Intracellular microrheology of motile Amoeba proteus

Extreme heterogeneity in the microrheology of lamellar surfactant gels analyzed with neural networks

The heterogeneity of the viscoelasticity of a lamellar gel network based on cetyl-trimethylammonium chloride and cetostearyl alcohol was studied using particle-tracking microrheology. A recurrent neural network (RNN) architecture was used for estimating the Hurst exponent, H, on small sections of tracks of probe spheres moving with fractional Brownian motion. Thus, dynamic segmentation of tracks via neural networks was used in microrheology and it is significantly more accurate than using mean square displacements (MSDs). An ensemble of 414 particles produces a MSD that is subdiffusive in time, t, with a power law of the form t^{0.74±0.02}, indicating power law viscoelasticity. RNN analysis of the probability distributions of H, combined with detailed analysis of the time-averaged MSDs of individual tracks, revealed diverse diffusion processes belied by the simple scaling of the ensemble MSD, such as caging phenomena, which give rise to the complex viscoelasticity of lamellar gels.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Topological damping in an ultrafast giant cell

Cellular systems are known to exhibit some of the fastest movements in biology, but little is known as to how single cells can dissipate this energy rapidly and adapt to such large accelerations without disrupting internal architecture. To address this, we investigate Spirostomum ambiguum-a giant cell (1-4 mm in length) well-known to exhibit ultrafast contractions (50% of body length) within 5 ms with a peak acceleration of 15[Formula: see text]. Utilizing transmitted electron microscopy and confocal imaging, we identify an association of rough endoplasmic reticulum (RER) and vacuoles throughout the cell-forming a contiguous fenestrated membrane architecture that topologically entangles these two organelles. A nearly uniform interorganelle spacing of 60 nm is observed between RER and vacuoles, closely packing the entire cell. Inspired by the entangled organelle structure, we study the mechanical properties of entangled deformable particles using a vertex-based model, with all simulation parameters matching 10 dimensionless numbers to ensure dynamic similarity. We demonstrate how entangled deformable particles respond to external loads by an increased viscosity against squeezing and help preserve spatial relationships. Because this enhanced damping arises from the entanglement of two networks incurring a strain-induced jamming transition at subcritical volume fractions, which is demonstrated through the spatial correlation of velocity direction, we term this phenomenon "topological damping." Our findings suggest a mechanical role of RER-vacuolar meshwork as a metamaterial capable of damping an ultrafast contraction event.

A Multipole Magnetoactive Elastomer for Vibration-Driven Locomotion

Smart materials such as magnetoactive elastomers (MAEs) combine elastic and magnetic properties that can be significantly changed in response to a magnetic field and therefore offer enormous potential for applications in both scientific research and engineering. When such an elastomer contains microsized hard magnetic particles, it can become an elastic magnet once magnetized in a strong magnetic field. This article studies a multipole MAE with the aim of utilizing it as an actuation element of vibration-driven locomotion robots. The elastomer beam has three magnetic poles overall with the same poles at the ends and possesses silicone bristles protruding from its underside. The quasi-static bending of the multipole elastomer in a uniform magnetic field is investigated experimentally. The theoretical model exploits the magnetic torque to describe the field-induced bending shapes. The unidirectional locomotion of the elastomeric bristle-bot is realized in two prototype designs using magnetic actuation of either an external or an integrated source of an alternating magnetic field. The motion principle is based on cyclic interplay of asymmetric friction and inertia forces caused by field-induced bending vibrations of the elastomer. The locomotion behavior of both prototypes shows a strong resonant dependency of the advancing speed on the frequency of applied magnetic actuation.

The Intracellular Amastigote of Trypanosoma cruzi Maintains an Actively Beating Flagellum

Throughout its complex life cycle, the uniflagellate parasitic protist, Trypanosoma cruzi, adapts to different host environments by transitioning between elongated motile extracellular stages and a nonmotile intracellular amastigote stage that replicates in the cytoplasm of mammalian host cells. Intracellular T. cruzi amastigotes retain a short flagellum that extends beyond the opening of the flagellar pocket with access to the extracellular milieu. Contrary to the long-held view that the T. cruzi amastigote flagellum is inert, we report that this organelle is motile and displays quasiperiodic beating inside mammalian host cells. Kymograph analysis determined an average flagellar beat frequency of ~0.7 Hz for intracellular amastigotes and similar beat frequencies for extracellular amastigotes following their isolation from host cells. Inhibitor studies reveal that flagellar motility in T. cruzi amastigotes is critically dependent on parasite mitochondrial oxidative phosphorylation. These novel observations reveal that flagellar motility is an intrinsic property of T. cruzi amastigotes and suggest that this organelle may play an active role in the parasite infection process. IMPORTANCE Understanding the interplay between intracellular pathogens and their hosts is vital to the development of new treatments and preventive strategies. The intracellular "amastigote" stage of the Chagas disease parasite, Trypanosoma cruzi, is a critical but understudied parasitic life stage. Previous work established that cytosolically localized T. cruzi amastigotes engage physically and selectively with host mitochondria using their short, single flagellum. The current study was initiated to examine the dynamics of the parasite flagellum-host mitochondrial interaction through live confocal imaging and led to the unexpected discovery that the T. cruzi amastigote flagellum is motile.

