Andrew C. Richardson

Three-dimensional optical control of individual quantum dots

We show that individual colloidal CdSe-core quantum dots can be optically trapped and manipulated in three dimensions by an infrared continuous wave laser operated at low laser powers. This makes possible utilizing quantum dots not only for visualization but also for manipulation, an important advantage for single molecule experiments. Moreover, we provide quantitative information about the magnitude of forces applicable to a single quantum dot and of the polarizability of an individual quantum dot.

Quantifying Noise in Optical Tweezers by Allan Variance

Much effort is put into minimizing noise in optical tweezers experiments because noise and drift can mask fundamental behaviours of, e.g., single molecule assays. Various initiatives have been taken to reduce or eliminate noise but it has been difficult to quantify their effect. We propose to use Allan variance as a simple and efficient method to quantify noise in optical tweezers setups.We apply the method to determine the optimal measurement time, frequency, and detection scheme, and quantify the effect of acoustic noise in the lab. The method can also be used on-the-fly for determining optimal parameters of running experiments.

Active-passive calibration of optical tweezers in viscoelastic media

In order to use optical tweezers as a force measuring tool inside a viscoelastic medium such as the cytoplasm of a living cell, it is crucial to perform an exact force calibration within the complex medium. This is a nontrivial task, as many of the physical characteristics of the medium and probe, e.g., viscosity, elasticity, shape, and density, are often unknown. Here, we suggest how to calibrate single beam optical tweezers in a complex viscoelastic environment. At the same time, we determine viscoelastic characteristics such as friction retardation spectrum and elastic moduli of the medium. We apply and test a method suggested [M. Fischer and K. Berg-Sørensen, J. Opt. A, Pure Appl. Opt. 9, S239 (2007)], a method which combines passive and active measurements. The method is demonstrated in a simple viscous medium, water, and in a solution of entangled F-actin without cross-linkers.

Quantitative determination of optical trapping strength and viscoelastic moduli inside living cells

With the success of in vitro single-molecule force measurements obtained in recent years, the next step is to perform quantitative force measurements inside a living cell. Optical traps have proven excellent tools for manipulation, also in vivo, where they can be essentially non-invasive under correct wavelength and exposure conditions. It is a pre-requisite for in vivo quantitative force measurements that a precise and reliable force calibration of the tweezers is performed. There are well-established calibration protocols in purely viscous environments; however, as the cellular cytoplasm is viscoelastic, it would be incorrect to use a calibration procedure relying on a viscous environment. Here we demonstrate a method to perform a correct force calibration inside a living cell. This method (theoretically proposed in Fischer and Berg-Sørensen (2007 J. Opt. A: Pure Appl. Opt. 9 S239)) takes into account the viscoelastic properties of the cytoplasm and relies on a combination of active and passive recordings of the motion of the cytoplasmic object of interest. The calibration procedure allows us to extract absolute values for the viscoelastic moduli of the living cell cytoplasm as well as the force constant describing the optical trap, thus paving the way for quantitative force measurements inside the living cell. Here, we determine both the spring constant of the optical trap and the elastic contribution from the cytoplasm, influencing the motion of naturally occurring tracer particles. The viscoelastic moduli that we find are of the same order of magnitude as moduli found in other cell types by alternative methods.

Non-harmonic potential of a single beam optical trap

Since the invention of optical traps based on a single laser beam, the potential experienced by a trapped specimen has been assumed harmonic, in the central part of the trap. It has remained unknown to what extent the harmonic region persists and what occurs beyond. By employing a new method, we have forced the trapped object to extreme positions, significantly further than previously achieved in a single laser beam, and thus experimentally explore an extended trapping potential. The potential stiffens considerably as the bead moves to extreme positions and therein is not well described by simple Uhlenbeck theories.

Significant improvement of optical traps by tuning standard water immersion objectives

Focused infrared lasers are widely used for micromanipulation and visualization of biological specimens. An inherent practical problem is that off-the-shelf commercial microscope objectives are designed for use with visible and not infrared wavelengths. Less aberration is introduced by water immersion objectives than by oil immersion ones, however, even water immersion objectives induce significant aberration. We present a simple method to reduce the spherical aberration induced by water immersion objectives, namely by tuning the correction collar of the objective to a value that is ∼10% lower than the physical thickness of the coverslip. This results in marked improvements in optical trapping strengths of up to 100% laterally and 600% axially from a standard microscope objective designed for use in the visible range. The results are generally valid for any water immersion objective with any numerical aperture.

