Motion Of Beads Research Articles

Near and far-wall effects on the three-dimensional motion of bacteria-driven microbeads

Bio-hybrid microrobots have been heavily studied due to their potential applications as minimally invasive medical microdevices. Though most researchers have focused on two-dimensional and near-wall motion, this letter uses a defocused optical tracking method to quantify the three-dimensional motion of 5 μm diameter polystyrene beads driven by attached Serratia marcescens bacteria. Away from walls the beads trace out helical trajectories, demonstrating kinematics produced by near-constant forces and torques. Near-wall motion is observed to be more stochastic. The motion of beads driven by single bacteria is analyzed in detail, providing an understanding of the forces and torques on the beads.

A Novel 3D Fibril Force Assay Implicates Src in Tumor Cell Force Generation in Collagen Networks

New insight into the biomechanics of cancer cell motility in 3D extracellular matrix (ECM) environments would significantly enhance our understanding of aggressive cancers and help identify new targets for intervention. While several methods for measuring the forces involved in cell-matrix interactions have been developed, previous to this study none have been able to measure forces in a fibrillar environment. We have developed a novel assay for simultaneously measuring cell mechanotransduction and motility in 3D fibrillar environments. The assay consists of a controlled-density fibrillar collagen gel atop a controlled-stiffness polyacrylamide (PAA) surface. Forces generated by living cells and their migration in the 3D collagen gel were measured with the 3D motion of tracer beads within the PAA layer. Here, this 3D fibril force assay is used to study the role of the invasion-associated protein kinase Src in mechanotransduction and motility. Src expression and activation are linked with proliferation, invasion, and metastasis, and have been shown to be required in 2D for invadopodia membranes to direct and mediate invasion. Breast cancer cell line MDA-MD-231 was stably transfected with GFP-tagged constitutively active Src or wild-type Src. In 3D fibrillar collagen matrices we found that, relative to wild-type Src, constitutively active Src: 1) increased the strength of cell-induced forces on the ECM, 2) did not significantly change migration speed, and 3) increased both the duration and the length, but not the number, of long membrane protrusions. Taken together, these results support the hypothesis that Src controls invasion by controlling the ability of the cell to form long lasting cellular protrusions to enable penetration through tissue barriers, in addition to its role in promoting invadopodia matrix-degrading activity.

Fundamental constraints on particle tracking with optical tweezers

A general quantum limit to the sensitivity of particle position measurements is derived following the simple principle of the Heisenberg microscope. The value of this limit is calculated for particles in the Rayleigh and Mie scattering regimes, and with parameters which are relevant to optical tweezers experiments. The minimum power required to observe the zero-point motion of a levitating bead is also calculated, with the optimal particle diameter always smaller than the wavelength. We show that recent optical tweezers experiments are within two orders of magnitude of quantum limited sensitivity, suggesting that quantum optical resources may soon play an important role in high sensitivity tracking applications.

Analysis of DNA Looping Kinetics in Tethered Particle Motion Experiments using Hidden Markov Models

Tethered particle motion (TPM) is a powerful method for measuring DNA-protein interactions at the single molecule level. TPM experiments monitor the Brownian motion of beads tethered to a microscope cover slip. The Brownian motion changes when a protein binds to and deforms the DNA 'leash', for example in the formation of a DNA loop. A complicating factor in the interpretation of TPM data is that the number of observable states, corresponding to different conformations of the DNA-protein complex, is often not known in advance. Moreover, conformational transitions that occur on time scales comparable to the diffusive motion of the bead are difficult to extract from the data. We present an analysis method for TPM data that overcomes these limitations in existing approaches. Our method relies on variational Bayesian inference on a variant of the Hidden Markov model. This variational approach allows us to determine the number of states directly from the data in a statistically principled manner. Moreover, by operating directly on the position data, we achieve significantly better time resolution compared to methods based on running averages of the bead root-mean-square distance from the tethering point. Finally, we show that hierarchical techniques developed in the context of single molecule FRET experiments can be adapted to our TPM methods to perform pooled analysis on many trajectories. This increases the accuracy of the method despite considerable bead-to-bead variability, and allows a more precise characterization of rare events. We apply our method to Lac-mediated loop formation on a short (107 bp) construct, and demonstrate direct interconversion between two different looped states, with implications for structual models of the looped Lac-DNA complex.

