to vibrations of the experimental apparatus, which we removed using a first order Butterworth filter at 0.05Hz cutoff frequency [@Vanzi2006]. To quantify bead excursion, we then used the square root of the sum of the variances of the drift corrected particle position $(x, y)$ along two orthogonal image-plane axes: $$\text{RMS}_{t} = \sqrt{{\langle (x-\bar{x})^2 + (y-\bar{y})^2\rangle}_{t}}
.\label{eq:rms}$$ Here $t$ is the time interval over which the RMS motion is measured (typically 4s); $\bar{x}$ and $\bar{y}$ represent the average of $x$ and $y$ over time $t$. is evaluated as a sliding filter at each point along the trajectory, and permits us to capture the tether dynamics using a single scalar quantity, as illustrated in below. The finite-sample means $\bar x, \bar y$ are subtracted as an additional method of eliminating instrumental drift not removed by the Butterworth filter; in practice, this subtraction has little effect. When simulating the motion numerically, we will compute the same quantity as , in order to make an appropriate comparison.

Data selection criteria
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Although single-particle tracking data can reveal detailed features of the dynamics of protein-DNA interactions, care must be taken to minimize experimental artifacts such as non-specific binding of the bead and DNA to each 