Glass-like characteristics of intracellular motion in human cells

The motion in the cytosol of microorganisms such as bacteria and yeast has been observed to undergo a dramatic slowing down upon cell energy depletion. These observations have been interpreted as the motion being "glassy," but whether this notion is useful also for active, motor-protein-driven transport in eukaryotic cells is less clear. Here, we use fluorescence microscopy of beads in human (HeLa) cells to probe the motion of membrane-surrounded structures that are carried along the cytoskeleton by motor proteins. Evaluating several hallmarks of glassy dynamics, we show that at short length scales, the motion is heterogeneous, is nonergodic, is well described by a model for the displacement distribution in glassy systems, and exhibits a decoupling of the exchange and persistence times. Overall, these results suggest that the short length scale behavior of objects that can be transported actively by motor proteins in human cells shares features with the motion in glassy systems.

Pinning dislocations in colloidal crystals with active particles that seek stacking faults

There is growing interest in functional, adaptive devices built from colloidal subunits of micron size or smaller. A colloidal material with dynamic mechanical properties could facilitate such microrobotic machines. Here we study via computer simulation how active interstitial particles in small quantities can be used to modify the bulk mechanical properties of a colloidal crystal. Passive interstitial particles are known to pin dislocations in metals, thereby increasing resistance to plastic deformation. We extend this tactic by employing anisotropic active interstitials that travel super-diffusively and bind strongly to stacking faults associated with partial dislocations. We find that: (1) interstitials that are effective at reducing plasticity compromise between strong binding to stacking faults and high mobility in the crystal bulk. (2) Reorientation of active interstitials in the crystal depends upon rotational transitions between high-symmetry crystal directions. (3) The addition of certain active interstitial shapes at concentrations as low as 60 per million host particles (0.006%) can create a shear threshold for dislocation migration. This work demonstrates how active materials in a dense matrix can locally sense their environment and lead to bulk property changes.

Evidence of conditioned behavior in amoebae

Associative memory is the main type of learning by which complex organisms endowed with evolved nervous systems respond efficiently to certain environmental stimuli. It has been found in different multicellular species, from cephalopods to humans, but never in individual cells. Here we describe a motility pattern consistent with associative conditioned behavior in the microorganism Amoeba proteus. We use a controlled direct-current electric field as the conditioned stimulus, and a specific chemotactic peptide as the unconditioned stimulus. The amoebae are capable of linking two independent past events, generating persistent locomotion movements that can prevail for 44 min on average. We confirm a similar behavior in a related species, Metamoeba leningradensis. Thus, our results indicate that unicellular organisms can modify their behavior during migration by associative conditioning.

Cell polarity: having and making sense of direction-on the evolutionary significance of the primary cilium/centrosome organ in Metazoa

Cell-autonomous polarity in Metazoans is evolutionarily conserved. I assume that permanent polarity in unicellular eukaryotes is required for cell motion and sensory reception, integration of these two activities being an evolutionarily constrained function. Metazoans are unique in making cohesive multicellular organisms through complete cell divisions. They evolved a primary cilium/centrosome (PC/C) organ, ensuring similar functions to the basal body/flagellum of unicellular eukaryotes, but in different cells, or in the same cell at different moments. The possibility that this innovation contributed to the evolution of individuality, in being instrumental in the early specification of the germ line during development, is further discussed. Then, using the example of highly regenerative organisms like planarians, which have lost PC/C organ in dividing cells, I discuss the possibility that part of the remodelling necessary to reach a new higher-level unit of selection in multi-cellular organisms has been triggered by conflicts among individual cell polarities to reach an organismic polarity. Finally, I briefly consider organisms with a sensorimotor organ like the brain that requires exceedingly elongated polarized cells for its activity. I conclude that beyond critical consequences for embryo development, the conservation of cell-autonomous polarity in Metazoans had far-reaching implications for the evolution of individuality.