Measurement of the Organ of Corti Mechanical Responses using a New Microchamber

The mammalian cochlea is an acoustic spectrum analyzer and pressure transducer with a remarkable operating range. In the cochlear sensory epithelium called the organ of Corti (OC), cellular mechanical force is transmitted to select and amplify acoustic vibrations. However, the amplification mechanism is still unclear. Diverse experiments in cochlear research have been developed to clarify the mechanics and physiology of the OC, but most experiments share some concerns (e.g., non-physiological electrical and chemical conditions of in vitro experiments; limited means of control over the subject of in vivo tests). Furthermore, most available data of cochlear mechanics are from the basal (high frequency) region.We developed a new microchamber system to overcome the limitations. The microchamber has two ports for solution circulation, two ports for sound delivery and exit, two slits for magnetic pole tips, a port for a ground electrode, and a slit for the cochlear tissue placement. An 800 μm long sensory epithelium was harvested from young (7-11 days old postnatal) gerbil cochlea. The tissue was transplanted to the microchamber. The tissue separated two fluid spaces filled and refreshed with different ionic solutions imitating the original chemical conditions of the endolymph and the perilymph. A target bead was attached to the tectorial membrane (an acellular matrix on top of the OC). Acoustic pressure was delivered through the bottom chamber and the motion of the target bead was measured using a laser interferometer (along the optical axis) and photo-diodes (in transverse plane). The motion trajectory was analyzed with our computational model of the OC.[Supported by NSF CMMI grant]

A pair of high resolution magnetic tweezers with illumination of total reflection evanescent field and its application in the study of DNA helicases

The resolution of conventional magnetic tweezers is limited by the Brown motion of magnetic beads. When the force is lower than ～10 pN, the resolution of magnetic tweezers decreases significantly because of the increased Brown motion. To improve the resolution of magnetic tweezers under low forces, we combine the total internal reflection fluorescence techniques with magnetic tweezers, and design a novel single molecule connection: magnetic bead-DNA linker-fluorescent bead-single molecule. With the improved magnetic tweezers, we study the folding dynamics of a DNA hairpin. The results reveal that a nanometer-scale resolution is obtained. By analyzing these results, we calibrate the penetration depth of the total internal reflection field. Finally, we investigate the unwinding dynamics of a BLM helicase core protein. Some preliminary results of the helicase unwinding experiments confirm the practicability of the improved magnetic tweezers in the field of single molecular research.

Decoupling Directed and Passive Motion in Dynamic Systems: Particle Tracking Microrheology of Sputum

Probing the physical properties of heterogeneous materials is essential to understand the structure, function and dynamics of complex fluids including cells, mucus, and polymer solutions. Particle tracking microrheology is a useful method to passively probe viscoelastic properties on micron length scales by tracking the thermal motion of beads embedded in the sample. However, errors associated with active motion have limited the implementation to dynamic systems. We present a simple method to decouple active and Brownian motion, enabling particle tracking to be applied to fluctuating heterogeneous systems. We use the movement perpendicular to the major axis of motion in time to calculate rheological properties. Through simulated data we demonstrate that this method removes directed motion and performs equally well when there is no directed motion, with an average percent error of <1%. We use this method to measure glycerol-water mixtures to show the capability to measure a range of materials. Finally, we use this technique to characterize the compliance of human sputum. We also investigate the effect of a liquefaction agent used to prepare sputum for diagnostic purposes. Our results suggest that the addition of high concentration sodium hydroxide increases sample heterogeneity by increasing the maximum observed creep compliance.

