Flow and Diffusion in Channel-Guided Cell Migration

Collective migration of mechanically coupled cell layers is a notable feature of wound healing, embryonic development, and cancer progression. In confluent epithelial sheets, the dynamics have been found to be highly heterogeneous, exhibiting spontaneous formation of swirls, long-range correlations, and glass-like dynamic arrest as a function of cell density. In contrast, the flow-like properties of one-sided cell-sheet expansion in confining geometries are not well understood. Here, we studied the short- and long-term flow of Madin-Darby canine kidney (MDCK) cells as they moved through microchannels. Using single-cell tracking and particle image velocimetry (PIV), we found that a defined averaged stationary cell current emerged that exhibited a velocity gradient in the direction of migration and a plug-flow-like profile across the advancing sheet. The observed flow velocity can be decomposed into a constant term of directed cell migration and a diffusion-like contribution that increases with density gradient. The diffusive component is consistent with the cell-density profile and front propagation speed predicted by the Fisher-Kolmogorov equation. To connect diffusion-mediated transport to underlying cellular motility, we studied single-cell trajectories and occurrence of vorticity. We discovered that the directed large-scale cell flow altered fluctuations in cellular motion at short length scales: vorticity maps showed a reduced frequency of swirl formation in channel flow compared with resting sheets of equal cell density. Furthermore, under flow, single-cell trajectories showed persistent long-range, random-walk behavior superimposed on drift, whereas cells in resting tissue did not show significant displacements with respect to neighboring cells. Our work thus suggests that active cell migration manifests itself in an underlying, spatially uniform drift as well as in randomized bursts of short-range correlated motion that lead to a diffusion-mediated transport.     

Directed cell migration on fibronectin gradients: effect of gradient slope

The migration of human microvascular endothelial cells (hMEC) was measured on a range of fibronectin gradient slopes. hMEC drift speed increased with increasing gradient slope with no concurrent change in cellular persistence time or random cell speed. The frequency of discrete cellular motion in the gradient direction increased with gradient slope. Morphological polarization of cells on the gradients is also characterized and correlated with cellular drift speed. These experiments present the first demonstration of cellular response to changing haptotactic gradient slope using an in vitro system for the quantitative study of cell migration.     

Human papillomavirus type 16 entry: retrograde cell surface transport along actin-rich protrusions

The lateral mobility of individual, incoming human papillomavirus type 16 pseudoviruses (PsV) bound to live HeLa cells was studied by single particle tracking using fluorescence video microscopy. The trajectories were computationally analyzed in terms of diffusion rate and mode of motion as described by the moment scaling spectrum. Four distinct modes of mobility were seen: confined movement in small zones (30-60 nm in diameter), confined movement with a slow drift, fast random motion with transient confinement, and linear, directed movement for long distances. The directed movement was most prominent on actin-rich cell protrusions such as filopodia or retraction fibres, where the rate was similar to that measured for actin retrograde flow. It was, moreover, sensitive to perturbants of actin retrograde flow such as cytochalasin D, jasplakinolide, and blebbistatin. We found that transport along actin protrusions significantly enhanced HPV-16 infection in sparse tissue culture, cells suggesting a role for in vivo infection of basal keratinocytes during wound healing.     

Multiscale mechanisms of cell migration during development: theory and experiment

Long-distance cell migration is an important feature of embryonic development, adult morphogenesis and cancer, yet the mechanisms that drive subpopulations of cells to distinct targets are poorly understood. Here, we use the embryonic neural crest (NC) in tandem with theoretical studies to evaluate model mechanisms of long-distance cell migration. We find that a simple chemotaxis model is insufficient to explain our experimental data. Instead, model simulations predict that NC cell migration requires leading cells to respond to long-range guidance signals and trailing cells to short-range cues in order to maintain a directed, multicellular stream. Experiments confirm differences in leading versus trailing NC cell subpopulations, manifested in unique cell orientation and gene expression patterns that respond to non-linear tissue growth of the migratory domain. Ablation experiments that delete the trailing NC cell subpopulation reveal that leading NC cells distribute all along the migratory pathway and develop a leading/trailing cellular orientation and gene expression profile that is predicted by model simulations. Transplantation experiments and model predictions that move trailing NC cells to the migratory front, or vice versa, reveal that cells adopt a gene expression profile and cell behaviors corresponding to the new position within the migratory stream. These results offer a mechanistic model in which leading cells create and respond to a cell-induced chemotactic gradient and transmit guidance information to trailing cells that use short-range signals to move in a directional manner.     

