Probing the cell membrane by magnetic particle actuation and Euler angle tracking

Association of Nanodiamond Rotation Dynamics with Cell Activities by Translation-Rotation Tracking

Correlated translation-orientation tracking of single particles can provide important information for understanding the dynamics of live systems and their interaction with the probes. However, full six-dimensional (6D) motion tracking has yet to be achieved. Here, we developed synchronized 3D translation and 3D rotation tracking of single diamond particles based on nitrogen-vacancy center sensing. We first performed 6D tracking of diamond particles attached to a giant plasma membrane vesicle to demonstrate the method. Quantitative analysis of diamond particles' motion allowed elimination of the geometric effect and revealed the net rotation on the vesicle. 6D tracking was then applied to measure live cell dynamics. Motion characteristics of nanodiamonds on cell membranes under various controlled physiological conditions suggest that the nanodiamonds' rotation is associated with cell metabolic activities. Our technique extends the toolbox of single particle tracking and provides a unique solution to problems where correlated analysis of translation and rotation is critical.

Rotating magnetic particles for lab-on-chip applications - a comprehensive review

Magnetic particles are widely used in lab-on-chip and biosensing applications, because they have a high surface-to-volume ratio, they can be actuated with magnetic fields and many biofunctionalization options are available. The most well-known actuation method is to apply a magnetic field gradient which generates a translational force on the particles and allows separation of the particles from a suspension. A more recently developed magnetic actuation method is to exert torque on magnetic particles by a rotating magnetic field. Rotational actuation can be achieved with a field that is uniform in space and it allows for a precise control of torque, orientation, and angular velocity of magnetic particles in lab-on-chip devices. A wide range of studies have been performed with rotating MPs, demonstrating fluid mixing, concentration determination of biological molecules in solution, and characterization of structure and function of biomolecules at the single-molecule level. In this paper we give a comprehensive review of the historical development of MP rotation studies, including configurations for field generation, physical model descriptions, and biological applications. We conclude by sketching the scientific and technological developments that can be expected in the future in the field of rotating magnetic particles for lab-on-chip applications.

Anisotropic mechanics and dynamics of a living mammalian cytoplasm

During physiological processes, cells can undergo morphological changes that can result in a significant redistribution of the cytoskeleton causing anisotropic behavior. Evidence of anisotropy in cells under mechanical stimuli exists; however, the role of cytoskeletal restructuring resulting from changes in cell shape in mechanical anisotropy and its effects remain unclear. In the present study, we examine the role of cell morphology in inducing anisotropy in both intracellular mechanics and dynamics. We change the aspect ratio of cells by confining the cell width and measuring the mechanical properties of the cytoplasm using optical tweezers in both the longitudinal and transverse directions to quantify the degree of mechanical anisotropy. These active microrheology measurements are then combined with intracellular movement to calculate the intracellular force spectrum using force spectrum microscopy (FSM), from which the degree of anisotropy in dynamics and force can be quantified. We find that unrestricted cells with aspect ratio (AR) ∼1 are isotropic; however, when cells break symmetry, they exhibit significant anisotropy in cytoplasmic mechanics and dynamics.

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.

Seeing the unseen: Imaging rotation in cells with designer anisotropic particles

Cellular functions are enabled by cascades of transient biological events. Imaging and tracking the dynamics of these events have proven to be a powerful means of understanding the principles of cellular processes. These studies have typically focused on translational dynamics. By contrast, investigations of rotational dynamics have been scarce, despite emerging evidence that rotational dynamics are an inherent feature of many cellular processes and may also provide valuable clues to understanding those cell functions. Such studies have been impeded by the limited availability of suitable rotational imaging probes. This has recently changed thanks to the advances in the development of anisotropic particles for rotational imaging. In this review, we will summarize current techniques for imaging rotation using particle probes that are anisotropic in shape or optical properties. We will highlight two studies that demonstrate how these techniques can be applied to explore important facets of cellular functions.

Measurement of the magnetic moment of single Magnetospirillum gryphiswaldense cells by magnetic tweezers

Magnetospirillum gryphiswaldense is a helix-shaped magnetotactic bacterium that synthesizes iron-oxide nanocrystals, which allow navigation along the geomagnetic field. The bacterium has already been thoroughly investigated at the molecular and cellular levels. However, the fundamental physical property enabling it to perform magnetotaxis, its magnetic moment, remains to be elucidated at the single cell level. We present a method based on magnetic tweezers; in combination with Stokesian dynamics and Boundary Integral Method calculations, this method allows the simultaneous measurement of the magnetic moments of multiple single bacteria. The method is demonstrated by quantifying the distribution of the individual magnetic moments of several hundred cells of M. gryphiswaldense. In contrast to other techniques for measuring the average magnetic moment of bacterial populations, our method accounts for the size and the helical shape of each individual cell. In addition, we determined the distribution of the saturation magnetic moments of the bacteria from electron microscopy data. Our results are in agreement with the known relative magnetization behavior of the bacteria. Our method can be combined with single cell imaging techniques and thus can address novel questions about the functions of components of the molecular magnetosome biosynthesis machinery and their correlation with the resulting magnetic moment.