Boundary conditions for creeping flow along periodic or random rough surfaces : experimental and theoretical results

Hydrodynamic interactions between particles and walls are relevant for the open problem of specifying boundary conditions for suspension flows. The Reynolds number around a small particle close to a wall is usually low and creeping flow equations apply. From the solution of these equations, the drag coefficient on a sphere becomes infinite when the gap between the sphere and a smooth wall vanishes, so that contact may not occur. Physically, the drag is finite because of various reasons, one of them being the particle and wall roughness. Then, for vanishing gap, even though some layers of fluid molecules may be left between the particle and wall roughness peaks, it may conventionally be said that contact occurs. In this paper, we are considering the example of a smooth sphere moving towards a rough wall. The roughness considered here consist of random rough planes or parallel periodic wedges, the characteristic length of which is small compared with the sphere radius. This problem is considered both experimentally and theoretically. The motion of a millimetre size bead settling towards a corrugated horizontal wall in a viscous oil is measured with laser interferometry giving an accuracy on the displacement of 0.2μm. Several random rough planes and wedge shaped walls were used, with various wavelengths and wedge angles. From the results, it is observed that the velocity of the sphere is, except for small gaps, similar to that towards a smooth plane that is shifted down from the top of corrugations.For the periodic wedges, the creeping flow is calculated as a series in the slope of the roughness grooves. The convergence of the series for the shift distance in term of the slope is accelerated by use of Euler transformation and of the existence of a limit for large slope. The cases of a flow along and across the grooves are considered separately. The shift is larger in the former case. Slightly flattened tops of the wedges used in experiments are also considered in the calculations. The effective theoretical shift for a sphere approaching a wall is obtained from Lorentz reciprocal theorem with an expansion for small roughness compared with the gap between the sphere and the wall. The effective shift is found to be the average of the shifts for shear flows in the two perpendicular directions. A good agreement is found between theory and experiment.The theoretical description of the flow close to the random rough wall represents a difficult, nearly insurmountable problem except in lattice Boltzmann simulations. Statistical analysis is presented in this paper to deduce the effective shift for sand-blasted rough surfaces. To overcome the difficulties of modelling, a regular perturbation expansion is developed, and from Lorentz reciprocal theorem, the first order correction to the drag force due to random roughness is evaluated.

Polymer unfolding and motion synchronization induced by spatially correlated noise

The problem of a spatially correlated noise affecting a complex system is studied in this paper. We present a comprehensive analysis of a two-dimensional model polymer chain, driven by the spatially correlated Gaussian noise, for which we have varied the amplitude and the correlation length. The chain model is based on a bead-spring approach, enriched with a global Lennard-Jones potential and angular interactions. We show that spatial correlations in the noise inhibit the chain geometry dynamics, enhancing the preservation of the polymer shape. This is supported by the analysis of correlation functions of both the module length and angles between neighboring modules, which have been measured for the noise amplitude ranging over three orders of magnitude. Moreover, we have observed the correlation length dependent bead motion synchronization and the spontaneous polymer unfolding, resulting from an interplay between chain potentials and the spatially structured noise.

DEM simulation of bead motion during wet bead milling using an enlarged particle model

A new model, an enlarged particle model, is proposed for simulating behavior of numerous tiny beads in wet beads milling using discrete element method (DEM). The enlarged particle model is assumed to be composed of several tiny beads. The behavior of enlarged particles in the stirred mill was simulated numerically using DEM. Furthermore, an experiment measuring the bead velocity in a transparent milling chamber using a high-speed camera was conducted to validate the enlarged particle model. The behaviors of 2 and 3mm beads in the stirred mill were also simulated using DEM. The velocity distributions of beads obtained from the simulation agree well with experimental ones when choosing the adequate frictional coefficient of beads. Then the virtual frictional coefficient was introduced into the enlarged particle model. The virtual frictional coefficient was determined so that the velocity distribution of the enlarged particles agrees with the distribution obtained from experiments. The adequate virtual frictional coefficient increases with an increase in the enlarged ratio, which is determined as a volume ratio of enlarged particle to bead. The correlation between the adequate virtual frictional coefficient and the enlarged ratio was apparent.

