of kθ = 0.042π/180 K. The weak upward trend illustrates that the dsDNA chain becomes more flexible as the temperature T increases because the average bending angle ⟨θ⟩ increases. The structural parameters showed that the average roll angle ρ increases, but the average tilt angle τ decreases as temperature T increases (see more data about the structural parameters in Table S2 of supplementary material), reflecting that the increase in local bending is directed toward the major groove.43 Then, we plotted the ratios between the thermal fluctuation for the tilt and roll angles Δρ2/Δτ2 as functions of temperature T as shown in Fig. 5(c). Here, Δρ2 and Δτ2 denote the mean square errors for the roll angle ρ and tilt angle τ, respectively. The ratio Δρ2/Δτ2 is about 3.8–4.0, which indicates the thermal fluctuations are greater in roll angles than those in tilt angle. This finding suggests that the bend elasticity is mainly from the roll angles for dsDNA.51 The Δρ2/Δτ2 slightly decreases with T in the slope of kρτ = −0.005/K, showing that the tilt angles have more contribution to the bending elasticity as T increases.

Two parameters, namely, the twist modulus KTT and twist persistence length lT, describe the twist elasticity of dsDNA, which can be measured in experiments. By calculating the matrix K in Eq. (2), we can arrive at

KTT=kBTL011ρLΦ21σΦ2,
(6)

where σΦ is the standard error of the cumulative H-twist angle Φ. We investigated the twist modulus KTT, according to Eq. (6) as shown in Fig. 6. We plotted the distributions of H-twist γ and showed two examples with T = 290 and 310 K in Fig. 6(a). Our simulations on p(γ) agree with the fact that the structural parameters fluctuated with Gaussian distributions in the WLC model.50,78 However, the difference between these two p(γ) values indicates the different twist moduli. We plotted the twist modulus KTT with various temperature values according to Eq. (6), as shown in Fig. 6(b). We observed that the twist modulus decreases from KTT = 455.2 ± 7.5 pN⋅nm2 at T = 280 K to KTT = 387.0 ± 7.9 pN⋅nm2 at T = 320 K with a linear relationship of slope of −1.68 pN⋅nm2/K. In particular, the present observation provides that KTT = 402.2 ± 7.2 pN⋅nm2 at T = 300 K. Our observations are in agreement with the previous MT experiments of twist persistence lengths (i.e., C = 410 ± 30 pN⋅nm2 and C = 436 ± 17 pN⋅nm2),110,111 where long-chain dsDNA were immersed in 100 mM NaCl solutions at room temperature (T = 296 ± 2 K). Recent coarse-grained MD studies reported that the dsDNA has KTT = 386 ± 3 pN⋅nm2112 and KTT = 399 ± 1 pN⋅nm2113 in 100 mM ion solutions at T = 300 K, respectively. These data were also inserted in Fig. 6(b), showing a good agreement with the current MD data. Previous MT experiments observed that the twist modulus are about 386–448 pN⋅nm2 at room temperatures,99,114 which also confirmed our MD data (see more data in Table S1 of supplementary material).

The twist persistence length lT is another experimentally accessible parameter measured in MT experiments.80,110,115,116 Actually, a series of theoretical works have contributed to the twist persistence length based on the twist WLC model using rigid base pairs,80–84,109,117,118 as well as the simulations based on the all-atom and coarse-grained models.51,117 Here, we reported the twist persistence length of dsDNA by all-atom MD depending on temperatures. We considered the temperature dependence of twist persistence length lT as shown in Fig. 7. We can statistically obtain the twist persistence lengths of dsDNA at various T values according to Eqs. (3) and (6) as shown in Fig. 7(a), where the data about T = 300 K were also inserted from the previous studies for convenient comparison. In the current MD simulations, we obtained lT = 95.6 ± 1.7 nm at T = 300 K and 100 mM NaCl. Recently, Skoruppa et al. carried out an all-atom MD simulation and reported that lT = 86 nm for 32 bp dsDNA with T = 298 K and 150 mM NaCl, which quantitatively confirmed our MD results.84 Caraglio et al. used MC method to predict that dsDNA has lT = 118 nm.82 The MT experiment observed that the twist persistence length is lT = 109 ± 4 nm for long chain dsDNA.99 These available data suggested that the twist persistence lengths lT is ∼100 nm (see more available data in Table S1 of supplementary material). Our observations on the twist persistence lengths lT are in good agreement with these data from the MC, MD, and MT methods, as well as the more simulation and experimental results. Skoruppa et al. also predicted that the dsDNA has lT = 105 nm at T = 295 K,117 which suggested that exploring the temperature dependence for the twist persistence length is desired. Our results predict that the twist persistence length has an obvious decreasing trend with increasing T values over the range of T = 280–320 K in a slope of −0.76 nm/K as shown in Fig. 7(a). The theoretical predictions and numerical calculations based on the twist WLC model suggested that the twist persistence lengths have a decreasing trend with temperature within the ranges of lT = 40–100 nm.80,83,109 Our observations are about lT = 85–116 nm, which are in approximate agreement with the previous studies about the temperature-dependent twist persistence lengths.80,109 The experiments and simulations showed that the elasticity has length-scale dependence for short dsDNA.51,108,119 This is a possible reason for the difference between the results from the current simulations and those from the previous experiments. For the long dsDNA chain, conformations, such as kinks, should be considered for the effects on persistence length, which leads to the possible modification of the theoretical prediction models and all-atom simulations.120 Here, the current simulations indicate that twist persistence length has an approximately linear decreasing with temperature over a wide range.