The Effects of the Interplay between Motor and Brownian Forces on the Rheology of Active Gels

Active gels perform key mechanical roles inside the cell, such as cell division, motion, and force sensing. The unique mechanical properties required to perform such functions arise from the interactions between molecular motors and semiflexible polymeric filaments. Molecular motors can convert the energy released in the hydrolysis of ATP into forces of up to piconewton magnitudes. Moreover, the polymeric filaments that form active gels are flexible enough to respond to Brownian forces but also stiff enough to support the large tensions induced by the motor-generated forces. Brownian forces are expected to have a significant effect especially at motor activities at which stable noncontractile in vitro active gels are prepared for rheological measurements. Here, a microscopic mean-field theory of active gels originally formulated in the limit of motor-dominated dynamics is extended to include Brownian forces. In the model presented here, Brownian forces are included accurately, at real room temperature, even in systems with high motor activity. It is shown that a subtle interplay, or competition, between motor-generated forces and Brownian forces has an important impact on the mass transport and rheological properties of active gels. The model predictions show that at low frequencies the dynamic modulus of active gels is determined mostly by motor protein dynamics. However, Brownian forces significantly increase the breadth of the relaxation spectrum and can affect the shape of the dynamic modulus over a wide frequency range even for ratios of motor to Brownian forces of more than a hundred. Since the ratio between motor and Brownian forces is sensitive to ATP concentration, the results presented here shed some light on how the transient mechanical response of active gels changes with varying ATP concentration.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

Unicellular organisms and other single cells often have to migrate towards food sources or away from predators by sensing chemicals present in the environment. There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain distance, or spatial sensing, where the cell senses the external chemical at two different locations on its cellular surface (e.g., the front and rear of the cell) simultaneously. It has been thought that small unicellular organisms employ temporal sensing as their small size prohibits sensing at two different locations on the cellular surface. Using computational modeling, we find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins. Predictions from our model agree with experimental observations over a wide range of cells, where a fast-moving, small cell performs better comparing the chemoattractant at different times in its trajectory; whereas, a slow-moving, big cell performs better by comparing the chemoattractant concentration at its two ends.

Integrated Analysis of Intracellular Dynamics of MenaINV Cancer Cells in a 3D Matrix

The intracellular environment is composed of a filamentous network that exhibits dynamic turnover of cytoskeletal components and internal force generation from molecular motors. Particle tracking microrheology enables a means to probe the internal mechanics and dynamics. Here, we develop an analytical model to capture the basic features of the active intracellular mechanical environment, including both thermal and motor-driven effects, and show consistency with a diverse range of experimental microrheology data. We further perform microrheology experiments, integrated with Brownian dynamics simulations of the active cytoskeleton, on metastatic breast cancer cells embedded in a three-dimensional collagen matrix with and without the presence of epidermal growth factor to probe the intracellular mechanical response in a physiologically mimicking scenario. Our results demonstrate that EGF stimulation can alter intracellular stiffness and power output from molecular motor-driven fluctuations in cells overexpressing an invasive isoform of the actin-associated protein Mena.

Active rotational and translational microrheology beyond the linear spring regime

Active particle tracking microrheometers have the potential to perform accurate broadband measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here whereby error in measurements of the complex shear modulus can be significantly reduced by analyzing the motion of a spherical particle driven by nonlinear forces. In some scenarios error can be further reduced by applying a variable transformation which linearizes the equation of motion. This enables normalization that eliminates error introduced by low frequency drift in the particle's equilibrium position. Our measurements indicate that this can further resolve an additional decade of viscoelasticity at high frequencies. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.

Cytoskeletal architecture and its evolutionary significance in amoeboid eukaryotes and their mode of locomotion

The cytoskeleton is the hallmark of eukaryotic evolution. The molecular and architectural aspects of the cytoskeleton have been playing a prominent role in our understanding of the origin and evolution of eukaryotes. In this study, we seek to investigate the cytoskeleton architecture and its evolutionary significance in understudied amoeboid lineages belonging to Amoebozoa. These amoebae primarily use cytoplasmic extensions supported by the cytoskeleton to perform important cellular processes such as movement and feeding. Amoeboid structure has important taxonomic significance, but, owing to techniques used, its potential significance in understanding diversity of the group has been seriously compromised, leading to an under-appreciation of its value. Here, we used immunocytochemistry and confocal microscopy to study the architecture of microtubules (MTs) and F-actin in diverse groups of amoebae. Our results demonstrate that all Amoebozoa examined are characterized by a complex cytoskeletal array, unlike what has been previously thought to exist. Our results not only conclusively demonstrate that all amoebozoans possess complex cytoplasmic MTs, but also provide, for the first time, a potential synapomorphy for the molecularly defined Amoebozoa clade. Based on this evidence, the last common ancestor of amoebozoans is hypothesized to have had a complex interwoven MT architecture limited within the granular cell body. We also generate several cytoskeleton characters related to MT and F-actin, which are found to be robust for defining groups in deep and shallow nodes of Amoebozoa.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Superdiffusion in dispersions of active colloids driven by an external field and their sedimentation equilibrium

