Control of relative radiation pressure in optical traps: application to phagocytic membrane binding studies

Making Hidden Cell Particle Interactions Visible by Thermal Noise Frequency Decomposition

Thermal noise drives cellular structures, bacteria, and viruses on different temporal and spatial scales. Their weak interactions with their environment can change on subsecond scales. However, particle interactions can be hidden or invisible-even when measured with thermal noise sensitivity, leading to misconceptions about their binding behavior. Here, it is demonstrated how invisible particle interactions at the cell periphery become visible by MHz interferometric thermal noise tracking and frequency decomposition at a spectral update rate of only 0.5 s. The particle fluctuations are analyzed in radial and lateral directions by a viscoelastic modulus G(ω,tex ) over the experiment time tex , revealing a surprisingly similar, frequency dependent response for different cell types. This response behavior can be explained by a mathematical model for molecular scale elasticity and damping. The method to reveal hidden interactions is tested at two examples: the stiffening of macrophage filopodia tips within 2 s with particle contact invisible by the fluctuation width. Second, the extent and stiffness of the soft cell glycocalyx is measured, which can be sensed by a particle only on microsecond-timescales, but which remains invisible on time-average. This concept study shows how to uncover hidden cellular interactions, if particle motions are measured at high-speed.

Pulling, failing, and adaptive mechanotransduction of macrophage filopodia

Macrophages use filopodia to withdraw particles toward the cell body for phagocytosis. This can require substantial forces, which the cell generates after bio-mechanical stimuli are transmitted to the filopodium. Adaptation mechanisms to mechanical stimuli are essential for cells, but can a cell iteratively improve filopodia pulling? If so, the underlying mechanic adaptation principles organized on the protein level are unclear. Here, we tackle this problem using optically trapped 1 μm beads, which we tracked interferometrically at 1 MHz during connection to the tips of dorsal filopodia of macrophages. We observe repetitive failures while the filopodium tries to pull the bead out of the optical trap. Analyses of mean bead motions and position fluctuations on the nano-meter and microsecond scale indicate mechanical ruptures caused by a force-dependent actin-membrane connection. We found that beads are retracted three times slower under any load between 5 and 40 pN relative to the no-load transport, which has the same speed as the actin retrograde flow obtained from fluorescent speckle tracking. From this duty ratio of pulling velocities, we estimated a continuous on/off binding with τoff = 2⋅τon, with measured off times τoff = 0.1-0.5 s. Remarkably, we see a gradual increase of filopodia pulling forces from 10 to 30 pN over time and after failures, which points toward an unknown adaptation mechanism. Additionally, we see that the attachment strength and friction between the bead and filopodium tip increases under load and over time. All observations are typical for catch-bond proteins such as integrin-talin complexes. We present a mechanistic picture of adaptive mechanotransduction, which formed by the help of mathematical models for repetitive tip ruptures and reconnections. The analytic mathematical model and the stochastic computer simulations, both based on catch-bond lifetimes, confirmed our measurements. Such catch-bond characteristics could also be important for other immune cells taking up counteracting pathogens.

Using blinking optical tweezers to study cell rheology during initial cell-particle contact

Phagocytosis is an important part of innate immunity and describes the engulfment of bacteria and other extracellular objects on the micrometer scale. The protrusion of the cell membrane around the bacteria during this process is driven by a reorganization of the actin cortex. The process has been studied on the molecular level to great extent during the past decades. However, a deep, fundamental understanding of the mechanics of the process is still lacking, in particular because of a lack of techniques that give access to binding dynamics below the optical resolution limit and cellular viscoelasticity at the same time. In this work, we propose a technique to characterize the mechanical properties of cells in a highly localized manner and apply it to investigate the early stages of phagocytosis. The technique can simultaneously resolve the contact region between a cell and an external object (in our application, a phagocytic target) even below the optical resolution limit. We used immunoglobulin-G-coated microparticles with a size of 2 μm as a model system and attached the particles to the macrophages with holographic optical tweezers. By switching the trap on and off, we were able to measure the rheological properties of the cells in a time-resolved manner during the first few minutes after attachment. The measured viscoelastic cellular response is consistent with power law rheology. The contact radius between particle and cell increased on a timescale of ∼30 s and converged after a few minutes. Although the binding dynamics are not affected by cytochalasin D, we observed an increase of the cellular compliance and a significant fluidization of the cortex after addition of cytochalasin D treatment. Furthermore, we report upper boundaries for the length- and timescale, at which cortical actin has been hypothesized to depolymerize during early phagocytosis.

