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.
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.
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 trap's 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.
We demonstrate an example of 'confocal-tweezers' wherein confocal images and precise optical force measurements,
using photodiodes, are obtained simultaneously in the x-y plane without moving the objective lens. The
optical trap is produced using a 1.064μm cw laser and is combined with Leica's TCS SP5 broadband confocal
microscope to trap and image living cells. The unique method by which the confocal images are created facilitates
the acquisition of images in areas far from the trapping location. In addition, because the scanning process
involves moving galvanic mirrors independently of the objective, the trap is held stable in position and is not
subject to any error in position for the x-y scan.
We have successfully trapped and confocally imaged 80nm gold colloids, 150nm gold colloids and 1μm
polystyrene beads whilst making quantitative measurements of the force applied by the trap on each bead.
To the best of our knowledge this is the first time that anyone has combined precise force measuring optical
tweezers with confocal microscopy. We also discuss some of the technical challenges involved in advancing the
experimental set up to make quantitative force measurements in combination with 3D stacking. Having proven
the potential of this system in 2D, we hope to develop it further to investigate the nano-mechanics of cell division
through the attachment of gold beads to fluorescently labelled organelles in S. pombe yeast cells.
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