Similar to stretch elasticity, we only considered the contribution of the standard error σΦ to the twist elasticity that described by the twist modulus and twist persistence length according to Eqs. (3) and (6). We investigated temperature dependence of 1/Δγ2 as shown in Fig. 7(b), where Δγ2 denotes the mean square error for H-twist γ and σΦ2=n2Δγ2 with the cumulative times n = 29. The results show that 1/Δγ2 decreases with T in a linear relationship of kγ = −0.02 × 1802/π2 K. Our simulations also show that the average twist and helical twist angles decrease very slightly with temperature (see more data about the structural parameters in Table S2 of supplementary material). However, the temperature dependence of twist modulus originates from the mean square deviations of twist angles, which is caused by the thermal fluctuation. Naturally, the higher temperature, the stronger thermal fluctuation, leading to the decrease in the twist modulus and twist persistence length. However, more obvious decrease occurred in the twist persistence length than those in twist modulus due to the factor of 1/kBT.

The coupling between elastic parameters plays an important role in the elastic behavior of dsDNA. In the full parameter space, a series of coupling combinations is present between the length and angle parameters. Here, we only concentrated on the stretch couplings with the twist angle as shown in Figs. 8 and 9. In the current work, we provide two calculational methods to demonstrate the twist–stretch coupling to conveniently compare with the experimental results.

We demonstrate the temperature dependence of twist–stretch coupling in Fig. 8, where the data were extracted from the all-atom MD. The H-rise and H-twist corrections are analyzed, and an example at T = 300 K is shown in Fig. 8(a), in which the data between the H-rise hz and H-twist γ have positive corrections with a positive slope of 0.015 × 180/π Å (more examples are provided in Fig. S1 of supplementary material). The positive correction indicates that the twist angle increases when the dsDNA stretches. In order to demonstrate this phenomenon clearly, we used the parameter dL/dN to characterize twist–stretch coupling, where dL is the change in contour length and dN denotes the change of helical turn.28,111,121 We obtained the twist–stretch coupling dL/dN = 0.53 ± 0.01 nm/turn at T = 300 K. Our calculations are in good agreement with several experimental measurements where the twist–stretch couplings are 0.5 ± 0.1 nm/turn,111 0.44 ± 0.1 nm/turn,99 and 0.42 ± 0.2 nm/turn.122 Our results also are in agreement with the all-atom MD results with dL/dN = 0.59 ± 0.02 nm/turn58 and dL/dN ∼ 0.61 nm/turn,61 where the 16 and 30 bp dsDNA were used in 1M NaCl solution, respectively. For convenience, we also listed these comparisons between the current all-atom MD simulations and the previous MT experiments or all-atom MD results in Fig. 8(b) (see more data in Table S1 of supplementary material). This difference is reasonable because the different DNA length and concentration of ion solution can cause the changes in twist–stretch couplings.28 However, all these MD simulation and MT experiments were performed at a constant temperature of T = 300 K. We calculated the twist–stretch coupling dL/dN at various temperatures T as shown in Fig. 8(c) to explore the temperature dependence of twist–stretch coupling. In particular, the twist–stretch coupling has dL/dN = 0.40 ± 0.01 nm/turn at T = 280 K and has dL/dN = 0.59 ± 0.01 nm/turn at T = 320 K. Expectedly, the twist–stretch coupling increases with increasing temperature T. The fitting result showed the twist–stretch coupling increases linearly with a slope of kln = 0.004 nm/turn K, indicating that the DNA overwinds obviously with increasing temperature in an approximately linear way.

The elasticity parameters can be calculated by the perturbed from the equilibrium related to the randomly thermal fluctuations in a polymer system.71 The twist–stretch coupling can be expressed by KST according to Eq. (2). By inversing the covariance matrix, we can arrive at

KST=kBTL0ρLΦ1ρLΦ21σLσΦ,
(7)

where ρ is Pearson coefficient between counter length L and cumulative H-twist angle Φ, σL, and σΦ are their standard errors, respectively. According to Eq. (7), we then obtained the twist–stretch coupling KST by analyzing the standard errors of H-rise and H-twist parameters and their Pearson correlation coefficient at various temperatures as shown in Fig. 9(a). In particular, we obtained the twist–stretch coupling KST = −116.7 ± 1.8 pN ⋅ nm at T = 300 K. This result is in agreement with the MT experiment, where the twist–stretch coupling is g = −90 ± 20 pN ⋅ nm at T = 296 ± 2 K111 and in good agreement with the coarse-grained MD results of KST ∼ −120 pN ⋅ nm.112,113 Actually, we can express the relationship between two coupling coefficients according to111 

dLdN=KSTKSS2π.
(8)

For example, we also obtained the twist–stretch coupling dL/dN = 0.53 ± 0.01 nm/turn at T = 300 K according to Eq. (8), which quantitatively agrees with the data in Fig. 8(c). According to Eq. (8), we plotted the twist–stretch coupling as a function of temperature in Fig. 9(b). Clearly, the theoretical results about the twist–stretch coupling also exhibit the similar trends with the temperature, which have been demonstrated in Fig. 8(c).

To demonstrate the origin of the increasing trend of twist–stretch coupling with temperature, we investigate the correlation between the random fluctuations about the stretch and twist according to Eq. (7), as shown in Figs. 9(c) and 9(d), where both ρ and 1/σLσΦ are shown at various temperatures. The results show that the ρ increases obviously with temperature T in a linear manner, namely, ρ increased from 0.11 to 0.18, whereas 1/σLσΦ decreased obviously from 22.9 to 15.7, as T varies from 280 to 320 K. Since ρ is between 0.11 and 0.18, the factor 1/(1ρLΦ2) can be ignored, the variation in KST comes from three terms: kBTL0, 1/σLσΦ, and ρ. The first term directly exhibits a linear relationship between KST and T because the L0 can be treated as a constant. The last two terms, 1/σLσΦ and ρ, are linear functions of T; the former is a negative correction, but the latter is a positive one. This result suggests that the increase in twist–stretch coupling KST is attributed to the ρ, but σLσΦ reduces the twist–stretch coupling as the T increases. From a viewpoint of statistical physics, the higher T leads to the stronger random thermal motions of molecules; thus, the thermal fluctuations of contour length L and cumulative H-twist angle Φ, i.e., σL and σΦ, increase with T. This naturally results in the decreasing of KST, according to Eq. (7). However, the Pearson’s correction coefficient ρ, which presents the corrections between the random thermal fluctuations of L and Φ, increases with T. That is to say, the ρ and σLσΦ play contrasting roles in the T-dependent KST.