Measuring Stepwise Binding of Thermally Fluctuating Particles to Cell Membranes without Fluorescence

Thermal motions enable a particle to probe the optimal interaction state when binding to a cell membrane. However, especially on the scale of microseconds and nanometers, position and orientation fluctuations are difficult to observe with common measurement technologies. Here, we show that it is possible to detect single binding events of immunoglobulin-G-coated polystyrene beads, which are held in an optical trap near the cell membrane of a macrophage. Changes in the spatial and temporal thermal fluctuations of the particle were measured interferometrically, and no fluorophore labeling was required. We demonstrate both by Brownian dynamic simulations and by experiments that sequential stepwise increases in the force constant of the bond between a bead and a cell of typically 20 pN/μm are clearly detectable. In addition, this technique provides estimates about binding rates and diffusion constants of membrane receptors. The simple approach of thermal noise tracking points out new strategies in understanding interactions between cells and particles, which are relevant for a large variety of processes, including phagocytosis, drug delivery, and the effects of small microplastics and particulates on cells.

Force Measurement of Living Professional Phagocytes of the Immune System

In higher organisms, the professional phagocytes of the immune system (dendritic cells, neutrophils, monocytes, and macrophages) are responsible for pathogen clearance, the development of immune responses via cytokine secretion and presentation of antigens derived from internalized material, and the normal turnover and remodelling of tissues and disposal of dead cells. These functions rely on the ability of phagocytes to migrate and adhere to sites of infection, dynamically probe their environments to make contact with phagocytic targets, and perform phagocytosis, a mechanism of internalization of large particles, microorganisms, and cellular debris for intracellular degradation. The cell-generated forces that are necessary for the professional phagocytes to act in their roles as ‘first responders’ of the immune system have been the subject of mechanical studies in recent years. Methods of force measurement such as atomic force microscopy, traction force microscopy, micropipette aspiration, magnetic and optical tweezers, and exciting new variants of these have accompanied classical biological methods to perform mechanical investigations of these highly dynamic immune cells.

Miniature scanning light-sheet illumination implemented in a conventional microscope

Living cells are highly dynamic systems responding to a large variety of biochemical and mechanical stimuli over minutes, which are well controlled by e.g. optical tweezers. However, live cell investigation through fluorescence microscopy is usually limited not only by the spatial and temporal imaging resolution but also by fluorophore bleaching. Therefore, we designed a miniature light-sheet illumination system that is implemented in a conventional inverted microscope equipped with optical tweezers and interferometric tracking to capture 3D images of living macrophages at reduced bleaching. The horizontal light-sheet is generated with a 0.12 mm small cantilevered mirror placed at 45° to the detection axis. The objective launched illumination beam is reflected by the micro-mirror and illuminates the sample perpendicular to the detection axis. Lateral and axial scanning of both Gaussian and Bessel beams, together with an electrically tunable lens for fast focusing, enables rapid 3D image capture without moving the sample or the objective lens. Using scanned Bessel beams and line-confocal detection, an average axial resolution of 0.8 µm together with a 10-15 fold improved image contrast is achieved.

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this paper, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane. II. Asymmetric motion

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 95, 013108 (2017)2470-004510.1103/PhysRevE.95.013108], where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero-frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a nonvanishing resistance toward shearing. We further compute the in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

Introduction to Optical Tweezers

Thirty years after their invention by Arthur Ashkin and colleagues at Bell Labs in 1986 [1], optical tweezers (or traps) have become a versatile tool to address numerous biological problems. Put simply, an optical trap is a highly focused laser beam that is capable of holding and applying forces to micron-sized dielectric objects. However, their development over the last few decades has converted these tools from boutique instruments into highly versatile instruments of molecular biophysics. This introductory chapter intends to give a brief overview of the field, highlight some important scientific achievements, and demonstrate why optical traps have become a powerful tool in the biological sciences. We introduce a typical optical setup, describe the basic theoretical concepts of how trapping forces arise, and present the quantitative position and force measurement techniques that are most widely used today.