Intrinsic fluctuations lead to broad range of transduced forces in tethered-bead single-molecule experiments

We build a theoretical platform for predicting the behavior of tethered-bead single-molecule experiments, accounting for bead translational and rotational fluctuations, the specific type of experimental setup, and the detailed application of tension to the tether molecule. Within this framework, the external force applied to the bead is distinguished from the instantaneous force transduced to the tether molecule, resulting in a distinction between the observable response of the bead and the underlying force fluctuations felt by the tether that directly affect the biomolecular processes being studied. Our theoretical model indicates that the spread of the distribution of tether forces increases with applied external force, resulting in substantial deviations between the external and tether forces. We find that the impact of rotational and translational fluctuations of the bead motion is larger in magnetic tweezers than optical tweezers. However, this distinction diminishes at large external forces, and our asymptotic expressions offer a simple route for experimental analyses. Overall, our theory demonstrates that fluctuations in the tether molecule due to bead rotation and translation lead to a broad range of tether forces.

Origin of multiplexing capabilities of multifrequency magnetic ratchets

Through a combination of theory, numerical simulation, and experiment, we investigate the motion of magnetic beads on the surface of a magnetic ratchet driven by multifrequency fields. Here, we focus on the influence of static forcing terms, which were not included in previous models, and we derive analytical models that show why the static forcing terms are responsible for inducing beads of two different sizes to move in opposite directions on the same ratchet potential. We begin our analysis with the simplest possible forcing model, and we show that the main effect of the static forcing terms is to delay the phase of flux reversal. From there, we move onto the full analysis and theoretically derive the phase range for which opposite motion among two different bead types is achieved. Based on these theoretical results, we conduct experimental investigations that explore the effects of bead size and static forcing coefficient on the direction of bead motion, which confirm most of the expected trends. These results shed light both on past experimental work both by ourselves and others, as well as elucidate the more general multiplexing capabilities of ratchets.

Influence of divalent cations on the cytoskeletal dynamics of K562 cells determined by nano-scale bead tracking

Cytoskeletal reorganization processes can be analyzed by studying the nanometer-scale spontaneous motion of beads bound to the cytoskeleton. The bead motion is determined by force fluctuations within the cytoskeletal network that originates from myosin motor activity and dynamic restructuring of cytoskeletal filaments. We investigated to what extend the spontaneous bead motion is influenced by the dynamics of the link between the bead and the cytoskeleton in the presence of divalent cations. Our data show that, when K562 cells expressing constitutively (alpha 5 beta 1) integrin and when stably transfected with (alpha v beta 3) integrin, spontaneous bead motion is dramatically affected by the presence of 1mM Mn2+ (integrin, activate state) compared to 1mM Ca2+/Mg2+ ions (integrin, inactive state). The directionality of the bead motion, which is influenced by the overall stability of the cytoskeletal network and by actomyosin-generated forces, is markedly different, whilst the persistence remained similar due to the specific binding of either Mn2+ or Mg2+/Ca2+ ions.

Liquid film flow on structured wires: Fluid dynamics and gas‐side mass transfer

The liquid film flow on different structured wires and chains is observed experimentally to assess the suitability of a structured packing consisting of vertical wires. The results show that liquid beads as they appear on cylindrical wires are inhibited by certain chain geometries. This increases the flooding gas load up to F = 12 Pa0.5. As the stabilized film shows no liquid bead motion, the liquid velocity at the interface is less which results in lower gas‐side mass‐transfer coefficients. An estimation of the packing characteristics for different chain geometries with an assumed wire packing density of 40,000 wires/m2 is made. The interfacial area, mass‐transfer coefficients, and consequently the separation efficiency strongly depend on the liquid load. However, the proposed gas‐side separation efficiencies are slightly lower compared to common structured packings but the advantages are higher load limits, a better liquid distribution, and lower pressure drop. © 2012 American Institute of Chemical Engineers AIChE J, 59: 295–302, 2013

