Mechanical signaling plays a key role in biological processes like embryo development and cancer growth. One prominent way to probe mechanical properties of tissues is to study their response to externally applied forces. Using a particle-based model featuring random apoptosis and environment-dependent division rates, we evidence a crossover from linear flow to a shear-thinning regime with increasing shear rate. To rationalize this non-linear flow we derive a theoretical mean-field scenario that accounts for the interplay of mechanical and active noise in local stresses. These noises are respectively generated by the elastic response of the cell matrix to cell rearrangements and by the internal activity.
The mechanics of biological tissues mainly proceeds from the cell cortex rheology. A direct, explicit link between cortex rheology and tissue rheology remains lacking, yet would be instrumental in understanding how modulations of cortical mechanics may impact tissue mechanical behaviour. Using an ordered geometry built on 3D hexagonal, incompressible cells, we build a mapping relating the cortical rheology to the monolayer tissue rheology. Our approach shows that the tissue low frequency elastic modulus is proportional to the rest tension of the cortex, as expected from the physics of liquid f…
Morphogenesis depends crucially on the complex rheological properties of cell tissues and on their ability to maintain mechanical integrity while rearranging at long times. In this paper, we study the rheology of polygonal cellular networks described by a vertex model in the presence of fluctuations. We use a triangulation method to decompose shear into cell shape changes and cell rearrangements. Considering the steady-state stress under constant shear, we observe nonlinear shear-thinning behavior at all magnitudes of the fluctuations, and an even stronger nonlinear regime at lower values of t…
When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly-responding cell is …
Adhesion differentials control the rheology of biomimetic emulsions
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Laboratoire Jean Perrin（让·佩兰实验室）；Inserm（法国国家健康与医学研究院）；Institut de Biologie Paris-Seine（巴黎塞纳生物学研究所）；Aix Marseille Univ（艾克斯-马赛大学）；Université de Toulon（土伦大学）；CPT (UMR 7332)（复杂系统物理中心（UMR 7332））；Turing Center for Living Systems（图灵生命系统中心）
Large-scale tissue deformation during biological processes such as morphogenesis requires cellular rearrangements. The simplest rearrangement in confluent cellular monolayers involves neighbor exchanges among four cells, called a T1 transition, in analogy to foams. But unlike foams, cells must execute a sequence of molecular processes, such as endocytosis of adhesion molecules, to complete a T1 transition. Such processes could take a long time compared to other timescales in the tissue. In this work, we incorporate this idea by augmenting vertex models to require a fixed, finite time for T1 tr…
Non-linear visco-elasto-plastic rheology of a viscous vertex model
Aix Marseille Univ, Université de Toulon, CNRS, CPT (UMR 7332), Turing Centre for Living systems（艾克斯-马赛大学，土伦大学，法国国家科学研究中心，理论物理与粒子物理中心（UMR 7332），图灵生命系统中心）；Institut für Theoretische Physik, Universität Innsbruck（因斯布鲁克大学理论物理研究所）
Exotic rheology of materials with active rearrangements
University of Bristol（布里斯托大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Exeter（埃克塞特大学）；Isaac Newton Institute for Mathematical Sciences（牛顿数学科学研究所）；Leiden University（莱顿大学）
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 …
Soft cellular systems, such as foams or biological tissues, exhibit highly complex rheological properties, even in the quasistatic regime, that numerical modeling can help to apprehend. We present a numerical implementation of quasistatic strain within the widely used cellular Potts model. The accuracy of the method is tested by simulating the quasistatic strain 2D dry foams, both ordered and disordered. The implementation of quasistatic strain in CPM allows the investigation of sophisticated interplays between stress-strain relationship and structural changes that take place in cellular syste…
Cell migration is important in many biological processes, including embryonic development, cancer metastasis, and wound healing. In these tissues, a cell's motion is often strongly constrained by its neighbors, leading to glassy dynamics. While self-propelled particle models exhibit a density-driven glass transition, this does not explain liquid-to-solid transitions in confluent tissues, where there are no gaps between cells and therefore the density is constant. Here we demonstrate the existence of a new type of rigidity transition that occurs in the well-studied vertex model for confluent ti…
Phase separation is as familiar as watching vinegar separating from oil in vinegrette. The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicate that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviours, which in turn may have biological significance. The aim of this perspective is to review the state…
