Nucleosome interactions in chromatin: Fiber stiffening and hairpin formation

We use Monte Carlo simulations to study attractive and excluded volume interactions between nucleosome core particles in $30\text{−}\mathrm{nm}$ chromatin fibers. The nucleosomes are treated as disklike objects having an excluded volume and short-range attraction modeled by a variant of the Gay-Berne potential. The nucleosomes are connected via bendable and twistable linker DNA in the crossed linker fashion. We investigate the influence of the nucleosomal excluded volume on the stiffness of the fiber. For parameter values that correspond to chicken erythrocyte chromatin, we find that the persistence length is governed to a large extent by that excluded volume whereas the soft linker backbone elasticity plays only a minor role. We further find that internucleosomal attraction can induce the formation of hairpin configurations. Tension-induced opening of such configurations into straight fibers manifests itself in a quasiplateau in the force-extension curve that resembles results from recent micromanipulation experiments. Such hairpins may play a role in the formation of higher-order structures in chromosomes like chromonema fibers.

Figure 1

Lhs: Portion of the model fiber including three nucleosomes (represented in this figure as green cylinders instead of ellipsoids to facilitate the identification of the nucleosome orientation) connected via stems (red) to the DNA linkers (blue). Also indicated are the two underlying angles: the deflection angle $\theta$ and the rotational angle $\varphi$. Rhs: Examples of two-angle fibers with the arrows denoting their position in the $(\theta ,\varphi )$-plane.

Figure 2

Effect of the excluded volume interaction on the bending persistence length of the fiber for two deflection angles $\theta$ with $\varphi =100°$ and $B=7.14\mathrm{nm}$. For a given linker length $B$, the fiber persistence length $l_p\left[\mathrm{nm}\right]$ grows with increasing disk size. For very small disk sizes, the measured persistence lengths converge to the analytical result, Eq. (97) of Ref. 23. On the rhs we show some snapshots of simulated fibers with varying disk sizes for $\theta =145°$ (top row) and $\theta =90°$ (bottom row).

Figure 3

Force-extension curves for fibers with $\theta =145°$, $\varphi =110°$, and $B=7.14\mathrm{nm}$. The curves correspond to fibers with different nucleosomal attraction, namely $ϵ=0$ (pure hardcore) and $ϵ=2,3,4k_{B}T$. At $ϵ=4k_{B}T$ occurs a force plateau around $2pN$. Snapshots of fibers with $\theta =145°$, $\varphi =110°$, and $B=7.14\mathrm{nm}$ at different stretching forces for $ϵ=4k_{B}T$. To facilitate the detection of hairpins, one half of the chain is shown in green while the other half is shown in cyan. The end nucleosomes are labeled red. The fiber at $f=0\mathrm{pN}$ shows a kink close to the center of the chain. Up to $f=2\mathrm{pN}$ the kink is still present, but the ends get pulled out. For $f=15\mathrm{pN}$ the fiber is stretched and nucleosomal contacts are broken.

Figure 4

Probability density of the end-to-end distance $R_E$ of a fiber with $\theta =145°$, $\varphi =110°$, and $B=7.14\mathrm{nm}$ for various GB energy well depths $\epsilon$ and stretching forces $f$ as specified in the legends. See text for details.

Figure 5

Contact matrix of the fiber with $ϵ=4k_{B}T$, $\theta =145°$, $\varphi =110°$, and $B=7.14\mathrm{nm}$. (a) At an external tension $f=3.5\mathrm{pN}$ the fiber is stretched and there is no hairpin. (b)–(d) Without an external force, $f=0\mathrm{pN}$, one can clearly detect hairpin structures. The simulation runs (b) and (c) show the occurrence of two hairpins, whereas in (d) only one hairpin can be identified.