In this work, we investigated the effects of temperature on the elasticity of dsDNA using an all-atom MD simulation. We selected a short dsDNA with 35 bp where only the center 29 bp were used to analyze the elastic properties of the dsDNA. We utilized the bending persistence length lB, twist persistence length lT, twist modulus KTT, and stretch modulus KSS to characterize the dsDNA bending, twist, and stretch elasticities. We used two types of twist–stretch coupling parameters, dL/dN and KST, to describe the twist–stretch couplings for dsDNA. We concentrated on the temperature dependence on these elastic parameters and their couplings, compared them with the available data for dsDNA.

The results showed that the stretch modulus KSS decreases in a linear manner, with a slope of −8.89 pN/K. Our observations on KSS were compared with the existing MT and MD data at room temperature, and the results are in good agreement. The decrease in KSS originates from the thermal fluctuation in contour length described by Δhz2, depending on the system temperature. The MD results showed that the bending persistence length lB decreases with temperature with a slope of −0.29 nm/K, which are in good agreement with the available data from the MT experiments. This is because that higher temperature leads to a bigger average bending angle θ in a linear relationship and subsequently leads to a smaller bending persistence length. The structural parameters showed that the bending flexibility of dsDNA mainly comes from the thermal fluctuation on roll angle Δρ2, but its proportion decreases linearly as T increases. We used the twist persistence length lT and the twist modulus KTT to analyze the twist elasticity for dsDNA chains by comparing with the available data at room temperature, and the results indicated that the dsDNA becomes flexible in twist elasticity in a linear manner as T increases because of the stronger thermal fluctuation on Δγ2.

We analyzed the twist–stretch coupling for dsDNA by two methods. One is the direct analysis of dL/dN from the corrections between the corresponding structural parameters and the other is to calculate the KST from modulus matrix K. Both methods were compared with the available data at room temperatures, and good agreements were obtained. Both these two methods predicted that the twist–stretch coupling become stronger as T increases. The method based on the modulus matrix K suggested that the correlations between thermal fluctuations of the contour length and twist angles contribute to the increase in twist–stretch coupling KST as the T increases, but the σLσΦ plays a contrasting role in twist–stretch coupling KST. Indeed, the T-dependent KST, or even other elastic parameters, are complex and the theoretical studies about the T-dependent KST elastic parameters are still needed. These findings provide a deeper understanding for the elastic nature of DNA and the regulation of DNA elasticity under various temperature environments and the development of DNA nanotechnology.

The supplementary material provided herein includes the correlation between the data about H-rise hz and H-twist γ at T = 280, 290, 310 and 320 K. The information provided in the supplementary material includes dsDNA elasticity parameters in the previous studies and the structural parameters and Pearson correlation coefficient ρ for dsDNA at different temperatures in present work.

We thank for the financial supports from the Program of National Natural Science Foundation of China (Grant Nos. 21973070 and 22273067).

The authors have no conflicts to disclose.

