DNA Spools under Tension

DNA spools, structures in which DNA is wrapped and helically coiled onto itself or onto a protein core, are ubiquitous in nature. We develop a general theory describing the nonequilibrium behavior of DNA spools under linear tension. Two puzzling and seemingly unrelated recent experimental findings, the sudden quantized unwrapping of nucleosomes and that of DNA toroidal condensates under tension, are theoretically explained and shown to be of the same origin. The study provides new insights into nucleosome and chromatin fiber stability and dynamics.

Figure 1

(a) An unfolding DNA-protein spool under tension is characterized by two angles: the desorption angle $\alpha$ and the tilt angle $\beta$. (b) The energy landscape of a DNA spool [as given by Eq. (1) for $A=50\mathrm{nm}$, $F=4\mathrm{pN}$, and ${\epsilon }_{\mathrm{ads}}=0.7k_{B}T/\mathrm{nm}$] and its unfolding pathway. Note that only states $b$ and $g$ correspond to (meta)stable states.

Figure 2

Kinetic barriers opposing DNA-spool unfolding as a function of applied tension computed for (a) the nucleosome ($R=4.2\mathrm{nm}$, $H=2.4\mathrm{nm}$, ${\epsilon }_{\mathrm{ads}}^0=0.7k_{B}T/\mathrm{nm}$, and $A=50k_{B}T/\mathrm{nm}$; cf. the text) for various interstrand repulsion energy densities ${\epsilon }_{\mathrm{es}}$, and, for (b) the DNA toroid ($R=50\mathrm{nm}$, $H=2.4\mathrm{nm}$, and $A=40k_{B}T/\mathrm{nm}$) for various adsorption energy densities ${\epsilon }_{\mathrm{ads}}$.

Figure 3

Optimal fits of the DFS data from Ref. 14 for various attempt frequencies give the corresponding electrostatic DNA-DNA repulsion ${\epsilon }_{\mathrm{es}}$.