Universality in RNA and DNA deformations induced by salt, temperature change, stretching force, and protein binding

Significance DNA and RNA deformations play crucial roles in biological processes, such as DNA packaging and nucleic acid recognition by proteins. The relevant understanding is limited due to the challenge in the precise measurement of nucleic acid deformations and the complexity of nucleic acid interactions. We solve these two issues using experiments, simulations, and theory. Magnetic tweezers experiments provide an excellent opportunity to precisely measure DNA and RNA twist changes induced by salt, temperature change, and stretching. Surprisingly, our simulations and theory find that common deformation pathways drive DNA and RNA deformations induced by different stimuli. Furthermore, the common deformation pathways appear to be utilized by protein binding to reduce the energy cost of DNA and RNA deformations.

concentration. (VI). Details of preparing torsion-constrained DNA constructs 43 (i-1) Prepare a multiple-biotin-labeled short DNA fragment by PCR using F and Rs as primers together with 30% 44 biotin-11-dUTP (Thermo Fisher Scientific) and using lambda DNA as the template.
(VII). Details of preparing torsion-constrained RNA construct (i-1) Make a short DNA template through PCR using F and Rs as primers and using lambda DNA as the template.

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(i-2) Make a long DNA fragment through PCR using FT7 and RlL as primers and using the lambda DNA as the template.

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(i-3) Make a long DNA fragment through PCR using F1L and RT7 as primers and using lambda DNA as the template.

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(i-4) Make a short DNA fragment through PCR using Fs and R as primers and using lambda DNA as the template.

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(ii-4) Then, generate the multiple-digoxigenin-labeled ssDNA through OSP using FsL as the primer together with 30% 59 digoxigenin-11-dUTP. 60 (iii) Anneal above two ssRNA strands and two ssDNA strands together equimolar through a temperature process containing 61 a one-hour incubation step at 65 • C followed by an over one-hour slow cooling process from 65 • C to 25 • C (-0.5 • C/min) 62 without purification after OSP or transcription.

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We used a set of primers for each sequence containing 43%, 57% or 36% GC percentage: Section S2. Effect of the change in refractive index on experimental measurement 99 We analyzed the change in refractive index and the effect of this change on extension measurement. The refractive index of As shown in Figure S2, before measuring twist-extension curves of RNA/DNA at each buffer condition, we built a library 105 containing the diffraction pattern of each bead at each vertical position of objective using a piezo scanner which changes the 106 thickness of objective oil by ∆zo. When measuring the twist-extension curves of RNA/DNA at each buffer condition, we 107 determined the change in RNA/DNA extension (∆z b ) by matching the bead's the diffraction pattern in the library. As the 108 same diffraction pattern of the bead meant the same optical length, we obtained ∆z b = (n0/n b )∆z0.
Section S3. Experimental results of RNA and DNA twist changes induced by switching the ion type 114 To measure the RNA (or DNA) twist change induced by switching the ion type, we fixed the concentration at 150 mM (around 115 physiological ionic strength) and measured the change in RNA (or DNA) twist change for the same RNA (or DNA) molecule 116 when changing the ion type. The results are shown in Figure S3A. For DNA, the trend for DNA agrees with a previous 117 study (4). Combining the result for RNA in Figure S3A. with the data in Fig. 2A Figure S4 shows noticeable changes in the twist-c salt curves for three RNA sequences. Such sequence effect may be caused 124 by sequence dependences of nucleic acid mechanical properties. And we did not observe a clear trend with varying the CG 125 percentage.

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For temperature-induced RNA twist changes, we also carried out experiments using the above three sequences. Figure S5 127 shows that the sequence effect is quite weak for temperature-induced RNA twist changes at 1 M KCl. We did not observe a 128 trend when varying the CG percentage.  Section S5. Details of all-atom molecular dynamics simulations Section S6. Details of the calculation of Ω(ω, G) Here we describe the calculation procedure of Ω(ω, G) in Eq. 1. We collected N conf = 5 × 10 4 dsRNA conformations from a 147 500 ns trajectory of one MD simulation at a given salt condition. For each dsRNA conformation, we computed ωi and Gi, 148 where i = 1, 2, . . . , N conf is the index of conformation. Then, these N conf data points of {ωi, Gi} were grouped into 10 × 10 149 bins according to the values of ω and G. For example, one bin corresponds to 30.4 • < ω ≤ 33.7 • and 0.25 nm < G ≤ 0.31 nm. 150 Finally, the number of data points in each bin is counted and recorded as Ω(ω, G). When converting Ω(ω, G) to Psim(ω, G) 151 using Eq. 1, we subtract a constant from Psim(ω, G) to make its minimum value to be zero. Section S7. Dependences of the twist-groove coupling constants on the salt, sequence, and force field We also performed additional simulations using three different dsRNA constructs (15) or the Parmbsc0 force field (16). The 158 calculated twist-groove coupling constants are shown in Table S4 and S7.

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159 Table S3. The twist-groove coupling per bp at different salt concentrations from 600 ns MD simulations. The uncertainties correspond to 95% confidence interval during the two-dimensional fitting.

