During migration cells exhibit a rich variety of seemingly random migration patterns, which makes unraveling the underlying mechanisms that control cell migration a daunting challenge. For efficient migration cells require a mechanism for polarization, so that traction forces are produced in the direction of motion, while adhesion is released to allow forward migration. To simplify the study of this process cells have been studied when placed along one-dimensional tracks, where single cells exhibit both smooth and stick-slip migration modes. The stick-slip motility mode is characterized by protrusive motion at the cell front, coupled with slow cell elongation, which is followed by rapid retractions of the cell back. In this study, we explore a minimal physical model that couples the force applied on the adhesion bonds to the length variations of the cell and the traction forces applied by the polarized actin retrograde flow. We show that the rich spectrum of cell migration patterns emerges from this model as different \emph{deterministic} dynamical phases. This result suggests a source for the large cell-to-cell variability (CCV) in cell migration patterns observed in single cells over time and within cell populations. The large heterogeneity can arise from small fluctuations in the cellular components that are greatly amplified due to moving the cells' internal state across the dynamical phase transition lines. Temporal noise is shown to drive random changes in the cellular polarization direction, which is enhanced during the stick-slip migration mode. These results offer a new framework to explain experimental observations of migrating cells, resulting from noisy switching between underlying deterministic migration modes.
Adhesive cell-substrate interactions are crucial for cell motility and are responsible for the necessary traction that propels cells. These interactions can also change the shape of the cell, analogous to liquid droplet wetting on adhesive substrates. To address how these shape changes affect cell migration and cell speed we model motility using deformable, 2D cross-sections of cells in which adhesion and frictional forces between cell and substrate can be varied separately. Our simulations show that increasing the adhesion results in increased spreading of cells and larger cell speeds. We pro…
The migration of cells through tight constricting spaces or along fibrous tracks in tissues is important for biological processes, such as embryogenesis, wound healing, and cancer metastasis, and depends on the mechanical properties of the cytoskeleton. Migratory cells often express and upregulate the intermediate filament protein vimentin. The viscoelasticity of vimentin networks in shear deformation has been documented, but its role in motility is largely unexplored. Here, we studied the effects of vimentin on cell motility and stiffness using mouse embryo fibroblasts derived from wild-type …
Recent experiments suggest that the interplay between cells and the mechanics of their substrate gives rise to a diversity of morphological and migrational behaviors. Here, we develop a Cellular Potts Model of polarizing cells on a visco-elastic substrate. We compare our model with experiments on endothelial cells plated on polyacrylamide hydrogels to constrain model parameters and test predictions. Our analysis reveals that morphology and migratory behavior are determined by an intricate interplay between cellular polarization and substrate strain gradients generated by traction forces exerte…
Shape matters: Inferring the motility of confluent cells from static images
Eindhoven University of Technology（埃因霍温理工大学）；Complutense University of Madrid（马德里康普顿斯大学）；Netherlands eScience Center（荷兰电子科学中心）；Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎大学）；Institute for Complex Molecular Systems, Eindhoven University of Technology（埃因霍温理工大学复杂分子系统研究所）
The dynamics of active matter driven by interacting molecular motors has a non-potential structure at the local scale. However, we show that there exists a quasi-potential effectively describing the collective self-organization of the motors propelling a cell at a continuum active gel level. Such a model allows us to understand cell motility as an active phase transition problem between the static and motile steady state configurations that minimize the quasi-potential. In particular both configurations can coexist in a metastable fashion and a small stochastic disorder in the gel is sufficien…
Suspensions of swimming micro-organisms provide examples of coordinated active dynamics. That has stimulated the study of a phenomenological theory combining synchronization and polar order in active matter. Here, we consider another example inspired by the traction forces of migrating cells. The novelty, in this case, is the global force-free nature of the traction force field. Such a constraint is absent in the case where the vector field describes swimming speeds in micro-organisms suspensions. Cell traction is characterized by means of a complex tensor quantity, that generalizes the nemati…
Collective cell migration in cohesive units is vital for tissue morphogenesis, wound repair, and immune response. While the fundamental driving forces for collective cell motion stem from contractile and protrusive activities of individual cells, it remains unknown how their balance is optimized to maintain tissue cohesiveness and the fluidity for motion. Here we present a cell-based computational model for collective cell migration during wound healing that incorporates mechanochemical coupling of cell motion and adhesion kinetics with stochastic transformation of active motility forces. We s…
While cell crawling on a solid surface is relatively well understood, and relies on substrate adhesion, some cells can also swim in the bulk, through mechanisms that are still largely unclear. Here, we propose a minimal model for in-bulk self-motility of a droplet containing an isotropic and compressible contractile gel, representing a cell extract containing a disordered actomyosin network. In our model, contraction mediates a feedback loop between myosin-induced flow and advection-induced myosin accumulation, which leads to clustering and a locally enhanced flow. Interactions of the emerging…
Cell migration is an indispensable physiological and pathological process for normal tissue development and cancer metastasis, which is greatly regulated by intracellular signal pathways and extracellular microenvironment (ECM). However, there is a lack of adequate tools to analyze the time-varying cell migration characteristics because of the effects of some factors, i.e., the ECM including the time-dependent local stiffness due to microstructural remodeling by migrating cells. Here, we develop an approach to derive the time-dependent motility parameters from cellular trajectories, based on t…
