101 research outputs found
Multicellular rosettes drive fluid-solid transition in epithelial tissues
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 fluid-to-solid transition
driven by rosette density and intracellular tensions. This transition exhibits
several hallmarks of a second-order phase transition such as a growing
correlation length and a universal critical scaling in the vicinity a critical
point. Further, we elucidate the nature of rigidity transitions in dense
biological tissues and other cellular structures using a generalized Maxwell
constraint counting approach. This answers a long-standing puzzle of the origin
of solidity in these systems.Comment: 11 pages, 5 figures + 8 pages, 7 figures in Appendix. To be appear in
PR
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 only on a few macroscopic parameters such as
temperature, pressure, volume, and energy. In this review article, we discuss
recent advances in establishing statistical ensembles for athermal materials.
The broad class of granular and particulate materials is immune from the
effects of thermal fluctuations because the constituents are macroscopic. In
addition, interactions between grains are frictional and dissipative, which
invalidates the fundamental postulates of equilibrium 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
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 [1,2], a special
class of granular solids created by pure shear, which is a strictly
non-equilbrium 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.Comment: 6 pages, 4 figure
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.Comment: accepted for publication in Physical Review X, 201
Controlled neighbor exchanges drive glassy behavior, intermittency and cell streaming in epithelial tissues
Cell neighbor exchanges are integral to tissue rearrangements in biology,
including development and repair. Often these processes occur via topological
T1 transitions analogous to those observed in foams, grains and colloids.
However, in contrast to in non-living materials the T1 transitions in
biological tissues are rate-limited and cannot occur instantaneously due to the
finite time required to remodel complex structures at cell-cell junctions. Here
we study how this rate-limiting process affects the mechanics and collective
behavior of cells in a tissue by introducing this important biological
constraint in a theoretical vertex-based model as an intrinsic single-cell
property. We report in the absence of this time constraint, the tissue
undergoes a motility-driven glass transition characterized by a sharp increase
in the intermittency of cell-cell rearrangements. Remarkably, this glass
transition disappears as T1 transitions are temporally limited. As a unique
consequence of limited rearrangements, we also find that the tissue develops
spatially correlated streams of fast and slow cells, in which the fast cells
organize into stream-like patterns with leader-follower interactions, and
maintain optimally stable cell-cell contacts. The predictions of this work is
compared with existing in-vivo experiments in Drosophila pupal development
Why Do Granular Materials Stiffen with Shear Rate? : Test of Novel Stress-Based Statistics
Peer reviewedPublisher PD
Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space
Solids are distinguished from fluids by their ability to resist shear. In
traditional solids, the resistance to shear is associated with the emergence of
broken translational symmetry as exhibited by a non-uniform density pattern,
which results from either minimizing the energy cost or maximizing the entropy
or both. In this work, we focus on a class of systems, where this paradigm is
challenged. We show that shear-driven jamming in dry granular materials is a
collective process controlled solely by the constraints of mechanical
equilibrium. We argue that these constraints lead to a broken translational
symmetry in a dual space that encodes the statistics of contact forces and the
topology of the contact network. The shear-jamming transition is marked by the
appearance of this broken symmetry. We extend our earlier work, by comparing
and contrasting real space measures of rheology with those obtained from the
dual space. We investigate the structure and behavior of the dual space as the
system evolves through the rigidity transition in two different shear
protocols. We analyze the robustness of the shear-jamming scenario with respect
to protocol and packing fraction, and demonstrate that it is possible to define
a protocol-independent order parameter in this dual space, which signals the
onset of rigidity.Comment: 14 pages, 17 figure
- …