A novel supervised trajectory segmentation algorithm identifies distinct types of human adenovirus motion in host cells

Biological trajectories can be characterized by transient patterns that may provide insight into the interactions of the moving object with its immediate environment. The accurate and automated identification of trajectory motifs is important for the understanding of the underlying mechanisms. In this work, we develop a novel trajectory segmentation algorithm based on supervised support vector classification. The algorithm is validated on synthetic data and applied to the identification of trajectory fingerprints of fluorescently tagged human adenovirus particles in live cells. In virus trajectories on the cell surface, periods of confined motion, slow drift, and fast drift are efficiently detected. Additionally, directed motion is found for viruses in the cytoplasm. The algorithm enables the linking of microscopic observations to molecular phenomena that are critical in many biological processes, including infectious pathogen entry and signal transduction.     

Pattern formation of vascular smooth muscle cells subject to nonuniform fluid shear stress: mediation by gradient of cell density

Smooth muscle cells (SMCs) are organized in various patterns in blood vessels. Whereas straight blood vessels mainly contain circumferentially aligned SMCs, curved blood vessels are composed of axially aligned SMCs in regions with vortex blood flow. The vortex flow-dependent feature of SMC alignment suggests a role for nonuniform fluid shear stress in regulating the pattern formation of SMCs. Here, we demonstrate that, in experimental models with vascular polymer implants designed for the observation of neointima formation and SMC migration under defined fluid shear stress, nonuniform shear stress possibly plays a role in regulating the direction of SMC migration and alignment in the neointima of the vascular implant. It was found that fluid shear stress inhibited cell growth, and the presence of nonuniform shear stress influenced the distribution of total cell density and induced the formation of cell density gradients, which in turn directed SMC migration and alignment. In contrast, uniform fluid shear stress in a control model influenced neither the distribution of total cell density nor the direction of SMC migration and alignment. In both the uniform and nonuniform shear models, the gradient of total cell density was consistent with the alignment of SMCs. These observations suggest that nonuniform shear stress may regulate the pattern formation of SMCs, possibly via mediating the gradient of cell density in the neointima of vascular polymer implants.     

Substrate stiffness regulates cadherin-dependent collective migration through myosin-II contractility

The mechanical microenvironment is known to influence single-cell migration; however, the extent to which mechanical cues affect collective migration of adherent cells is not well understood. We measured the effects of varying substrate compliance on individual cell migratory properties in an epithelial wound-healing assay. Increasing substrate stiffness increased collective cell migration speed, persistence, and directionality as well as the coordination of cell movements. Dynamic analysis revealed that wounding initiated a wave of motion coordination from the wound edge into the sheet. This was accompanied by a front-to-back gradient of myosin-II activation and establishment of cell polarity. The propagation was faster and farther reaching on stiff substrates, indicating that substrate stiffness affects the transmission of directional cues. Manipulation of myosin-II activity and cadherin–catenin complexes revealed that this transmission is mediated by coupling of contractile forces between neighboring cells. Thus, our findings suggest that the mechanical environment integrates in a feedback with cell contractility and cell–cell adhesion to regulate collective migration.     

