Mathematical Models for Cell Migration with Real-Time Cell Cycle Dynamics

The fluorescent ubiquitination-based cell cycle indicator, also known as FUCCI, allows the visualization of the G1 and S/G2/M cell cycle phases of individual cells. FUCCI consists of two fluorescent probes, so that cells in the G1 phase fluoresce red and cells in the S/G2/M phase fluoresce green. FUCCI reveals real-time information about cell cycle dynamics of individual cells, and can be used to explore how the cell cycle relates to the location of individual cells, local cell density, and different cellular microenvironments. In particular, FUCCI is used in experimental studies examining cell migration, such as malignant invasion and wound healing. Here we present, to our knowledge, new mathematical models that can describe cell migration and cell cycle dynamics as indicated by FUCCI. The fundamental model describes the two cell cycle phases, G1 and S/G2/M, which FUCCI directly labels. The extended model includes a third phase, early S, which FUCCI indirectly labels. We present experimental data from scratch assays using FUCCI-transduced melanoma cells, and show that the predictions of spatial and temporal patterns of cell density in the experiments can be described by the fundamental model. We obtain numerical solutions of both the fundamental and extended models, which can take the form of traveling waves. These solutions are mathematically interesting because they are a combination of moving wavefronts and moving pulses. We derive and confirm a simple analytical expression for the minimum wave speed, as well as exploring how the wave speed depends on the spatial decay rate of the initial condition.     

Gaussian Curvature Directs Stress Fiber Orientation and Cell Migration

We show that substrates with nonzero Gaussian curvature influence the organization of stress fibers and direct the migration of cells. To study the role of Gaussian curvature, we developed a sphere-with-skirt surface in which a positive Gaussian curvature spherical cap is seamlessly surrounded by a negative Gaussian curvature draping skirt, both with principal radii similar to cell-length scales. We find significant reconfiguration of two subpopulations of stress fibers when fibroblasts are exposed to these curvatures. Apical stress fibers in cells on skirts align in the radial direction and avoid bending by forming chords across the concave gap, whereas basal stress fibers bend along the convex direction. Cell migration is also strongly influenced by the Gaussian curvature. Real-time imaging shows that cells migrating on skirts repolarize to establish a leading edge in the azimuthal direction. Thereafter, they migrate in that direction. This behavior is notably different from migration on planar surfaces, in which cells typically migrate in the same direction as the apical stress fiber orientation. Thus, this platform reveals that nonzero Gaussian curvature not only affects the positioning of cells and alignment of stress fiber subpopulations but also directs migration in a manner fundamentally distinct from that of migration on planar surfaces.     

Collective Cell Migration in Embryogenesis Follows the Laws of Wetting

Collective cell migration is a fundamental process during embryogenesis and its initial occurrence, called epiboly, is an excellent in vivo model to study the physical processes involved in collective cell movements that are key to understanding organ formation, cancer invasion, and wound healing. In zebrafish, epiboly starts with a cluster of cells at one pole of the spherical embryo. These cells are actively spreading in a continuous movement toward its other pole until they fully cover the yolk. Inspired by the physics of wetting, we determine the contact angle between the cells and the yolk during epiboly. By choosing a wetting approach, the relevant scale for this investigation is the tissue level, which is in contrast to other recent work. Similar to the case of a liquid drop on a surface, one observes three interfaces that carry mechanical tension. Assuming that interfacial force balance holds during the quasi-static spreading process, we employ the physics of wetting to predict the temporal change of the contact angle. Although the experimental values vary dramatically, the model allows us to rescale all measured contact-angle dynamics onto a single master curve explaining the collective cell movement. Thus, we describe the fundamental and complex developmental mechanism at the onset of embryogenesis by only three main parameters: the offset tension strength, α, that gives the strength of interfacial tension compared to other force-generating mechanisms; the tension ratio, δ, between the different interfaces; and the rate of tension variation, λ, which determines the timescale of the whole process.     

Vinculin Force-Sensitive Dynamics at Focal Adhesions Enable Effective Directed Cell Migration

Cell migration is a complex process, requiring coordination of many subcellular processes including membrane protrusion, adhesion, and contractility. For efficient cell migration, cells must concurrently control both transmission of large forces through adhesion structures and translocation of the cell body via adhesion turnover. Although mechanical regulation of protein dynamics has been proposed to play a major role in force transmission during cell migration, the key proteins and their exact roles are not completely understood. Vinculin is an adhesion protein that mediates force-sensitive processes, such as adhesion assembly under cytoskeletal load. Here, we elucidate the mechanical regulation of vinculin dynamics. Specifically, we paired measurements of vinculin loads using a Förster resonance energy transfer-based tension sensor and vinculin dynamics using fluorescence recovery after photobleaching to measure force-sensitive protein dynamics in living cells. We find that vinculin adopts a variety of mechanical states at adhesions, and the relationship between vinculin load and vinculin dynamics can be altered by the inhibition of vinculin binding to talin or actin or reduction of cytoskeletal contractility. Furthermore, the force-stabilized state of vinculin required for the stabilization of membrane protrusions is unnecessary for random migration, but is required for directional migration along a substrate-bound cue. These data show that the force-sensitive dynamics of vinculin impact force transmission and enable the mechanical integration of subcellular processes. These results suggest that the regulation of force-sensitive protein dynamics may have an underappreciated role in many cellular processes.     

Topotaxis: A New Mechanism of Directed Cell Migration in Topographic ECM Gradients

Living cells orient the cytoskeleton polarity and directional migration in response to spatial gradients of multiple types of cues. The resulting tactic behaviors are critical for the proper cell localization in the context of complex single-cell and tissue behaviors. In this perspective, we highlight the recent discovery of, to our knowledge, a new -taxis phenomenon, the topotaxis, which mediates directional cell migration in response to the gradients of such topographic features as the density of extracellular matrix fibers. The direction of topotactic migration critically depends on the effective stiffness of the cortical cytoskeleton, which is controlled by the balance between two parallel signaling pathways activated by the extracellular matrix input. Topotaxis can account for such striking cell behaviors as the opposite directionality of migration of benign and metastatic cancer cells and certain aspects of the wound-healing process. We anticipate that, in conjunction with other tactic phenomena, topotaxis can provide critical information for understanding and design of tissue structure and function.     

Excessive Cell Growth Causes Cytoplasm Dilution And Contributes to Senescence

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Apical Junctional Fluctuations Lead to Cell Flow while Maintaining Epithelial Integrity

Epithelial sheet integrity is robustly maintained during morphogenesis, which is essential to shape organs and embryos. While maintaining the planar monolayer in three-dimensional space, cells dynamically flow via rearranging their connections between each other. However, little is known about how cells maintain the plane sheet integrity in three-dimensional space and provide cell flow in the in-plane sheet. In this study, using a three-dimensional vertex model, we demonstrate that apical junctional fluctuations allow stable cell rearrangements while ensuring monolayer integrity. In addition to the fluctuations, direction-dependent contraction on the apical cell boundaries, which corresponds to forces from adherens junctions, induces cell flow in a definite direction. We compared the kinematic behaviors of this apical-force-driven cell flow with those of typical cell flow that is driven by forces generated on basal regions and revealed the characteristic differences between them. These differences can be used to distinguish the mechanism of epithelial cell flow observed in experiments, i.e., whether it is apical- or basal-force-driven. Our numerical simulations suggest that cells actively generate fluctuations and use them to regulate both epithelial integrity and plasticity during morphogenesis.     

Loss of Paneth Cell Autophagy Causes Acute Susceptibility to Toxoplasma gondii-Mediated Inflammation

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