Frederick Gittes

Interference model for back-focal-plane displacement detection in optical tweezers

The lateral position of an optically trapped object in a microscope can be monitored with a quadrant photodiode to within nanometers or better by measurement of intensity shifts in the back focal plane of the lens that is collimating the outgoing laser light. This detection is largely independent of the position of the trap in the field of view. We provide a model for the essential mechanism of this type of detection, giving a simple, closed-form analytic solution with simplifying assumptions. We identify intensity shifts as first-order far-field interference between the outgoing laser beam and scattered light from the trapped particle, where the latter is phase advanced owing to the Gouy phase anomaly. This interference also reflects momentum transfer to the particle, giving the spring constant of the trap. Our response formula is compared with the results of experiments.

Laser-Induced Heating in Optical Traps

In an optical tweezers experiment intense laser light is tightly focused to intensities of MW/cm(2) in order to apply forces to submicron particles or to measure mechanical properties of macromolecules. It is important to quantify potentially harmful or misleading heating effects due to the high light intensities in biophysical experiments. We present a model that incorporates the geometry of the experiment in a physically correct manner, including heat generation by light absorption in the neighborhood of the focus, balanced by outward heat flow, and heat sinking by the glass surfaces of the sample chamber. This is in contrast to the earlier simple models assuming heat generation in the trapped particle only. We find that in the most common experimental circumstances, using micron-sized polystyrene or silica beads, absorption of the laser light in the solvent around the trapped particle, not in the particle itself, is the most important contribution to heating. To validate our model we measured the spectrum of the Brownian motion of trapped beads in water and in glycerol as a function of the trapping laser intensity. Heating both increases the thermal motion of the bead and decreases the viscosity of the medium. We measured that the temperature in the focus increased by 34.2 +/- 0.1 K/W with 1064-nm laser light for 2200-nm-diameter polystyrene beads in glycerol, 43.8 +/- 2.2 K/W for 840-nm polystyrene beads in glycerol, 41.1 +/- 0.7 K/W for 502-nm polystyrene beads in glycerol, and 7.7 +/- 1.2 K/W for 500-nm silica beads and 8.1 +/- 2.1 K/W for 444-nm silica beads in water. Furthermore, we observed that in glycerol the heating effect increased when the bead was trapped further away from the cover glass/glycerol interface as predicted by the model. We show that even though the heating effect in water is rather small it can have non-negligible effects on trap calibration in typical biophysical experimental circumstances and should be taken into consideration when laser powers of more than 100 mW are used.

Microscopic Viscoelasticity: Shear Moduli of Soft Materials Determined from Thermal Fluctuations

We describe a high-resolution, high-bandwidth technique for determining the local viscoelasticity of soft materials such as polymer gels. Loss and storage shear moduli are determined from the power spectra of thermal fluctuations of embedded micron-sized probe particles, observed with an interferometric microscope. This provides a passive, small-amplitude measurement of rheological properties over a much broader frequency range than previously accessible to microrheology. We study both F-actin biopolymer solutions and polyacrylamide (PAAm) gels, as model semiflexible and flexible systems, respectively. We observe high-frequency

TWO-DIMENSIONAL TRACKING OF NCD MOTILITY BY BACK FOCAL PLANE INTERFEROMETRY

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Signals and noise in micromechanical measurements.

scaling of the shear modulus in F-actin solutions, in contrast to

Thermal noise limitations on micromechanical experiments

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DIRECTIONAL LOADING OF THE KINESIN MOTOR MOLECULE AS IT BUCKLES A MICROTUBULE

scaling for PAAm.

Optical trapping near resonance absorption

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.

Metastable intermediates in the condensation of semiflexible polymers.

Publisher Summary This chapter discusses the signals and noise in micromechanical measurements. A variety of single-molecule experiments, ranging from optical tweezers and scanned-tip microscopies to single-molecule fluorescence methods, have recently begun to explore the new territory. Researchers are faced with a multitude of challenging problems, one of which is noise that sets limits on the resolution of single-molecule measurement. Instrumentation must be designed with enough stability to make measurements on nm-length scales, and a thorough understanding of the subtleties of data analysis is necessary to push the limits of detection and to avoid artifacts. The chapter discusses noise issues mainly in the context of optical tweezers experiments, but much of the discussion applies to other micromechanical experiments as well. Optical tweezers, also known as laser trapping, is a micromechanical technique that is finding increasing use in a broad spectrum of experiments in biology. Optical trapping of particles uses the momentum transfer from light scattered or diffracted by an object immersed in a medium with an index of refraction different from its own.

Counting cell nuclei with random sections: The effect of shape and size

Abstract Thermal motions of microscopic probes limit the possibilities of experiments that are designed to resolve single-macromolecule dynamics in aqueous conditions. We investigate theoretical strategies for maximizing signal-to-noise ratios or resolution in typical situations, illustratin+g our discussion with examples from optical tweezers and atomic force microscopy experiments. A central result is that the viscous drag on a micromechanical probe is more important than the compliance of the probe. Within limits, increased stiffness of an AFM cantilever or of an optical trap does not increase resolution, and decreased stiffness does not provide the possibility of less invasive measurements.