Forming superhelix of double stranded DNA from local deformation

TL;DR

This work argues that the formation of a 1.7-turn DNA superhelix around a core can be understood through geometrical constraints on base-pair deformation, distinct from elastic energetics. It develops a bend-twist coupling framework using 3DNA variables within the Marko–Siggia formalism, deriving how tilt, roll, and twist interrelate and how an additional twist arises from bending. Coarse-grained simulations with oxDNA1/oxDNA2 around a nanoparticle validate the geometry-driven mechanism, revealing sequence-dependent effects and the critical role of the major-minor groove in achieving the 1.7-turn curvature, quantified via a curvature kurtosis measure $\mathcal{K}$. The results highlight geometry as a key contributor to nucleosomal-like DNA wrapping and provide a pathway to incorporate protein interactions and topological constraints in future models.

Abstract

The formation of 1.7 turns of the superhelix of DNA strands is the quintessential step of DNA packaging. In this paper, the geometrical constraints of the base pair in a curved DNA strand are derived separately from its elasticity as addressing the deformation characteristics during superhelix formation around a simplified core structure. The constraints that base pair has from its inherent helicity characterize the conditional affinity in the bend-twist coupling deformation and the 1.7 turns in the superhelix structure. Coarse-grained molecular dynamics simulation validates the description of the curvature formation process.

Figures (6)

• Figure 1: Schematic figure of a base pair in the superhelix curvature. When $O_c$ and $\vec{R}_c$ are the center of the curvature and the radius of the curvature that the strand draws at n th base pair, a hollow red circle indicates the contact point between $\vec{R}_c$ and the circumference of the cross section disk of a base pair. $O_{bp}$ in the right inset is the center of the cross section of the base pair, which has two red dots as the location of the nucleotides. $\vec{r}_1$ and $\vec{r}_2$ are the two vectors towards each nucleotide from $O_{bp}$. $\vec{R}_{bp}$ is the vector from $O_{bp}$ to the contact point and the contact angle is defined between $\hat{e}_2$ and $\vec{R}_{bp}$ or $\vec{R}_c$. $\vec{\Omega}$ is the rotation vector of the base pair aligned parallel to the tangential line of the circumference at the contact point. Reprinted figure with rearrangement by the authors with permission from Nomidis et al.Nomidis2019b,doi:10.1103/PhysRevE.99.032414.
• Figure 2: A-a. Arrangement between $n-1$ th(blue) and $n$ th(red) base pairs. $\theta_{\omega}$ is the angle for inherent helicity, which is from 32.4 $^{\circ}$. Two solid dots represent two nucleotides for each base pair, A-b. Modified twist angle, $\theta^{'}_{\omega}$ with $\Delta L_y$, A-c. Additional twist angle $\Delta \theta_{\omega}$ for $\theta^{'}_{\omega} = \theta_{\omega}+\Delta \theta_{\omega}$ with $\Delta L_y$ and $\Delta L_x$. Note that $\Delta \theta_{\omega}$ is measured from the median of $n$ th base pair, B. The quantification result from the derivation in Eq.(\ref{['eq:eq1']})$\sim$Eq.(\ref{['eq:eq8']}).
• Figure 3: The angle between the contact point and the center of the base pair is measured as shown by spatiotemporal distribution. y axis is time, x axis is the index of base pair along the strands. The left inset is about the conformation change during the wrapping process of c1 strand. The angle and contact point are measured only when the distance from the center of NP to that of dsDNA is within 6 nm, B. Three rotational deformations along roll($\rho$), tilt($\tau$) and twist($\omega$) in curvature unit on each base pair in the strand. Each deformation is normalized by its maximum value. Purple means zero deformation. Clear patterns in the approximately 11 base pair period are observed both in A and B.
• Figure 4: Total energy during wrapping process in 30 ns using oxDNA2 and new thermostat. A. c1 (pink) proves its minimum free energy level and rapid completion of wrapping. c2(grey) and c3(blue) strands have major re-arrangement of strands around the NP at 10 $\sim$20 ns, which delays the completion of wrapping. B. EXAT(blue) has a more stable condition than IAT(grey) according to the minimum energy (in parentheses). The peak at 25 ns in the IAT result bolsters the wrapping process of IAT, which is completed slowly compared to EXAT.
• Figure 5: A. Wrapping using the CG model with major-minor groove(oxDNA2), B. Wrapping from CG model without major-minor groove(oxDNA). The distance between strands in wrapping conformation(red arrow) in the oxDNA case is narrower than that calculated using the oxDNA2 case(blue arrow). For the simulation, 375 bps strand with AT(red) and CG(gray) combination is used with one end fixed.