Computational modelling has made many useful contributions to the field of optical tweezers. One aspect in which it can be applied is the simulation of the dynamics of particles in optical tweezers. This can be useful for systems with many degrees of freedom, and for the simulation of experiments. While modelling of the optical force is a prerequisite for simulation of the motion of particles in optical traps, non-optical forces must also be included; the most important are usually Brownian motion and viscous drag. We discuss some applications and examples of such simulations. We review the theory and practical principles of simulation of optical tweezers, including the choice of method of calculation of optical force, numerical solution of the equations of motion of the particle, and finish with a discussion of a range of open problems.

Abstractα-catenin is a crucial protein at cell junctions that provides connection between the actin cytoskeleton and the cell membrane. At adherens junctions (AJs), α-catenin forms heterodimers with β-catenin that are believed to resist force on F-actin. Outside AJs, α-catenin forms homodimers that regulates F-actin organization and directly connect the cell membrane to the actin cytoskeleton, but their mechanosensitive properties are inherently unknown. By using ultra-fast laser tweezers we found that a single α-β-catenin heterodimer does not resist force but instead slips along F-actin in the direction of force. Conversely, the action of 5 to 10 α-β-catenin heterodimers together with force applied toward F-actin pointed end engaged a molecular switch in α-catenin, which unfolded and strongly bound F-actin as a cooperative catch bond. Similarly, an α-catenin homodimer formed an asymmetric catch bond with F-actin triggered by protein unfolding under force. Our data suggest that α-catenin clustering together with intracellular tension engage a fluid-to-solid phase transition at the membrane-cytoskeleton interface.

Force measurement with an optical trap requires calibration of it. With a suitable detector, such as a position-sensitive detector (PSD), it is possible to calibrate the detector so that the force can be measured for arbitrary particles and arbitrary beams without further calibration; such a calibration can be called an “absolute calibration”. Here, we present a simple method for the absolute calibration of a PSD. Very often, paired position and force measurements are required, and even if synchronous measurements are possible with the position and force detectors used, knowledge of the force–position curve for the particle in the trap can be highly beneficial. Therefore, we experimentally demonstrate methods for determining the force–position curve with and without synchronous force and position measurements, beyond the Hookean (linear) region of the trap. Unlike the absolute calibration of the force and position detectors, the force–position curve depends on the particle and the trapping beam, and needs to be determined in each individual case. We demonstrate the robustness of our absolute calibration by measuring optical forces on microspheres as commonly trapped in optical tweezers, and other particles such a birefringent vaterite microspheres, red blood cells, and a deformable “blob”.

Optical tweezers are tools made of light that enable contactless pushing, trapping, and manipulation of objects ranging from atoms to space light sails. Since the pioneering work by Arthur Ashkin in the 1970s, optical tweezers have evolved into sophisticated instruments and have been employed in a broad range of applications in life sciences, physics, and engineering. These include accurate force and torque measurement at the femtonewton level, microrheology of complex fluids, single micro- and nanoparticle spectroscopy, single-cell analysis, and statistical-physics experiments. This roadmap provides insights into current investigations involving optical forces and optical tweezers from their theoretical foundations to designs and setups. It also offers perspectives for applications to a wide range of research fields, from biophysics to space exploration.

Exquisite manipulations of light can be performed with devices such as spatial light modulators (SLMs) and digital micromirror devices (DMDs). These devices can be used to simulate transverse paraxial beam wavefunction eigenstates such as the Hermite–Laguerre–Gaussian mode families. We investigate several beam shaping methods in terms of the wavefunctions of scattered light. Our analysis of the efficiency, behaviour and limitations of beam shaping methods is applied to both theory and experiment. The deviation from the ideal output from a valid beam shaping method is shown to be due to experimental factors which are not necessarily being accounted for. Incident beam mode shape, aberration, and the amplitude/phase transfer functions of the DMD and SLM impact the distribution of scattered light and hence the effectiveness and efficiency of a beam shaping method. Correcting for these particular details of the optical system accounts for all differences in efficiency and mode fidelity between experiment and theory. We explicitly show the impact of experimental parameter variations so that these problems may be diagnosed and corrected in an experimental beam shaping apparatus. We show that several beam shaping methods can be used for the production of beam modes in a single pass and the choice is based on the particular experimental conditions.

We demonstrate how optical tweezers combined with a three-dimensional force detection system and high-speed camera are used to study the swimming force and behavior of trapped micro-organisms. By utilizing position sensitive detection, we measure the motility force of trapped particles, regardless of orientation. This has the advantage of not requiring complex beam shaping or microfluidic controls for aligning trapped particles in a particular orientation, leading to unambiguous measurements of the propulsive force at any time. Correlating the direct force measurements with position data from a high-speed camera enables us to determine changes in the particle’s behavior. We demonstrate our technique by measuring the swimming force and observing distinctions between swimming and tumbling modes of the Escherichia coli (E. coli) strain MC4100. Our method shows promise for application in future studies of trappable but otherwise arbitrary-shaped biological swimmers and other active matter.

Cell adhesions dynamically tune their mechanical properties during tissue development and homeostasis. Fluid connections required for cell mobility can switch to solid links to maintain the mechanical rigidity of epithelial layers 1,2 . Changes in the composition and clustering of adhesion molecules have been proposed to modulate cell junction fluidity, but the underlying mechanisms are unclear 3,4 . acatenin has been shown to play a fundamental role in different adhesion sites. At adherens cell-cell junctions (AJ), a-catenin localizes in cadherin-catenin complexes, where it provides a mechanical link between b-catenin and the actin cytoskeleton 5 . However, its function is controversial owing to the low affinity between actin and the a-b-catenin heterodimer 6 . Outside AJ, a-catenin binds itself to form homodimers that connect the cell membrane to the actin cytoskeleton to promote adhesion and migration, but its mechanosensitive properties are inherently unknown 7,8 . Here, using ultra-fast laser tweezers 9 we show that a single mammalian a-catenin molecule displays very different force-bearing properties depending on whether it is associated to b-catenin or not. We found that a single a-b-catenin heterodimer slips along an actin filament in the direction of force, while a single a-catenin homodimer forms a strong asymmetric catch-bond with actin, in which the bond lifetime increases, and the protein unfolds with force. Importantly, assemblies of multiple ab-catenin heterodimers show force-bearing and unfolding properties similar to the acatenin homodimer. Our results indicate that, outside AJ, single a-catenin homodimers act as a mechanical link with the actin cytoskeleton that resists force efficiently. Nonetheless, inside AJ, a-catenin's capability to hold cell-cell connections under physiological loads critically depends on the recruitment of multiple (5-10) complexes. Our data support a molecular model in which a-catenin clustering and intercellular tension engage a fluid-to-solid phase transition at the membranecytoskeleton interface.In any living cell, an array of mechanotransductor proteins responds to mechanical cues to trigger complex molecular signaling, driving cell morphology and gene expression profiles 10 . Among these proteins, a-catenin has been reported to act as a mechanosensor that regulates adherens junctions (AJ) in response to mechanical cues from neighboring cells in a tissue 5 . It is widely accepted that a-catenin in AJ binds b-catenin, which, in turn, connects to the cytoplasmatic portion of E-cadherin to constitute the cadherin-catenin complex (CCC). Since a-catenin also binds actin, a-catenin has been indicated as a major candidate for providing a link between the CCC and the actin cytoskeleton. This molecular link is required

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