Related papers: Rigidity of Epithelial Tissues as a Double Optimiz…
Many animal cells change their shape depending on the stiffness of the substrate on which they are cultured: they assume small, rounded shapes in soft ECMs, they elongate within stiffer ECMs, and flatten out on hard substrates. Cells tend…
We introduce a novel model, comprising self-avoiding surfaces and incorporating edges and tubules, that is designed to characterize the structural morphologies and transitions observed within the endoplasmic reticulum (ER). By employing…
Cross-sections of cell shapes in a tissue monolayer typically resemble a tiling of convex polygons. Yet, examples exist where the polygons are not convex with curved cell-cell interfaces, as seen in the adaxial epidermis. To date,…
Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer/substrate modulus ratio is…
Animal morphogenesis involves complex tissue deformation processes, which require tight control over tissue rheology. Yet, it remains insufficiently understood how tissue rheology results from the interplay between cellular packing and…
The mechanical environment of a substrate plays a key role in influencing the behavior of adherent biological cells. Traditional tunable substrates have limitations as their mechanical properties cannot be dynamically altered in-situ during…
Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements.…
The majority of solid tumours arise in epithelia and therefore much research effort has gone into investigating the growth, renewal and regulation of these tissues. Here we review different mathematical and computational approaches that…
A new class of micromechanically motivated chain network models for soft biological tissues is presented. On the microlevel, it is based on the statistics of long chain molecules. A wormlike chain model is applied to capture the behavior of…
The hydrodynamic theory of active nematics has been often used to describe the spatio-temporal dynamics of cell flows and motile topological defects within soft confluent tissues. Those theories, however, often rely on the assumption that…
Collective cell migration governs a range of physiological and pathological processes, from tissue morphogenesis to cancer invasion, in which topological defects arise as an inevitable consequence of frequent cellular rearrangement and…
In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…
We consider a free boundary problem for a system of PDEs, modeling the growth of a biological tissue. A morphogen, controlling volume growth, is produced by specific cells and then diffused and absorbed throughout the domain. The geometric…
Shape transformations of epithelial tissues in three dimensions, which are crucial for embryonic development or in vitro organoid growth, can result from active forces generated within the cytoskeleton of the epithelial cells. How the…
There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale.…
A constitutive relation between stress and strain relative to a reference state is the basic assumption of elasticity theory. However, in living matter, force generation is governed by motor molecule activity, which does not depend on…
We introduce an Active Vertex Model (AVM) for cell-resolution studies of the mechanics of confluent epithelial tissues consisting of tens of thousands of cells, with a level of detail inaccessible to similar methods. The AVM combines the…
Over the last two decades, scientific literature has been blooming with various means of simulating epithelial cell colonies. Each of these simulations can be separated by their respective efficiency (expressed in terms of consumed…