The present work presents a density-functional microscopic model of soft biological tissue. The model was based on a prototype molecular structure from experimentally resolved collagen peptide residues and water clusters and has the objective to capture some well-known experimental features of soft tissues. It was obtained the optimized geometry, binding and coupling energies and dipole moments. The results concerning the stability of the confined water clusters, the water-water and water-collagen interactions within the CLBM framework were successfully correlated to some important trends obse…
In the theory of weakly non-linear elasticity, Hamilton et al. [J. Acoust. Soc. Am. \textbf{116} (2004) 41] identified $W = μI_2 + (A/3)I_3 + D I_2^2$ as the fourth-order expansion of the strain-energy density for incompressible isotropic solids. Subsequently, much effort focused on theoretical and experimental developments linked to this expression in order to inform the modeling of gels and soft biological tissues. However, while many soft tissues can be treated as incompressible, they are not in general isotropic, and their anisotropy is associated with the presence of oriented collagen fib…
Collective cell motility is crucial to many biological processes including morphogenesis, wound healing, and cancer invasion. Recently, the biology and biophysics communities have begun to use the term cell jamming to describe the collective arrest of cell motion in tissues. Although this term is widely used, the underlying mechanisms are varied. In this review, we highlight three independent mechanisms that can potentially drive arrest of cell motion -- crowding, tension-driven rigidity, and reduction of fluctuations -- and propose a speculative phase diagram that includes all three. Since mu…
Vertex models are a popular approach to modeling the mechanical and dynamical properties of dense biological tissues, describing the tissue as a network of connected polygons representing the cells. Recently a class of two-dimensional vertex models was shown to exhibit a disordered rigidity transition controlled by the preferred cellular geometry, echoing experimental findings. An attractive variant of these models uses a Voronoi tessellation to describe the cells and endows them with a non-equilibrium model of cellular motility, leading to rich, glassy behavior. This glassy behavior was sugge…
We propose a nonlinear extension of the standard tube model for semidilute solutions of freely-sliding semiflexible polymers. Non-affine filament deformations at the entanglement scale, the renormalisation of direct interactions by thermal fluctuations, and the geometry of large deformations are systematically taken into account. The stiffening response predicted for athermal solutions of stiff rods is found to be thermally suppressed. Instead, we obtain a broad linear response regime, supporting the interpretation of shear stiffening at finite frequencies in polymerised actin solutions as ind…
The rheological properties of cells and tissues are central to embryonic development and homoeostasis in adult tissues and organs and are closely related to their physiological activities. In this work, we present our study of rheological experiments on cell monolayer under serum starvation compared to that of healthy cell monolayer with full serum. The normal functioning of cells depends on the micronutrient supply provided by the serum in the growth media. Serum starvation is one of the most widely used procedures in cell biology. Serum deficiency may lead to genomic instability, variation i…
The rheology of biological tissues is important for their function, and we would like to better understand how single cells control global tissue properties such as tissue fluidity. A confluent tissue can fluidize when cells diffuse by executing a series of cell rearrangements, or T1 transitions. In a disordered 2D vertex model, the tissue fluidizes when the T1 energy barriers disappear as the target shape index approaches a critical value ($s^*_{0} \sim 3.81$), and the shear modulus describing the linear response also vanishes at this same critical point. However, the ordered ground states of…
We investigate the system size dependent rheological response of branched type I collagen gels. When subjected to a shear strain, the highly interconnected mesh dynamically reorients, resulting in overall stiffening of the network. When a continuous shear strain is applied to a collagen network, we observe that the local apparent modulus, in the strain-stiffening regime, is strongly dependent on the gel thickness. In addition, we demonstrate that the overall network failure is determined by the ratio of the gel thickness to the mesh size. These findings have broad implications for cell-matrix …