Rectified Cell Migration on Saw-Like Micro-Elastically Patterned Hydrogels with Asymmetric Gradient Ratchet Teeth

To control cell motility is one of the essential technologies for biomedical engineering. To establish a methodology of the surface design of elastic substrate to control the long-range cell movements, here we report a sophisticated cell culture hydrogel with a micro-elastically patterned surface that allows long-range durotaxis. This hydrogel has a saw-like pattern with asymmetric gradient ratchet teeth, and rectifies random cell movements. Durotaxis only occurs at boundaries in which the gradient strength of elasticity is above a threshold level. Consequently, in gels with unit teeth patterns, durotaxis should only occur at the sides of the teeth in which the gradient strength of elasticity is above this threshold level. Therefore, such gels are expected to support the long-range biased movement of cells via a mechanism similar to the Feynman-Smoluchowski ratchet, i.e., rectified cell migration. The present study verifies this working hypothesis by using photolithographic microelasticity patterning of photocurable gelatin gels. Gels in which each teeth unit was 100–120 µm wide with a ratio of ascending:descending elasticity gradient of 1:2 and a peak elasticity of ca. 100 kPa supported the efficient rectified migration of 3T3 fibroblast cells. In addition, long-range cell migration was most efficient when soft lanes were introduced perpendicular to the saw-like patterns. This study demonstrates that asymmetric elasticity gradient patterning of cell culture gels is a versatile means of manipulating cell motility.     

Pelagic-benthic transition of the harmful alga, Heterosigma akashiwo: Changes in swimming and implications for benthic cell distributions

Many harmful algal blooming (HAB) species transition between a vegetative, motile phase in the water column and a dormant, non-motile resting phase in the sediments. These life history transitions potentially regulate the timing, location and persistence of bloom events. Motility promotes aggregation and influences vertical distributions in the water column. However, the contribution of this behavior to benthic distributions of resting cells is currently unknown. We used video-tracking techniques to test the hypothesis that algal cells use active down-swimming during pelagic-benthic transition to favorably influence benthic distributions. In an experimental water column, we monitored cell swimming trajectories of Heterosigma akashiwo for 14 days after cells were signaled to enter the benthic resting stage. Using the statistical characteristics of individual cell trajectories, we developed a video-based motion assay to assign each tracked Heterosigma cell to one of three cell states known to occur during pelagic-benthic transition: induced motile, transitional and resting. The primary swimming characteristic influencing benthic distribution, net vertical velocity, was essentially the same for all three cell states. Hence, we found no evidence that active down-swimming influences benthic distributions. Our data suggest that benthic distributions of Heterosigma resting cells are similar to distributions of slowly sedimenting passive particles. These observations suggest that Heterosigma benthic resting cell distributions can be predicted by modeling the effects of cell sedimentation rates combined with geophysical flow patterns.     

A stochastic description of Dictyostelium chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells.     

Real-Time Motion Analysis Reveals Cell Directionality as an Indicator of Breast Cancer Progression

Cancer cells alter their migratory properties during tumor progression to invade surrounding tissues and metastasize to distant sites. However, it remains unclear how migratory behaviors differ between tumor cells of different malignancy and whether these migratory behaviors can be utilized to assess the malignant potential of tumor cells. Here, we analyzed the migratory behaviors of cell lines representing different stages of breast cancer progression using conventional migration assays or time-lapse imaging and particle image velocimetry (PIV) to capture migration dynamics. We find that the number of migrating cells in transwell assays, and the distance and speed of migration in unconstrained 2D assays, show no correlation with malignant potential. However, the directionality of cell motion during 2D migration nicely distinguishes benign and tumorigenic cell lines, with tumorigenic cell lines harboring less directed, more random motion. Furthermore, the migratory behaviors of epithelial sheets observed under basal conditions and in response to stimulation with epidermal growth factor (EGF) or lysophosphatitic acid (LPA) are distinct for each cell line with regard to cell speed, directionality, and spatiotemporal motion patterns. Surprisingly, treatment with LPA promotes a more cohesive, directional sheet movement in lung colony forming MCF10CA1a cells compared to basal conditions or EGF stimulation, implying that the LPA signaling pathway may alter the invasive potential of MCF10CA1a cells. Together, our findings identify cell directionality as a promising indicator for assessing the tumorigenic potential of breast cancer cell lines and show that LPA induces more cohesive motility in a subset of metastatic breast cancer cells.     