Measuring Local Viscosities near Plasma Membranes of Living Cells with Photonic Force Microscopy

The molecular processes of particle binding and endocytosis are influenced by the locally changing mobility of the particle nearby the plasma membrane of a living cell. However, it is unclear how the particle's hydrodynamic drag and momentum vary locally and how they are mechanically transferred to the cell. We have measured the thermal fluctuations of a 1 μm-sized polystyrene sphere, which was placed in defined distances to plasma membranes of various cell types by using an optical trap and fast three-dimensional (3D) interferometric particle tracking. From the particle position fluctuations on a 30 μs timescale, we determined the distance-dependent change of the viscous drag in directions perpendicular and parallel to the cell membrane. Measurements on macrophages, adenocarcinoma cells, and epithelial cells revealed a significantly longer hydrodynamic coupling length of the particle to the membrane than those measured at giant unilamellar vesicles (GUVs) or a plane glass interface. In contrast to GUVs, there is also a strong increase in friction and in mean first passage time normal to the cell membrane. This hydrodynamic coupling transfers a different amount of momentum to the interior of living cells and might serve as an ultra-soft stimulus triggering further reactions.

Interaction dynamics of two diffusing particles: contact times and influence of nearby surfaces

Interactions of diffusing particles are governed by hydrodynamics on different length and timescales. The local hydrodynamics can be influenced substantially by simple interfaces. Here, we investigate the interaction dynamics of two micron-sized spheres close to plane interfaces to mimic more complex biological systems or microfluidic environments. Using scanned line optical tweezers and fast 3D interferometric particle tracking, we are able to track the motion of each bead with precisions of a few nanometers and at a rate of 10 kilohertz. From the recorded trajectories, all spatial and temporal information is accessible. This way, we measure diffusion coefficients for two coupling particles at varying distances h to one or two glass interfaces. We analyze their coupling strength and length by cross-correlation analysis relative to h and find a significant decrease in the coupling length when a second particle diffuses nearby. By analysing the times the particles are in close contact, we find that the influence of nearby surfaces and interaction potentials reduce the diffusivity strongly, although we found that the diffusivity hardly affects the contact times and the binding probability between the particles. All experimental results are compared to a theoretical model, which is based on the number of possible diffusion paths following the Catalan numbers and a diffusion probability, which is biased by the spheres' surface potential. The theoretical and experimental results agree very well and therefore enable a better understanding of hydrodynamically coupled interaction processes.

Surfing along Filopodia: A Particle Transport Revealed by Molecular-Scale Fluctuation Analyses

Filopodia perform cellular functions such as environmental sensing or cell motility, but they also grab for particles and withdraw them leading to an increased efficiency of phagocytic uptake. Remarkably, withdrawal of micron-sized particles is also possible without noticeable movements of the filopodia. Here, we demonstrate that polystyrene beads connected by optical tweezers to the ends of adherent filopodia of J774 macrophages, are transported discontinuously toward the cell body. After a typical resting time of 1-2 min, the cargo is moved with alternating velocities, force constants, and friction constants along the surface of the filopodia. This surfing-like behavior along the filopodium is recorded by feedback-controlled interferometric three-dimensional tracking of the bead motions at 10-100 kHz. We measured transport velocities of up to 120 nm/s and transport forces of ∼ 70 pN. Small changes in position, fluctuation width, and temporal correlation, which are invisible in conventional microscopy, indicate molecular reorganization of transport-relevant proteins in different phases of the entire transport process. A detailed analysis implicates a controlled particle transport with fingerprints of a nanoscale unbinding/binding behavior. The manipulation and analysis methods presented in our study may also be helpful in other fields of cellular biophysics.

How to calibrate an object-adapted optical trap for force sensing and interferometric shape tracking of asymmetric structures

Optical traps have shown to be a flexible and powerful tool for 3D manipulations on the microscale. However, when it comes to sensitive measurements of particle displacements and forces thorough calibration procedures are required, which can be already demanding for trapped spheres. For asymmetric structures, with more complicated shapes, such as helical bacteria, novel calibration schemes need to be established. The paper describes different methods of how to extract various calibration parameters of a tiny helical bacterium, which is trapped and tracked in shape by scanning line optical tweezers. Tiny phase differences of the light scattered at each slope of the bacterium are measured by back focal plane interferometry, providing precise and high bandwidth information about fast deformations of the bacterium. A simplified theoretical model to estimate the optical forces on a chain like structure is presented. The methods presented here should be of interest to people that investigate optical trapping and tracking of asymmetric particles.