Yahong Zhang: Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (lead); Visualization (equal); Writing – original draft (equal). Linli He: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (equal). Shiben Li: Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Resources (equal); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
T. J.
Richmond
and
C. A.
Davey
, “
The structure of DNA in the nucleosome core
,”
Nature
423
,
145
150
(
2003
).
2.
J. P.
Peters
and
L. J.
Maher
, “
DNA curvature and flexibility in vitro and in vivo
,”
Q. Rev. Biophys.
43
,
23
63
(
2010
).
3.
R.
Vafabakhsh
,
K. S.
Lee
, and
T.
Ha
, “
Recent advances in studying mechanical properties of DNA
,”
Adv. Chem. Phys.
150
,
169
186
(
2012
).
4.
J.
Lipfert
,
S.
Doniach
,
R.
Das
, and
D.
Herschlag
, “
Understanding nucleic acid–ion interactions
,”
Annu. Rev. Biochem.
83
,
813
841
(
2014
).
5.
L.
Bao
,
X.
Zhang
,
L.
Jin
, and
Z.-J.
Tan
, “
Flexibility of nucleic acids: From DNA to RNA
,”
Chin. Phys. B
25
,
018703
(
2016
).
6.
A.
Aggarwal
,
S.
Naskar
,
A. K.
Sahoo
,
S.
Mogurampelly
,
A.
Garai
, and
P. K.
Maiti
, “
What do we know about DNA mechanics so far?
,”
Curr. Opin. Struct. Biol.
64
,
42
50
(
2020
).
7.
A.
Basu
,
D. G.
Bobrovnikov
, and
T.
Ha
, “
DNA mechanics and its biological impact
,”
J. Mol. Biol.
433
,
166861
(
2021
).
8.
T.
Schlick
,
R.
Collepardo-Guevara
,
L. A.
Halvorsen
,
S.
Jung
, and
X.
Xiao
, “
Biomolecular modeling and simulation: A field coming of age
,”
Q. Rev. Biophys.
44
,
191
228
(
2011
).
9.
N. C.
Seeman
, “
DNA nanotechnology at 40
,”
Nano Lett.
20
,
1477
1478
(
2020
).
10.
R.
Saran
,
Y.
Wang
, and
I. T. S.
Li
, “
Mechanical flexibility of DNA: A quintessential tool for DNA nanotechnology
,”
Sensors
20
,
7019
(
2020
).
11.
J. Y.
Lee
,
M.
Kim
,
C.
Lee
, and
D.-N.
Kim
, “
Characterizing and harnessing the mechanical properties of short single-stranded DNA in structured assemblies
,”
ACS Nano
15
,
20430
20441
(
2021
).
12.
H.
Dohnalová
and
F.
Lankaš
, “
Deciphering the mechanical properties of B-DNA duplex
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
12
,
e1575
(
2022
).
13.
J. R.
Wenner
,
M. C.
Williams
,
I.
Rouzina
, and
V. A.
Bloomfield
, “
Salt dependence of the elasticity and overstretching transition of single DNA molecules
,”
Biophys. J.
82
,
3160
3169
(
2002
).
14.
X.
Qiu
,
D. C.
Rau
,
V. A.
Parsegian
,
L. T.
Fang
,
C. M.
Knobler
, and
W. M.
Gelbart
, “
Salt-dependent DNA–DNA spacings in intact bacteriophage λ reflect relative importance of DNA self-repulsion and bending energies
,”
Phys. Rev. Lett.
106
,
028102
(
2011
).
15.
A.
Savelyev
, “
Do monovalent mobile ions affect DNA’s flexibility at high salt content?
,”
Phys. Chem. Chem. Phys.
14
,
2250
(
2012
).
16.
G. S.
Manning
, “
The response of DNA length and twist to changes in ionic strength
,”
Biopolymers
103
,
223
226
(
2015
).
17.
A.
Garai
,
S.
Saurabh
,
Y.
Lansac
, and
P. K.
Maiti
, “
DNA elasticity from short DNA to nucleosomal DNA
,”
J. Phys. Chem. B
119
,
11146
11156
(
2015
).
18.
A.
Brunet
,
C.
Tardin
,
L.
Salomé
,
P.
Rousseau
,
N.
Destainville
, and
M.
Manghi
, “
Dependence of DNA persistence length on ionic strength of solutions with monovalent and divalent salts: A joint theory–experiment study
,”
Macromolecules
48
,
3641
3652
(
2015
).
19.
S.
Naskar
and
P. K.
Maiti
, “
Mechanical properties of DNA and DNA nanostructures: Comparison of atomistic, Martini and oxDNA models
,”
J. Mater. Chem. B
9
,
5102
5113
(
2021
).
20.
C.
Zhang
,
F.
Tian
,
Y.
Lu
,
B.
Yuan
,
Z.-J.
Tan
,
X.-H.
Zhang
, and
L.
Dai
, “
Twist–diameter coupling drives DNA twist changes with salt and temperature
,”
Sci. Adv.
8
,
eabn1384
(
2022
).
21.
C. G.
Baumann
,
S. B.
Smith
,
V. A.
Bloomfield
, and
C.
Bustamante
, “
Ionic effects on the elasticity of single DNA molecules
,”
Proc. Natl. Acad. Sci. U. S. A.
94
,
6185
6190
(
1997
).
22.
A. V.
Drozdetski
,
I. S.
Tolokh
,
L.
Pollack
,
N.
Baker
, and
A. V.
Onufriev
, “
Opposing effects of multivalent ions on the flexibility of DNA and RNA
,”
Phys. Rev. Lett.
117
,
028101
(
2016
).
23.
T.
Sun
,
A.
Mirzoev
,
N.
Korolev
,
A. P.
Lyubartsev
, and
L.
Nordenskiöld
, “
All-atom MD simulation of DNA condensation using ab initio derived force field parameters of cobalt(III)-hexammine
,”
J. Phys. Chem. B
121
,
7761
7770
(
2017
).
24.
A.
Garai
,
D.
Ghoshdastidar
,
S.
Senapati
, and
P. K.
Maiti
, “
Ionic liquids make DNA rigid
,”
J. Chem. Phys.
149
,
045104
(
2018
).
25.
S.
Guilbaud
,
L.
Salomé
,
N.
Destainville
,
M.
Manghi
, and
C.
Tardin
, “
