Stephen Keen

Measuring the accuracy of particle position and force in optical tweezers using high-speed video microscopy

We assess the performance of a CMOS camera for the measurement of particle position within optical tweezers and the associated autocorrelation function and power spectrum. Measurement of the displacement of the particle from the trap center can also be related to the applied force. By considering the Allan variance of these measurements, we show that such cameras are capable of reaching the thermal limits of nanometer and femtonewton accuracies, and hence are suitable for many of the applications that traditionally use quadrant photodiodes. As an example of a multi-particle measurement we show the hydrodynamic coupling between two particles.

Comparison of a high-speed camera and a quadrant detector for measuring displacements in optical tweezers

We compare the performance of a high-speed camera and a quadrant detector for measuring the displacement of micron-sized particles in optical tweezers. For trapping powers up to 100 mW, the standard deviation of the particle displacements measured by the two techniques shows excellent agreement. This comparison also provides a method for calibrating one technique against the other.

Direct measurement of the skew angle of the Poynting vector in a helically phased beam

We measure the local skew angle of the Poynting vector within a helically-phased, exp (il phi), beam using a Shack Hartmann wavefront sensor. It is the skew angle of the Poynting vector with respect to the beam axis that gives rise to the orbital angular momentum of a light beam. We confirm that this skew angle is l/kr, corresponding to an orbital angular momentum of l? per photon. Measurement of orbital angular momentum in this way is an alternative to interferometric techniques giving a non-ambiguous result to both the magnitude and sign of l from a single measurement, without any restriction on the optical bandwidth.

Multipoint viscosity measurements in microfluidic channels using optical tweezers

We demonstrate the technique of multipoint viscosity measurements incorporating the accurate calibration of micron sized particles. We describe the use of a high-speed camera to measure the residual motion of particles trapped in holographic optical tweezers, enabling us to calculate the fluid viscosity at multiple points across the field-of-view of the microscope within a microfluidic system.

Hydrodynamic interactions in two dimensions

We measure hydrodynamic interactions between colloidal particles confined in a thin sheet of fluid. The reduced dimensionality, compared to a bulk fluid, increases dramatically the range of couplings. Using optical tweezers we force a two body system along the eigenmodes of the mobility tensor and find that eigenmobilities change logarithmically with particle separation. At a hundred radii distance, the mobilities for rigid and relative motions differ by a factor of 2, whereas in bulk fluids, they would be practically indistinguishable. A two dimensional counterpart of Oseen hydrodynamic tensor quantitatively reproduces the observed behavior, once the relevant boundary conditions are recognized. These results highlight the importance of dimensionality for transport and interactions in colloidal systems and proteins in biological membranes.

The effect of external forces on discrete motion within holographic optical tweezers

Holographic optical tweezers is a widely used technique to manipulate the individual positions of optically trapped micron-sized particles in a sample. The trap positions are changed by updating the holographic image displayed on a spatial light modulator. The updating process takes a finite time, resulting in a temporary decrease of the intensity, and thus the stiffness, of the optical trap. We have investigated this change in trap stiffness during the updating process by studying the motion of an optically trapped particle in a fluid flow. We found a highly nonlinear behavior of the change in trap stiffness vs. changes in step size. For step sizes up to approximately 300 nm the trap stiffness is decreasing. Above 300 nm the change in trap stiffness remains constant for all step sizes up to one particle radius. This information is crucial for optical force measurements using holographic optical tweezers.

Underdamped modes in a hydrodynamically coupled microparticle system

When micron-sized particles are trapped in a linear periodic array, for example, by using optical tweezers, they interact only through the hydrodynamic forces between them. This couples the motion of the spheres and it has been predicted that an extended system might behave as an elastic medium that could support underdamped propagating waves. In practice, these underdamped modes can be observed only with massive particles in very stiff traps and very low viscosity fluids. We have been able to realize these conditions by trapping water droplets in air. Even with a system of just two particles we were able to observe the coupled oscillatory motion predicted: underdamping of the symmetric (collective) mode and overdamping of the asymmetric (relative) mode.

An exploration of the microrheological environment around the distal ileal villi and proximal colonic mucosa of the possum (Trichosurus vulpecula)

Multiple particle-tracking techniques were used to quantify the thermally driven motion of ensembles of naked polystyrene (0.5 µm diameter) microbeads in order to determine the microrheological characteristics around the gut mucosa. The microbeads were introduced into living ex vivo preparations of the wall of the terminal ileum and proximal colon of the brushtail possum (Trichosurus vulpecula). The fluid environment surrounding both the ileal villi and colonic mucosa was heterogeneous; probably comprising discrete viscoelastic regions suspended in a continuous Newtonian fluid of viscosity close to water. Neither the viscosity of the continuous phase, the elastic modulus (G’) nor the sizes of viscoelastic regions varied significantly between areas within 20 µm and areas more than 20 µm from the villous mucosa nor from the tip to the sides of the villous mucosa. The viscosity of the continuous phase at distances further than 20 µm from the colonic mucosa was greater than that at the same distance from the ileal villous mucosa. Furthermore, the estimated sizes of viscoelastic regions were significantly greater in the colon than in the ileum. These findings validate the sensitivity of the method and call into question previous hypotheses that a contiguous layer of mucus envelops all intestinal mucosa and restricts diffusive mass transfer. Our findings suggest that, in the terminal ileum and colon at least, mixing and mass transfer are governed by more complex dynamics than were previously assumed, perhaps with gel filtration by viscoelastic regions that are suspended in a Newtonian fluid.

DNA visualization in single molecule studies carried out with optical tweezers: Covalent versus non-covalent attachment of fluorophores.

In this study, we investigated the use of the covalent attachment of fluorescent dyes to double-stranded DNA (dsDNA) stretched between particles using optical tweezers (OT) and compared the mechanical properties of the covalently-functionalized chain to that of unmodified DNA and to DNA bound to a previously uncharacterized groove-binder, SYBR-gold. Modified DNA species were obtained by covalently linking azide-functionalized organic fluorophores onto the backbone of DNA chains via the alkyne moieties of modified bases that were incorporated during PCR. These DNA molecules were then constructed into dumbbells by attaching polystyrene particles to the respective chain ends via biotin or digoxigenin handles that had been pre-attached to the PCR primers which formed the ends of the synthesized molecule. Using the optical tweezers, the DNA was stretched by separating the two optically trapped polystyrene particles. Displacements of the particles were measured in 3D using an interpolation-based normalized cross-correlation method and force-extension curves were calculated and fitted to the worm-like chain model to parameterize the mechanical properties of the DNA. Results showed that both the contour and persistence length of the covalently-modified dsDNAs were indistinguishable from that of the unmodified dsDNA, whereas SYBR-gold binding perturbed the contour length of the chain in a force-dependent manner.

A Practical Review of Microrheological Techniques

Microrheology is a method for the study of the viscoelastic properties of materials [1, 2]. It has many potential benefits including requiring only microlitres of sample and applying on‐ ly microscopic strains, making it ideal for costly, rare or fragile samples. Ever since the earli‐ est papers began emerging in the biophysical arena some ten to fifteen years ago [3,4], to more current publications [5-8] fascinating insights into the material properties of the cell and its constituent biopolymers have been revealed by microrheological studies. It can ex‐ tract information about the underlying heterogeneities in soft materials of interest, and can measure viscoelastic properties to high frequencies compared to traditional rheological measurements [9]. This paper reviews the limits of speed and accuracy achievable with cur‐ rent advances in instrumentation, such as state-of-the-art correlators and cameras, by direct‐ ly comparing different methodologies and equipment.