Comparing individual-based models of collective cell motion in a benchmark flow geometry.

Collectively coordinated cell migration plays a role in tissue embryogenesis, cancer, homeostasis and healing. To study these processes, different cell-based modelling approaches have been developed, ranging from lattice-based cellular automata to lattice-free models that treat cells as point-like particles or extended detailed cell shape contours. In the spirit of what Osborne et al. [PLOS Comput. Biol., 2017, 13, 1-34] did for cellular tissue structure simulation models, we here compare five simulation models of collective cell migration, chosen to be representatives in increasing order of included detail. They are Vicsek-Grégoire particles, Szabó-like particles, self-propelled Voronoi model, cellular Potts model, and multiparticle cells, where each model includes cell motility. We examine how these models compare when applied to the same biological problem, and what differences in behaviour are due to different model assumptions and abstractions. For this purpose, we use a benchmark that discriminates between complex material flow models, and that can be experimentally approached using cell cultures: the flow within a channel around a circular obstacle, that is, the geometry Stokes used in his historical 1851 experiment. For each model we explain how to best implement it; vary cell density, attraction force and alignment interaction; draw the resulting maps of velocity, density and deformation fields; and eventually discuss its respective advantages and limitations. We thus provide a recommendation on how to select a model to answer a given question, and we examine whether models of motile particles and motile cells display similar collective effects.

Live 3D imaging and mapping of shear stresses within tissues using incompressible elastic beads.

To investigate the role of mechanical constraints in morphogenesis and development, we have developed a pipeline of techniques based on incompressible elastic sensors. These techniques combine the advantages of incompressible liquid droplets, which have been used as precise in situ shear stress sensors, and of elastic compressible beads, which are easier to tune and to use. Droplets of a polydimethylsiloxane mix, made fluorescent through specific covalent binding to a rhodamin dye, are produced by a microfluidics device. The elastomer rigidity after polymerization is adjusted to the tissue rigidity. Its mechanical properties are carefully calibrated in situ, for a sensor embedded in a cell aggregate submitted to uniaxial compression. The local shear stress tensor is retrieved from the sensor shape, accurately reconstructed through an active contour method. In vitro, within cell aggregates, and in vivo, in the prechordal plate of the zebrafish embryo during gastrulation, our pipeline of techniques demonstrates its efficiency to directly measure the three dimensional shear stress repartition within a tissue.

Collective cell migration without proliferation: density determines cell velocity and wave velocity.

Collective cell migration contributes to embryogenesis, wound healing and tumour metastasis. Cell monolayer migration experiments help in understanding what determines the movement of cells far from the leading edge. Inhibiting cell proliferation limits cell density increase and prevents jamming; we observe long-duration migration and quantify space-time characteristics of the velocity profile over large length scales and time scales. Velocity waves propagate backwards and their frequency depends only on cell density at the moving front. Both cell average velocity and wave velocity increase linearly with the cell effective radius regardless of the distance to the front. Inhibiting lamellipodia decreases cell velocity while waves either disappear or have a lower frequency. Our model combines conservation laws, monolayer mechanical properties and a phenomenological coupling between strain and polarity: advancing cells pull on their followers, which then become polarized. With reasonable values of parameters, this model agrees with several of our experimental observations. Together, our experiments and model disantangle the respective contributions of active velocity and of proliferation in monolayer migration, explain how cells maintain their polarity far from the moving front, and highlight the importance of strain-polarity coupling and density in long-range information propagation.

Modulation of junction tension by tumor suppressors and proto-oncogenes regulates cell-cell contacts.

Tumor suppressors and proto-oncogenes play crucial roles in tissue proliferation. Furthermore, de-regulation of their functions is deleterious to tissue architecture and can result in the sorting of somatic rounded clones minimizing their contact with surrounding wild-type (wt) cells. Defects in the shape of somatic clones correlate with defects in proliferation, cell affinity, cell-cell adhesion, oriented cell division and cortical contractility. Combining genetics, live-imaging, laser ablation and computer simulations, we aim to analyze whether distinct or similar mechanisms can account for the common role of tumor suppressors and proto-oncogenes in cell-cell contact regulation. In Drosophila epithelia, the tumor suppressors Fat (Ft) and Dachsous (Ds) regulate cell proliferation, tissue morphogenesis, planar cell polarity and junction tension. By analyzing the evolution over time of ft mutant cells and clones, we show that ft clones reduce their cell-cell contacts with the surrounding wt tissue in the absence of concomitant cell divisions and over-proliferation. This contact reduction depends on opposed changes of junction tensions in the clone bulk and its boundary with neighboring wt tissue. More generally, either clone bulk or boundary junction tension is modulated by the activation of Yorkie, Myc and Ras, yielding similar contact reductions with wt cells. Together, our data highlight mechanical roles for proto-oncogene and tumor suppressor pathways in cell-cell interactions.

Robustness of force and stress inference in an epithelial tissue.

During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time (~minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.

PTEN controls junction lengthening and stability during cell rearrangement in epithelial tissue.

Planar cell rearrangements control epithelial tissue morphogenesis and cellular pattern formation. They lead to the formation of new junctions whose length and stability determine the cellular pattern of tissues. Here, we show that during Drosophila wing development the loss of the tumor suppressor PTEN disrupts cell rearrangements by preventing the lengthening of newly formed junctions that become unstable and keep on rearranging. We demonstrate that the failure to lengthen and to stabilize is caused by the lack of a decrease of Myosin II and Rho-kinase concentration at the newly formed junctions. This defect results in a heterogeneous cortical contractility at cell junctions that disrupts regular hexagonal pattern formation. By identifying PTEN as a specific regulator of junction lengthening and stability, our results uncover how a homogenous distribution of cortical contractility along the cell cortex is restored during cell rearrangement to control the formation of epithelial cellular pattern.

Mechanical control of morphogenesis by Fat/Dachsous/Four-jointed planar cell polarity pathway.

During animal development, several planar cell polarity (PCP) pathways control tissue shape by coordinating collective cell behavior. Here, we characterize by means of multiscale imaging epithelium morphogenesis in the Drosophila dorsal thorax and show how the Fat/Dachsous/Four-jointed PCP pathway controls morphogenesis. We found that the proto-cadherin Dachsous is polarized within a domain of its tissue-wide expression gradient. Furthermore, Dachsous polarizes the myosin Dachs, which in turn promotes anisotropy of junction tension. By combining physical modeling with quantitative image analyses, we determined that this tension anisotropy defines the pattern of local tissue contraction that contributes to shaping the epithelium mainly via oriented cell rearrangements. Our results establish how tissue planar polarization coordinates the local changes of cell mechanical properties to control tissue morphogenesis.

The role of fluctuations and stress on the effective viscosity of cell aggregates.

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses ("fluctuation-induced flow"). If not, changing the aggregate's shape requires a sufficiently large applied stress ("stress-induced flow"). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress tau*, the aggregate as a whole flows with an apparent viscosity eta*, and at higher stress it is a shear-thinning fluid. An increasing cell-cell tension results in a higher eta* (and thus a slower stress relaxation time t(c)). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find t(c) of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration.