such as those in . For very small $\delta t$ we get $S\to 1$. For large $\delta t$, we have $S\to0$.

To predict the experimental data we should thus take the theoretical prediction and correct it by a factor of $S$. This correction is trivial to apply (comes out of the statistical averaging), because $S$ is independent of $\rho_0$. The curves in show that a correction of the form of fits the data well; this correction was applied when drawing the curves in .

Applications to DNA Looping
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![\[fig:loopsensitivity\] Two typical $\Jrmsfour$ trajectories in the presence of Lac repressor, showing events of loop formation and breakdown. Total length of the DNA tether is $L=901\,$bp Operator center to center distance is 325.5bp. ](calibrationfigPN/sensitivity_comp.eps "fig:"){width="4truein"} ![\[fig:loopsensitivity\] Two typical $\Jrmsfour$ trajectories in the presence of Lac repressor, showing events of loop formation and breakdown. Total length of the DNA tether is $L=901\,$bp Operator center to center distance is 325.5bp. ](bitmaps/sensitivity_comp.eps "fig:"){width="4truein"}

One of the key applications of the tethered particle method has been its use in studying DNA looping. Many transcriptional regulatory motifs involve the binding of transcription factors that bind at more than one site simultaneously, forming a loop of the 