Related papers: A bulk-surface reaction-diffusion system for cell …
The bulk-surface wave pinning model is a reaction-diffusion system for studying cell polarisation. It is constituted by a surface reaction-diffusion equation, coupled to a bulk diffusion equation with a non-linear boundary condition. Cell…
When it is polarised, a cell develops an asymmetric distribution of specific molecular markers, cytoskeleton and cell membrane shape. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signalling…
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a…
A cell is polarised when it has developed a main axis of organisation through the reorganisation of its cytosqueleton and its intracellular organelles. Polarisation can occur spontaneously or be triggered by external signals, like gradients…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
The amplification of an external signal is a key step in direction sensing of biological cells. We consider a simple model for the response to a time-depending signal, which was previously proposed by the last three authors. The model…
Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and…
Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signalling. In this paper, a minimal, mass-conserving model of cell-polarization on a curved membrane is…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
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,…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
Cued and un-cued cell polarization is a fundamental mechanism in cell biology. As an alternative to the classical Turing bifurcation, it has been proposed that the cell polarity might onset by means of the well-known phenomenon of…
In multicellular organisms, epithelial cells form layers separating compartments responsible for different physiological functions. At the early stage of epithelial layer formation, each cell of an aggregate defines an inner and an outer…
The motion of a eukaryotic cell presents a variety of interesting and challenging problems from both a modeling and a computational perspective. The processes span many spatial scales (from molecular to tissue) as well as disparate time…
Many cellular processes require a polarization axis which generally initially emerges as an inhomogeneous distribution of molecular markers in the cell. We present a simple analytical model of a general mechanism of cell polarization taking…
Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions.…
Cell polarity refers to the spatial asymmetry of molecules on the cell membrane. Altschuler, Angenent, Wang and Wu have proposed a stochastic model for studying the emergence of polarity in the presence of feedback between molecules. We…
We present and analyse a model for cell signalling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces, and both inter- and intracellular signalling. Using techniques from the theory of…
Cell polarization underlies many cellular processes, such as differentiation, migration, and budding. Many living cells, such as budding yeast and fission yeast, use cytoskeletal structures to actively transport proteins to one location on…
In this work, we investigate the dynamics of a non-local model describing spontaneous cell polarisation. It consists in a drift-diffusion equation set in the half-space, with the coupling involving the trace value on the boundary. We…