The diffusive behaviors of active colloids with run-and-tumble movement are explored by dissipative particle dynamics simulations for self-propelled particles (force dipole) and external field-driven particles (point force). The self-diffusion of tracers (solvent) is investigated as well. The influences of the active force, run time, and concentration associated with active particles are studied. For the system of self-propelled particles, the normal diffusion is observed for both active particles and tracers. The diffusivity of the former is significantly greater than that of the latter. For the system of field-driven particles, the superdiffusion is seen for both active particles and tracers. In contrast, it is found that the anomalous diffusion exponent of the former is slightly less than that of the latter. The anomalous diffusion is caused by the many-body, long-range hydrodynamic interactions. In spite of the superdiffusion, the sedimentation equilibrium of field-driven particles can be acquired and the density profile is still exponentially decayed. The sedimentation length of field-driven particles is always greater than that of self-propelled particles.

Impact of dimensionality and network disruption on microrheology of cancer cells in 3D environments

Dimensionality is a fundamental component that can have profound implications on the characteristics of physical systems. In cell biology, however, the majority of studies on cell physical properties, from rheology to force generation to migration, have been performed on 2D substrates, and it is not clear how a more realistic 3D environment influences cell properties. Here, we develop an integrated approach and demonstrate the combination of mitochondria-tracking microrheology, microfluidics, and Brownian dynamics simulations to explore the impact of dimensionality on intracellular mechanics and on the effects of intracellular disruption. Additionally, we consider both passive thermal and active motor-driven processes within the cell and demonstrate through modeling how active internal fluctuations are modulated via dimensionality. Our results demonstrate that metastatic breast cancer cells (MDA-MB-231) exhibit more solid-like internal motions in 3D compared to 2D, and actin network disruption via Cytochalasin D has a more pronounced effect on internal cell fluctuations in 2D. Our computational results and modeling show that motor-induced active stress fluctuations are enhanced in 2D, leading to increased local intracellular particle fluctuations and apparent fluid-like behavior.

Biomechanical properties at the cellular and subcellular levels are important in providing proper biological functions, from cell migratory capabilities to intracellular transport. Deregulation in these properties can lead to disease states such as cancer metastasis. We develop and demonstrate an integrated experimental and computational approach to study intracellular mechanics. We demonstrate that a key environmental factor, dimensionality, plays a significant role in modulating intracellular mechanical behavior. This is important as typical cell biology and mechanics experiments are performed on 2D substrates, which do not capture the physiological features of 3D matrices and may not induce physiologically accurate cell properties. We further develop an effective temperature model to describe how dimensionality changes intracellular particle motion by altering the activity of molecular motors.

Reconstruction of active regular motion in amoeba extract: dynamic cooperation between sol and gel states

Amoeboid locomotion is one of the typical modes of biological cell migration. Cytoplasmic sol–gel conversion of an actomyosin system is thought to play an important role in locomotion. However, the mechanisms underlying sol–gel conversion, including trigger, signal, and regulating factors, remain unclear. We developed a novel model system in which an actomyosin fraction moves like an amoeba in a cytoplasmic extract. Rheological study of this model system revealed that the actomyosin fraction exhibits shear banding: the sol–gel state of actomyosin can be regulated by shear rate or mechanical force. Furthermore, study of the living cell indicated that the shear-banding property also causes sol–gel conversion with the same order of magnitude as that of shear rate. Our results suggest that the inherent sol–gel transition property plays an essential role in the self-regulation of autonomous translational motion in amoeba.

Role of ion channels and transporters in cell migration

Cell motility is central to tissue homeostasis in health and disease, and there is hardly any cell in the body that is not motile at a given point in its life cycle. Important physiological processes intimately related to the ability of the respective cells to migrate include embryogenesis, immune defense, angiogenesis, and wound healing. On the other side, migration is associated with life-threatening pathologies such as tumor metastases and atherosclerosis. Research from the last ≈ 15 years revealed that ion channels and transporters are indispensable components of the cellular migration apparatus. After presenting general principles by which transport proteins affect cell migration, we will discuss systematically the role of channels and transporters involved in cell migration.

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.

Python algorithms in particle tracking microrheology

BACKGROUND

Particle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors.

RESULTS

We report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner.

CONCLUSIONS

The presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%.

