of the RMS-filtered trajectory for various values of window size $t$ (see ). Here $\langle\ldots \rangle$ denotes two averages: (1) over the $(200\,\sunit/t) $ windows that make up each bead’s time series, and (2) over nominally identical tethered particles with the same bead size and tether length. The DNA lengths varied from 199bp to 2625bp, and we tested beads with three different diameters: 200nm, 490nm and 970nm.

![\[fig:winsize\] *Top:* Average RMS excursion and *bottom:* standard deviation of $\Jrmst$ as functions of window time $t$ in for different bead sizes (columns) and lengths $L$ of the DNA tether (colored lines). As discussed in the text, black dotted lines indicate “large enough” choices of $t$.](calibrationfigPN/winsize-motionallclean1.eps "fig:"){width="4.4truein"} ![\[fig:winsize\] *Top:* Average RMS excursion and *bottom:* standard deviation of $\Jrmst$ as functions of window time $t$ in for different bead sizes (columns) and lengths $L$ of the DNA tether (colored lines). As discussed in the text, black dotted lines indicate “large enough” choices of $t$.](bitmaps/winsize-motionallclean1.eps "fig:"){width="4.4truein"}

Calibration of motion
---------------------

In order for TPM experiments to detect discrete conformational changes of biopolymers such as in DNA looping, it is necessary to quantify how tether length affects particle motion. Precise calibration data also indicates the minimum 