a function of applied tensile force in the femtonewton range. The DNA samples used in this study were prepared in a similar way to that of other TPM experiments [9]. We surface-tethered a 1316-bp ds-DNA molecule with two symmetric lac operators spaced 305 bp apart and then attached an 800 nm polystyrene microsphere to the other end, which was trapped within the linear regime of the optical potential. The total tension in the DNA was carefully calibrated to account for the applied optical force [9] and volume exclusion effects arising from entropic interactions between the microsphere and the coverslip [10]. The looping and unlooping lifetimes were measured under four different forces: 60 ( ± 5), 78 ( ± 6), 121 ( ± 9), and 183 ( ± 15) fN in the presence of 100 pM of LacI protein. In each measurement, the surface-tethered ds-DNA molecule was stretched by a contant force while the CCD camera captured defocused images of the tethered microsphere at a frame rate of 100 fps. The looped and unlooped states of the DNA molecule, which correspond to different axial positions of the microsphere, can be measured by analyzing the resulting images, as shown in Fig. 1b. By directly observing changes in the axial position of the microsphere, the temporal resolution for detecting loop formation and breakdown events in our experiment is as low as 300 ms, an order of magnitude better than conven- tional TPM. However, as we decrease the applied tension, it becomes increasingly difficult to resolve changes in the size of the microsphere, and at zero optical force, we must resort to conventional TPM. Moreover, even in the absence of an optical force, a residual entropic force from excluded volume effects remains. For this reason, we were not able to obtain a direct measure of the force free loop formation and breakdown rates. The data was analyzed by first extracting the elapsed times between loop formation and breakdown events from time traces like the one in Fig. 1b. Then, for each force condition, the lifetime of each state was determined from a fit to the cumulative probability distribution, as shown in Fig. 2. The resulting distribution displayed by the looped state is well fit by a single exponential function with time constant τ . However, the data of the unlooped state is poorly fit to a single exponential function, but is well fit to a biexponential function with time constants τ$_{1}$ and τ$_{2}$ , and dimensionless fitting parameter c . Results of the fits are 4 P$_{2}$ ( t ; τ$_{1}$, τ$_{2}$ ) = cP ( t ; τ$_{1}$ ) + (1 − c ) P ( t ; τ$_{2}$ ) , (2) P ( t ; τ ) = 1 − e − $^{t/τ}$, (1)