plot of the trajectory in (a) shows it to be symmetric. (e) Scatter plot of the motion in (b) shows it to be asymmetric. The DNA used in (a–e) are 1206bp long and the bead size is 490nm in diameter. (f) Distribution of bead excursions and the number of beads that pass successive application of the selection criteria (see text) [@Blumberg2005]. Red: original data. Cyan: after application of minimal motion filter. Blue: after application of symmetry filter. Green: after application of uniformity filter. The DNA used in (f) are 901bp long and bead size is 490nm diameter. ](bitmaps/selectioneff.eps "fig:"){width="3in"}

“Minimum motion” discards beads that cannot be differentiated from beads stuck to the glass substrate (or otherwise compromised in their mobility). $\Jrmsfour$ from a control experiment with beads but no DNA is shown in (green line), and is substantially smaller than that for a tethered bead (blue line). Data sets exhibiting average excursions, $\Jrmsfour$, lower than 30nm cannot be differentiated from stuck beads and are therefore rejected.

“Motion symmetry” requires that a tethered particle should exhibit symmetric in-plane motion about its anchor point, and is calculated from the covariance matrix [@Blumberg2005; @Nelson2006]: $$C= \begin{pmatrix} \sigma_{x_{1}x_{1}} & \sigma_{x_{1}x_{2}} \\
\sigma_{x_{2}x_{1}} &
\sigma_{x_{2}x_{2}}  