The motility of a cell can be triggered or inhibited not only by an applied force but also by a mechanically neutral force couple. This type of loading, represented by an applied stress and commonly interpreted as either squeezing or stretching, can originate from extrinsic interaction of a cell with its neighbors. To quantify the effect of applied stresses on cell motility we use an analytically transparent one-dimensional model accounting for active myosin contraction and induced actin turnover. We show that stretching can polarize static cells and initiate cell motility while squeezing can …
Eukaryotic cells adhere to extracellular matrix during the normal development of the organism, forming static adhesion as well as during cell motility. We study this process by considering a simplified coarse-grained model of a vesicle that has uniform adhesion energy with a flat substrate, mobile curved membrane proteins and active forces. We find that a high concentration of curved proteins alone increases the spreading of the vesicle, by the self-organization of the curved proteins at the high curvature vesicle-substrate contact line, thereby reducing the bending energy penalty at the vesic…
The one-dimensional crawling movement of a cell is considered in this theoretical study. Our active gel model shows that for a cell with weakly mechanosensitive adhesion complexes, as myosin contractility increases, a cell starts to move at a constant velocity. As the mechanosensitivity of the adhesion complexes increases, a cell can exhibit stick-slip motion. Finally, a cell with highly mechanosensitive adhesion complexes exhibits periodic back-and-forth migration. A simplified model which assumes that the cell crawling dynamics are controlled by the evolution of the myosin density dipole and…
Cell motility is one of the most fundamental phenomena underlying biological processes that maintain living organisms alive. Here we introduce a simple model to describe the motility of cells which include not only time-correlated internal forces but also the biological variability which is inherent of the intra-cellular biochemical processes. Such model allow us to derive exact expressions for the mean-squared displacement and the effective time-dependent diffusion coefficient which are compared to numerical results obtained from non-markovian stochastic simulations. In addition, we show that…
We study the clustering of a model cyanobacterium \textit{Synechocystis} into microcolonies. The bacteria are allowed to diffuse onto surfaces of different hardness, and interact with the others by aggregation and detachment. We find that soft surfaces give rise to more microcolonies than hard ones. This effect is related to the amount of heterogeneity of bacteria's dynamics as given by the proportion of motile cells. A kinetic model that emphasizes specific interactions between cells, complemented by extensive numerical simulations considering various amounts of motility, describes the experi…
The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity, and (iii) when the polarity direction executes a persistent random walk.In all three cases, we observe a sharp transition from a jammed state (…
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell l…
Many bacteria rely on active cell appendages, such as type IV pili, to move over substrates and interact with neighboring cells. Here, we study the motion of individual cells and bacterial colonies, mediated by the collective interactions of multiple pili. It was shown experimentally that the substrate motility of Neisseria gonorrhoeae cells can be described as a persistent random walk with a persistence length that exceeds the mean pili length. Moreover, the persistence length increases for a higher number of pili per cell. With the help of a simple, tractable stochastic model, we test whethe…
Many mature bacterial colonies and biofilms are complex three-dimensional (3D) structures. One key step in their developmental program is a transition from a two-dimensional (2D) monolayer into a 3D architecture. Despite the importance of controlling the growth of microbial colonies and biofilms in a variety of medical and industrial settings, the underlying physical mechanisms behind single-cell dynamics, collective behaviors of densely-packed cells, and 3D complex colony expansion remain largely unknown. In this work, we explore the mechanisms behind the 2D-to-3D transition of motile Pseudom…
The ability of cells to move through small spaces depends on the mechanical properties of the cellular cytoskeleton and on nuclear deformability. In mammalian cells, the cytoskeleton is comprised of three interacting, semi-flexible polymer networks: actin, microtubules, and intermediate filaments (IF). Recent experiments of mouse embryonic fibroblasts with and without vimentin have shown that the IF vimentin plays a role in confined cell motility. We, therefore, develop a minimal model of cells moving through confined geometries that effectively includes all three types of cytoskeletal filamen…
Combining high-resolution single cell tracking experiments with numerical simulations, we show that starvation-induced fruiting body (FB) formation in Myxococcus xanthus is a phase separation driven by cells that tune their motility over time. The phase separation can be understood in terms of cell density and a dimensionless Peclet number that captures cell motility through speed and reversal frequency. Our work suggests that M. xanthus take advantage of a self-driven non-equilibrium phase transition that can be controlled at the single cell level.
Peritrichous bacteria such as Escherichia coli swim in viscous fluids by forming a helical bundle of flagellar filaments. The filaments are spatially distributed around the cell body to which they are connected via a flexible hook. To understand how the swimming direction of the cell is determined, we theoretically investigate the elastohydrodynamic motility problem of a multi-flagellated bacterium. Specifically, we consider a spherical cell body with a number N of flagella which are initially symmetrically arranged in a plane in order to provide an equilibrium state. We analytically solve the…
Epithelial cell clusters often move collectively on a substrate. Mechanical signals play a major role in organizing this behavior. There are a number of experimental observations in these systems which await a comprehensive explanation. These include: the internal strains are tensile even for clusters that expand by proliferation; the tractions on the substrate are often confined to the edges of the cluster; there can exist density waves within the cluster; clusters can exhibit collective durotaxis when individual cells show no effect; and for cells in an annulus there is a transition between …
Drosophila melanogaster hemocytes are highly motile cells that are crucial for successful embryogenesis and have important roles in the organism's immunological response. Hemocyte motion was measured using selective plane illumination microscopy. Every hemocyte cell in one half of an embryo was tracked during embryogenesis and analysed using a deep learning neural network. The anomalous transport of the cells was well described by fractional Brownian motion that was heterogeneous in both time and space. Hemocyte motion became less persistent over time. LanB1 and SCAR mutants disrupted the coll…