High-efficiency magnetophoretic separation based on synergy of magnetic force field and flow field in microchannels

Magnetophoresis is one of the most important separation methods in biological and chemical engineering. In this paper, a novel impact parameter on separation efficiency, i.e., the angle between the vectors of magnetic force and fluid velocity, was derived from the basic equation describing the motion of magnetic beads in microchannels. It is proposed that one of the most important approaches for separation efficiency enhancement is to improve the coordination of magnetic force field and fluid flow field. A T-shaped microchannel magnetophoretic separator was designed based on the angle. And then a two-dimensional dynamic model of magnetic beads moving in microchannels was established to study the separation efficiency of T-shaped microseparator by combined use of finite element method and Runge-Kutta method. The results show that the capture efficiency of T-shaped microseparator is much higher than that of the straight microseparator at the same conditions. For small magnetic beads at high fluid velocities, the designed T-shaped microseparator could still keep high separation efficiency whereas the conventional straight microseparator fails to separate the magnetic beads. Further analysis shows that the mechanism of separation efficiency enhancement lies in the synergy of magnetic force field and flow field, which directly leads to large deflected velocity of the magnetic beads from the main stream, and thus increasing the separation efficiency. It is anticipated that the results in this paper are theoretically helpful for the optimum design of highly efficient magnetophoretic separators.

Vascular Wall Engineering Via Femtosecond Laser Ablation: Scaffolds with Self-Containing Smooth Muscle Cell Populations

For tissue-engineered vascular grafts to reach their full potential, three-dimensional (3D) cellular micro-integration will be necessary. In this study, we utilize femtosecond laser ablation to produce microchannels inside electrospun polycaprolactone (PCL) scaffolds. These microchannels potentially provide spatially controlled cell distributions approaching those observed in vivo. The ability of such laser-ablated microchannels to direct cell seeding was evaluated. The dimensions chosen were 100 μm wide, 100 μm deep and 10 mm long. Femtosecond laser ablation successfully produced these microchannels in the scaffolds without substantially altering the ~900 nm diameter fibers. Flow within these microchannels was studied by injecting fluorescent polystyrene bead solutions. Direct measurement of bead motion yielded an inlet velocity of 2.78 cm s(-1). This was used for modeling two-dimensional (2D) flow using computational fluid dynamics to estimate flow profiles within the microchannel. Successful demonstrations of bead flow were followed by seeding of 500,000 human coronary artery smooth muscle cells (HCASMCs) in proliferative medium at a rate of ~500 μL min(-1). Confocal microscopy and scanning electron microscopy confirmed that the HCASMCs were seeded down the full 10-mm length of the microchannel and stayed within its boundaries. Both nuclei and F-actin were observed within the seeded cells. The presence of F-actin filaments shows that the cells were adhered strongly to the scaffold and remained viable throughout the culture. The concept of "vascular wall engineering" producing intricate cell seeding through microchannels produced via femtosecond laser ablation was validated.

Contractile Forces Contribute to Increased Glycosylphosphatidylinositol-anchored Receptor CD24-facilitated Cancer Cell Invasion

