Collective cell migration over long time scales reveals distinct phenotypes.

INTRODUCTION: Migratory phenotypes of metastasizing tumor cells include single and collective cell migration. While migration of tumor cells is generally less cooperative than that of normal epithelial cells, our understanding of precisely how they differ in long time behavior is incomplete. OBJECTIVES: We measure in a model system how cancer progression affects collective migration on long time scales, and determine how perturbation of cell-cell adhesions, specifically reduced E-cadherin expression, affects the collective migration phenotype. METHODS: Time lapse imaging of cellular sheets and particle image velocimetry (PIV) are used to quantitatively study the dynamics of cell motion over ten hours. Long time dynamics are measured via finite time Lyapunov exponents (FTLE) and changes in FTLE with time. RESULTS: We find that non-malignant MCF10A cells are distinguished from malignant MCF10CA1a cells by both their short time (minutes) and long time (hours) dynamics. In addition, short time dynamics distinguish non-malignant E-cadherin knockdown cells from the control, but long time dynamics and increasing spatial correlations remain unchanged. DISCUSSION: Epithelial sheet collective behavior includes long time dynamics that cannot be captured by metrics that assess cooperativity based on short time dynamics, such as instantaneous speed or directionality. The use of metrics incorporating migration data over hours instead of minutes allows us to more precisely describe how E-cadherin, a clinically relevant adhesion molecule, affects collective migration. We predict that the long time scale metrics described here will be more robust and predictive of malignant behavior than analysis of instantaneous velocity fields alone.

Microstructural view of burrowing with a bioinspired digging robot.

RoboClam is a burrowing technology inspired by Ensis directus, the Atlantic razor clam. Atlantic razor clams should only be strong enough to dig a few centimeters into the soil, yet they burrow to over 70 cm. The animal uses a clever trick to achieve this: by contracting its body, it agitates and locally fluidizes the soil, reducing the drag and energetic cost of burrowing. RoboClam technology, which is based on the digging mechanics of razor clams, may be valuable for subsea applications that could benefit from efficient burrowing, such as anchoring, mine detonation, and cable laying. We directly visualize the movement of soil grains during the contraction of RoboClam, using a novel index-matching technique along with particle tracking. We show that the size of the failure zone around contracting RoboClam can be theoretically predicted from the substrate and pore fluid properties, provided that the timescale of contraction is sufficiently large. We also show that the nonaffine motions of the grains are a small fraction of the motion within the fluidized zone, affirming the relevance of a continuum model for this system, even though the grain size is comparable to the size of RoboClam.

Granular dynamics during impact.

We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. We vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of the linear depth-dependent term in the stopping force. We propose a simple model to account for the strain dependence of this term, owing to increased pressure in the pile. Interestingly, we find that the presence of the fluid does not affect the impact dynamics, suggesting that dynamic friction is not a factor. Using a laser sheet scanning technique to visualize internal grain motion, we measure the trajectory of each grain throughout an impact. Microscopically, our results indicate that weaker initial force chains result in more irreversible, plastic rearrangements, suggesting static friction between grains does play a substantial role in the energy dissipation.

Analysis of multiple physical parameters for mechanical phenotyping of living cells.

Since the cytoskeleton is known to regulate many cell functions, an increasing amount of effort to characterize cells by their mechanical properties has occured. Despite the structural complexity and dynamics of the multicomponent cytoskeleton, mechanical measurements on single cells are often fit to simple models with two to three parameters, and those parameters are recorded and reported. However, different simple models are likely needed to capture the distinct mechanical cell states, and additional parameters may be needed to capture the ability of cells to actively deform. Our new approach is to capture a much larger set of possibly redundant parameters from cells' mechanical measurement using multiple rheological models as well as dynamic deformation and image data. Principal component analysis and network-based approaches are used to group parameters to reduce redundancies and develop robust biomechanical phenotyping. Network representation of parameters allows for visual exploration of cells' complex mechanical system, and highlights unexpected connections between parameters. To demonstrate that our biomechanical phenotyping approach can detect subtle mechanical differences, we used a Microfluidic Optical Cell Stretcher to mechanically stretch circulating human breast tumor cells bearing genetically-engineered alterations in c-src tyrosine kinase activation, which is known to influence reattachment and invasion during metastasis.