Quantifying and pinpointing sources of noise in optical tweezers experiments

One limitation on the performance of optical traps is the noise inherently present in every setup. Therefore, it is the desire of most experimentalists to minimize and possibly eliminate noise from their optical trapping experiments. A step in this direction is to quantify the actual noise in the system and to evaluate how much each particular component contributes to the overall noise. For this purpose we present Allan variance analysis as a straightforward method. In particular, it allows for judging the impact of drift which gives rise to low-frequency noise, which is extremely difficult to pinpoint by other methods. We show how to determine the optimal sampling time for calibration, the optimal number of data points for a desired experiment, and we provide measurements of how much accuracy is gained by acquiring additional data points. Allan variances of both micrometersized spheres and asymmetric nanometer-sized rods are considered.One limitation on the performance of optical traps is the noise inherently present in every setup. Therefore, it is the desire of most experimentalists to minimize and possibly eliminate noise from their optical trapping experiments. A step in this direction is to quantify the actual noise in the system and to evaluate how much each particular component contributes to the overall noise. For this purpose we present Allan variance analysis as a straightforward method. In particular, it allows for judging the impact of drift which gives rise to low-frequency noise, which is extremely difficult to pinpoint by other methods. We show how to determine the optimal sampling time for calibration, the optimal number of data points for a desired experiment, and we provide measurements of how much accuracy is gained by acquiring additional data points. Allan variances of both micrometer-sized spheres and asymmetric nanometer-sized rods are considered.

Validation of FDT calibration method in complex media

Optical tweezers constitute an obvious choice as the experimental technique for manipulation and trapping of organelles in living cells. For quantitative determination of the forces exerted in such in vivo systems, however, tools for reliable calibration of the optical tweezers are required. This is complicated by the fact that the viscoelastic properties of the cytoplasm are a priori unknown. We elaborate on a previously reported theoretical calibration procedure and verify its authenticity experimentally. With this approach, we may at the same time determine the trapping characteristics of the optical tweezers and the viscoelastic properties of the cytoplasm. The method employs the fluctuation-dissipation theorem (FDT) which is assumed valid for the situations considered. This allows for extracting the requested properties from two types of measurements that we denote as passive and active. In the passive part, the Brownian motion of a particle inside the trap is observed. In the active part, the system is slightly perturbed and the response of the trapped particle is tracked. Gently oscillating the stage on which the sample is mounted allows the delay between the position of the stage and the response of the trapped bead, using a quadrant photodiode, to be quantified. No assumptions about the particle radius or geometry or about the frequency-dependent friction coefficient are needed. The paper contains the theoretical background of the method in terms of convenient formulations of the fluctuation-dissipation theorem and application of the method in two types of experiments. Further we discuss experimental concerns which are i) the choice of driving characteristics in the active part of the calibration procedure and ii) statistical errors.

Extending the lateral trapping force of optical tweezers

By increasing the axial trap stiffness, we demonstrate an increase of at least 50% in the maximum lateral trapping force that can be applied using optical tweezers. It has previously been shown that, using a novel method of compensating for spherical aberrations, the axial trap stiffness at any particular chosen depth within a sample can be increased. However, to our knowledge, the present paper is the first time this method has been used in combination with the drag force method for the purpose of more accurately determining the maximum lateral trapping force applicable by optical tweezers. Previous studies have substantially shown that before the actual maximum lateral trapping force can be reached, the particle escapes in the axial direction. Using a conventional setup, our studies support this conclusion. However, by employing the above mentioned method for improving the axial trap stiffness, we observed that the displacement of the bead in the lateral direction is increased by approximately 10%. This allows progress towards a more accurate determination of the maximum lateral force that can be applied using optical tweezers and could also permit a mapping of the trapping potential further from the traps central region. Theoretical predictions made, show that the point where the maximum lateral force could be applied is at 0.9 a, where a is the radius of the trapped particle. However, the experimentally measured limit 0.55 a has until now been far lower than that theoretically predicted 0.9 a. In this proceeding, we demonstrate that the experimental limit can be extended to 0.61 a because of the decreased axial displacement of the bead.