Section S8. The effective twist rigidity for dsRNA
We can calculate the effective twist rigidity for a dsRNA molecule from k bp ω , k bp G and k bp ωG . Eq. 2 can be reformed as: [S1]

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For every twist angle ∆ω, the major groove of dsRNA will be relaxed toward ∆G = (∆ω) 2 . So, the effective twist rigidity is While we define the twist rigidity for a base pair, another definition is P = Section S9. Theoretical calculation of ∆ω using other values of P-P distance 170 We have used the P-P distance of r = 0.6 nm in the calculation of effective force in Eq. 7. Here, we show that other values of r 171 combining adjusting the rescale factor also produce agreeable results, as shown in Figure S8. Section S10. Effect of ion type on the ion distribution around RNA and RNA twist change As shown in Fig. 2, RNA twist change depends on not only the ion concentration but also the ion type. To understand the 174 ion-type dependence, we analyzed the ion distributions around RNA for different ion types, as shown in Figures S9-S13.

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To obtain an additional reason for the different deformation pathways between DNA and RNA, we compare ion distributions 176 between DNA and RNA in Figure S14. It is obvious that RNA can capture much more ions in the major groove. Accordingly,

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RNA major groove width is significantly affected by ions, which mediates RNA twist change.
178 Fig. S9. Two-dimensional ion distribution of Na + around RNA from MD simulations.   Section S11. Sequence effect on salt-induced RNA twist changes the effects of base pair step number on RNA twist changes. As shown in Figure S15, higher pyrimidine-purine step content 181 significantly increases RNA twist. The higher pyrimidine-purine step number also increases twist deformability, as proved by 182 the smaller twist rigidity in Figure S16. This sequence-dependent result of RNA is consistent with the sequence dependence of 183 DNA, where pyrimidine-purine basepair step has much higher twist flexibility than other basepair steps (20). 184 50% 0% 50% Section S12. Discussion about other possible deformation pathways in dsRNA and dsDNA Gma as a function of the salt concentration in Figure S18.

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The coupling of ω with D, Gmi, and Gma can be estimated through the correlation coefficients in Table S7. For dsDNA, coupling constant for dsRNA appears to be weaker than the ω − D coupling constant for dsDNA, dsRNA responds to the 208 salt more profoundly than dsDNA. The reason is that dsRNA has a soft major groove width, relative to the stiff diameter of 209 dsDNA. As illustrated in Figure S17, the combination of two steps determines the sensitivity of salt-induced twist change. 210 We also compare the magnitudes of the changes of many RNA structural parameters to verify the contribution of major      Section S13. RNA and DNA deformations induced by protein binding Fig. 7A shows the results of dsRNA deformations within three dsRNA-protein complexes (21, 22). The reason why selected 217 these three complexes is that in these three complexes, proteins mainly bind on the major grooves, which are likely to vary the 218 major groove width. Basically, these three dsRNA-protein complexes are "clean" systems to analyze the correlation between the 219 twist change and the major groove width during dsRNA deformations. In these three complexes, double-stranded RNA binding 220 domains (dsRBD) mainly recognize the major groove by the N-terminal tip of helix α2 (23). For simplicity, we calculated 221 the major groove width using the phosphate-phosphate distance perpendicular to the adjacent phosphate cubic spline curves 222 across the major groove, which is similar to the groove parameters definition in 3DNA and Curves+ (6, 24). Overall, the 223 results in Fig. 7A suggest that the protein-binding induced dsRNA deformations, in terms of ∆ω and ∆G, are along the 224 direction of twist-groove coupling in dsRNA, which should reduce dsRNA deformation energies during protein binding. The 225 dsRNA structural parameters for dsRNA-protein complexes were extracted directly from the structures in the PDB, while the 226 standalone dsRNA structural parameters were obtained from our MD simulations of the dsRNA molecules with the specific 227 sequences.

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Then, we roughly estimate the contribution of the twist-groove coupling to the dsRNA deformation energy. The dsRNA 229 deformation energy in the absence of the twist-groove coupling would be Here, N bp is the number of RNA base pairs deformed by the protein binding. The dsRNA deformation energy with the 232 twist-groove coupling is The contribution of the twist-groove coupling to the dsRNA deformation energy is We also analyze the normalized magnitudes of the changes of many structural parameters induced by protein binding. As 237 shown by Table S11, the variations of major groove width appear to be most significant among other structural parameters.

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Similarly, we selected three dsDNA-protein complexes to analyze dsDNA deformations upon protein binding. In these 239 three complexes, proteins surround dsDNA molecules and affect dsDNA diameters. Fig. 7B shows the results for these three 240 dsDNA-protein complexes (25, 26). The results suggest that the twist change and diameter change induced by protein binding 241 are along the same direction as the twist-diameter coupling for DNA, which should reduce dsDNA deformation energies during 242 protein binding. The contribution of the twist-diameter coupling to the dsDNA deformation energy is also estimated in Table   243 S10.
244 Table S10. DsDNA deformation energy reduced by twist-diameter coupling obtained from 600 ns MD simulations .  Table S11. Normalized change of structural parameters by standard deviation among twist, major groove width, roll (bend), and tilt of dsRNAprotein complexes with protein binding from our 600 ns MD simulations.