Granular convection in microgravity.

We investigate the role of gravity on convection in a dense granular shear flow. Using a microgravity-modified Taylor-Couette shear cell under the conditions of parabolic flight microgravity, we demonstrate experimentally that secondary, convective-like flows in a sheared granular material are close to zero in microgravity and enhanced under high-gravity conditions, though the primary flow fields are unaffected by gravity. We suggest that gravity tunes the frictional particle-particle and particle-wall interactions, which have been proposed to drive the secondary flow. In addition, the degree of plastic deformation increases with increasing gravitational forces, supporting the notion that friction is the ultimate cause.

Microstructure evolution during impact on granular matter.

We study the impact of an intruder on a dense granular material. The process of impact and interaction between the intruder and the granular particles is modeled using discrete element simulations in two spatial dimensions. In the first part of the paper we discuss how the intruder's dynamics depends on (1) the intruder's properties, including its size, shape and composition, (2) the properties of the grains, including friction, polydispersity, structural order, and elasticity, and (3) the properties of the system, including its size and gravitational field. It is found that polydispersity and related structural order, and frictional properties of the granular particles, play a crucial role in determining impact dynamics. In the second part of the paper we consider the response of the granular system itself. We discuss the force networks that develop, including their topological evolution. The influence of friction and structural order on force propagation, including the transition from hyperbolic-like to elastic-like behavior is discussed, as well as the affine and nonaffine components of the grain dynamics. Several broad observations include the following: tangential forces between granular particles are found to play a crucial role in determining impact dynamics; both force networks and particle dynamics are correlated with the dynamics of the intruder itself.

Path to fracture in granular flows: dynamics of contact networks.

Capturing the dynamics of granular flows at intermediate length scales can often be difficult. We propose studying the dynamics of contact networks as a new tool to study fracture at intermediate scales. Using experimental three-dimensional flow fields with particle-scale resolution, we calculate the time evolving broken-links network and find that a giant component of this network is formed as shear is applied to this system. We implement a model of link breakages where the probability of a link breaking is proportional to the average rate of longitudinal strain (elongation) in the direction of the edge and find that the model demonstrates qualitative agreement with the data when studying the onset of the giant component. We note, however, that the broken-links network formed in the model is less clustered than our experimental observations, indicating that the model reflects less localized breakage events and does not fully capture the dynamics of the granular flow.

Feedback control of unstable cellular solidification fronts.

We present a feedback control scheme to stabilize unstable cellular patterns during the directional solidification of a binary alloy. The scheme is based on local heating of cell tips which protrude ahead of the mean position of all tips in the array. The feasibility of this scheme is demonstrated using phase-field simulations and, experimentally, using a real-time image processing algorithm, to track cell tips, coupled with a movable laser spot array device to heat the tips locally. We demonstrate, both numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable with uniform spacing through the feedback control which is maintained with minimal heating.

Distinguishing modes of eukaryotic gradient sensing.

We develop a mathematical model of phosphoinositide-mediated gradient sensing that can be applied to chemotactic behavior in highly motile eukaryotic cells such as Dictyostelium and neutrophils. We generate four variants of our model by adjusting parameters that control the strengths of coupled positive feedbacks and the importance of molecules that translocate from the cytosol to the membrane. Each variant exhibits a qualitatively different mode of gradient sensing. Simulations of characteristic behaviors suggest that differences between the variants are most evident at transitions between efficient gradient detection and failure. Based on these results, we propose criteria to distinguish between possible modes of gradient sensing in real cells, where many biochemical parameters may be unknown. We also identify constraints on parameters required for efficient gradient detection. Finally, our analysis suggests how a cell might transition between responsiveness and nonresponsiveness, and between different modes of gradient sensing, by adjusting its biochemical parameters.

Ordered clusters and dynamical states of particles in a vibrated fluid.