Similarly to their biological counterparts, suspensions of chemically-active autophoretic swimmers exhibit nontrivial dynamics involving self-organization processes as a result of inter-particle interactions. Using a kinetic model for a dilute suspension of autochemotactic Janus particles, we analyse the effect of a confined pressure-driven flow on these collective behaviours and the impact of chemotactic aggregation on the effective viscosity of the active fluid. Four dynamic regimes are identified when increasing the strength of the imposed pressure-driven flow, each associated with a differ…
In the last decade, rapid advances have been made in the field of micro-rheology of cells and tissues. Given the complexity of living systems, there is a need for the development of new types of nano- and micron-sized probes, and in particular of probes with controlled interactions with the surrounding medium. In the present paper, we evaluate the use of micron-sized wires as potential probes of the mechanical properties of cells. The wire-based micro-rheology technique is applied to living cells such as murine fibroblasts and canine kidney epithelial cells. The mean-squared angular displaceme…
In this paper we derive a model to describe the important inelastic features associated with the cyclic softening, often referred to as stress-softening, of soft biological tissue. The model developed here includes the notion of multiple stress-strain cycles with increasing values of the maximum strain. The model draws upon the similarities between the cyclic softening associated with carbon-filled rubber vulcanizates and soft biological tissue. We give non-linear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain. These idea…
In order to understand the mechanisms for glassy dynamics in biological tissues and shed light on those in non-biological materials, we study the low-temperature disordered phase of 2D vertex-like models. Recently it has been noted that vertex models have quite unusual behavior in the zero-temperature limit, with rigidity transitions that are controlled by residual stresses and therefore exhibit very different scaling and phenomenology compared to particulate systems. Here we investigate the finite-temperature phase of two-dimensional Voronoi and Vertex models, and show that they have highly u…
Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlle…
The size and shape of a large variety of polymeric particles, including biological cells, star polymers, dendrimes, and microgels, depend on the applied stresses as the particles are extremely soft. In high-density suspensions these particles deform as stressed by their neighbors, which implies that the interparticle interaction becomes of many-body type. Investigating a two-dimensional model of cell tissue, where the single particle shear modulus is related to the cell adhesion strength, here we show that the particle deformability affects the melting scenario. On increasing the temperature, …
Magnetic resonance imaging (MRI) is the method of choice for noninvasive studies of micrometer-scale structures in biological tissues via their effects on the time/frequency-dependent ("restricted") and anisotropic self-diffusion of water. Traditional MRI relies on pulsed magnetic field gradients to encode the signal with information about translational motion in the direction of the gradient, which convolves fundamentally different aspects-such as bulk diffusivity, restriction, anisotropy, and flow-into a single effective observable lacking specificity to distinguish between biologically plau…
Surface tension governed by differential adhesion can drive fluid particle mixtures to sort into separate regions, i.e., demix. Does the same phenomenon occur in confluent biological tissues? We begin to answer this question for epithelial monolayers with a combination of theory via a vertex model and experiments on keratinocyte monolayers. Vertex models are distinct from particle models in that the interactions between the cells are shape-based, as opposed to distance-dependent. We investigate whether a disparity in cell shape or size alone is sufficient to drive demixing in bidisperse vertex…
The rheology of biological cells is not only determined by their cytoskeletal networks, but also by the molecular motors that crosslink and contract them. Recently it has been found that the assemblies of myosin II molecular motors in non-muscle cells are mixtures of fast and slow motor variants. Using computer simulations and an analytical mean field theory of a crossbridge model for myosin II motors, here we show that such motor ensembles effectively behave as active Maxwell elements. We calculate storage and loss moduli as a function of the model parameters and show that the rheological pro…
We propose a PDE-constrained shape registration algorithm that captures the deformation and growth of biological tissue from imaging data. Shape registration is the process of evaluating optimum alignment between pairs of geometries through a spatial transformation function. We start from our previously reported work, which uses 3D tensor product B-spline basis functions to interpolate 3D space. Here, the movement of the B-spline control points, composed with an implicit function describing the shape of the tissue, yields the total deformation gradient field. The deformation gradient is then s…