Label-free biosensing over a wide concentration range with photonic force microscopy

We present a label-free biosensor that measures molecular interactions between biomolecules on the surface of a probe bead and substrate over a wide concentration range. This system is capable of detecting target biomolecules with concentrations varying from 10 nM to 0.1 pM, with high selectivity and sensitivity.

Induced phagocytic particle uptake into a giant unilamellar vesicle

Phagocytosis, the uptake and ingestion of solid particles into living cells, is a central mechanism of our immune system. Due to the complexity of the uptake mechanism, the different forces involved in this process are only partly understood. Therefore the usage of a giant unilamellar vesicle (GUV) as the simplest biomimetic model for a cell allows one to investigate the influence of the lipid membrane on the energetics of the uptake process. Here, a photonic force microscope (PFM) is used to approach an optically trapped 1 μm latex bead to an immobilized GUV to finally insert the particle into the GUV. By analysing the mean displacement and the position fluctuations of the trapped particle during the uptake process in 3D with nanometre precision, we are able to record force and energy profiles, as well as changes in the viscous drag and the stiffness. After observing a global followed by a local deformation of the GUV, we measured uptake energies of 2000 kT to 5500 kT and uptake forces of 4 pN to 16 pN for Egg-PC GUVs with sizes of 18-26 μm and varying membrane tension. The measured energy profiles, which are compared to a Helfrich energy model for local and global deformation, show good coincidence with the theoretical results. Our proof-of-principle study opens the door to a large number of similar experiments with GUVs containing more biochemical components and complexity. This bottom-up strategy should allow for a better understanding of the physics of phagocytosis.

Comparison of the force exerted by hippocampal and DRG growth cones

Mechanical properties such as force generation are fundamental for neuronal motility, development and regeneration. We used optical tweezers to compare the force exerted by growth cones (GCs) of neurons from the Peripheral Nervous System (PNS), such as Dorsal Root Ganglia (DRG) neurons, and from the Central Nervous System (CNS) such as hippocampal neurons. Developing GCs from dissociated DRG and hippocampal neurons were obtained from P1-P2 and P10-P12 rats. Comparing their morphology, we observed that the area of GCs of hippocampal neurons was 8-10 µm² and did not vary between P1-P2 and P10-P12 rats, but GCs of DRG neurons were larger and their area increased from P1-P2 to P10-P12 by 2-4 times. The force exerted by DRG filopodia was in the order of 1-2 pN and never exceeded 5 pN, while hippocampal filopodia exerted a larger force, often in the order of 5 pN. Hippocampal and DRG lamellipodia exerted lateral forces up to 20 pN, but lamellipodia of DRG neurons could exert a vertical force larger than that of hippocampal neurons. Force-velocity relationships (Fv) in both types of neurons had the same qualitative behaviour, consistent with a common autocatalytic model of force generation. These results indicate that molecular mechanisms of force generation of GC from CNS and PNS neurons are similar but the amplitude of generated force is influenced by their cytoskeletal properties.

Simultaneous detection of biomolecular interactions and surface topography using photonic force microscopy

We developed a photonic force microscope that can map multiple parameters simultaneously, including the surface topography and biomolecular interactions. To track the position of the probe bead and to determine contact position with the sample surface, we adopted a video analysis method using the diffraction pattern of monochromatic light passing through the probe bead. To demonstrate the capability of the microscope, we report the simultaneous measurement of the molecule distribution of DNA oligonucleotides on the surface, the binding strength of DNA hybridization between the bead and surface, and the topography of the smooth molded surface.

The formation of actin waves during regeneration after axonal lesion is enhanced by BDNF

During development, axons of neurons in the mammalian central nervous system lose their ability to regenerate. To study the regeneration process, axons of mouse hippocampal neurons were partially damaged by an UVA laser dissector system. The possibility to deliver very low average power to the sample reduced the collateral thermal damage and allowed studying axonal regeneration of mouse neurons during early days in vitro. Force spectroscopy measurements were performed during and after axon ablation with a bead attached to the axonal membrane and held in an optical trap. With this approach, we quantified the adhesion of the axon to the substrate and the viscoelastic properties of the membrane during regeneration. The reorganization and regeneration of the axon was documented by long-term live imaging. Here we demonstrate that BDNF regulates neuronal adhesion and favors the formation of actin waves during regeneration after axonal lesion.