Fluid-mediated interactions between particles in a vibrating fluid lead to both long range attraction and short range repulsion. The resulting patterns include hexagonally ordered microcrystallites, time-periodic structures, and chaotic fluctuating patterns with complex dynamics. A model based on streaming flow gives a good quantitative account of the attractive part of the interaction.

Frictional properties of bidisperse granular matter: effect of mixing ratio.

The frictional response of granular binary mixtures to an applied shear stress is studied experimentally by sliding a rough plate across a granular surface. The static friction force is found to be up to 25% larger than a linear interpolation between the frictional properties of each component. The dynamical friction coefficient can exhibit a maximum, a minimum, or an oscillatory behavior as a function of mixing ratio, depending on the size ratio or shape of the two components. In addition, visualization of the granular flow makes it possible to show that the shear layer thickness and the characteristic shear displacement, over which a steady state dilation is reached, change linearly with the mass concentration.

Two-dimensional granular Poiseuille flow on an incline: multiple dynamical regimes.

We investigate experimentally the flow of a monolayer of spherical beads through a channel on a smooth incline that is bounded by rough sidewalls. Using high-speed video imaging and particle tracking, we measure the positions and velocities of all particles in the field of view. We find that the flows are accelerating and dilute if the channel exit is open. On the other hand, if the exit is constricted, flows can reach a state in which the local time-averaged velocity is invariant along the stream. In the latter case, we find a continuous transition from an oscillatory two-phase flow (2PF) regime with wide density variations to a uniform dense flow regime, depending on the channel width and the mean flow speed. These two regimes exhibit distinct density variation, time regularity, and transverse profiles. The rough sidewalls are found to be necessary for the 2PF regime. In the dense regions of both flows, particles exhibit temporary arches, long-range correlated velocities, inhomogenuous propagation of disturbances, and hexagonal lattice structures. On the other hand, the dilute regions of the two-phase flow are nearly collisionless. Existing models can neither fully describe the dynamics of both the dense and the dilute regions nor explain the spontaneous switching between them.

Granular shear flow dynamics and forces: experiment and continuum theory.

We analyze the main features of granular shear flow through experimental measurements in a Couette geometry and a comparison to a locally Newtonian, continuum model of granular flow. The model is based on earlier hydrodynamic models, adjusted to take into account the experimentally observed coupling between fluctuations in particle motion and mean-flow properties. Experimentally, the local velocity fluctuations are found to decrease more slowly with distance from the shear surface than the velocity. This can be explained by an effective viscosity that diverges more rapidly as the random-close-packing density is approached than is predicted by Enskog theory for dense hard-sphere systems. Experiment and theory are in good agreement, especially for the following key features of granular flow: The flow is confined to a small shear band, fluctuations decay approximately exponentially away from the sheared wall, and the shear stress is approximately independent of the shear velocity. The functional forms of the velocity and fluctuation profiles predicted by the model agree with the experimental results.

Front propagation of spatiotemporal chaos.

We study the dynamics of the front separating a spatiotemporally chaotic region from a stable steady region using a simple model applicable to periodically forced systems. In particular, we investigate both the coarsening of the front induced by the inherent "noise" of the chaotic region, and the long wavelength dynamics causing the front to develop cusps.

Mechanisms for slow strengthening in granular materials

Several mechanisms cause a granular material to strengthen over time at low applied stress. The strength is determined from the maximum frictional force F(max) experienced by a shearing plate in contact with wet or dry granular material after the layer has been at rest for a waiting time tau. The layer strength increases roughly logarithmically with tau only if a shear stress is applied during the waiting time. The mechanisms of strengthening are investigated by sensitive displacement measurements, and by imaging of particle motion in the shear zone. Granular matter can strengthen due to a slow shift in the particle arrangement under shear stress. Humidity also leads to strengthening, but is found not to be its sole cause. In addition to these time dependent effects, the static friction coefficient can also be increased by compaction of the granular material under some circumstances, and by a cycling of the applied shear stress.