Dependence of DNA persistence length on ionic strength and ion type
,”
Phys. Rev. Lett.
122
,
028102
(
2019
).
26.
H.
Fu
,
C.
Zhang
,
X.-W.
Qiang
,
Y.-J.
Yang
,
L.
Dai
,
Z.-J.
Tan
, and
X.-H.
Zhang
, “
Opposite effects of high-valent cations on the elasticities of DNA and RNA duplexes revealed by magnetic tweezers
,”
Phys. Rev. Lett.
124
,
058101
(
2020
).
27.
N.
Li
,
Z.
Liao
,
S.
He
,
X.
Chen
,
S.
Huang
,
Y.
Wang
, and
G.
Yang
, “
Demonstration of pH-controlled DNA–surfactant manipulation for biomolecules
,”
RSC Adv.
11
,
15099
15105
(
2021
).
28.
X.-W.
Qiang
,
C.
Zhang
,
H.-L.
Dong
,
F.-J.
Tian
,
H.
Fu
,
Y.-J.
Yang
,
L.
Dai
,
X.-H.
Zhang
, and
Z.-J.
Tan
, “
Multivalent cations reverse the twist–stretch coupling of RNA
,”
Phys. Rev. Lett.
128
,
108103
(
2022
).
29.
M. C.
Williams
,
J. R.
Wenner
,
I.
Rouzina
, and
V. A.
Bloomfield
, “
Effect of pH on the overstretching transition of double-stranded DNA: Evidence of force-induced DNA melting
,”
Biophys. J.
80
,
874
881
(
2001
).
30.
C. M.
Muntean
,
L.
Dostál
,
R.
Misselwitz
, and
H.
Welfle
, “
DNA structure at low pH values, in the presence of Mn2+ ions: A Raman study
,”
J. Raman Spectrosc.
36
,
1047
1051
(
2005
).
31.
H.-Y.
Zhang
,
C.
Ji
,
Y.-R.
Liu
,
W.
Li
,
H.
Li
,
S.-X.
Dou
,
W.-C.
Wang
,
L.-Y.
Zhang
,
P.
Xie
, and
P.-Y.
Wang
, “
Effects of pH on oxaliplatin-induced condensation of single DNA molecules
,”
Chin. Phys. Lett.
31
,
028701
(
2014
).
32.
Z.
Guo
,
Y.
Wang
,
A.
Yang
, and
G.
Yang
, “
The effect of pH on charge inversion and condensation of DNA
,”
Soft Matter
12
,
6669
6674
(
2016
).
33.
C.
Wang
,
Z.
Huang
,
Y.
Lin
,
J.
Ren
, and
X.
Qu
, “
Artificial DNA nano-spring powered by protons
,”
Adv. Mater.
22
,
2792
2798
(
2010
).
34.
J. J.
Delrow
,
P. J.
Heath
, and
J. M.
Schurr
, “
On the origin of the temperature dependence of the supercoiling free energy
,”
Biophys. J.
73
,
2688
2701
(
1997
).
35.
J.-S.
Park
,
K. J.
Lee
,
S.-C.
Hong
, and
J.-Y.
Hyon
, “
Temperature dependence of DNA elasticity and cisplatin activity studied with a temperature-controlled magnetic tweezers system
,”
J. Korean Phys. Soc.
52
,
1927
1931
(
2008
).
36.
R. A.
Forties
,
R.
Bundschuh
, and
M. G.
Poirier
, “
The flexibility of locally melted DNA
,”
Nucleic Acids Res.
37
,
4580
4586
(
2009
).
37.
S.
Geggier
,
A.
Kotlyar
, and
A.
Vologodskii
, “
Temperature dependence of DNA persistence length
,”
Nucleic Acids Res.
39
,
1419
1426
(
2011
).
38.
S.
Meyer
,
D.
Jost
,
N.
Theodorakopoulos
,
M.
Peyrard
,
R.
Lavery
, and
R.
Everaers
, “
Temperature dependence of the DNA double helix at the nanoscale: Structure, elasticity, and fluctuations
,”
Biophys. J.
105
,
1904
1914
(
2013
).
39.
F.
Kriegel
,
C.
Matek
,
T.
Dršata
,
K.
Kulenkampff
,
S.
Tschirpke
,
M.
Zacharias
,
F.
Lankaš
, and
J.
Lipfert
, “
The temperature dependence of the helical twist of DNA
,”
Nucleic Acids Res.
46
,
7998
8009
(
2018
).
40.
A.
Brunet
,
L.
Salomé
,
P.
Rousseau
,
N.
Destainville
,
M.
Manghi
, and
C.
Tardin
, “
How does temperature impact the conformation of single DNA molecules below melting temperature?
,”
Nucleic Acids Res.
46
,
2074
2081
(
2018
).
41.
J. M.
Schurr
, “
Temperature-dependence of the bending elastic constant of DNA and extension of the two-state model. Tests and new insights
,”
Biophys. Chem.
251
,
106146
(
2019
).
42.
R. P. C.
Driessen
,
G.
Sitters
,
N.
Laurens
,
G. F.
Moolenaar
,
G. J. L.
Wuite
,
N.
Goosen
, and
R. T.
Dame
, “
Effect of temperature on the intrinsic flexibility of DNA and its interaction with architectural proteins
,”
Biochemistry
53
,
6430
6438
(
2014
).
43.
H.
Dohnalová
,
T.
Dršata
,
J.
Šponer
,
M.
Zacharias
,
J.
Lipfert
, and
F.
Lankaš
, “
Compensatory mechanisms in temperature dependence of DNA double helical structure: Bending and elongation
,”
J. Chem. Theory Comput.
16
,
2857
2863
(
2020
).
44.
V.
Ortiz
and
J. J.
de Pablo
, “
Molecular origins of DNA flexibility: Sequence effects on conformational and mechanical properties
,”
Phys. Rev. Lett.
106
,
238107
(
2011
).
45.
J. S.
Mitchell
,
J.
Glowacki
,
A. E.
Grandchamp
,
R. S.
Manning
, and
J. H.
Maddocks
, “
Sequence-dependent persistence lengths of DNA
,”
J. Chem. Theory Comput.
13
,
1539
1555
(
2017
).
46.
J. M.
Schurr
, “
Effects of sequence changes on the torsion elastic constant and persistence length of DNA. Applications of the two-state model
,”
J. Phys. Chem. B
123
,
7343
7353
(
2019
).
47.
X.-W.
Qiang
,
H.-L.
Dong
,
K.-X.
Xiong
,
W.
Zhang
, and
Z.-J.
Tan
, “
Understanding sequence effect in DNA bending elasticity by molecular dynamic simulations
,”
Commun. Theor. Phys.
73
,
075601
(