Fast parallel interferometric 3D tracking of numerous optically trapped particles and their hydrodynamic interaction

Multi-dimensional, correlated particle tracking is a key technology to reveal dynamic processes in living and synthetic soft matter systems. In this paper we present a new method for tracking micron-sized beads in parallel and in all three dimensions - faster and more precise than existing techniques. Using an acousto-optic deflector and two quadrant-photo-diodes, we can track numerous optically trapped beads at up to tens of kHz with a precision of a few nanometers by back-focal plane interferometry. By time-multiplexing the laser focus, we can calibrate individually all traps and all tracking signals in a few seconds and in 3D. We show 3D histograms and calibration constants for nine beads in a quadratic arrangement, although trapping and tracking is easily possible for more beads also in arbitrary 2D arrangements. As an application, we investigate the hydrodynamic coupling and diffusion anomalies of spheres trapped in a 3 × 3 arrangement.

Interface shear microrheometer with an optically driven oscillating probe particle

We report the first experimental demonstration of an active interfacial shear microrheometer (ISMR) that uses a particle trapped by oscillating optical tweezers (OT) to probe the shear modulus G(s)(*)(ω) of a gas/liquid interface. The most significant advantages of the oscillating OT in a rheology study are: (1) very high sensitivity compared to other active microrheology methods and (2) the ability to measure both the real and imaginary components of the complex shear modulus without relying on the use of Kramers-Kronig relation, which can be problematic at low frequencies for most of the passive methods. We demonstrate the utilities of our ISMR in two case studies: (1) a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine monolayer and (2) a composite of poly(styrene sulfonate) and dioctadecyldimethylammonium at the air/water interface in regimes where no other active instruments can explore.

Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We put forward the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle reproduces the stochastic nature of lamellipodia protrusion (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is a well-known signature of self-organized criticality and is confirmed by unique optical tweezer measurements performed in vivo on neuronal growth cones.

Survey on indirect optical manipulation of cells, nucleic acids, and motor proteins

Optical tweezers have emerged as a promising technique for manipulating biological objects. Instead of direct laser exposure, more often than not, optically-trapped beads are attached to the ends or boundaries of the objects for translation, rotation, and stretching. This is referred to as indirect optical manipulation. In this paper, we utilize the concept of robotic gripping to explain the different experimental setups which are commonly used for indirect manipulation of cells, nucleic acids, and motor proteins. We also give an overview of the kind of biological insights provided by this technique. We conclude by highlighting the trends across the experimental studies, and discuss challenges and promising directions in this domain of active current research.

Control and manipulation of pathogens with an optical trap for live cell imaging of intercellular interactions

The application of live cell imaging allows direct visualization of the dynamic interactions between cells of the immune system. Some preliminary observations challenge long-held beliefs about immune responses to microorganisms; however, the lack of spatial and temporal control between the phagocytic cell and microbe has rendered focused observations into the initial interactions of host response to pathogens difficult. This paper outlines a method that advances live cell imaging by integrating a spinning disk confocal microscope with an optical trap, also known as an optical tweezer, in order to provide exquisite spatial and temporal control of pathogenic organisms and place them in proximity to host cells, as determined by the operator. Polymeric beads and live, pathogenic organisms (Candida albicans and Aspergillus fumigatus) were optically trapped using non-destructive forces and moved adjacent to living cells, which subsequently phagocytosed the trapped particle. High resolution, transmitted light and fluorescence-based movies established the ability to observe early events of phagocytosis in living cells. To demonstrate the broad applicability of this method to immunological studies, anti-CD3 polymeric beads were also trapped and manipulated to form synapses with T cells in vivo, and time-lapse imaging of synapse formation was also obtained. By providing a method to exert fine control of live pathogens with respect to immune cells, cellular interactions can be captured by fluorescence microscopy with minimal perturbation to cells and can yield powerful insight into early responses of innate and adaptive immunity.

