detectable change in tether length. Sensitive measurements may also allow detection of more subtle changes, such as kinking of the DNA upon protein binding or multiple loop topologies.

![\[fig:calibration\] RMS excursion of bead as a function of the tether length for different sized microspheres, . Each red square is the average of equilibrium amplitude of RMS motion over 20 to 200 qualified beads, which is calculated by using with $t = 5\,$s for $R = 100\,$nm (bottom data set), $t = 10\, $s for $R = 245\, $nm (middle data set) and $t = 20\,$s for $R = 485\, $nm (top data set). Using $t=4\,\sunit$ for the same data systematically underestimates the motion of larger beads (green circles). The curves are empirical polynomial fits to the datasets(see Table \[tab:fit\]). ](calibrationfigPN/cali-curve-eq4sclean1.eps "fig:"){width="4truein"} ![\[fig:calibration\] RMS excursion of bead as a function of the tether length for different sized microspheres, . Each red square is the average of equilibrium amplitude of RMS motion over 20 to 200 qualified beads, which is calculated by using with $t = 5\,$s for $R = 100\,$nm (bottom data set), $t = 10\, $s for $R = 245\, $nm (middle data set) and $t = 20\,$s for $R 