Particle dynamics in sheared granular matter

The particle dynamics and shear forces of granular matter in a Couette geometry are determined experimentally. The normalized tangential velocity V(y) declines strongly with distance y from the moving wall, independent of the shear rate and of the shear dynamics. Local rms velocity fluctuations deltaV(y) scale with the local velocity gradient to the power 0.4+/-0.05. These results agree with a locally Newtonian, continuum model, where the granular medium is assumed to behave as a liquid with a local temperature [deltaV(y)](2) and density dependent viscosity.

Propagating front in an excited granular layer.

A partial monolayer of approximately 20 000 uniform spherical steel beads, vibrated vertically on a flat plate, shows remarkable ordering transitions and cooperative behavior just below 1g maximum acceleration. We study the stability of a quiescent disordered or "amorphous" state formed when the acceleration is switched off in the excited "gaseous" state. The transition from the amorphous state back to the gaseous state upon increasing the plate's acceleration is generally subcritical: An external perturbation applied to one bead initiates a propagating front that produces a rapid transition. We measure the front velocity as a function of the applied acceleration. This phenomenon is explained by a model based on a single vibrated particle with multiple attractors that is perturbed by collisions. A simulation shows that a sufficiently high rate of interparticle collisions can prevent trapping in the attractor corresponding to the nonmoving ground state.

Frictional mechanics of wet granular material.

The mechanical response of a wet granular layer to imposed shear is studied experimentally at low applied normal stress. The granular material is immersed in water and the shear is applied by sliding a plate resting on the upper surface of the layer. We monitor simultaneously the horizontal and the vertical displacements of the plate to submicron accuracy with millisecond time resolution. The relations between the plate displacement, the dilation of the layer and the measured frictional force are analyzed in detail. When slip begins, the dilation increases exponentially over a slip distance comparable to the particle radius. We find that the total dilation and the steady state frictional force do not depend on the driving velocity, but do depend linearly on the applied normal stress. The frictional force also depends linearly on the dilation rate (rather than the dilation itself), and reaches a maximum value during the transient acceleration. We find that the layer can temporarily sustain a shear stress that is in excess of the critical value that will eventually lead to slip. We describe an empirical model that describes much of what we observe. This model differs in some respects from those used previously at stresses 10(6) times larger.

Velocity statistics in excited granular media.

We present an experimental study of velocity statistics for a partial layer of inelastic colliding beads driven by a vertically oscillating boundary. Over a wide range of parameters (accelerations 3-8 times the gravitational acceleration), the probability distribution P(v) deviates measurably from a Gaussian for the two horizontal velocity components. It can be described by P(v) approximately exp(-mid R:v/v(c)mid R:(1.5)), in agreement with a recent theory. The characteristic velocity v(c) is proportional to the peak velocity of the boundary. The granular temperature, defined as the mean square particle velocity, varies with particle density and exhibits a maximum at intermediate densities. On the other hand, for free cooling in the absence of excitation, we find an exponential velocity distribution. Finally, we examine the sharing of energy between particles of different mass. The more massive particles are found to have greater kinetic energy. (c) 1999 American Institute of Physics.

Evolution of dendritic patterns during alloy solidification: onset of the initial instability.

The evolution of a dendritic pattern from a planar solid-liquid interface during directional solidification of a binary alloy was investigated experimentally. The model alloy used was the transparent organic crystal succinonitrile doped with the laser dye coumarin 152. The buildup of solute ahead of the initially stable planar interface and the subsequent instability of the planar front were measured in detail and compared with recent theoretical calculations by Warren and Langer [Warren, J. A. & Langer, J. S. (1993) Phys. Rev. E 47, 2702- 2712]. The fluorescence of coumarin 152 was used for direct observations of the evolution of the solute concentration profile ahead of the initially planar solid-liquid interface. UV absorption was used to produce thermal perturbations of the sample that generated spatially periodic modulations of the planar interface. This technique allows for measurement of both positive and negative linear growth coefficients (determined from the growth or decay rate of the modulation after the perturbation is switched off) for a large range of wave vectors. Measurements of the evolution of the concentration profile and the linear growth coefficients, and the occurrence of the initial instability, were in good agreement with the Warren-Langer predictions.