Rotational response of a DNA-bead tether.

<p><b>A</b> The response of a DNA-bead tether subject to a rotating external magnet pair (frequency of rotation ω_mag) that is misaligned with respect to the axis of rotation of the magnet pair and for which the DNA attachment position is eccentric, is a combination of a precessional motion with radius, R_prec and frequency ω = 2ω_mag (panel I) and a rotational motion around the DNA attachement point with radius, R_att and frequency ω = ω_mag (panel II). The bi-circular rotation pattern describes a roulette that is a special case of the epitrochoid: the Limaçon (panel III). <b>B</b> Measurement of the rotational response for a DNA-bead tether at different positions in the field of view The * denotes the position of the rotation axis of the magnet. For clarity in presentation, the patterns were scaled up by a factor 37.5 compared to the scale of the field of view. <b>C</b> R_att and R_prec as function of the distance of the tether position to the center of the magnet. R_att is independent of the position of the tether in the field of view, as expected. R_prec increases with the distance to the center of the magnet. Red line is prediction based on calculations of the 3D force field (as in Fig. 2).