Leader cell positioning drives wound-directed collective migration in TGFβ-stimulated epithelial sheets

During wound healing and cancer metastasis, cells are frequently observed to migrate in collective groups. This mode of migration relies on the cooperative guidance of leader and follower cells throughout the collective group. The upstream determinants and molecular mechanisms behind such cellular guidance remain poorly understood. We use live-cell imaging to track the behavior of epithelial sheets of keratinocytes in response to transforming growth factor β (TGFβ), which stimulates collective migration primarily through extracellular regulated kinase 1/2 (Erk1/2) activation. TGFβ-treated sheets display a spatial pattern of Erk1/2 activation in which the highest levels of Erk1/2 activity are concentrated toward the leading edge of a sheet. We show that Erk1/2 activity is modulated by cellular density and that this functional relationship drives the formation of patterns of Erk1/2 activity throughout sheets. In addition, we determine that a spatially constrained pattern of Erk1/2 activity results in collective migration that is primarily wound directed. Conversely, global elevation of Erk1/2 throughout sheets leads to stochastically directed collective migration throughout sheets. Our study highlights how the spatial patterning of leader cells (cells with elevated Erk1/2 activity) can influence the guidance of a collective group of cells during wound healing.     

Cell Volume Fluctuations in MDCK Monolayers

Cells moving collectively in tissues constitute a form of active matter, in which collective motion depends strongly on driven fluctuations at the single-cell scale. Fluctuations in cell area and number density are often seen in monolayers, yet their role in collective migration is not known. Here we study density fluctuations at the single- and multicell level, finding that single-cell volumes oscillate with a timescale of 4 h and an amplitude of 20%; the timescale and amplitude are found to depend on cytoskeletal activity. At the multicellular scale, density fluctuations violate the central limit theorem, highlighting the role of nonequilibrium driving forces in multicellular density fluctuations.     

Diffusional and electrokinetic redistribution at the synapse: a physicochemical basis of synaptic competition

Coinnervating nerve terminals may compete for "stabilizing factors" confined within the postsynaptic cell. The competition could be achieved through a diffusion-mediated trapping the factor, facilitated by an activity-dependent electrokinetic migration of the factor toward the synaptic site. We have examined the evidence for diffusional and electrokinetic motions of cell surface and cytoplasmic components, the profile and magnitude of the electric field produced by the synaptic current, and the plausibility that these motions underlie the process of synaptic competition.     

A cellular automaton model for the migration of glioma cells

We present a study of in vitro cell migration in two dimensions as a first step towards understanding the mechanisms governing the motility of glioma cells. Our study is based on a cellular automaton model which aims at reproducing the kinetics of a lump of glioma cells deposited on a substrate of collagen. The dynamical effects of cell attraction and motion inertia are introduced through adequate automaton rules. We compare the density profiles given by the model to those obtained experimentally. The result of the best fit indicates a substantial cell-cell attraction due to cell-cell communication through gap junctions (or chemotaxis) and negligible inertia effects during migration. Tracking of individual migrating cells indicates highly convoluted cell trajectories.     

Differential effects of EGF gradient profiles on MDA-MB-231 breast cancer cell chemotaxis

Chemotaxis, directed cell migration in a gradient of chemoattractant, is an important biological phenomenon that plays pivotal roles in cancer metastasis. Newly developed microfluidic chemotaxis chambers (MCC) were used to study chemotaxis of metastatic breast cancer cells, MDA-MB-231, in EGF gradients of well-defined profiles. Migration behaviors of MDA-MB-231 cells in uniform concentrations of EGF (0, 25, 50, and 100 ng/ml) and EGF (0-25, 0-50, and 0-100 ng/ml) with linear and nonlinear polynomial profiles were investigated. MDA-MB-231 cells exhibited increased speed and directionality upon stimulation with uniform concentrations of EGF. The cells were viable and motile for over 24 h, confirming the compatibility of MCC with cancer cells. Linear concentration gradients of different ranges were not effective in inducing chemotactic movement as compared to nonlinear gradients. MDA-MB-231 cells migrating in EGF gradient of 0-50 ng/ml nonlinear polynomial profile exhibited marked directional movement toward higher EGF concentration. This result suggests that MDA-MB-231 cancer cell chemotaxis depends on the shape of gradient profile as well as on the range of EGF concentrations.     