Hydrodynamic interaction between particles near elastic interfaces

We present an analytical calculation of the hydrodynamic interaction between two spherical particles near an elastic interface such as a cell membrane. The theory predicts the frequency dependent self- and pair-mobilities accounting for the finite particle size up to the 5th order in the ratio between particle diameter and wall distance as well as between diameter and interparticle distance. We find that particle motion towards a membrane with pure bending resistance always leads to mutual repulsion similar as in the well-known case of a hard-wall. In the vicinity of a membrane with shearing resistance, however, we observe an attractive interaction in a certain parameter range which is in contrast to the behavior near a hard wall. This attraction might facilitate surface chemical reactions. Furthermore, we show that there exists a frequency range in which the pair-mobility for perpendicular motion exceeds its bulk value, leading to short-lived superdiffusive behavior. Using the analytical particle mobilities we compute collective and relative diffusion coefficients. The appropriateness of the approximations in our analytical results is demonstrated by corresponding boundary integral simulations which are in excellent agreement with the theoretical predictions.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements, which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a nonvanishing resistance toward shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

On-chip electromagnetic tweezers - 3-dimensional particle actuation using microwire crossbar arrays

Emerging miniaturization technologies for biological and bioengineering applications require precise control over position and actuation of microparticles. While many of these applications call for high-throughput approaches, common tools for particle manipulation, such as magnetic or optical tweezers, suffer from low parallelizability. To address this issue, we introduce a chip-based platform that enables flexible three-dimensional control over individual magnetic microparticles. Our system relies on microwire crossbar arrays for simultaneous generation of magnetic and dielectric forces, which actuate the particles along highly localized traps. We demonstrate the precise spatiotemporal control of individual particles by tracing complex trajectories in three dimensions and investigate the forces that can be generated along different axes. Furthermore, we show that our approach for particle actuation can be parallelized by simultaneously controlling the position and movement of 16 particles in parallel.

Interfacial rheometry of polymer at a water-oil interface by intra-pair magnetophoresis

We describe an interfacial rheometry technique based on pairs of micrometer-sized magnetic particles at a fluid-fluid interface. The particles are repeatedly attracted and repelled by well-controlled magnetic dipole-dipole forces, so-called interfacial rheometry by intra-pair magnetophoresis (IPM). From the forces (∼pN), displacements (∼μm) and velocities (∼μm s(-1)) of the particles we are able to quantify the interfacial drag coefficient of particles within a few seconds and over very long timescales. The use of local dipole-dipole forces makes the system insensitive to fluid flow and suited for simultaneously recording many particles in parallel over a long period of time. We apply IPM to study the time-dependent adsorption of an oil-soluble amino-modified silicone polymer at a water-oil interface using carboxylated magnetic particles. At low polymer concentration the carboxylated particles remain on the water side of the water-oil interface, while at high polymer concentrations the particles transit into the oil phase. Both conditions show a drag coefficient that does not depend on time. However, at intermediate polymer concentrations data show an increase of the interfacial drag coefficient as a function of time, with an increase over more than three orders of magnitude (10(-7) to 10(-4) N s m(-1)), pointing to a strong polymer-polymer interaction at the interface. The time-dependence of the interfacial drag appears to be highly sensitive to the polymer concentration and to the ionic strength of the aqueous phase. We foresee that IPM will be a very convenient technique to study fluid-fluid interfaces for a broad range of materials systems.

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.

Force spectroscopy measurements show that cortical neurons exposed to excitotoxic agonists stiffen before showing evidence of bleb damage

In ischemic and traumatic brain injury, hyperactivated glutamate (N-methyl-D-aspartic acid, NMDA) and sodium (Nav) channels trigger excitotoxic neuron death. Na⁺, Ca⁺⁺ and H₂O influx into affected neurons elicits swelling (increased cell volume) and pathological blebbing (disassociation of the plasma membrane’s bilayer from its spectrin-actomyosin matrix). Though usually conflated in injured tissue, cell swelling and blebbing are distinct processes. Around an injury core, salvageable neurons could be mildly swollen without yet having suffered the bleb-type membrane damage that, by rendering channels leaky and pumps dysfunctional, exacerbates the excitotoxic positive feedback spiral. Recognizing when neuronal inflation signifies non-lethal osmotic swelling versus blebbing should further efforts to salvage injury-penumbra neurons. To assess whether the mechanical properties of osmotically-swollen versus excitotoxically-blebbing neurons might be cytomechanically distinguishable, we measured cortical neuron elasticity (gauged via atomic force microscopy (AFM)-based force spectroscopy) upon brief exposure to hypotonicity or to excitotoxic agonists (glutamate and Nav channel activators, NMDA and veratridine). Though unperturbed by solution exchange per se, elasticity increased abruptly with hypotonicity, with NMDA and with veratridine. Neurons then invariably softened towards or below the pre-treatment level, sometimes starting before the washout. The initial channel-mediated stiffening bespeaks an abrupt elevation of hydrostatic pressure linked to NMDA or Nav channel-mediated ion/H₂O fluxes, together with increased [Ca⁺⁺]_int-mediated submembrane actomyosin contractility. The subsequent softening to below-control levels is consistent with the onset of a lethal level of bleb damage. These findings indicate that dissection/identification of molecular events during the excitotoxic transition from stiff/swollen to soft/blebbing is warranted and should be feasible.

A method for time-resolved measurements of the mechanics of phagocytic cups

The internalization of matter by phagocytosis is of key importance in the defence against bacterial pathogens and in the control of cancerous tumour growth. Despite the fact that phagocytosis is an inherently mechanical process, little is known about the forces and energies that a cell requires for internalization. Here, we use functionalized magnetic particles as phagocytic targets and track their motion while actuating them in an oscillating magnetic field, in order to measure the translational and rotational stiffnesses of the phagocytic cup as a function of time. The measured evolution of stiffness reveals a characteristic pattern with a pronounced peak preceding the finalization of uptake. The measured stiffness values and their time dependence can be interpreted with a model that describes the phagocytic cup as a prestressed membrane connected to an elastically deformable actin cortex. In the context of this model, the stiffness peak is a direct manifestation of a previously described mechanical bottleneck, and a comparison of model and data suggests that the membrane advances around the particle at a speed of about 20 nm s(-1). This approach is a novel way of measuring the progression of emerging phagocytic cups and their mechanical properties in situ and in real time.