The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multi-phase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solid-like state and a fluid-like state tuned by cell motility and deformability - the ratio of the energetic costs of steric cell-cell repulsion and cell surface tension. When perturbed, solid tissues exhibit yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different, and point to ways in which it can be controlled.
Recent experiments on monolayers of spindle-like cells plated on adhesive stripe-shaped domains have provided a convincing demonstration that certain types of collective phenomena in epithelia are well described by active nematic hydrodynamics. While recovering some of the hallmark predictions of this framework, however, these experiments have also revealed a number of unexpected features that could be ascribed to the existence of chirality over length scales larger than the typical size of a cell. In this article we elaborate on the microscopic origin of chiral stresses in nematic cell monola…
Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resu…
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric component has been widely reported, at least for planar monolayers. Here we consider the stress attributed to the neighbourhood of each tricellular junction, evaluating in particular its leading-order antisymmetric component and the associated couple stresses, which characterise the degree to which individual cells experience (and resist) in-plane bending deformati…
We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cel…
Coordinated motion of cell monolayers during epithelial wound healing and tissue morphogenesis involves mechanical stress generation. Here we propose a model for the dynamics of epithelial expansion that couples mechanical deformations in the tissue to contractile activity and polarization in the cells. A new ingredient of our model is a feedback between local strain, polarization and contractility that naturally yields a mechanism for viscoelasticity and effective inertia in the cell monolayer. Using a combination of analytical and numerical techniques, we demonstrate that our model quantitat…
Collective cell migration plays a crucial role in many developmental processes that underlie morphogenesis, wound healing, or cancer progression. In such coordinated behaviours, cells are organised in coherent structures and actively migrate to serve different biological purposes. In some contexts, namely during epithelial wound healing, it is well known that a migrating free-edge monolayer develops finger-like instabilities, yet the onset is still under debate. Here, by means of theory and numerical simulations, we shed light on the main mechanisms driving the instability process, analysing t…
During the early-stages of embryo development, morphogenesis--- the emergence of shape and form in living organisms--- is almost exclusively associated with monolayers of tightly bound epithelial cells. To understand how such tissues change their shape, we construct a fully covariant active-hydrodynamic theory. At the cellular scale, stresses arise from apical contractility, mechanical response and the constraint of constant cell volume. Tissue-scale deformations emerge due to the balance between such cell-autonomous stresses and the displacement and shear of a low Reynolds number embedding fl…
Epithelial cell monolayers exhibit traveling mechanical waves. We rationalize this observation thanks to a hydrodynamic description of the monolayer as a compressible, active and polar material. We show that propagating waves of the cell density, polarity, velocity and stress fields may be due to a Hopf bifurcation occurring above threshold values of active coupling coefficients.
In developing organisms, internal cellular processes generate mechanical stresses at the tissue scale. The resulting deformations depend on the material properties of the tissue, which can exhibit long-ranged orientational order and topological defects. It remains a challenge to determine these properties on the time scales relevant for developmental processes. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. Specifically, we use a hydrodynamic description to characterize the stationary states of compressible active polar fluids around defec…
Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges $\pm 1/2$ are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive …
Many fascinating phenomena such as large-scale collective flows, enhanced fluid mixing and pattern formation have been observed in so-called active fluids, which are composed of particles that can absorb energy and dissipate it into the fluid medium. For active particles immersed in liquids, fluid-mediated viscous stresses can play an important role on the emergence of collective behavior. Here, we experimentally investigate their role in the dynamics of self-assembling magnetically-driven colloidal particles which can rapidly form organized hexagonal structures. We find that viscous stresses …
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…
We consider a monolayer of particles floating at a horizontal liquid-gas interface -- a particle raft. Upon compressing the monolayer in a Langmuir trough, the particles at first pack but ultimately the monolayer buckles out of the plane. We measure the stress profile within the raft at the onset of buckling and show for the first time that such systems exhibit a Janssen effect: the stress decays exponentially away from the compressing barriers over a length scale that depends on the width of the trough. We find quantitative agreement between the rate of decay and the simple theory presented b…
There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle elongation, emerge in monolayers of cells with isotropic shapes is an outstanding question. In this article we present a minimal model of cellular monolayers based on cell deformation and force transmission at the cell-cell interface that explains the formation of topological defects and captures the flow-field and stress patterns around them. By including mech…
It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects mechanical properties at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the ins…
We show that a small crystal trapped within a potential well and in contact with its own fluid, responds to large compressive stresses by a novel mechanism -- the transfer of complete lattice layers across the solid-fluid interface. Further, when the solid is impacted by a momentum impulse set up in the fluid, a coherently ejected lattice layer carries away a definite quantity of energy and momentum, resulting in a sharp peak in the calculated phonon absorption spectrum. Apart from its relevance to studies of stability and failure of small sized solids, such coherent nanospallation may be used…
Inspired by the recent realization of a 2D chiral fluid as an active monolayer droplet moving atop a 3D Stokesian fluid, we formulate mathematically its free-boundary dynamics. The surface droplet is described as a general 2D linear, incompressible, and isotropic fluid, having a viscous shear stress, an active chiral driving stress, and a Hall stress allowed by the lack of time-reversal symmetry. The droplet interacts with itself through its driven internal mechanics and by driving flows in the underlying 3D Stokes phase. We pose the dynamics as the solution to a singular integral-differential…
Monolayers of anisotropic cells exhibit long-ranged orientational order and topological defects. During the development of organisms, orientational order often influences morphogenetic events. However, the linkage between the mechanics of cell monolayers and topological defects remains largely unexplored. This holds specifically at the time scales relevant for tissue morphogenesis. Here, we build on the physics of liquid crystals to determine material parameters of cell monolayers. In particular, we use a hydrodynamical description of an active polar fluid to study the steady-state mechanical …
Mechanical forces influence the development and behavior of biological tissues. In many situations these forces are exerted or resisted by elastic compliant structures such as the own-tissue cellular matrix or other surrounding tissues. This kind of tissue-elastic body interactions are also at the core of many state-of-the-art {\it in situ} force measurement techniques employed in biophysics. This creates the need to model tissue interaction with the surrounding elastic bodies that exert these forces, raising the question: which are the minimum ingredients needed to describe such interactions?…
Using three-dimensional representation of confluent cell layers, we map the amorphous solid to fluid phase transition in active cell layers onto the two-dimensional (2D) site percolation universality class. Importantly, we unify two distinct, predominant, pathways associated with this transition; namely (i) cell-cell adhesion and (ii) active traction forces. For each pathway, we independently vary the corresponding control parameter and focus on the emergent mechanical stress patterns as the monolayer transitions from a glassy- to a fluid-like state. Through finite-size scaling analyses, our r…
The fcc Lennard-Jones crystal is used as a generic model of solid to study the elastic properties of thin films as a function of thickness and temperature. The Monte Carlo algorithm is used to calculate the average deformations along the axes in the isostress-isothermal ensemble that mimics a real uniaxial loading experiment. The four independent parameters (tetragonal symmetry The fcc Lennard-Jones crystal is used as a generic model of solid to study the elastic properties of thin films as a function of thickness and temperature. The Monte Carlo algorithm is used to calculate the average defo…
We report on the emergence of stable self-propelled bound defects in monolayers of active nematics, which form virtual full-integer topological defects in the form of vortices and asters. Through numerical simulations and analytical arguments, we identify the phase-space of the bound defect formation in active nematic monolayers. It is shown that an intricate synergy between the nature of active stresses and the flow-aligning behaviour of active particles can stabilise the motion of self-propelled positive half-integer defects into specific bound structures. Our findings uncover new complexiti…