Single-vesicle tracking reveals the potential correlation of the movement of cell-bound membrane vesicles (CBMVs) with cell migration

The movement of cell-bound membrane vesicles (CBMVs) on migrating cells is poorly understood. We hypothesized that the movement of CBMVs on migrating cells is different from that on non-migrating cells and can be interfered by external stimuli. To test it, single-vesicle tracking was performed to analyze motion type, speed, displacement, and direction of CBMVs on migrating cells treated with different reagents (Ang-1, TNF-α, LPS, VEGFα, endostatin, Cytochalasin D, and nocodazole) among which the former four promoted cell migration whereas the others inhibited cell migration. We found that cell migration changed CBMVs from non-directed to directed motion and that most CBMVs on untreated migrating cells moved along the migration axis. Interestingly, the migration-promoting reagents played positive roles in CBMV movement (improving directed motion, speed and/or maximal displacement, upregulating the amount of vesicles moving in migration direction) whereas the migration-inhibiting reagents played negative roles (impairing/abolishing directed motion, speed and/or maximal displacement, downregulating the vesicles moving forward or causing an even distribution of motion direction). The cytoskeleton (particularly microtubules) probably played vital roles in CBMV movement on migrating cells and mediated the effects of stimuli on vesicle movement. The data may provide important information for understanding the properties, behaviors, and functions of CBMVs.     

Influence of the safety factor inhomogeneity on collisionless current generation in tokamaks

An improved scaling for the current density generated due to collisionless motion of α-particles in a tokamak is proposed. The dependence of the current density on the radial profile of the safety factor q is investigated. Monotonically increasing q profiles are considered, as well as q profiles with a minimum in the axial region of the plasma column. It is shown that the current density depends on the variation in q along the charged particle trajectories, rather than on the q value at the starting magnetic surface. The dependence of the current density on the gradient of q is strongest in the plasma core because of the large deviation of the drift surfaces from the magnetic ones in this region. At the plasma edge, the larger the second derivative of the plasma density, the greater the contribution of the gradient of q. For conventional plasma density profiles, the poloidal-angle-averaged current density calculated for a varying safety factor q is always lower than that calculated for a constant q. The effect of the nonuniformity of the safety factor on the current generation at the magnetic axis of a tokamak is investigated.     

Centrosome reorientation in wound-edge cells is cell type specific

The reorientation of the microtubule organizing center during cell migration into a wound in the monolayer was directly observed in living wound-edge cells expressing gamma-tubulin tagged with green fluorescent protein. Our results demonstrate that in CHO cells, the centrosome reorients to a position in front of the nucleus, toward the wound edge, whereas in PtK cells, the centrosome lags behind the nucleus during migration into the wound. In CHO cells, the average rate of centrosome motion was faster than that of the nucleus; the converse was true in PtK cells. In both cell lines, centrosome motion was stochastic, with periods of rapid motion interspersed with periods of slower motion. Centrosome reorientation in CHO cells required dynamic microtubules and cytoplasmic dynein/dynactin activity and could be prevented by altering cell-to-cell or cell-to-substrate adhesion. Microtubule marking experiments using photoactivation of caged tubulin demonstrate that microtubules are transported in the direction of cell motility in both cell lines but that in PtK cells, microtubules move individually, whereas their movement is more coherent in CHO cells. Our data demonstrate that centrosome reorientation is not required for directed migration and that diverse cells use distinct mechanisms for remodeling the microtubule array during directed migration.     

Lateral diffusion in an archipelago. Single-particle diffusion.

Several laboratories have measured lateral diffusion of single particles on the cell surface, and these measurements may reveal an otherwise inaccessible level of submicroscopic organization of cell membranes. Pitfalls in the interpretation of these experiments are analyzed. Random walks in unobstructed systems show structure that could be interpreted as free diffusion, obstructed diffusion, directed motion, or trapping in finite domains. To interpret observed trajectories correctly, one must consider not only the trajectories themselves but also the probabilities of occurrence of various trajectories. Measures of the asymmetry of obstructed and unobstructed random walks are calculated, and probabilities are evaluated for random trajectories that resemble either directed motion or diffusion in a bounded region.