Two-Dimensional Tracking of ncd Motility by Back Focal Plane Interferometry

Abstract

A technique for detecting the displacement of micron-sized optically trapped probes using far-field interference is introduced, theoretically explained, and used to study the motility of the ncd motor protein. Bead motions in the focal plane relative to the optical trap were detected by measuring laser intensity shifts in the back-focal plane of the microscope condenser by projection on a quadrant diode. This detection method is two-dimensional, largely independent of the position of the trap in the field of view and has approximately 10-micros time resolution. The high resolution makes it possible to apply spectral analysis to measure dynamic parameters such as local viscosity and attachment compliance. A simple quantitative theory for back-focal-plane detection was derived that shows that the laser intensity shifts are caused primarily by a far-field interference effect. The theory predicts the detector response to bead displacement, without adjustable parameters, with good accuracy. To demonstrate the potential of the method, the ATP-dependent motility of ncd, a kinesin-related motor protein, was observed with an in vitro bead assay. A fusion protein consisting of truncated ncd (amino acids 195-685) fused with glutathione-S-transferase was adsorbed to silica beads, and the axial and lateral motions of the beads along the microtubule surface were observed with high spatial and temporal resolution. The average axial velocity of the ncd-coated beads was 230 +/- 30 nm/s (average +/- SD). Spectral analysis of bead motion showed the increase in viscous drag near the surface; we also found that any elastic constraints of the moving motors are much smaller than the constraints due to binding in the presence of the nonhydrolyzable nucleotide adenylylimidodiphosphate.

Calibrating bead displacements in optical tweezers using acousto-optic deflectors

“…13,14 Bead movement is often detected using back-focal-plane ͑BFP͒ interferometry. 15,16 In this method, the intensity distribution of the trapping laser in the BFP of the condenser ͑typically͒ used to collect the laser light downstream from the trap is imaged on a quadrant photodiode ͑QPD͒. The normalized difference signals from the quadrants depend linearly on the lateral displacement of the bead in the plane normal to the optical axis close to the trap center.…”

“…A widely used method to measure the detector calibration factor consists of moving a fixed bead over a known distance across the laser beam waist, while recording the signals from the QPD. [16][17][18][19] Apart from the advantage of a direct measurement, this method also has several disadvantages: ͑i͒ calibration is usually not performed with the same bead and not at the same position in the sample as the actual experiment, the latter being especially important when the focus gets distorted with increasing distance from the surface due to spherical aberration; 20,21 ͑ii͒ it is critical, but difficult in practice, to position the fixed calibration bead correctly with respect to the laser in x , y, and z directions; and ͑iii͒ the proximity of the cover slip could influence the measured response.…”

Twin optical traps for two-particle cross-correlation measurements: Eliminating cross-talk

“…Twin optical traps with one laser Figure 1 shows a sketch of our custom-built inverted microscope 13,31 which is equipped with two optical traps. We use a linearly polarized near infrared laser ͑ND: YV0 4 cw, = 1064 nm, maximum power= 4 W, Compass, Coherent Inc., Santa Clara, CA͒, protected against back reflections to enhance stability with an optical isolator ͑OI͒ ͑37 dB isolation, Optics for Research, Caldwell, NJ͒.…”

Extending the bandwidth of optical-tweezers interferometry

“…7 The signals were then digitized with an analog-to-digital conversion board sampling at 195 kHz per channel ͑AD16 board on a ChicoPlus PC-card, Innovative Integration, Simi Valley, CA͒. This board is based on ⌺⌬ technology; hence, no external anti-alias filters were needed.…”

“…Tied to momentum transfer to the particle is an equal and opposite change of momentum ͑i.e., primarily a change of the angular distribution͒ in the light beam which can be used to measure the exerted force or the particle displacement. [5][6][7] Using segmented photodiodes, displacement and force can be measured with nanometer and piconewton resolution. The technique has in principle a wide bandwidth, from hours ͑limited by the mechanical drift of the instrument͒ down to microseconds ͑limited by shot noise and electronics͒.…”