The malignancy of a tumor depends on the capability of cancer cells to metastasize. The process of metastasis involves cell invasion through connective tissue and transmigration through endothelial monolayers. The expression of the glycosylphosphatidylinositol-anchored receptor CD24 is increased in several tumor types and is consistently associated with increased metastasis formation in patients. Furthermore, the localization of β1-integrins in lipid rafts depends on CD24. Cell invasion is a fundamental biomechanical process and usually requires cell adhesion to the extracellular matrix (ECM) mainly through β1 heterodimeric integrin receptors. Here, we studied the invasion of A125 human lung cancer cells with different CD24 expression levels in three-dimensional ECMs. We hypothesized that CD24 expression increases cancer cell invasion through increased contractile forces. To analyze this, A125 cells (CD24 negative) were stably transfected with CD24 and sorted for high and low CD24 expression. The invasiveness of the CD24(high) and CD24(low) transfectants was determined in three-dimensional ECMs. The percentage of invasive cells and their invasion depth was increased in CD24(high) cells compared with CD24(low) cells. Knockdown of CD24 and of the β1-integrin subunit in CD24(high) cells decreased their invasiveness, indicating that the increased invasiveness is CD24- and β1-integrin subunit-dependent. Fourier transform traction microscopy revealed that the CD24(high) cells generated 5-fold higher contractile forces compared with CD24(low) cells. To analyze whether contractile forces are essential for CD24-facilitated cell invasion, we performed invasion assays in the presence of myosin light chain kinase inhibitor ML-7 as well as Rho kinase inhibitor Y27632. Cell invasiveness was reduced after addition of ML-7 and Y27632 in CD24(high) cells but not in CD24(neg) cells. Moreover, after addition of lysophosphatidic acid or calyculin A, an increase in pre-stress in CD24(neg) cells was observed, which enhanced cellular invasiveness. In addition, inhibition of the Src kinase or STAT3 strongly reduced the invasiveness of CD24(high) cells, slightly reduced that of CD24(low) cells, and did not alter the invasiveness of CD24(neg) cells. Taken together, these results suggest that CD24 enhances cell invasion through increased generation or transmission of contractile forces.

Transport of superparamagnetic beads through a two-dimensional potential energy landscape

The nonlinear dynamic behavior of superparamagnetic beads transported through a two-dimensional potential energy landscape is explored empirically and through numerical simulation. The beads are driven through a periodic array of micromagnets by an external rotating field oriented at an angle θ relative to the magnetization direction of the substrate. The bead's motion was highly sensitive to the angle of the driving field near critical angles and to various system parameters, including bead size, rotation frequency, and substrate pole density. Our results suggest the possibility of using this behavior in a highly discriminative colloidal separation system, in which two different bead types can be tuned to move in orthogonal directions.

Actin-based propulsion of spatially extended objects

We propose a mathematical model of the actin-based propulsion of spatially extended obstacles. It starts from the properties of individual actin filaments and includes transient attachment to the obstacle, polymerization as well as cross-linking. Two particular geometries are discussed, which apply to the motion of protein-coated beads in a cell-like medium and the leading edge of a cell protrusion, respectively. The model gives rise to both steady and saltatory movement of beads and can explain the experimentally observed transitions of the dynamic regime with changing bead radius and protein surface density. Several spatiotemporal patterns are obtained with a soft obstacle under tension, including the experimentally observed spontaneous emergence of lateral traveling waves in crawling cells. Thus, we suggest a unifying mechanism for systems that are currently described by differential concepts.

Probing Membrane-Surface Interactions via Brownian Motion of Micro-Sized Beads

Interactions between a free standing bilayer lipid membrane and various surfaces have been investigated by monitoring the Brownian motion of micron-sized silica beads on a GMO membrane. This membrane was suspended across a 200 µm Teflon aperture in either water or buffer solution using the painting method. Silica beads with diameters ranging from 0.7 µm - 5 µm were spread on the membrane and their motions were recorded at a rate of 10 frames/sec. The beads were either left unfunctionalized after cleaning or further functionalized with various chemical groups, including amine, PEG, methyl, octadecyl, avidin as well as the membrane itself. Since the interface interactions between the membrane and the beads leads to increased friction, it would be detected if the bead slowed in comparison with free Brownian motion. Experiments showed that the membrane functions as a near-perfect surface, lacking non-specific interactions. In all cases, only the avidin-biotin and membrane-membrane interactions lead to retarded motion and only in a buffered solution. This study on the Brownian motion of micron-sized beads on a membrane provides a convenient novel probe to detect interface interactions. As the beads used in these experiments have similar sizes to most bacteria and cells, they can be treated as bacteria/cell analogues and used to simulate the adsorption of bacteria /cells on another membraned bioorganism.