First-passage-probability analysis of active transport in live cells

The first-passage-probability can be used as an unbiased method for determining the phases of motion of individual organelles within live cells. Using high speed microscopy, we observe individual lipid droplet tracks and analyze the motor protein driven motion. At short passage lengths (<10(-2)μm), a log-normal distribution in the first-passage-probability as a function of time is observed, which switches to a Gaussian distribution at longer passages due to the running motion of the motor proteins. The mean first-passage times (<t(FPT)>) as a function of the passage length (L), averaged over a number of runs for a single lipid droplet, follow a power law distribution <t(FPT)>~L(α), α>2, at short times due to a passive subdiffusive process. This changes to another power law at long times where 1<α<2, corresponding to sub-ballistic superdiffusive motion, an active process. Subdiffusive passive mean square displacements are observed as a function of time, <r(2)>~t(β), where 0<β<1 at short times again crossing over to an active sub-ballistic superdiffusive result 1<β<2 at longer times. Consecutive runs of the lipid droplets add additional independent Gaussian peaks to a cumulative first-passage-probability distribution indicating that the speeds of sequential phases of motion are independent and biochemically well regulated. As a result we propose a model for motor driven lipid droplets that exhibits a sequential run behavior with occasional pauses.

Splinelike interpolation in particle tracking microrheology

Converting time dependent creep compliance to frequency dependent complex shear modulus is an important step in analyzing the results of particle tracking microrheology. Fitting a function to the whole time range and transforming it to calculate the shear modulus is one way of solving this problem. However, the creep compliance of many samples, such as gels of biopolymers, shows different trends under different time regimes. Fitting in these regimes segmentwise results in a function which usually cannot be transformed in a closed analytical form. In general, unlike for beta and cubic splines, also the continuity of the first derivative cannot be ensured. In this paper, we present a method for using segmentwise fitting and numerical conversion, discussing interpolation for improving the transition between the fitted ranges, and propose a dynamic sampling technique to control the accuracy of the resultant complex shear modulus.

Analytical tools to distinguish the effects of localization error, confinement, and medium elasticity on the velocity autocorrelation function

Single particle tracking is a powerful technique for investigating the dynamic behavior of biological molecules. However, many of the analytical tools are prone to generate results that can lead to mistaken interpretations of the underlying transport process. Here, we explore the effects of localization error and confinement on the velocity autocorrelation function, Cυ. We show that calculation of Cυ across a range of discretizations can distinguish the effects of localization error, confinement, and medium elasticity. Thus, under certain regimes, Cυ can be used as a diagnostic tool to identify the underlying mechanism of anomalous diffusion. Finally, we apply our analysis to experimental data sets of chromosomal loci and RNA-protein particles in Escherichia coli.

High-throughput ballistic injection nanorheology to measure cell mechanics

High-throughput ballistic injection nanorheology is a method for the quantitative study of cell mechanics. Cell mechanics are measured by ballistic injection of submicron particles into the cytoplasm of living cells and tracking the spontaneous displacement of the particles at high spatial resolution. The trajectories of the cytoplasm-embedded particles are transformed into mean-squared displacements, which are subsequently transformed into frequency-dependent viscoelastic moduli and time-dependent creep compliance of the cytoplasm. This method allows for the study of a wide range of cellular conditions, including cells inside a 3D matrix, cell subjected to shear flows and biochemical stimuli, and cells in a live animal. Ballistic injection lasts <1 min and is followed by overnight incubation. Multiple particle tracking for one cell lasts <1 min. Forty cells can be examined in <1 h.

Magnetic nanomanipulations inside living cells compared with passive tracking of nanoprobes to get consensus for intracellular mechanics

During the last decade, the development of nanomaterials to penetrate inside living cells has been the focus of a large number of studies, with applications for the biomedical field. However, the further dynamics of these nanomaterials inside the cells is dictated by the intracellular environment and in particular its mechanical properties. The mechanical characteristics of the cell interior can be probed with either active or passive microrheological approaches. However, active intracellular microrheology is still in its infancy, owing to the difficulty of inserting probes that can be manipulated by external forces. Here we review recent active microrheology studies using magnetic nanoprobes inserted into endosomes or phagosomes as useful approaches for measuring frequency-dependent viscoelasticity, for mapping the viscoelastic landscape, as well as for identifying the contribution of individual cytoskeleton components and the influence of cell motility. The results of such direct measurements challenge the validity of more typical passive approaches in which the spontaneous displacement of embedded nanoprobes is measured. Here we discuss that one must distinguish probes suitable for use in conditions of thermal equilibrium, whose movements reflect the mechanical environment from probes that interact actively with the cytoplasm and cytoskeleton, in a state of nonequilibrium for which fluctuation-dissipation theorem no longer holds. However, when data on these probes' viscoelastic microenvironment is available, such passive probe movements can yield useful information on the forces responsible for intracellular activity.

Different diffusive regimes, generalized Langevin and diffusion equations

We investigate a generalized Langevin equation (GLE) in the presence of an additive noise characterized by the mixture of the usual white noise and an arbitrary one. This scenario lead us to a wide class of diffusive processes, in particular the ones whose noise correlation functions are governed by power laws, exponentials, and Mittag-Leffler functions. The results show the presence of different diffusive regimes related to the spreading of the system. In addition, we obtain a fractional diffusionlike equation from the GLE, confirming the results for long time.