The complex spatiotemporal flow patterns in living tissues, driven by active forces, have many of the characteristics associated with inertial turbulence even though the Reynolds number is extremely low. Analyses of experimental data from two-dimensional epithelial monolayers in combination with agent-based simulations show that cell division and apoptosis lead to directed cell motion for hours, resulting in rapid topological transitions in neighboring cells. These transitions in turn generate both long ranged and long lived clockwise and anticlockwise vortices, which gives rise to turbulent-l…
Models for confluent biological tissues often describe the network formed by cells as a triple-junction network, similar to foams. However, higher order vertices or multicellular rosettes are prevalent in developmental and {\it in vitro} processes and have been recognized as crucial in many important aspects of morphogenesis, disease, and physiology. In this work, we study the influence of rosettes on the mechanics of a confluent tissue. We find that the existence of rosettes in a tissue can greatly influence its rigidity. Using a generalized vertex model and effective medium theory we find a …
We suggest a simple model for reversible cross-links, binding and unbinding to/from a network of semiflexible polymers. The resulting frequency dependent response of the network to an applied shear is calculated via Brownian dynamics simulations. It is shown to be rather complex with the timescale of the linkers competing with the excitations of the network. If the lifetime of the linkers is the longest timescale, as is indeed the case in most biological networks, then a distinct low frequency peak of the loss modulus develops. The storage modulus shows a corresponding decay from its plateau v…
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 v…
Compression stiffening, or an increase in shear modulus with increasing compressive strain, has been observed in recent rheometry experiments on brain, liver, and fat tissues. Here, we extend the known types of biomaterials exhibiting this phenomenon to include agarose gel and fruit flesh. Further, we show that two different results from classic elasticity theory can account for the phenomenon of linear compression stiffening. One result is due to Barron and Klein, extended here to the relevant geometry and pre-stresses; the other is due to Birch. For incompressible materials, there are no adj…
In vertebrates, insufficient availability of calcium and phosphate ions in extracellular fluids leads to loss of bone density and neuronal hyper-excitability. To counteract this problem, calcium ions are present at high concentrations throughout body fluids -- at concentrations exceeding the saturation point. This condition leads to the opposite situation where unwanted mineral sedimentation may occur. Remarkably, ectopic or out-of-place sedimentation into soft tissues is rare, in spite of the thermodynamic driving factors. This fortunate fact is due to the presence of auto-regulatory proteins…
Many problems in mechanobiology urgently require characterisation of the micromechanical properties of the fibrous proteins of cells and tissues. Brillouin light scattering has been proposed as a new optical elastography technique to meet this need, but the information contained in the Brillouin spectrum is still a matter of debate. Here we investigate this question using gelatin as a model system in which the macroscopic physical properties can be manipulated to mimic all the relevant biological states of matter, ranging from the liquid to the gel and the glassy phase. We demonstrate that Bri…
Metastatic tumors often invade healthy neighboring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a 2D circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model th…
Vibrational spectroscopy has been widely employed to unravel physical-chemical properties of biological systems. Due to its high sensitivity to monitor real time "in situ" changes, Raman spectroscopy has been successfully employed, e.g., in biomedicine, metabolomics, and biomedical engineering. The grounds of interpretation of Raman spectra in these cases is the isolated macromolecules constituent vibrational assignment. Due to this, probe the anharmonic interactions or the mutual interactions among specific moieties/side chains to name but a few is a challenge. We present a complete vibration…
Many soft biological tissues possess a considerable surface stress, which plays a significant role in their biophysical functions, but most previous methods for characterizing their mechanical properties have neglected the effects of surface stress. In this work, we investigate the micropipette aspiration to measure the mechanical properties of cells and soft tissues with surface effects. The neo-Hookean constitutive model is adopted to describe the hyperelasticity of the measured biological material, and the surface effect is considered through the finite element method. It is found that when…
