Unwrapping of DNA-protein complexes under external stretching

A DNA-protein complex modeled by a semiflexible chain and an attractive spherical core is studied in the situation when an external stretching force is acting on one end monomer of the chain while the other end monomer is kept fixed in space. Without a stretching force, the chain is wrapped around the core. By applying an external stretching force, unwrapping of the complex is induced. We study the statics and dynamics of the unwrapping process by computer simulations and simple phenomenological theory. We find two different scenarios depending on the chain stiffness: For a flexible chain, the extension of the complex scales linearly with the external force applied. The sphere-chain complex is disordered; i.e., there is no clear winding of the chain around the sphere. For a stiff chain, on the other hand, the complex structure is ordered, which is reminiscent of nucleosome. There is a clear winding number, and the unwrapping process under external stretching is discontinuous with jumps of the distance-force curve. This is associated with discrete unwinding processes of the complex. Our predictions are of relevance for experiments, which measure force-extension curves of DNA-protein complexes, such as nucleosome, using optical tweezers.

Figure 1

Schematic sketch of the complex under external stretching. The first end monomer is fixed at ${\mathit{r}}_1$, the protein sphere with radius $R$ is fixed at the origin, and the other end monomer is pulled by the force $f$ along the $x$ axis. The chain extension $r$ and the tilt angle $\varphi$, which can be defined for the ordered complex, are also shown.

Figure 2

(Dots) Force-extension relation of the sphere-chain complex obtained by computer simulations for different chain stiffnesses $\kappa =2$, 5, and 10. In the case of a bimodal distribution of $r$, we plot both peak positions. (Line) Theoretical force-extension relation of the disordered sphere-chain complex. The parameters are estimated from the corresponding system in the simulation with $\kappa =2$: $a_1=-7$, $a_2=0.12$, $L_0=44$, and ${\lambda }_p=1.5$.

Figure 3

Probability distribution of the order parameter $\eta$ for complexes made from chains with different stiffnesses $\kappa =2$, 5, and 10 under a stretching force $f=0.2$.

Figure 4

Typical simulation snapshots of the sphere-chain complex. Top: an ordered wrapping with wrapping number $w=2$ for $\kappa =10$, $f=1$. Middle: an ordered wrapping with $w=1$ for $\kappa =10$, $f=2.5$. Bottom: a disordered state for $\kappa =2$, $f=1$.

Figure 5

Specific heat as a function of the stretching force for different chain stiffnesses $\kappa =2$, 5, and 10.

Figure 6

Probability distribution of the chain extension $r$ (a) below $(f=1.6)$ and (b) above $(f=1.8)$ the critical stretching force to induce the unwrapping transition from $w=2\text{to}1$ for a chain stiffness of $\kappa =10$.

Figure 7

Unwrapping process by stretching an end monomer by a constant speed for the chain stiffness parameter $\kappa =10$. (a) Force-extension relation. The result from the force constant ensemble is also plotted by circles for comparison. (b) Tilting angle-extension relation. (c) Bending energy-extension relation. (d) Adsorption energy-extension relation.