Superdiffusion induced by a long-correlated external random force

We consider a particle immersed in a thermal reservoir and simultaneously subjected to an external random force that drives the system to a nonequilibrium situation. Starting from a Langevin equation description, we derive exact expressions for the mean-square displacement and the velocity autocorrelation function of the diffusing particle. An effective temperature is introduced to characterize the deviation from the internal equilibrium situation. Using a power-law force autocorrelation function, the mean-square displacement and the velocity autocorrelation function are analytically obtained in terms of Mittag-Leffler functions. In this case, we show that the present model exhibits a superdiffusive regime as a consequence of the competition between passive and active processes.

The physics of cancer: the role of physical interactions and mechanical forces in metastasis

Metastasis is a complex, multistep process responsible for >90% of cancer-related deaths. In addition to genetic and external environmental factors, the physical interactions of cancer cells with their microenvironment, as well as their modulation by mechanical forces, are key determinants of the metastatic process. We reconstruct the metastatic process and describe the importance of key physical and mechanical processes at each step of the cascade. The emerging insight into these physical interactions may help to solve some long-standing questions in disease progression and may lead to new approaches to developing cancer diagnostics and therapies.

Surprisingly simple mechanical behavior of a complex embryonic tissue

BACKGROUND

Previous studies suggest that mechanical feedback could coordinate morphogenetic events in embryos. Furthermore, embryonic tissues have complex structure and composition and undergo large deformations during morphogenesis. Hence we expect highly non-linear and loading-rate dependent tissue mechanical properties in embryos.

METHODOLOGY/PRINCIPAL FINDINGS

We used micro-aspiration to test whether a simple linear viscoelastic model was sufficient to describe the mechanical behavior of gastrula stage Xenopus laevis embryonic tissue in vivo. We tested whether these embryonic tissues change their mechanical properties in response to mechanical stimuli but found no evidence of changes in the viscoelastic properties of the tissue in response to stress or stress application rate. We used this model to test hypotheses about the pattern of force generation during electrically induced tissue contractions. The dependence of contractions on suction pressure was most consistent with apical tension, and was inconsistent with isotropic contraction. Finally, stiffer clutches generated stronger contractions, suggesting that force generation and stiffness may be coupled in the embryo.

CONCLUSIONS/SIGNIFICANCE

The mechanical behavior of a complex, active embryonic tissue can be surprisingly well described by a simple linear viscoelastic model with power law creep compliance, even at high deformations. We found no evidence of mechanical feedback in this system. Together these results show that very simple mechanical models can be useful in describing embryo mechanics.

Probing GFP-actin diffusion in living cells using fluorescence correlation spectroscopy

The cytoskeleton of eukaryotic cells is continuously remodeled by polymerization and depolymerization of actin. Consequently, the relative content of polymerized filamentous actin (F-actin) and monomeric globular actin (G-actin) is subject to temporal and spatial fluctuations. Since fluorescence correlation spectroscopy (FCS) can measure the diffusion of fluorescently labeled actin it seems likely that FCS allows us to determine the dynamics and hence indirectly the structural properties of the cytoskeleton components with high spatial resolution. To this end we investigate the FCS signal of GFP-actin in living Dictyostelium discoideum cells and explore the inherent spatial and temporal signatures of the actin cytoskeleton. Using the free green fluorescent protein (GFP) as a reference, we find that actin diffusion inside cells is dominated by G-actin and slower than diffusion in diluted cell extract. The FCS signal in the dense cortical F-actin network near the cell membrane is probed using the cytoskeleton protein LIM and is found to be slower than cytosolic G-actin diffusion. Furthermore, we show that polymerization of the cytoskeleton induced by Jasplakinolide leads to a substantial decrease of G-actin diffusion. Pronounced fluctuations in the distribution of the FCS correlation curves can be induced by latrunculin, which is known to induce actin waves. Our work suggests that the FCS signal of GFP-actin in combination with scanning or spatial correlation techniques yield valuable information about the local dynamics and concomitant cytoskeletal properties.

