Structural dynamics of double-stranded DNA with epigenome modification

Abstract Modification of cytosine plays an important role in epigenetic regulation of gene expression and genome stability. Cytosine is converted to 5-methylcytosine (5mC) by DNA methyltransferase; in turn, 5mC may be oxidized to 5-hydroxymethylcytosine (5hmC) by ten-eleven translocation enzyme. The structural flexibility of DNA is known to affect the binding of proteins to methylated DNA. Here, we have carried out a semi-quantitative analysis of the dynamics of double-stranded DNA (dsDNA) containing various epigenetic modifications by combining data from imino 1H exchange and imino 1H R1ρ relaxation dispersion NMR experiments in a complementary way. Using this approach, we characterized the base-opening (kopen) and base-closing (kclose) rates, facilitating a comparison of the base-opening and -closing process of dsDNA containing cytosine in different states of epigenetic modification. A particularly striking result is the increase in the kopen rate of hemi-methylated dsDNA 5mC/C relative to unmodified or fully methylated dsDNA, indicating that the Watson–Crick base pairs undergo selective destabilization in 5mC/C. Collectively, our findings imply that the epigenetic modulation of cytosine dynamics in dsDNA mediates destabilization of the GC Watson–Crick base pair to allow base-flipping in living cells.


Supplementary method
The influence of cross-relaxation on 1

H R1ρ relaxation dispersion
For 15 N relaxation experiments such as R1, R2, and R1ρ rate measurements, the contribution of 15 N-15 N cross-relaxation to effective relaxation rates is usually negligible because of its small gyromagnetic ratio and the relatively long distances between adjacent 15 N atoms in proteins and nucleic acids. For the 1 H R1ρ relaxation experiment conducted in this study, however, 1 H-1 H cross-relaxation in the rotating frame, known as the rotating-frame Overhauser effect (ROE), must be taken into account because it may change the effective 1 H R1ρ relaxation rate ( eff R1ρ = R2 0 + Rex). Because proton density is lower in DNA than in protein, the contribution of 1 H-1 H cross-relaxation in the rotating frame to 1 H R1ρ relaxation should be smaller in DNA. To our knowledge, however, no theoretical examination of this matter has been conducted.
Below, we have simulated the 1 H R1ρ relaxation of imino protons of guanine and thymine in the doublestrand DNA (dsDNA) sample, including the effect of 1 H-1 H cross-relaxation.
In the case of an n-spin system, a set of coupled differential equations describes the time evolution of the magnetization of the individual spins. The matrix form of the differential equations can be written as , where M(t) is the column vector with 1 H peak intensities after a spin-lock time of t. R is the matrix that contains auto-relaxation rates, ρii, as the diagonal elements; and cross-relaxation rates, σ ROE ij, as the nondiagonal elements. Because matrix R does not contain the terms that describe chemical exchange, the amplitude of the relaxation due to chemical exchange, Rex, cannot be simulated. However, cross-relaxation does not alter Rex, which is determined by the exchange rate, populations, chemical shift differences between the interconvertible states, and the offset from the carrier frequency (2). These parameters are independent of cross-relaxation. In the simulation, therefore, we focused only on the contribution of crossrelaxation to the intrinsic relaxation rate, R2 0 .
For each pair of 1 H-1 H 2-spin systems, σ ROE can be calculated by using the following equations under the assumption that dsDNA is treated as a cylinder shape molecule and undergoes axially symmetric rotation around the cylinder axis (1,3): where h is the Planck constant, μ0 is the vacuum permeability, γH is the gyromagnetic ratio for 1 H, and r is the interatomic distance between an imino proton of interest and another proton (see below). S 2 denotes the generalized order parameter, which represents the rigidity of a H-N (or H-C) bond vector; S 2 ranges from 0 to 1, but here we set S 2 as 0.8, which is a typical S 2 value for dsDNA (4,5). Ak and τk (k = 1, 2, and 3) are defined as A1 = (3cos 2 θ -1) 2 /4, A2 = 3sin 2 θcos 2 θ, A3 = 3sin 4 θ/4, τ1 = (6D ⊥ ) -1 , τ2 = (5D ⊥ + D || ) -1 , and Here, θ is the angle between the H-N (or H-C) bond vector and the cylinder axis.
