Dapeng Bi

Jamming by shear

A broad class of disordered materials including foams, glassy molecular systems, colloids and granular materials can form jammed states. A jammed system can resist small stresses without deforming irreversibly, whereas unjammed systems flow under any applied stresses. The broad applicability of the Liu–Nagel jamming concept has attracted intensive theoretical and modelling interest but has prompted less experimental effort. In the Liu–Nagel framework, jammed states of athermal systems exist only above a certain critical density. Although numerical simulations for particles that do not experience friction broadly support this idea, the nature of the jamming transition for frictional grains is less clear. Here we show that jamming of frictional, disk-shaped grains can be induced by the application of shear stress at densities lower than the critical value, at which isotropic (shear-free) jamming occurs. These jammed states have a much richer phenomenology than the isotropic jammed states: for small applied shear stresses, the states are fragile, with a strong force network that percolates only in one direction. A minimum shear stress is needed to create robust, shear-jammed states with a strong force network percolating in all directions. The transitions from unjammed to fragile states and from fragile to shear-jammed states are controlled by the fraction of force-bearing grains. The fractions at which these transitions occur are statistically independent of the density. Jammed states with densities lower than the critical value have an anisotropic fabric (contact network). The minimum anisotropy of shear-jammed states vanishes as the density approaches the critical value from below, in a manner reminiscent of an order–disorder transition.

A density-independent rigidity transition in biological tissues

Cells moving in a tissue undergo a rigidity transition resembling that of active particles jamming at a critical density—but the tissue density stays constant. A new type of rigidity transition implicates the physical properties of the cells.

Unjamming and cell shape in the asthmatic airway epithelium

From coffee beans flowing in a chute to cells remodelling in a living tissue, a wide variety of close-packed collective systems-both inert and living-have the potential to jam. The collective can sometimes flow like a fluid or jam and rigidify like a solid. The unjammed-to-jammed transition remains poorly understood, however, and structural properties characterizing these phases remain unknown. Using primary human bronchial epithelial cells, we show that the jamming transition in asthma is linked to cell shape, thus establishing in that system a structural criterion for cell jamming. Surprisingly, the collapse of critical scaling predicts a counter-intuitive relationship between jamming, cell shape and cell-cell adhesive stresses that is borne out by direct experimental observations. Cell shape thus provides a rigorous structural signature for classification and investigation of bronchial epithelial layer jamming in asthma, and potentially in any process in disease or development in which epithelial dynamics play a prominent role.

Motility-driven glass and jamming transitions in biological tissues

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 controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.

Energy barriers govern glassy dynamics in tissues

Recent observations demonstrate that confluent tissues exhibit features of glassy dynamics, such as caging behavior and dynamical heterogeneities, although it has remained unclear how single-cell properties control this behavior. Here we develop numerical and theoretical models to calculate energy barriers to cell rearrangements, which help govern cell migration in cell monolayers. In contrast to work on sheared foams, we find that energy barrier heights are exponentially distributed and depend systematically on the cells number of neighbors. Based on these results, we predict glassy two-time correlation functions for cell motion, with a timescale that increases rapidly as cell activity decreases. These correlation functions are used to construct simple random walks that reproduce the caging behavior observed for cell trajectories in experiments. This work provides a theoretical framework for predicting collective motion of cells in wound-healing, embryogenesis and cancer tumorogenesis.

The Statistical Physics of Athermal Materials

At the core of equilibrium statistical mechanics lies the notion of statistical ensembles: a collection of microstates, each occurring with a given a priori probability that depends on only a few macroscopic parameters,suchastemperature,pressure,volume,andenergy.Inthis review, we discuss recent advances in establishing statistical ensembles for athermal materials. The broad class of granular and particulate materials is immune to the effects of thermal fluctuations because the constituents are macroscopic. In addition, interactions between grains are frictional and dissipative, which invalidates the fundamental postulates ofequilibrium statistical mechanics. However, granular materials exhibit distributions of microscopic quantities that are reproducible and often depend on only a few macroscopic parameters. We explore the history of statistical ensemble ideas in the context of granular materials, clarify the nature of such ensembles and their foundational principles, highlight advances in testing key ideas, and discuss applications of ensembles to analyze the collective behavior of granular materials.

Why do granular materials stiffen with shear rate? Test of novel stress-based statistics.

Recent experiments exhibit a rate dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, gamma. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence of (ln(gamma))(1/2).

Rheology of granular materials: dynamics in a stress landscape

We present a framework for analysing the rheology of dense driven granular materials, based on a recent proposal of a stress-based ensemble. In this ensemble, fluctuations in a granular system near jamming are controlled by a temperature-like parameter, the angoricity, which is conjugate to the stress of the system. In this paper, we develop a model for slowly driven granular materials based on the stress ensemble and the idea of a landscape in stress space. The idea of an activated process driven by the angoricity has been shown by Behringer et al. (Behringer et al. 2008 Phys. Rev. Lett. 101, 268301) to describe the logarithmic strengthening of granular materials. Just as in the soft glassy rheology (SGR) picture, our model represents the evolution of a small patch of granular material (a mesoscopic region) in a stress-based trap landscape. The angoricity plays the role of the fluctuation temperature in the SGR. We determine (i) the constitutive equation, (ii) the yield stress, and (iii) the distribution of stress dissipated during granular shearing experiments, and compare these predictions with the experiments of Hartley & Behringer (Hartley & Behringer 2003 Nature 421, 928–931.).

Fluctuations in shear-jammed states: A statistical ensemble approach

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full utility of this statistical framework in shear-jammed (SJ) experimental states, a special class of granular solids created by pure shear, which is a strictly non-equilibrium protocol for creating solids. We demonstrate that the stress ensemble provides an excellent quantitative description of fluctuations in experimental SJ states. We show that the stress fluctuations are controlled by a single tensorial quantity: the angoricity of the system, which is a direct analog of the thermodynamic temperature. SJ states exhibit significant correlations in local stresses and are thus inherently different from density-driven, isotropically jammed (IJ) states.

Correlating cell shape and cellular stress in motile confluent tissues

Significance Using a self-propelled Voronoi model of epithelia known to predict a liquid–solid transition, we examine the interplay between cell motility and cell shape, tuned by cortex contractility and cell–cell adhesion, in controlling the mechanical properties of tissue. Our work provides a unifying framework for existing, seemingly distinct notions of stress in tissues and relates stresses to material properties. In particular, we show that the temporal correlation function of shear stresses can be used to define an effective tissue viscosity that diverges at the liquid–solid transition. This finding suggests a unique way of analyzing traction force microscopy data that may provide information on tissue rheology. Collective cell migration is a highly regulated process involved in wound healing, cancer metastasis, and morphogenesis. Mechanical interactions among cells provide an important regulatory mechanism to coordinate such collective motion. Using a self-propelled Voronoi (SPV) model that links cell mechanics to cell shape and cell motility, we formulate a generalized mechanical inference method to obtain the spatiotemporal distribution of cellular stresses from measured traction forces in motile tissues and show that such traction-based stresses match those calculated from instantaneous cell shapes. We additionally use stress information to characterize the rheological properties of the tissue. We identify a motility-induced swim stress that adds to the interaction stress to determine the global contractility or extensibility of epithelia. We further show that the temporal correlation of the interaction shear stress determines an effective viscosity of the tissue that diverges at the liquid–solid transition, suggesting the possibility of extracting rheological information directly from traction data.