Experimental configuration. (a) DNA–microsphere dumbbell geometry. Two microspheres of radii r₁ and r₂ tethered by a molecule of dsDNA of stiffness k_DNA are held in separate optical traps of stiffnesses k₁ and k₂. At a given tension, the molecule is extended by ξ, and the microspheres are displaced from the center of each trap by x₁ and x₂ and separated by a distance R₁₂. (b) Schematic layout of the dual-trap optical tweezers. The linearly polarized light of a 200-mW, 845-nm fiber-coupled laser (DL) (Lumics, Berlin) is magnified and collimated by the first telescope (T1). This beam is split by polarization at the first polarizing beam splitter (PB1). A computer-controlled, motorized half waveplate (WP) allows remote control of the relative power between the beams. The s-polarized beam is deflected by a two-axis piezo-steerable mirror (SM) (Mad City Labs, Madison, WI), whereas the p-polarized beam is deflected by a fixed mirror, and the two beams are then recombined at the second polarizing beam splitter (PB2). A second telescope (T2) provides the final magnification of the beams and images the plane (∗) of the steerable mirror onto the back focal plane of a 1.2 numerical aperture 60× water immersion objective (O1) (Nikon, Melville, NY). The objective focuses the beams to two diffraction-limited spots in the center of a 200-μm-thick fluidics chamber (FC). A second, identical objective (O2) collects the forward scattered light, which is split again by polarization at a third polarizing beam splitter (PB3) and imaged onto two separate position-sensitive photodetectors (PD1 and PD2) (Pacific Silicon Detectors, Westlake Village, CA). A light-emitting diode provides light for Kohler illumination, and the second objective and an additional tube lens image the specimen plane onto a charge-coupled device camera (CM).

Measured and predicted SNR as a function of trap stiffness. (a) SNR for identical, tethered, 860-nm microspheres as measured in the trap 1 (green diamonds) and trap 2 (orange triangles) coordinates, the difference coordinate (blue circles), and the optimal coordinate (red squares) as the trap stiffnesses are changed. Measurements from six different DNA–microsphere dumbbells are plotted. (b) SNR for an 800-nm microsphere in trap 1 tethered to a 997-nm microsphere in trap 2 as the trap stiffnesses are changed. The coordinates are labeled as in a. Measurements from four different DNA tethers are plotted. The slight increase in SNR_opt in a over that in b reflects the fact that γ_eff is smaller for two 860-nm microspheres than for one 800-nm and one 997-nm microsphere. The displayed SNR are scaled by the square-root of the measurement bandwidth divided by the step size as in Fig. 2, and the patterned areas are 1-σ confidence regions for the predicted SNR (Eqs. 3, 6, and 8).

Measured and predicted SNR for two tethered, 860-nm microspheres in traps of equal stiffness as a function of the DNA stiffness. The data and predictions are scaled by the square-root of the bandwidth divided by the step size and thus correspond to the SNR for a 1-nm step on a 1-Hz bandwidth. The SNR measured in the optimal coordinate (red squares) (also the difference coordinate) increases linearly with DNA stiffness, whereas the SNR measured in the single-trap coordinate (green diamonds) saturates. To reflect the uncertainty in the experimental parameters, the predicted SNR (Eqs. 3 and 8) are plotted as shaded, 1-σ confidence intervals. The observed spread in the data is dominated not by measurement error but by the inherent stochasticity in finite measurements of spatial resolution. Disagreement between measured and predicted SNR at high DNA stiffness results from systematic errors due to nonlinearities in the traps at high force. Data from six DNA–microsphere dumbbells are plotted, with one of three data points displayed.

Improvement in spatial resolution from dual-trap detection. (a) Observed displacements for two 860-nm microspheres tethered by 3.4-kb dsDNA at a tension of 7.3 ± 0.1 pN as the distance between the traps is increased by 3.4 Å every 2 s. The displacement of the microsphere in trap 1 (lower trace) and the optimal coordinate (upper trace) are filtered with a sliding boxcar filter to 100 Hz (gray traces) and to 2 Hz (blue for the lower trace and red for the upper trace). (b) Pairwise distance histogram for the optimal coordinate in a averaged to 2 Hz. Peaks corresponding to the distance between each of the seven steps confirm the presence of these steps. (c) Similar peaks are not present in the pairwise distance histogram for the displacement of a single microsphere. The observed signals in the optimal coordinate are ≈2.3 Å, smaller than the 3.4 Å changes in the trap separation, as expected for finite trap stiffness (see Supporting Text).