Because the DNA base planes are approximately perpendicular to the cylinder axis, θ is set to 90˚. The base planes are actually 1.2˚ inclined; however, this small deviation does not change σ ROE , as far as we tested. D ⊥ and D || are the perpendicular and parallel rotational diffusion constants, respectively. dsDNA can be treated as a cylinder shape molecule with length L (number of base pairs × 3.38 Å), diameter d (~20 Å), and aspect ratio p (p = L/d). For this type of cylinder, D || and D ⊥ are calculated by using the equations (6): , where k is the Boltzmann constant, T is the absolute temperature, and η0 is the viscosity of the solvent.
Regarding the interatomic distance, r, we measured distances from imino protons of interest to other protons in the structure of the dsDNA sample used in the present study. For imino protons in guanine, the most adjacent nonlabile proton was the imino proton in the preceding or succeeding base. For those in thymine, H2 in adenine that is base-paired with the thymine under analysis was the nearest. The distances used in the σ ROE calculations are summarized in Table S1. It should be noted that resonances of adenine H2 are usually separate from those of imino protons: according to the Biological Magnetic Resonance Data Bank (http://www.bmrb.wisc.edu/), the averaged chemical shifts of adenine H2, the imino proton in guanine (guanine H1), and the imino proton in thymine (thymine H3) are 7.65, 11.88, and 13.00 ppm, respectively. In the 1 H R1ρ relaxation experiments conducted in this study, the carrier frequency was set to one of the imino proton resonances. Therefore, the effective magnetic field at the resonance frequency of adenine H2 is tilted at a weak spin-lock power, ω1, and thus σ ROE is scaled by sinα (Supplementary Figure   S1). Here, α = tan -1 (ω1/Ω) and Ω is the chemical shift difference between the spin-lock carrier frequency and the resonance frequency of adenine H2 (7). Although the contribution of σ ROE to the effective 1 H R1ρ relaxation rate depends on ω1, here we calculated σ ROE with sinα = 1 to understand its maximum contribution to the effective 1 H R1ρ relaxation rate.
The parameter values used in the simulation of 1 H R1ρ relaxation were as follows: h = 6.626 × 10 -34 J·s, μ0 = 1.257 × 10 -6 N·A -2 , γH = 2.675 × 10 8 T -1 ·s -1 , ωH = 3.770 × 10 9 rad·s -1 , S 2 = 0.  Figure S2). The deviations between the decay profiles with and without σ ROE were very small, but those for thymine were slightly larger than those for guanine because of the cross-relaxation from adenine H2, which is closest to the imino proton in thymine (Supplementary Table S1). The resultant effective 1 H R1ρ relaxation rates calculated with σ ROE were in a good agreement with those without σ ROE (Supplementary Table S2) within the experimental error ( Figure 5). The effective 1 H R1ρ relaxation rates are not significantly dependent on the R2 0 values, but the differences between the rates with and without σ ROE become smaller as R2 0 increases.
In conclusion, we have shown by the simulation that the contribution of 1 H-1 H cross-relaxation to the effective 1 H R1ρ relaxation rates is negligible in the case of the dsDNA sample used in the present study, especially for the imino proton in guanine. However, the contribution of 1 H-1 H cross-relaxation depends on auto-relaxation rates, which are closely correlated with molecular weight or the number of base pairs. Therefore, it is recommended that a similar simulation should be performed for each dsDNA sample. Coloring: C/C 5mC/C 5mC/5mC C/5mC 5hmC/C 5hmC/5mC   Figure S5. Average angle at C6:G to G9:C base pairs for C/C (black), 5mC/C (cyan), 5mC/5mC (blue), C/5mC (magenta), 5hmC/C (red), and 5hmC/5mC (green).  Coloring: C/C 5caC/5caC (A) 5'-G 1 C 2 A 3 A 4 T 5 C 6 caC 7 G 8 G 9 T 10 A 11 G 12 -3' 3'-C 1 G 2 T 3 T 4 A 5 G 6 G 7 caC 8 C 9 A 10 T 11 C 12 -5'