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This article is the second of a three-part series that derives a self-consistent theoretical framework of the electromechanics of arbitrarily curved lipid membranes. Existing continuum theories commonly treat lipid membranes as strictly…
Curvature and mechanics are intimately connected for thin materials, and this coupling between geometry and physical properties is readily seen in folded structures from intestinal villi and pollen grains, to wrinkled membranes and…
Morphogenesis involves the transformation of initially simple shapes, such as multicellular spheroids, into more complex $3D$ shapes. These shape changes are governed by mechanical forces including molecular motor-generated forces as well…
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…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
Modeling membrane interactions with arbitrarily shaped colloidal particles, such as environmental micro- and nanoplastics, at the cell scale remains particularly challenging, owing to the complexity of particle geometries and the need to…
We establish the existence of a cusp in the curvature of a solid sheet at its contact with a liquid subphase. We study two configurations in floating sheets where the solid-vapor-liquid contact line is a straight line and a circle,…
The locomotion of flexible membrane-like organisms on top of curved surfaces appears in different contexts and scales. Still, such dynamics have not yet been quantitatively modeled and no realization of such motion in manmade systems has…
Cell spreading and motility on an adhesive substrate are driven by the active physical forces generated by the actin cytoskeleton. We have recently shown that coupling curved membrane complexes to protrusive forces, exerted by the actin…
The growth of several biological tissues is known to be controlled in part by local geometrical features, such as the curvature of the tissue interface. This control leads to changes in tissue shape that in turn can affect the tissue's…
In this paper, we present a 2D numerical model developed to simulate the dynamics of soft, deformable particles. To accommodate significant particle deformations, the particle surface is represented as a narrow shell composed of mass points…
We propose a sharp-interface model for a hyperelastic material consisting of two phases. In this model, phase interfaces are treated in the deformed configuration, resulting in a fully Eulerian interfacial energy. In order to penalize large…
Epithelial morphogenesis, a signature problem of tissue biology and tissue mechanics, continues to inspire biologists and physicists alike. Many treatments focus on tissue fluidization, apical/basal ratio changes, or mechanical…
A theoretical model for stratified epithelium is presented. The viscoelastic properties of the tissue is assumed to be dependent on the spatial distribution of proliferative and differentiated cells. Based on this assumption, a hydrodynamic…
We use a simple and efficient computer model to investigate the physical properties of bilayer membranes. The amphiphilic molecules are modeled as short rigid trimers with finite range pair interactions between them. The pair potentials…
Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…
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…
Cellularized tissue and polymer networks can both transition from floppy to rigid as a function of their control parameters, and, yet, the two systems often mechanically interact, which may affect their respective rigidities. To study this…
Cellular membranes exhibit a large variety of shapes, strongly coupled to their function. Many biological processes involve dynamic reshaping of membranes, usually mediated by proteins. This interaction works both ways: while proteins…
Membrane bending is an extensively studied problem from both modeling and experimental perspectives because of the wide implications of curvature generation in cell biology. Many of the curvature generating aspects in membranes can be…