Removal of DNA-bound proteins by DNA twisting

We present a simple model of how local torsional stress in DNA can eject a DNA-bound protein. An estimate of the torque ${\mathrm{\tau }}^{\mathrm{*}}$ required to eject a typical DNA-bound protein is made through a two-state model of the equilibrium between the bound and unbound states of the protein. For the familiar case of a nucleosome octamer bound to double-stranded DNA, we find this critical torque to be $\approx {9k}_{B}T.\mathrm{}$ More weakly bound proteins and large (≈kilobase) loops of DNA are shown to be destabilized by smaller torques of only a few $k_{B}T.\mathrm{}$ We then use our model to estimate the maximum range $R_{\max }$ at which a protein can be removed by a transient source of twisting. We model twist strain propagation along DNA by simple dissipative dynamics in order to estimate $R_{\max }.$ Given twist pulses of the type expected to be generated by RNA polymerase and DNA gyrase, we find $R_{\max }\approx 70$ and 450 bp, respectively, for critical torques of $\approx {2k}_{B}T.\mathrm{}$