Geometry and symbols used for describing a dual-trap “dumbbell” experiment.
Dual-trap optical tweezers instrument with two detection lasers. Dashed lines indicate optically conjugate planes. Components inside the dotted line are mounted on/inside the microscope body. Trap laser (1064), shutter (SH), lens (L), half-wave plate (HWP), Faraday isolator (FI), polarizing beam-splitter (PBS), single-mode fiber (SMF), output coupler (OC), mirror (M), dichroic mirror (D), objective (OBJ), piezo-electric stage (PZT), condenser (COND), filter (F), position-sensitive photodiode (PD), tube-lens (TL).
Electrical schematic of real-time force-clamp instrument. Data acquisition card (PCI-7833R) with field-programmable gate-array (FPGA) featuring analog-to-digital (ADC) and digital-to-analog (DAC) converters. The signal from a position sensitive photodiode (PD) is amplified (INA111) and low-pass anti-alias filtered (AAF). Digital outputs control digital direct synthesizers (DDS) which drive acousto-optic deflectors (AOD).
A sample chamber (top) was assembled by drilling 1.6 mm holes in a 75 × 25 × 1 mm 3 microscope slide (a) and by glueing 0.25 mm i.d. PEEK tubing (b) to the slide using UV-curing epoxy (Norland NOA81). A 3-lane pattern was then cut into a 200 μm thick double-stick tape spacer (c, Tesa) which was glued to the slide. The chamber was sealed with a 60 × 24 × 0.17 mm 3 coverslip (d, Corning). (bottom) Experiments were performed by trapping beads in channel 1, finding a DNA-tether in channel 2, and performing force-extension and force-clamp experiments in channel 3.
(a) Time-series of force-signal, collected at 200 kS/s, during a force-clamp experiment. The set-point force was 6 pN. The proportional gain G P and the integral gain G I were adjusted every 2 s. (b) Histograms of the force remain Gaussian, which indicates harmonic trapping. (c) Time-series of trap position x T2, collected at 200 kS/s, during the force-clamp experiment, and its corresponding histogram (D). The black traces show data low-pass filtered to 100 Hz.
Power spectral densities of force (a), steerable bead position (b), trap position (c), and tether extension (d). The predicted PSD (Eq. (7)) is shown in black and (a) is shown with dashed lines proportional to f 2 and f −2 as a guide to the eye.
(a) Measured force and (b) tether extension during the enzymatic activity of lambda exonuclease. The solid line in (a) shows the force set-point, 3.4 pN, for the force clamp control. The measured force signal is shown both at 2 kHz bandwidth, and low-pass filtered to 100 Hz. (c) Rate of the extension change calculated from time-series in (b) (see text). (d) Histogram of the rates showing an average rate of 9 ± 6 nm/s.
Single-frame excerpt from video recording of force clamp experiment with lamda exonuclease. In the first part of the video a force-extension curve (bottom panel) is obtained using manual control. In the second part, after t = 20 s, the tether is held force clamped at 3.4 pN (force shown in top panel). The video is at normal speed (1X) while the force extension curve is measured. During ∼13 min of force-clamp control the video is sped up 25-fold. The gradual conversion from a double-stranded tether to a single-stranded tether is seen as a decrease in the extension (middle panel). The tether broke at t = 880 s. Scale-bar 5 μm. (enhanced online). [URL: http://dx.doi.org/10.1063/1.3615309.1]10.1063/1.3615309.1
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