Related papers: Three-dimensional phase field model for actin-base…
We perform an analytical investigation of the cell interface dynamics in the framework of a minimal phase field model of cell motility suggested in [1], which consists of two coupled evolution equations for the order parameter and a…
We suggest a 3D phase field model to describe 3D cell spreading on a flat substrate. The model is a simplified version of a minimal model that was developed in [1]. Our model couples the order parameter $u$ with 3D polarization…
The basic process of the innate immune system when phagocyte (white blood cell) engulf or swallow a target particle (bacterium or dead cell), is called phagocytosis. We apply the phase field approach in the spirit of [1], that couples the…
Cell spreading is investigated at various scales in order to understand motility of living cells which is essential for a range of physiological activities in higher organisms as well as in microbes. At a microscopic scale, it has been seen…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
This work presents the development, analysis and numerical simulations of a biophysical model for 3D cell deformation and movement, which couples biochemical reactions and biomechanical forces. We propose a mechanobiochemical model which…
We consider a system of two PDEs arising in modeling of motility of eukariotic cells on substrates. This system consists of the Allen-Cahn equation for the scalar phase field function coupled with another vectorial parabolic equation for…
This letter is concerned with asymptotic analysis of a PDE model for motility of a eukaryotic cell on a substrate. This model was introduced in [1], where it was shown numerically that it successfully reproduces experimentally observed…
Inspired by recent experimental observation of patterning at the membrane of a living cell, we propose a generic model for the dynamics of a fluctuating interface driven by particle-like inclusions which stimulate its growth. We find that…
Many processes in eukaryotic cells, including cell motility, rely on the growth of branched actin networks from surfaces. Despite its central role the mechano-chemical coupling mechanisms which guide the growth process are poorly…
We present a generic model of cell motility generated by acto-myosin contraction of the cell cortex. We identify analytically dynamical instabilities of the cortex and show that they trigger spontaneous cortical flows which in turn can…
Cell shape changes are largely controlled by the actin cytoskeleton, a dynamic filament network beneath the plasma membrane. Several cell types can form extended free-standing protrusions not supported by an extracellular substrate or…
The phase transition kinetics in three phase systems was investigated using the numerically efficient cell dynamics method. A phasefield model with a simple analytical free energy and single order parameter was used to study the kinetics…
The initiation of directional cell motion requires symmetry breaking that can happen both with or without external stimuli. During cell crawling, forces generated by the cytoskeleton and their transmission through mechanosensitive adhesions…
This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…
We propose and study a simple, physical model for phagocytosis, i.e. the active, actin-mediated uptake of micron-sized particles by biological cells. The cell is described by the phase field method and the driving mechanisms of uptake are…
The development of traction-force microscopy, in the past two decades, has created the unprecedented opportunity of performing direct mechanical measurements on living cells as they adhere or crawl on uniform or micro-patterned substrates.…
A living cell actively generates traction forces on its environment with its actin cytoskeleton. These forces deform the cell elastic substrate which, in turn, affects the traction forces exerted by the cell and can consequently modify the…
In the framework of a phase field model of a single cell crawling on a substrate, we investigate how the properties of the cell membrane affect the shape and motility of the cell. Since the membrane influences the cell dynamics on multiple…
An analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations…