Related papers: A simple model of Keratocyte membrane dynamics
To explain the differentiation of stem cells in terms of dynamical systems theory, models of interacting cells with intracellular protein expression dynamics are analyzed and simulated. Simulations were carried out for all possible protein…
We propose a simple mathematical model to describe the mechanical relaxation of cells within a curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This model generalises previous one-dimensional models…
We model the spatiotemporal dynamics of cellular protein concentrations near membranes composed of different lipids using a three-variable continuum model for membrane-bound protein, cytosolic protein, and the local composition of a binary…
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…
Migratory and tissue resident cells exhibit highly branched morphologies to perform their function and to adapt to the microenvironment. Immune cells, for example, display transient branched shapes while exploring the surrounding tissues.…
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 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…
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…
Substrate-based cell motility is essential for fundamental biological processes, such as tissue growth, wound healing and immune response. Even if a comprehensive understanding of this motility mode remains elusive, progress has been…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
We consider a continuum mechanical model for the migration of multiple cell populations through parts of tissue separated by thin membranes. In this model, cells belonging to different populations may be characterised by different…
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…
Eukaryotic cell motility involves a complex network of interactions between biochemical components and mechanical processes. The cell employs this network to polarize and induce shape changes that give rise to membrane protrusions and…
Recent research has shown that motile cells can adapt their mode of propulsion to the mechanical properties of the environment in which they find themselves--crawling in some environments while swimming in others. The latter can involve…
We investigate the dynamics of membranes that are held by freely-rotating tethers in fluid flows. The tethered boundary condition allows periodic and chaotic oscillatory motions for certain parameter values. We characterize the oscillations…
A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell…
Microphase separation of membrane components is thought to play an important role in many physiological processes, from cell signaling to endocytosis and cellular trafficking. Here, we study how variations in the membrane composition can be…
Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for explaining observed collective behaviors such as those in…