Related papers: Three-dimensional phase field model for actin-base…
Adhesion-independent migration is a prominent mode of cell motility in confined environments, yet the physical principles that guide such movement remain incompletely understood. We present a phase-field model for simulating the motility of…
We present an overview of phase field modeling of active matter systems as a tool for capturing various aspects of complex and active interfaces. We first describe how interfaces between different phases are characterized in phase field…
Actin filaments are critical components of the eukaryotic cytoskeleton, playing important roles in a number of cellular functions, such as cell migration, organelle transport, and mechanosensation. They are helical polymers with a…
The orientation of cell division is a major determinant of three-dimensional plant morphogenesis. Whether and how a simple division orientation rule explains the establishment of symmetric body plans is a fundamental question. Testing such…
We consider a system of two coupled parabolic PDEs introduced in [1] to model motility of eukaryotic cells. We study the asymptotic behavior of solutions in the limit of a small parameter related to the width of the interface in phase field…
The biological membrane, which compartmentalizes the cell and its organelles, exhibit wide variety of macroscopic shapes of varying morphology and topology. A systematic understanding of the relation of membrane shapes to composition,…
Experiments suggest that the migration of some cells in the three-dimensional extra cellular matrix bears strong resemblance to one-dimensional cell migration. Motivated by this observation, we construct and study a minimal one-dimensional…
The motility of a fish keratocyte on a flat substrate exhibits two distinct regimes: the non-migrating and the migrating one. In both configurations the shape is fixed in time and, when the cell is moving, the velocity is constant in…
Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have…
Observations of single epidermal cells on flat adhesive substrates have revealed two distinct morphological and functional states, namely a non-migrating symmetric unpolarized state and a migrating asymmetric polarized state. These states…
Phase-field models have recently had great success in describing the dynamic morphologies and motility of eukaryotic cells. In this work we investigate the minimal phase-field model introduced in [Berlyand, Potomkin, Rybalko (2017)].…
We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with…
This study develops an equation for describing three-dimensional membrane transformation through proliferation of its component cells regulated by morphogen density distributions on the membrane. The equation is developed in a…
T cells use sophisticated shape dynamics (morphodynamics) to migrate towards and neutralise infected and cancerous cells. However, there is limited quantitative understanding of the migration process in 3D extracellular matrices (ECMs) and…
Many models have been developed to study the role of branching actin networks in motility. One important component of those models is the distribution of filament orientations relative to the cell membrane. Two mean-field models previously…
The cell motility problem has been investigated for a long time. Today, many biologists, physicists, and mathematicians are looking for new research instruments for this process. A simple 2D model of a free-boundary cell moving on a…
During cell migration, cells become polarized, change their shape, and move in response to various internal and external cues. Cell polarization is defined through the spatio-temporal organization of molecules such as PI3K or small GTPases,…
We study dynamics of a membrane and its matrix regularisation. We present the matrix regularisation for a membrane propagating in a curved space-time geometry in the presence of an arbitrary 3-form field. In the matrix regularisation, we…
The essential features of many interfaces driven out of equilibrium are described by the same equation---the Kardar-Parisi-Zhang (KPZ) equation. How do living interfaces, such as the cell membrane, fit into this picture? In an endeavour to…
Based on symmetry consideration of migration and shape deformations, we formulate phenomenologically the dynamics of cell crawling in two dimensions. Forces are introduced to change the cell shape. The shape deformations induce migration of…