Characterization of hydrogel microstructure using laser tweezers particle tracking and confocal reflection imaging

Hydrogels are commonly used as extracellular matrix mimetics for applications in tissue engineering and increasingly as cell culture platforms with which to study the influence of biophysical and biochemical cues on cell function in 3D. In recent years, a significant number of studies have focused on linking substrate mechanical properties to cell function using standard methodologies to characterize the bulk mechanical properties of the hydrogel substrates. However, current understanding of the correlations between the microstructural mechanical properties of hydrogels and cell function in 3D is poor, in part because of a lack of appropriate techniques. Here we have utilized a laser tracking system, based on passive optical microrheology instrumentation, to characterize the microstructure of viscoelastic fibrin clots. Trajectories and mean square displacements were observed as bioinert PEGylated (PEG: polyethylene glycol) microspheres (1, 2 or 4.7 μm in diameter) diffused within confined pores created by the protein phase of fibrin hydrogels. Complementary confocal reflection imaging revealed microstructures comprised of a highly heterogeneous fibrin network with a wide range of pore sizes. As the protein concentration of fibrin gels was increased, our quantitative laser tracking measurements showed a corresponding decrease in particle mean square displacements with greater resolution and sensitivity than conventional imaging techniques. This platform-independent method will enable a more complete understanding of how changes in substrate mechanical properties simultaneously influence other microenvironmental parameters in 3D cultures.

Multiphase flow models of biogels from crawling cells to bacterial biofilms

This article reviews multiphase descriptions of the fluid mechanics of cytoplasm in crawling cells and growing bacterial biofilms. These two systems involve gels, which are mixtures composed of a polymer network permeated by water. The fluid mechanics of these systems is essential to their biological function and structure. Their mathematical descriptions must account for the mechanics of the polymer, the water, and the interaction between these two phases. This review focuses on multiphase flow models because this framework is natural for including the relative motion between the phases, the exchange of material between phases, and the additional stresses within the network that arise from nonspecific chemical interactions and the action of molecular motors. These models have been successful in accounting for how different forces are generated and transmitted to achieve cell motion and biofilm growth and they have demonstrated how emergent structures develop though the interactions of the two phases. A short description of multiphase flow models of tumor growth is included to highlight the flexibility of the model in describing diverse biological applications.

Experimental evidence of strong anomalous diffusion in living cells

We evaluated the transport of polymeric particles internalized into living cancer cells. The mean-square displacement demonstrates superdiffusion with a scaling exponent of 1.25. Scaling exponents of a range of displacement moments are bilinear with moment order, exhibiting slopes of 0.6 and 0.8. Thus, we present experimental evidence of strong anomalous diffusion. Bilinearity indicates that particle motion is composed of subdiffusive regimes separated by active yet nonballistic flights. We discuss the results in terms of particle interactions with their microenvironment.

Impact of external stimuli and cell micro-architecture on intracellular transport states

A living cell is a complex out-of-equilibrium system, in which a great variety of biochemical and physical processes have to be coordinated to ensure viability. We investigate properties of intracellular transport in single cells of the amoeba Dictyostelium discoideum, a relevant model organism due to its cytoskeleton simplicity. In the cells, vesicles undergo two types of motion: directed transport, driven by molecular motors on filaments, or thermal diffusion in a crowded active medium. We present results obtained with our recently developed TRAnSpORT algorithm, which performs a high-resolution temporal analysis of the track of endosomal superparamagnetic particles and splits intracellular transport into different motion states. It results in a two-state model, distinguishing active and passive transport phenomena. We can extract the precise effect of cellular micro- and nanoarchitecture on endosomal transport by disturbing the cytoskeleton through the use of depolymerizing drugs (Benomyl for microtubules, and Latrunculin A for F-actin). Further, we investigate how cytoskeleton filaments act together in order to maintain cell integrity, by applying external mechanical force on the magnetic particle and influencing its motion.

Cell mechanics: dissecting the physical responses of cells to force

It is now widely appreciated that normal tissue morphology and function rely upon cells' ability to sense and generate forces appropriate to their correct tissue context. Although the effects of forces on cells have been studied for decades, our understanding of how those forces propagate through and act on different cell substructures remains at an early stage. The past decade has seen a resurgence of interest, with a variety of different micromechanical methods in current use that probe cells' dynamic deformation in response to a time-varying force. The ability of researchers to carefully measure the mechanical properties of cells subjected to a variety of pharmacological and genetic interventions, however, currently outstrips our ability to quantitatively interpret the data in many cases. Despite these challenges, the stage is now set for the development of detailed models for cell deformability, motility, and mechanosensing that are rooted at the molecular level.

Particle-tracking microrheology of living cells: principles and applications

A multitude of cellular and subcellular processes depend critically on the mechanical deformability of the cytoplasm. We have recently introduced the method of particle-tracking microrheology, which measures the viscoelastic properties of the cytoplasm locally and with high spatiotemporal resolution. Here we establish the basic principles of particle-tracking microrheology, describing the advantages of this approach over more conventional approaches to cell mechanics. We present basic concepts of molecular mechanics and polymer physics relevant to the microrheological response of cells. Particle-tracking microrheology can probe the mechanical properties of live cells in experimentally difficult, yet more physiological, environments, including cells embedded inside a 3D matrix, adherent cells subjected to shear flows, and cells inside a developing embryo. Particle-tracking microrheology can readily reveal the lost ability of diseased cells to resist shear forces.

