content_image/334737.jpg
<img src='content_image/334737.jpg'>

in the figure, the lifetime of the looped state is independent of the fluctuations. This is consistent with previous findings that the looped state is insensitive to femtonewton forces [7]. The lifetime of the unlooped state, however, is clearly seen to decrease as we increase the fluctuations. At 2 σ , approximately 95% of the noise distribution is accounted for. Since volume exclusion forces are on the order of 35 fN [9], σ = 60 fN or T$_{α}$/T = 0 . 12 are the largest fluctuations we can apply to the DNA without significantly clipping the distribution. 

We fit the cumulative probability distributions using the kinetic scheme detailed in [7] to extract loop dissociation and association lifetimes. In summary, the looped lifetimes are simply fit by a single exponential function parametrized by the looped lifetime τ$_{L}$ : S(t)=1 − exp( − t/τ$_{L}$ ). The unlooped kinetics, however, are more complicated, and may accurately be described by collecting all time intervals beginning with an unlooping event and ending 

