Calibration of TPM: Theory

To gain more confidence in our understanding of the apparatus and analysis, we compared our experimental calibration curve to one we generated from a mathematical model of the system, following [1, 2]. The root-mean-square excursion of the projected bead location away from its tether point is controlled by various competing effects: (i) In the absence of any bead or wall, the chain’s endpoint would execute 3D Brownian motion subject to a restoring force from the tether. (ii) But the bead’s rotatory Brownian motion implies that its center, which is what we observe, lies a considerable distance away from the chain endpoint. (iii) The bead–wall exclusion pushes the bead upward, reducing its transverse excursions. To account for all these effects, we modified the Gaussian sampling Monte Carlo technique previously used in [1, 2, 3] (see supplement). Our code generated many simulated DNA chains and bead orientations, applied the steric constraints [1], and reported the RMS deviation of the bead center from the attachment point. We applied a correction to this theoretical result, to account for the bead’s motion during the rather long shutter time (about 31msec, see supplement). Fig. 1 shows that an a priori calculation of the expected motion matches the data fairly well. The remaining discrepancy with our data may reflect unremoved instrumental drift, for example high-frequency motion that our Butterworth filter cannot distinguish from true Brownian motion. The variance of such noise would add in quadrature with the true Brownian motion.