Mapping of spatiotemporal heterogeneous particle dynamics in living cells

Colloidal particles embedded in the cytoplasm of living mammalian cells have been found to display remarkable heterogeneity in their amplitude of motion. However, consensus on the significance and origin of this phenomenon is still lacking. We conducted experiments on Hmec-1 cells loaded with about 100 particles to reveal the intracellular particle dynamics as a function of both location and time. Central quantity in our analysis is the amplitude (A) of the individual mean-squared displacement (iMSD), averaged over a short time. Histograms of A were measured, (1) over all particles present at the same time and (2) for individual particles as a function of time. Both distributions showed significant broadening compared to particles in Newtonian liquid, indicating that the particle dynamics varies with both location and time. However, no systematic dependence of A on intracellular location was found. Both the (strong) spatial and (weak) temporal variations were further analyzed by correlation functions of A . Spatial cross correlations were rather weak down to interparticle distances of 1 microm , suggesting that the precise intracellular probe distribution is not crucial for observing a dynamic behavior that is representative for the whole cell. Temporal correlations of A decayed at approximately 10 s , possibly suggesting an intracellular reorganization at this time scale. These findings imply (1) that both individual particle dynamics and the ensemble averaged behavior in a given cell can be measured if there are enough particles per cell and (2) that the amplitude and power-law exponent of iMSDs can be used to reveal local dynamics. We illustrate this by showing how superdiffusive and subdiffusive behaviors may be hidden under an apparently diffusive global dynamics.

Quantitative imaging of colloidal flows

We present recent advances in the instrumentation and analysis methods for quantitative imaging of concentrated colloidal suspensions under flow. After a brief review of colloidal imaging, we describe various flow geometries for two and three-dimensional (3D) imaging, including a 'confocal rheoscope'. This latter combination of a confocal microscope and a rheometer permits simultaneous characterization of rheological response and 3D microstructural imaging. The main part of the paper discusses in detail how to identify and track particles from confocal images taken during flow. After analyzing the performance of the most commonly used colloid tracking algorithm by Crocker and Grier extended to flowing systems, we propose two new algorithms for reliable particle tracking in non-uniform flows to the level of accuracy already available for quiescent systems. We illustrate the methods by applying it to data collected from colloidal flows in three different geometries (channel flow, parallel plate shear and cone plate rheometry).

Micro- and macrorheology of mucus

Mucus is a complex biological material that lubricates and protects the human lungs, gastrointestinal (GI) tract, vagina, eyes, and other moist mucosal surfaces. Mucus serves as a physical barrier against foreign particles, including toxins, pathogens, and environmental ultrafine particles, while allowing rapid passage of selected gases, ions, nutrients, and many proteins. Its selective barrier properties are precisely regulated at the biochemical level across vastly different length scales. At the macroscale, mucus behaves as a non-Newtonian gel, distinguished from classical solids and liquids by its response to shear rate and shear stress, while, at the nanoscale, it behaves as a low viscosity fluid. Advances in the rheological characterization of mucus from the macroscopic to nanoscopic levels have contributed critical understanding to mucus physiology, disease pathology, and the development of drug delivery systems designed for use at mucosal surfaces. This article reviews the biochemistry that governs mucus rheology, the macro- and microrheology of human and laboratory animal mucus, rheological techniques applied to mucus, and the importance of an improved understanding of the physical properties of mucus to advancing the field of drug and gene delivery.

Microrheology of bacterial biofilms in vitro: Staphylococcus aureus and Pseudomonas aeruginosa

The rheology of bacterial biofilms at the micron scale is an important step to understanding the communal lifecycles of bacteria that adhere to solid surfaces, as it measures how they mutually adhere and desorb. Improvements in particle-tracking software and imaging hardware have allowed us to successfully employ particle-tracking microrheology to measuring single-species bacterial biofilms, based on Staphlococcus aureus and Pseudomonas aeruginosa. By tracking displacements of the cells at a range of timescales, we separate active and thermal contributions to the cell motion. The S. aureus biofilms in particular show power-law rheology, in common with other dense colloidal suspensions. By calculating the mean compliance of S. aureus biofilms, we observe them becoming less compliant during growth, and more compliant during starvation. The biofilms are rheologically inhomogeneous on the micron scale, as a result of the strength of initial adhesion to the flow cell surface, the arrangement of individual bacteria, and larger-scale structures such as flocs of P. aeruginosa. Our S. aureus biofilms became homogeneous as a function of height as they matured: the rheological environment experienced by a bacterium became independent of how far it lived from the flow cell surface. Particle-tracking microrheology provides a quantitative measure of the "strength" of a biofilm. It may therefore prove useful in identifying drug targets and characterizing the effect of specific molecular changes on the micron-scale rheology of biofilms.