2L2K
Standard deviation before protein binding, δ Section S14. Modification of the force field parameters for Na +

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As shown in Fig. 2, the simulation results of K + and Rb + agree well with the experimental results, while the simulation 246 results of Na + deviate from the experimental results. Considering that all-atom MD force fields keep evolving to better match 247 experiments, we take advantage of our experimental results and modify the force field parameters for better agreement with 248 experiments. We hope such attempts of modification can be useful in future development of force field parameters for Na + .

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The force field parameters of Na + include the sigma and epsilon for the Lennard-Jones interaction. We modified the sigma 250 and epsilon independently, carried out new MD simulations, and then compared simulation and experimental results ( Figure   251 S19 and Table S12). It is interesting that increasing sigma can substantially increase the number of Na + in major groove width 252 (Table S13), which is probably the reason why the modified LJ parameter can better match experimental results. Eventually, we 253 find that slightly increasing the sigma from 0.243928 nm to 0.29000 nm (modified parameters 4) can achieve a good agreement.
254 Table S12. Comparison of original parameters using the Joung-Cheatham model (7) and our modified parameters obtained from 600 ns MD simulations.   Section S15. The role of twist-groove coupling in temperature-induced twist change twist change, our MD simulations for temperature-induced RNA twist change yield PMF with respect to the major groove 257 width under various temperatures ( Figure S20), which allows us to separate the contributions of interaction energy U and 258 conformational entropy S to RNA free energy:

Na
where U (G) is the internal energy and S(G) is the entropy, both as a function of the major groove width. Taking the PMF in 1 261 M KCl at 22 • C as a reference, we subtract it from the PMF at one another temperature (RNA in 1 M KCl at 27 • C) to give 262 the PMF difference.
where a is the constant independent of G. Dividing Eq. S7 by the prefactor of S(G), we obtain S(G) plus a constant: Here we just need how S changes as a function of G instead of the absolute value of S. As shown in Fig. 5B, we find that [S9]

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The value of ∂S/∂G ≈ 0.024 kJ/(mol · K · nm) was obtained from the simulation result in Figure S20. In the main manuscript, 273 we have obtained the relationship between the effective force that tends to change the major groove width and hence twist.

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It means the temperature-dependent RNA twist change has a coefficient kT : kSG.
[S11] Section S16. Comparison of temperature-induced RNA and DNA twist changes 283 In Figure S21, we compare temperature dependence for DNA and RNA. The slopes are similar for DNA and RNA. The 284 mechanisms are presented in the flowchart.

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The reason why RNA and DNA have opposite twist-stretch coupling is illustrated by the flowchart ( Figure S22). The 286 opposition comes from the first step (stretching → major groove width and stretching → diameter  Section S17. A simple helical model for RNA twist-groove coupling 291 RNA twist-groove coupling and DNA twist-diameter coupling can be simply and roughly explained using a simple helical model.

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Two adjacent bases are connected by a fragment of sugar-phosphate backbone, whose length, s, is roughly fixed. The length, s, 293 can be written as s = (Dω/2) 2 + h 2 , where h is the helical rise per bp. Under the condition that s is fixed, there are two 294 cases. (i) When h is fixed, ω and D are negatively correlated, i.e., twist-diameter coupling in DNA. This explanation was used 295 in our previous study (27). (ii) When D is fixed, ω and h are negatively correlated. Considering the strong positive correlation 296 between h and the major groove width G, one obtains the negative correlation between ω and G in RNA (Fig. 3A, 3C).

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Section S18. Confirmation of RNA twist-groove coupling using MD simulations with external forces on major 298 grooves 299 We performed additional simulations with artificial forces to enlarge RNA major grooves and then observe RNA twist changes.

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For each pair of P atoms across the RNA major groove, we imposed two springs that pull each P atom toward the other P 301 atom (see the left panel in Figure S23). We set the spring constant to be negative such that the spring force tends to enlarge 302 RNA major grooves. We set five values of spring constant so that the spring forces equal 1, 2, 3, 4, and 5 pN, respectively. The 303 distance for the P-P pair across RNA major groove is around 0.8353 nm, and hence the spring constants are roughly -0.6022, 304 -1.2044, -1.8066, -2.4088, and -3.011 kJ · mol −1 · nm −2 . Figure S23 shows the corresponding RNA twist changes for these five 305 springs. Each data point corresponds to a simulation of 600 ns. The scatter points are close to the ones for salt-induced RNA 306 twist changes, which supports that the variation of major groove width plays a major role in mediating RNA twist change.

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Enlarging major groove width, G by external forces Fig. S23. Illustration of adding force to enlarge major groove of RNA (left) and the force-induced twist-groove curve agrees with that obtained from salt variation by 600 ns MD simulations (right).