Cell motility in higher organisms (eukaryotes) is crucial to biological functions ranging from wound healing to immune response, and also implicated in diseases such as cancer. For cells crawling on hard surfaces, significant insights into motility have been gained from experiments replicating such motion in vitro. Such experiments show that crawling uses a combination of actin treadmilling (polymerization), which pushes the front of a cell forward, and myosin-induced stress (contractility), which retracts the rear. Here we present a simplified physical model of a crawling cell, consisting of a droplet of active polar fluid with contractility throughout, but treadmilling connected to a thin layer near the supporting wall. The model shows a variety of shapes and/or motility regimes, some closely resembling cases seen experimentally. Our work strongly supports the view that cellular motility exploits autonomous physical mechanisms whose operation does not need continuous regulatory effort.
The mechanics of crawling cells on a substrate is investigated by using a minimal model that satisfies the force-free condition. A cell is described by two subcellular elements connected by a linear actuator that changes the length of the cell cyclically in time, together with periodic alternation of adhesive characters at the interface between the cell and the substrate. Here the key model parameters are the phase shifts between the elongation of the actuator and the alternation of the adhesion of the two elements. We emphasize that the phase shifts determine not only the efficiency of the cr…
Eukaryotic cell motility is crucial during development, wound healing, the immune response, and cancer metastasis. Some eukaryotic cells can swim, but cells more commonly adhere to and crawl along the extracellular matrix. We study the relationship between hydrodynamics and adhesion that describe whether a cell is swimming, crawling, or combining these motions. Our simple model of a cell, based on the three-sphere swimmer, is capable of both swimming and crawling. As cell-matrix adhesion strength increases, the influence of hydrodynamics on migration diminish. Cells with significant adhesion c…
The mechanosensitivity of cells, which determines how they are able to respond to mechanical signals received from their environment, is crucial for the functioning of all biological systems. In experiments, cells placed on cyclically stretched substrates have been shown to reorient in a direction that depends not only on the type of cell, but also on the mechanical properties of the substrate, and the amplitude and rate of stretching. However, the underlying biochemical and mechanical mechanisms responsible for this realignment are still not completely understood. In this study, we introduce …
Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a…
A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the cell dynamics. By considering a cell constrained to move along a one-dimensional thin track, we take advantage of the problem geometry to explicitly derive the effective law that describes the non-local frictional contact between the cell and the deformable substrate. We then couple such a law with one of the simplest model of the active flow within the cell…
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…
Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with ext…
There is increasing evidence that mammalian cells not only crawl on substrates but can also swim in fluids. To elucidate the mechanisms of the onset of motility of cells in suspension, a model which couples actin and myosin kinetics to fluid flow is proposed and solved for a spherical shape. The swimming speed is extracted in terms of key parameters. We analytically find super- and subcritical bifurcations from a non-motile to a motile state and also spontaneous polarity oscillations that arise from a Hopf bifurcation. Relaxing the spherical assumption, the obtained shapes show appealing trend…
Numerous physical models have been proposed to explain how cell motility emerges from internal activity, mostly focused on how crawling motion arises from internal processes. Here we offer a classification of self-propulsion mechanisms based on general physical principles, showing that crawling is not the only way for cells to move on a substrate. We consider a thin drop of active matter on a planar substrate and fully characterize its autonomous motion for all three possible sources of driving: (i) the stresses induced in the bulk by active components, which allow in particular tractionless m…
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…
The migration of cells is relevant for processes such as morphogenesis, wound healing, and invasion of cancer cells. In order to move, single cells deform cyclically. However, it is not understood how these shape oscillations influence collective properties. Here we demonstrate, using numerical simulations, that the interplay of directed motion, shape oscillations, and excluded volume enables cells to locally "synchronize" their motion and thus enhance collective migration. Our model captures elongation and contraction of crawling ameboid cells controlled by an internal clock with a fixed peri…
Experimental evidence shows that there is a feedback between cell shape and cell motion. How this feedback impacts the collective behavior of dense cell monolayers remains an open question. We investigate the effect of a feedback that tends to align the cell crawling direction with cell elongation in a biological tissue model. We find that the alignment interaction promotes nematic patterns in the fluid phase that eventually undergo a non-equilibrium phase transition into a quasi-hexagonal solid. Meanwhile, highly asymmetric cells do not undergo the liquid-to-solid transition for any value of …
Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves--crawling in some environments while swimming in others. The latter can involve movement by blebbing or other cyclic shape changes, and both highlysimplified and more realistic models of these modes have been studied previously. Herein we study swimming that is driven by membrane tension gradients that arise from flows in the actin cortex underlying the membrane, and does not involve imposed cyclic shape changes. Such gradients can lead to…
The dynamical phase-space of axisymmetric Canham-Helfrich (CH) cells is constructed from a Hamiltonian field recapitulating membrane curvature-elasticity and systemic restrictions. Guiding principles are reparametrization to convert a static geometric system into a dynamical system, and Galilean transformation, to build a transformed Lagrangian invariant with respect to the action described by the CH free-energy. Building on the fluidity postulate, this Lagrangian describes the cellular membrane as an inverted harmonic oscillator driven by bending elasticity and effective friction governed by …
The cell cortex, a thin film of active material assembled below the cell membrane, plays a key role in cellular symmetry breaking processes such as cell polarity establishment and cell division. Here, we present a minimal model of the self-organization of the cell cortex that is based on a hydrodynamic theory of curved active surfaces. Active stresses on this surface are regulated by a diffusing molecular species. We show that coupling of the active surface to a passive bulk fluid enables spontaneous polarization and the formation of a contractile ring on the surface via mechano-chemical insta…
The actin cytoskeleton of cells is in continuous motion due to both polymerization of new filaments and their contraction by myosin II molecular motors. Through adhesion to the substrate, such intracellular flow can be converted into cell migration. Recently, optogenetics has emerged as a new powerful experimental method to control both actin polymerization and myosin II contraction. While optogenetic control of polymerization can initiate cell migration by generating protrusion, it is less clear if and how optogenetic control of contraction can also affect cell migration. Here we analyze the …
We present a minimal computational model, which allows very fast, on-the-fly construction of three dimensional haploid interphase genomes from single cell Hi-C contact maps using the HOOMD-blue molecular dynamics package on graphics processing units. Chromosomes are represented by a string of connected beads, each of which corresponds to 100,000 base pairs, and contacts are mediated via a structure-based harmonic potential. We suggest and test two minimization protocols which consistently fold into conformationally similar low energy states. The latter are similar to previously published struc…
In this thesis we develop minimal models of the relationship between motility, growth, and evolution of cancer cells. We utilise simple simulations of a population of individual cells in space to examine how changes in mechanical properties of invasive cells and their surroundings can affect the speed of cell migration. We also find that the growth rate of large lesions depends weakly on the migration speed of escaping cells, and has stronger and more complex dependencies on the rates of other stochastic processes in the model, namely the rate at which cells transition to being motile and the …
