相关论文: A mass conserved reaction-diffusion system capture…
Motile eukaryotic cells display distinct modes of migration that often occur within the same cell type. It remains unclear, however, whether transitions between the migratory modes require changes in external conditions, or whether the…
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…
The process of polarization determines the head and tail of single cells. A mechanism of this kind frequently precedes the subsequent cell locomotion and it determines the direction of motion. The process of polarization has frequently been…
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…
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…
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…
The combination of protrusions and retractions in the movement of polarized cells leads to understand the effect of possible synchronisation between the two ends of the cells. This synchronisation, in turn, could lead to different dynamics…
Cell migration is a fundamental process underlying the survival and function of both unicellular and multicellular organisms. Crawling motility in eukaryotic cells arises from cyclic protrusion and retraction driven by the cytoskeleton,…
Eukaryotic cells demonstrate a wide variety of dynamic patterns of filamentous actin (F-actin) and its regulators. Some of these patterns play important roles in cell functions, such as distinct motility modes, which motivate this study. We…
Control of the cytoskeleton and mechanical contacts with the extracellular environment are essential component of motility in eukaryotic cells. In the absence of signals, cells continuously rebuild the cytoskeleton and periodically extend…
We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical…
We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…
Experimental studies of cell motility in culture have shown that under adequate conditions these living organisms possess the ability to organize themselves into complex structures. Such structures may exhibit a synergy that greatly…
Cell polarization requires redistribution of specific proteins to the nascent front and back of a eukarytotic cell. Among these proteins are Rac and Rho, members of the small GTPase family that regulate the actin cytoskeleton. Rac promotes…
Mass-conserving reaction-diffusion systems with bistable nonlinearity are useful models for studying cell polarity formation, which is a key process in cell division and differentiation. We rigorously show the existence and stability of…
Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how…
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…
Intracellular protein patterns govern essential cellular functions by dynamically redistributing proteins between membrane-bound and cytosolic states, conserving their total numbers. This review presents a theoretical framework for…
Collective cell migration in response to a chemical cue occurs in many biological processes such as morphogenesis and cancer metastasis. Clusters of migratory cells in these systems are capable of responding to gradients of less than 1%…
Cell polarization and directional cell migration can display random, persistent and oscillatory dynamic patterns. However, it is not clear if these polarity patterns can be explained by the same underlying regulatory mechanism. Here, we…