DNA spontaneously wrapping around a histone core prefers negative supercoiling: A Brownian dynamics study

Abstract

In eukaryotes, DNA achieves a highly compact structure primarily due to its winding around the histone cores. The nature wrapping of DNA around histone core form a 1.7 left-handed superhelical turns, contributing to negative supercoiling in chromatin. During transcription, negative supercoils generated behind the polymerase during transcription may play a role in triggering nucleosome reassembly. To elucidate how supercoils influence the dynamics of wrapping of DNA around the histone cores, we developed a novel model to simulate the intricate interplay between DNA and histone. Our simulations reveal that both positively and negatively supercoiled DNAs are capable of wrapping around histone cores to adopt the nucleosome conformation. Notably, our findings confirm a strong preference for negative supercoiled DNA during nucleosome wrapping, and reveal that the both of the negative writhe and twist are beneficial to the formation of the DNA wrapping around histone. Additionally, the simulations of the multiple nucleosomes on the same DNA template indicate that the nucleosome tends to assemble in proximity to the original nucleosome. This advancement in understanding the spontaneous formation of nucleosomes may offer insights into the complex dynamics of chromatin assembly and the fundamental mechanisms governing the structure and function of chromatin.

Fig 1. Schematic view of histone-DNA interaction model.

The histone core is modeled as a sphere entity, possessing 22 interaction points along a left-handed helical path that enable the DNA to be wound around the histone core. The axial vector A of the helical path on the sphere describes the orientation of the histone core. The DNA is modeled as N discrete segements. The i-th segment is defined by vertices i and i + 1, attached by $f_i$, $g_i$ and $e_i$. The vectors define the bending angle ${\beta }_i=\arccos (e_{i-1}\cdot e_i)$, and the twisting angle ${\theta }_i={\alpha }_i+{\gamma }_i$ by introducing an auxiliary vector $p_i=e_{i-1}\times e_i$. (Right) Two views of a nucleosome structure generated by VMD from the simulations.

Fig 2. Generation of initial supercoiled DNA and representative snapshots of DNA winding around a histone core.

(Left) The initial DNA supercoils were introduced by rotating the base vectors $f_N$ and $g_N$ about $e_N$ attached to the end DNA segment. A single histone core interacts with a positively supercoiled DNA (ΔLk = 3) at length of 1000 bp (100 segments) under tension f = 0 . 3pN. A complete simulation trajectory includes the sequential steps: histone core searching the DNA chain(a), the histone touching the DNA(b), DNA winding around histone (c) and finally completing the nucleosome wrapping (d and e). The first passage time (τ) of nucleosome-wrapping is defined by the time interval between (b) and (d).

Fig 3. Nucleosome-wrapping driven by interactions between DNA and histone.

(A) Schematic illustration of the nucleosome wrapping process. Before completely nucleosome wrapping (Energetic minimum), the system explores a vast number of conformations of the mis-wrapped state (out of left-handed helix path) and partially wrapped state. (B) The mean first passage time (MFPT) for the completion of the nucleosome wrapping depends on the interaction energy strength ϵ and the supercoil degree. Each dot was obtained from 20 simulations trajectories with 10ms of each (It should be noted that no data was captured for ΔLk = 5 and ϵ = 4, $5{\text{k}}_{\text{B}}\text{T}$ within 10 ms). For each given linking number, the DNA is stretched under constant force f = 0 . 3pN.

Fig 4. Preference for negative supercoiling.

(A) Schematics for a single histone interacting with a supercoiled DNA under stretching force f = 1 . 0pN. (B) The MFPT for completing nucleosome wrapping with $ϵ=6{\text{k}}_{\text{B}}\text{T}$ is supercoiling-dependent and force-dependent. Each dot was obtained from 20 simulations trajectories with 10 ms of each.

Fig 5. Multiple nucleosomes assembling.

(A)Distribution of nucleosome assembling distance along a DNA chain at length of 1000 bp. The first nucleosome is constrained at z = 20nm, and then the second histone is wound by DNA to form a new nucleosome. The second nucleosome tends to successfully assemble near the first nucleosome. The distribution of the distance d between two nucleosomes was obtained from 100 simulation trajectories of 100 μs each. (B)Average number of nucleosomes. An initially naked DNA chain with different linking numbers interact with 6 histone cores and form multiple nucleosomes. Compared with the DNA without supercoil (ΔLk = 0), the highly supercoiled DNA (ΔLk = - 5) enhances efficiency of the nucleosome assembling. Each line is the average over 10 simulation trajectories with 75 μs of each.

Fig 6. Extension, twist and writhe changes of DNA during nucleosome-wrapping.

(A) The extension increment of the supercoiled DNA due to the nucleosome wrapping.Under tensional forces, the nucleosome wrapping increases the extension of the negatively supercoiled DNA while reducing the extension of the positively supercoiled DNA. (B) The mean extension increment resulting from nucleosome wrapping is a function of supercoil and stretching force. The positive increment in DNA extension due to nucleosome wrapping causes the decrease of the potential energy of the extended DNA, which is energetically favored. (C) Changes in the twist (ΔTw) and writhe (Wr) of the unconstrained DNA due to nucleosome-wrapping. (D)The changes in twist and writhe of (positive supercoils) DNA during winding around histone core. (Left) Extendedly (+) supercoiled DNA wraps around a histone under small force, e.g, f = 0 . 1pN. The induced  + 1 linking number is mainly attributed to writhe, which causes work done during nucleosome wrapping. (Right) Highly tensional (+) supercoiled DNA wraps around a histone under large force, e.g, f = 10pN. The induced  + 1 linking number is mainly attributed to twist, which increases twisting energy during nucleosome wrapping.