Force generation in lamellipodia is a probabilistic process with fast growth and retraction events

Polymerization of actin filaments is the primary source of motility in lamellipodia and it is controlled by a variety of regulatory proteins. The underlying molecular mechanisms are only partially understood and a precise determination of dynamical properties of force generation is necessary. Using optical tweezers, we have measured with millisecond (ms) temporal resolution and picoNewton (pN) sensitivity the force-velocity (Fv) relationship and the power dissipated by lamellipodia of dorsal root ganglia neurons. When force and velocity are averaged over 3-5 s, the Fv relationships can be flat. On a finer timescale, random occurrence of fast growth and subsecond retractions become predominant. The maximal power dissipated by lamellipodia over a silica bead with a diameter of 1 microm is 10(-16) W. Our results clarify the dynamical properties of force generation: i), force generation is a probabilistic process; ii), underlying biological events have a bandwidth up to at least 10 Hz; and iii), fast growth of lamellipodia leading edge alternates with local retractions.

Improved interferometric tracking of trapped particles using two frequency-detuned beams

For most optical tweezer applications, precise and reliable tracking of the trapped particle is an important requirement. Backfocal-plane interferometry is the fastest and most accurate tracking technique if the particle displacements are limited to half of the focal width. Especially for positive axial displacements, the nonlinear detector response can lead to incorrect tracking results. Here we show how the linear detection range around the trap center can be extended by a factor of 2 to 4 in the axial direction using a second frequency-detuned tracking focus that is generated by the same laser as the optical trap. Additionally, we show how the noise in the axial signal can be decreased significantly using a second detector.

Axial optical trapping efficiency through a dielectric interface

Axial trapping through a dielectric interface is investigated in the framework of the angular spectrum representation and of the generalized Lorenz-Mie theory. We determine the optical force for an arbitrarily polarized non-paraxial, strongly aberrated, axially symmetric focusing beam and apply this description to the case of an arbitrarily positioned dielectric microsphere, commonly employed in optical tweezers, not taking into account the contribution of evanescent waves at the interface. We derive the analytical expression of the force profile, finding that the incident polarization does not affect the axial optical force. In addition, we derive an approximated expression for the axial force as a function of beam displacement just outside the microsphere and we show how the information provided by the ripple structure of the optical trapping efficiency versus sphere displacement curve, due to the aberration effect, could be exploited to calibrate the bead axial position versus the experimental beam positioning controls.

Filopodia act as phagocytic tentacles and pull with discrete steps and a load-dependent velocity

Filopodia are thin, spike-like cell surface protrusions containing bundles of parallel actin filaments. So far, filopodial dynamics has mainly been studied in the context of cell motility on coverslip-adherent filopodia by using fluorescence and differential interference contrast (DIC) microscopy. In this study, we used an optical trap and interferometric particle tracking with nanometer precision to measure the three-dimensional dynamics of macrophage filopodia, which were not attached to flat surfaces. We found that filopodia act as cellular tentacles: a few seconds after binding to a particle, filopodia retract and pull the bound particle toward the cell. We observed F-actin-dependent stepwise retraction of filopodia with a mean step size of 36 nm, suggesting molecular motor activity during filopodial pulling. Remarkably, this intracellular stepping motion, which was measured at counteracting forces of up to 19 pN, was transmitted to the extracellular tracked particle via the filopodial F-actin bundle and the cell membrane. The pulling velocity depended strongly on the counteracting force and ranged between 600 nm/s at forces <1 pN and approximately 40 nm/s at forces >15 pN. This result provides an explanation of the significant differences in filopodial retraction velocities previously reported in the literature. The measured filopodial retraction force-velocity relationship is in agreement with a model for force-dependent multiple motor kinetics.

DNA as a metrology standard for length and force measurements with optical tweezers

Optical tweezers have broad applications in studies of structures and processes in molecular and cellular biophysics. Use of optical tweezers for quantitative molecular-scale measurement requires careful calibration in physical units. Here we show that DNA molecules may be used as metrology standards for force and length measurements. Analysis of DNA molecules of two specific lengths allows simultaneous determination of all essential measurement parameters. We validate this biological-calibration method experimentally and with simulated data, and show that precisions in determining length scale factor ( approximately 0.2%), length offset ( approximately 0.03%), force scale factor ( approximately 2%), and compliance of the traps ( approximately 3%) are limited only by current measurement variation, much of which arises from polydispersity of the microspheres ( approximately 2%). We find this procedure to be simpler and more convenient than previous methods, and suggest that it provides an easily replicated standard that can insure uniformity of measurements made in different laboratories.