2021
).
48.
J. M.
Schurr
, “
A quantitative model of a cooperative two-state equilibrium in DNA: Experimental tests, insights, and predictions
,”
Q. Rev. Biophys.
54
,
e5
(
2021
).
49.
P. A.
Wiggins
,
T.
van der Heijden
,
F.
Moreno-Herrero
,
A.
Spakowitz
,
R.
Phillips
,
J.
Widom
,
C.
Dekker
, and
P. C.
Nelson
, “
High flexibility of DNA on short length scales probed by atomic force microscopy
,”
Nat. Nanotechnol.
1
,
137
141
(
2006
).
50.
A. K.
Mazur
, “
Wormlike chain theory and bending of short DNA
,”
Phys. Rev. Lett.
98
,
218102
(
2007
).
51.
A.
Noy
and
R.
Golestanian
, “
Length scale dependence of DNA mechanical properties
,”
Phys. Rev. Lett.
109
,
228101
(
2012
).
52.
A. K.
Mazur
and
M.
Maaloum
, “
DNA flexibility on short length scales probed by atomic force microscopy
,”
Phys. Rev. Lett.
112
,
068104
(
2014
).
53.
Y.-Y.
Wu
,
L.
Bao
,
X.
Zhang
, and
Z.-J.
Tan
, “
Flexibility of short DNA helices with finite-length effect: From base pairs to tens of base pairs
,”
J. Chem. Phys.
142
,
125103
(
2015
).
54.
M.
Zoli
, “
End-to-end distance and contour length distribution functions of DNA helices
,”
J. Chem. Phys.
148
,
214902
(
2018
).
55.
M.
Zoli
, “
Short DNA persistence length in a mesoscopic helical model
,”
Europhys. Lett.
123
,
68003
(
2018
).
56.
R. S.
Mathew-Fenn
,
R.
Das
, and
P. A. B.
Harbury
, “
Remeasuring the double helix
,”
Science
322
,
446
449
(
2008
).
57.
E. F.
Pettersen
,
T. D.
Goddard
,
C. C.
Huang
,
G. S.
Couch
,
D. M.
Greenblatt
,
E. C.
Meng
, and
T. E.
Ferrin
, “
UCSF Chimera—A visualization system for exploratory research and analysis
,”
J. Comput. Chem.
25
,
1605
1612
(
2004
).
58.
J.-H.
Liu
,
K.
Xi
,
X.
Zhang
,
L.
Bao
,
X.
Zhang
, and
Z.-J.
Tan
, “
Structural flexibility of DNA–RNA hybrid duplex: Stretching and twist–stretch coupling
,”
Biophys. J.
117
,
74
86
(
2019
).
59.
A.
Srivastava
,
R.
Timsina
,
S.
Heo
,
S. W.
Dewage
,
S.
Kirmizialtin
, and
X.
Qiu
, “
Structure-guided DNA–DNA attraction mediated by divalent cations
,”
Nucleic Acids Res.
48
,
7018
7026
(
2020
).
60.
I.
Hamilton
,
M.
Gebala
,
D.
Herschlag
, and
R.
Russell
, “
Direct measurement of interhelical DNA repulsion and attraction by quantitative cross-linking
,”
J. Am. Chem. Soc.
144
,
1718
1728
(
2022
).
61.
L.
Bao
,
X.
Zhang
,
Y.-Z.
Shi
,
Y.-Y.
Wu
, and
Z.-J.
Tan
, “
Understanding the relative flexibility of RNA and DNA duplexes: Stretching and twist–stretch coupling
,”
Biophys. J.
112
,
1094
1104
(
2017
).
62.
S.
Izadi
,
R.
Anandakrishnan
, and
A. V.
Onufriev
, “
Building water models: A different approach
,”
J. Phys. Chem. Lett.
5
,
3863
3871
(
2014
).
63.
I. S.
Joung
and
T. E.
Cheatham
, “
Determination of alkali and halide monovalent ion parameters for use in explicitly solvated biomolecular simulations
,”
J. Phys. Chem. B
112
,
9020
9041
(
2008
).
64.
G.
Bussi
,
D.
Donadio
, and
M.
Parrinello
, “
Canonical sampling through velocity rescaling
,”
J. Chem. Phys.
126
,
014101
(
2007
).
65.
Q.
Ke
,
X.
Gong
,
S.
Liao
,
C.
Duan
, and
L.
Li
, “
Effects of thermostats/barostats on physical properties of liquids by molecular dynamics simulations
,”
J. Mol. Liq.
365
,
120116
(
2022
).
66.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
, “
GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulation
,”
J. Chem. Theory Comput.
4
,
435
447
(
2008
).
67.
M. J.
Abraham
,
T.
Murtola
,
R.
Schulz
,
S.
Páll
,
J. C.
Smith
,
B.
Hess
, and
E.
Lindahl
, “
GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
,”
SoftwareX
1-2
,
19
25
(
2015
).
68.
R.
Galindo-Murillo
,
J. C.
Robertson
,
M.
Zgarbová
,
J.
Šponer
,
M.
Otyepka
,
P.
Jurečka
, and
T. E.
Cheatham
, “
Assessing the current state of Amber force field modifications for DNA
,”
J. Chem. Theory Comput.
12
,
4114
4127
(
2016
).
69.
I.
Ivani
,
P. D.
Dans
,
A.
Noy
,
A.
Pérez
,
I.
Faustino
,
A.
Hospital
,
J.
Walther
,
P.
Andrio
,
R.
Goñi
,
A.
Balaceanu
,
G.
Portella
,
F.
Battistini
,
J. L.
Gelpí
,
C.
González
,
M.
Vendruscolo
,
C. A.
Laughton
,
S. A.
Harris
,
D. A.
Case
, and
M.
Orozco
, “
Parmbsc1: A refined force field for DNA simulations
,”
Nat. Methods
13
,
55
58
(
2016
).
70.
X.
Kai-Xin
,
X.
Kun
,
B.
Lei
,
Z.
Zhong-Liang
, and
T.
Zhi-Jie
, “
Molecular dynamics simulations on DNA flexibility: A comparative study of amber bsc1 and bsc0 force fields
,”
Acta Phys. Sin.
67
,
108701
(
2018
).
71.
F.
Lankaš
,
O.
Gonzalez
,
L. M.
Heffler
,
G.
Stoll
,
M.
Moakher
, and
J. H.
Maddocks
, “
On the parameterization of rigid base and basepair models of DNA from molecular dynamics simulations
,”
Phys. Chem. Chem. Phys.
11
,
10565
