subsets labeled by $i=1,\ldots10$. In subset $i$, we calculate $\Jrmsfour$ over each 4s window and then average these, defining $A_{i}\equiv\langle\text{RMS}_\mathrm{4\,s}\rangle_i$. Then we define $u$ as the standard deviation of $\{A_1,\ldots A_{10}\}$, normalized by the overall average $\Jrmsfour$. Only data sets with relative standard deviation $u<0.2$ are accepted. For example, the bead shown in (c) meets the motion and symmetry criterions; however, it displays a non-specific binding event at $~30\sunit$. In short, our third criterion removes tethers with temporal inconsistency in their Brownian motion.

The first two selection criteria discard tethers that are permanently defective, whereas the third eliminates time series with undesirable transient events. Note that if the purpose of the experiment is to identify interesting molecular binding events, such as those leading to DNA looping or bending, then the last criterion cannot be applied, because these transient events can appear similar to the sticking events rejected by the uniformity criterion. In the present work we aimed at characterizing uniform DNA tethers, so we enforced all three criteria. Prior to applying the selection criteria, (f) displays a broad distribution in the measured $\Jrmsfour$ (red). Afterwards, $\sim50\%$ of the data are qualified and exhibit well-defined Brownian motion (green bars). This figure 