Arnau Farré

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ · β (where κ is the trap stiffness and 1/β is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

A force detection technique for single-beam optical traps based on direct measurement of light momentum changes

Despite the tremendous success of force-measuring optical traps in recent years, the calibration methods most commonly used in the field have been plagued with difficulties and limitations. Force sensing based on direct measurement of light momentum changes stands out among these as an exception. Especially significant is this methods potential for working within living cells, with non-spherical particles or with non-Gaussian beams. However, so far, the technique has only been implemented in counter-propagating dual-beam traps, which are difficult to align and integrate with other microscopy techniques. Here, we show the feasibility of a single-beam gradient-trap system working with a force detection technique based on this same principle.

Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers.

The well calibrated force-extension behaviour of single double-stranded DNA molecules was used as a standard to investigate the performance of phase-only holographic optical tweezers at high forces. Specifically, the characteristic overstretch transition at 65 pN was found to appear where expected, demonstrating (1) that holographic optical trap calibration using thermal fluctuation methods is valid to high forces; (2) that the holographic optical traps are harmonic out to >250 nm of 2.1 mum particle displacement; and (3) that temporal modulations in traps induced by the spatial light modulator (SLM) do not affect the ability of optical traps to hold and steer particles against high forces. These studies demonstrate a new high-force capability for holographic optical traps achievable by SLM technologies.

Positional stability of holographic optical traps

The potential of digital holography for complex manipulation of micron-sized particles with optical tweezers has been clearly demonstrated. By contrast, its use in quantitative experiments has been rather limited, partly due to fluctuations introduced by the spatial light modulator (SLM) that displays the kinoforms. This is an important issue when high temporal or spatial stability is a concern. We have investigated the performance of both an analog-addressed and a digitally-addressed SLM, measuring the phase fluctuations of the modulated beam and evaluating the resulting positional stability of a holographic trap. We show that, despite imparting a more unstable modulation to the wavefront, our digitally-addressed SLM generates optical traps in the sample plane stable enough for most applications. We further show that traps produced by the analog-addressed SLM exhibit a superior pointing stability, better than 1 nm, which is comparable to that of non-holographic tweezers. These results suggest a means to implement precision force measurement experiments with holographic optical tweezers (HOTs).

Understanding Optical Trapping Phenomena: A Simulation for Undergraduates

Optical trapping is an attractive and multidisciplinary topic that has become the center of attention to a large number of researchers. Moreover, it is a suitable subject for advanced students that requires a knowledge of a wide range of topics. As a result, it has been incorporated into some syllabuses of both undergraduate and graduate programs. In this paper, basic concepts in laser trapping theory are reviewed. To provide a better understanding of the underlying concepts for students, a Java application for simulating the behavior of a dielectric particle trapped in a highly focused beam has been developed. The program illustrates a wide range of theoretical results and features, such as the calculation of the force exerted by a beam in the Mie and Rayleigh regimes or the calibration of the trap stiffness. Some examples that are ready to be used in the classroom or in the computer lab are also supplied.

Measuring stall forces in vivo with optical tweezers through light momentum changes

The stall forces of processive molecular motors have been widely studied previously in vitro. Even so, in vivo experiments are required for determining the actual performance of each molecular motor in its natural environment. We report the direct measurement of light momentum changes in single beam optical tweezers as a suitable technique for measuring forces inside living cells, where few alternatives exist. The simplicity of this method, which does not require force calibration for each trapped object, makes it convenient for measuring the forces involved in fast dynamic biological processes such us intracellular traffic. Here we present some measurements of the stall force of processive molecular motors inside living Allium cepa cells.

Extending calibration-free force measurements to optically-trapped rod-shaped samples

Optical trapping has become an optimal choice for biological research at the microscale due to its non-invasive performance and accessibility for quantitative studies, especially on the forces involved in biological processes. However, reliable force measurements depend on the calibration of the optical traps, which is different for each experiment and hence requires high control of the local variables, especially of the trapped object geometry. Many biological samples have an elongated, rod-like shape, such as chromosomes, intracellular organelles (e.g., peroxisomes), membrane tubules, certain microalgae, and a wide variety of bacteria and parasites. This type of samples often requires several optical traps to stabilize and orient them in the correct spatial direction, making it more difficult to determine the total force applied. Here, we manipulate glass microcylinders with holographic optical tweezers and show the accurate measurement of drag forces by calibration-free direct detection of beam momentum. The agreement between our results and slender-body hydrodynamic theoretical calculations indicates potential for this force-sensing method in studying protracted, rod-shaped specimens.

Holographic optical tweezers combined with back-focal-plane displacement detection

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Artificially-induced organelles are optimal targets for optical trapping experiments in living cells

Optical trapping supplies information on the structural, kinetic or rheological properties of inner constituents of the cell. However, the application of significant forces to intracellular objects is notoriously difficult due to a combination of factors, such as the small difference between the refractive indices of the target structures and the cytoplasm. Here we discuss the possibility of artificially inducing the formation of spherical organelles in the endoplasmic reticulum, which would contain densely packed engineered proteins, to be used as optimized targets for optical trapping experiments. The high index of refraction and large size of our organelles provide a firm grip for optical trapping and thereby allow us to exert large forces easily within safe irradiation limits. This has clear advantages over alternative probes, such as subcellular organelles or internalized synthetic beads.

Holographic optical manipulation of motor-driven membranous structures in living NG-108 cells

Optical tweezer experiments have partially unveiled the me- chanical properties of processive motor proteins while driving polysty- rene or silica microbeads in vitro. However, the set of forces underlying the more complex transport mechanisms in living samples remains poorly understood. Several studies have shown that optical tweezers are capable of trapping vesicles and organelles in the cytoplasm of living cells, which can be used as handles to mechanically interact with en- gaged active motors, or other components regulating transport. This may ultimately enable the exploration of the mechanics of this trafficking mechanism in vivo. These cell manipulation experiments have been car- ried out using different strategies to achieve dynamic beam steering ca- pable of trapping these subcellular structures. We report here the first trapping and manipulation, to our knowledge, of such small motor- propelled cargos in living cells using holographic technology.