(
2009
).
72.
I.
Faustino
,
A.
Pérez
, and
M.
Orozco
, “
Toward a consensus view of duplex RNA flexibility
,”
Biophys. J.
99
,
1876
1885
(
2010
).
73.
T.
Dršata
and
F.
Lankaš
, “
Theoretical models of DNA flexibility
,”
Wiley Interdiscip. Rev. Comput. Mol. Sci.
3
,
355
363
(
2013
).
74.
T.
Dršata
,
A.
Pérez
,
M.
Orozco
,
A. V.
Morozov
,
J.
Šponer
, and
F.
Lankaš
, “
Structure, stiffness and substates of the Dickerson–Drew dodecamer
,”
J. Chem. Theory Comput.
9
,
707
721
(
2013
).
75.
J.
Singh
and
P. K.
Purohit
, “
Elasticity as the basis of allostery in DNA
,”
J. Phys. Chem. B
123
,
21
28
(
2019
).
76.
A. K.
Mazur
, “
Evaluation of elastic properties of atomistic DNA models
,”
Biophys. J.
91
,
4507
4518
(
2006
).
77.
Q.
Du
,
C.
Smith
,
N.
Shiffeldrim
,
M.
Vologodskaia
, and
A.
Vologodskii
, “
Cyclization of short DNA fragments and bending fluctuations of the double helix
,”
Proc. Natl. Acad. Sci. U. S. A.
102
,
5397
5402
(
2005
).
78.
A.
Polley
,
J.
Samuel
, and
S.
Sinha
, “
Bending elasticity of macromolecules: Analytic predictions from the wormlike chain model
,”
Phys. Rev. E
87
,
012601
(
2013
).
79.
J. D.
Moroz
and
P.
Nelson
, “
Torsional directed walks, entropic elasticity, and DNA twist stiffness
,”
Proc. Natl. Acad. Sci. U. S. A.
94
,
14418
14422
(
1997
).
80.
S. K.
Nomidis
,
F.
Kriegel
,
W.
Vanderlinden
,
J.
Lipfert
, and
E.
Carlon
, “
Twist–bend coupling and the torsional response of double-stranded DNA
,”
Phys. Rev. Lett.
118
,
217801
(
2017
).
81.
E.
Skoruppa
,
S. K.
Nomidis
,
J. F.
Marko
, and
E.
Carlon
, “
Bend-induced twist waves and the structure of nucleosomal DNA
,”
Phys. Rev. Lett.
121
,
088101
(
2018
).
82.
M.
Caraglio
,
E.
Skoruppa
, and
E.
Carlon
, “
Overtwisting induces polygonal shapes in bent DNA
,”
J. Chem. Phys.
150
,
135101
(
2019
).
83.
M.
Segers
,
A.
Voorspoels
,
T.
Sakaue
, and
E.
Carlon
, “
Mechanical properties of nucleic acids and the non-local twistable wormlike chain model
,”
J. Chem. Phys.
156
,
234105
(
2022
).
84.
E.
Skoruppa
,
A.
Voorspoels
,
J.
Vreede
, and
E.
Carlon
, “
Length-scale-dependent elasticity in DNA from coarse-grained and all-atom models
,”
Phys. Rev. E
103
,
042408
(
2021
).
85.
M.
Zoli
, “
Thermodynamics of twisted DNA with solvent interaction
,”
J. Chem. Phys.
135
,
115101
(
2011
).
86.
M.
Zoli
, “
Helix untwisting and bubble formation in circular DNA
,”
J. Chem. Phys.
138
,
205103
(
2013
).
87.
M.
Zoli
, “
Twisting and bending stress in DNA minicircles
,”
Soft Matter
10
,
4304
(
2014
).
88.
M.
Zoli
, “
J-factors of short DNA molecules
,”
J. Chem. Phys.
144
,
214104
(
2016
).
89.
M.
Zoli
, “
DNA size in confined environments
,”
Phys. Chem. Chem. Phys.
21
,
12566
12575
(
2019
).
90.
R.
Lavery
and
H.
Sklenar
, “
Defining the structure of irregular nucleic acids: Conventions and principles
,”
J. Biomol. Struct. Dyn.
6
,
655
667
(
1989
).
91.
R. E.
Dickerson
, “
Definitions and nomenclature of nucleic acid structure components
,”
Nucleic Acids Res.
17
,
1797
1803
(
1989
).
92.
W. K.
Olson
,
M.
Bansal
,
S. K.
Burley
,
R. E.
Dickerson
,
M.
Gerstein
,
S. C.
Harvey
,
U.
Heinemann
,
X.-J.
Lu
,
S.
Neidle
,
Z.
Shakked
,
H.
Sklenar
,
M.
Suzuki
,
C.-S.
Tung
,
E.
Westhof
,
C.
Wolberger
, and
H. M.
Berman
, “
A standard reference frame for the description of nucleic acid base-pair geometry
,”
J. Mol. Biol.
313
,
229
237
(
2001
).
93.
K.
Liebl
,
T.
Drsata
,
F.
Lankas
,
J.
Lipfert
, and
M.
Zacharias
, “
Explaining the striking difference in twist–stretch coupling between DNA and RNA: A comparative molecular dynamics analysis
,”
Nucleic Acids Res.
43
,
gkv1028
(
2015
).
94.
Z.-J.
Tan
and
S.-J.
Chen
, “
Electrostatic correlations and fluctuations for ion binding to a finite length polyelectrolyte
,”
J. Chem. Phys.
122
,
044903
(
2005
).
95.
Z.-J.
Tan
and
S.-J.
Chen
, “
RNA helix stability in mixed Na+/Mg2+ solution
,”
Biophys. J.
92
,
3615
3632
(
2007
).
96.
Z.-J.
Tan
and
S.-J.
Chen
, “
Electrostatic free energy landscapes for DNA helix bending
,”
Biophys. J.
94
,
3137
3149
(
2008
).
97.
R.
Lavery
,
M.
Moakher
,
J. H.
Maddocks
,
D.
Petkeviciute
, and
K.
Zakrzewska
, “
Conformational analysis of nucleic acids revisited: Curves+
,”
Nucleic Acids Res.
37
,
5917
5929
(
2009
).
98.
N.
Ma
and
A.
van der Vaart
, “
Anisotropy of B-DNA groove bending
,”
J. Am. Chem. Soc.
138
,
9951
9958
(
2016
).
99.
J.
Lipfert
,
G. M.
Skinner
,
J. M.
Keegstra
,
T.
Hensgens
,
T.
Jager
,
D.
Dulin
,
M.
Köber
,
Z.
Yu
,
S. P.
Donkers
,
F.-C.
Chou
,
R.
Das
, and
N. H.
Dekker
, “
Double-stranded RNA under force and torque: Similarities to and striking differences from double-stranded DNA
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
15408
15413
(
2014
).
100.
A.
Marin-Gonzalez
,
J. G.
Vilhena
,
R.
Perez
, and
F.
Moreno-Herrero
, “
Understanding the mechanical response of double-stranded DNA and RNA under constant stretching forces using all-atom molecular dynamics
,”
Proc. Natl. Acad. Sci. U. S. A.
114
,
7049
7054
(
2017
).
101.
P.
Gross
,
N.
Laurens
,
L. B.
Oddershede
,
U.
Bockelmann
,
E. J. G.
Peterman
, and
G. J. L.
Wuite
, “
Quantifying how DNA stretches, melts and changes twist under tension
,”
Nat. Phys.
7
,
731
736
(
2011
).
102.
O. D.
Broekmans
,
G. A.
King
,
G. J.
Stephens
, and
G. J. L.
Wuite
, “
DNA twist stability changes with magnesium(2+) concentration
,”
Phys. Rev. Lett.
116
,
258102
(
2016
).
103.
J. B.
Mills
, “
Origin of the intrinsic rigidity of DNA
,”
Nucleic Acids Res.
32
,
4055
4059
(
2004
).
104.
G. S.
Manning
, “
The persistence length of DNA is reached from the persistence length of its null isomer through an internal electrostatic stretching force
,”
Biophys. J.
91
,
3607
3616
(
2006
).
105.
E.
Herrero-Galán
,
M. E.
Fuentes-Perez
,
C.
Carrasco
,
J. M.
Valpuesta
,
J. L.
Carrascosa
,
F.
Moreno-Herrero
, and
J. R.
Arias-Gonzalez
, “
Mechanical identities of RNA and DNA double helices unveiled at the single-molecule level
,”
J. Am. Chem. Soc.
135
,
122
131
(
2013
).
106.
R.
Vafabakhsh
and
T.
Ha
, “
Extreme bendability of DNA less than 100 base pairs long revealed by single-molecule cyclization
,”
Science
337
,
1097
1101
(
2012
).
107.
T. T.
Le
and
H. D.
Kim
, “
Measuring shape-dependent looping probability of DNA
,”
Biophys. J.
104
,
2068
2076
(
2013
).
108.
C.
Yuan
,
H.
Chen
,
X. W.
Lou
, and
L. A.
Archer
, “
DNA bending stiffness on small length scales
,”
Phys. Rev. Lett.
100
,
018102
(
2008
).
109.
S. K.
Nomidis
,
E.
Skoruppa
,
E.
Carlon
, and
J. F.
Marko
, “
Twist–bend coupling and the statistical mechanics of the twistable wormlike-chain model of DNA: Perturbation theory and beyond
,”
Phys. Rev. E
99
,
032414
(
2019
).
110.
Z.
Bryant
,
M. D.
Stone
,
J.
Gore
,
S. B.
Smith
,
N. R.
Cozzarelli
, and
C.
Bustamante
, “
Structural transitions and elasticity from torque measurements on DNA
,”
Nature
424
,
338
341
(
2003
).
111.
J.
Gore
,
Z.
Bryant
,
M.
Nöllmann
,
M. U.
Le
,
N. R.
Cozzarelli
, and
C.
Bustamante
, “
DNA overwinds when stretched
,”
Nature
442
,
836
839
(
2006
).
112.
S.
Assenza
and
R.
Pérez
, “
Accurate sequence-dependent coarse-grained model for conformational and elastic properties of double-stranded DNA
,”
J. Chem. Theory Comput.
18
,
3239
3256
(
2022
).
113.
B. E. K.
Snodin
,
F.
Randisi
,
M.
Mosayebi
,
P.
Šulc
,
J. S.
Schreck
,
F.
Romano
,
T. E.
Ouldridge
,
R.
Tsukanov
,
E.
Nir
,
A. A.
Louis
, and
J. P. K.
Doye
, “
Introducing improved structural properties and salt dependence into a coarse-grained model of DNA
,”
J. Chem. Phys.
142
,
234901
(
2015
).
114.
M. Y.
Sheinin
and
M. D.
Wang
, “
Twist–stretch coupling and phase transition during DNA supercoiling
,”
Phys. Chem. Chem. Phys.
11
,
4800
(
2009
).
115.
J.
Lipfert
,
J. W. J.
Kerssemakers
,
T.
Jager
, and
N. H.
Dekker
, “
Magnetic torque tweezers: Measuring torsional stiffness in DNA and RecA-DNA filaments
,”
Nat. Methods
7
,
977
980
(
2010
).
116.
F.-C.
Chou
,
J.
Lipfert
, and
R.
Das
, “
Blind predictions of DNA and RNA tweezers experiments with force and torque
,”
PLoS Comput. Biol.
10
,
e1003756
(
2014
).
117.
E.
Skoruppa
,
M.
Laleman
,
S. K.
Nomidis
, and
E.
Carlon
, “
DNA elasticity from coarse-grained simulations: The effect of groove asymmetry
,”
J. Chem. Phys.
146
,
214902
(
2017
).
118.
S. K.
Nomidis
,
M.
Caraglio
,
M.
Laleman
,
K.
Phillips
,
E.
Skoruppa
, and
E.
Carlon
, “
Twist–bend coupling, twist waves, and the shape of DNA loops
,”
Phys. Rev. E
100
,
022402
(
2019
).
119.
S.
Xiao
,
H.
Liang
, and
D. J.
Wales
, “
The contribution of backbone electrostatic repulsion to DNA mechanical properties is length-scale-dependent
,”
J. Phys. Chem. Lett.
10
,
4829
4835
(
2019
).
120.
K. A.
Simonov
, “
Strong deformations of DNA: Effect on the persistence length
,”
Eur. Phys. J. E
41
,
114
(
2018
).
121.
J.
Wei
,
L.
Czapla
,
M. A.
Grosner
,
D.
Swigon
, and
W. K.
Olson
, “
DNA topology confers sequence specificity to nonspecific architectural proteins
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
16742
16747
(
2014
).
122.
T.
Lionnet
,
S.
Joubaud
,
R.
Lavery
,
D.
Bensimon
, and
V.
Croquette
, “
Wringing out DNA
,”
Phys. Rev. Lett.
96
,
178102
(
2006
).

Supplementary Material