A one-dimensional model of cell diffusion and aggregation, incorporating volume filling and cell-to-cell adhesion

2008 ◽  
Vol 58 (3) ◽  
pp. 395-427 ◽  
Author(s):  
K. Anguige ◽  
C. Schmeiser
Keyword(s):  
Cell Adhesion ◽  
Dimensional Model ◽  
Volume Filling ◽  
One Dimensional ◽  
Cell To Cell Adhesion

Multi-phase Stefan problems for a non-linear one-dimensional model of cell-to-cell adhesion and diffusion

2010 ◽  
Vol 21 (2) ◽  
pp. 109-136 ◽  
Author(s):  
K. ANGUIGE
Keyword(s):  
Cell Adhesion ◽  
Existence Theory ◽  
Dimensional Model ◽  
One Dimensional ◽  
Stefan Problems ◽  
Non Linear ◽  
Long Time ◽  
Multi Phase ◽  
Cell To Cell Adhesion ◽  
And Diffusion

We consider a family of multi-phase Stefan problems for a certain one-dimensional model of cell-to-cell adhesion and diffusion, which takes the form of a non-linear forward–backward parabolic equation. In each material phase the cell density stays either high or low, and phases are connected by jumps across an ‘unstable’ interval. We develop an existence theory for such problems which allows for the annihilation of phases and the subsequent continuation of solutions. Stability results for the long-time behaviour of solutions are also obtained, and, where necessary, the analysis is complemented by numerical simulations.

scholarly journals A one-dimensional model for the interaction between cell-to-cell adhesion and chemotactic signalling

2011 ◽  
Vol 22 (4) ◽  
pp. 291-316 ◽  
Author(s):  
K. ANGUIGE
Keyword(s):  
Cell Adhesion ◽  
Discrete Model ◽  
Continuum Limit ◽  
Numerical Solutions ◽  
Problem Formulation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Spatial Oscillations ◽  
Cell To Cell Adhesion ◽  
The Continuum

We develop and analyse a discrete, one-dimensional model of cell motility which incorporates the effects of volume filling, cell-to-cell adhesion and chemotaxis. The formal continuum limit of the model is a non-linear generalisation of the parabolic-elliptic Keller–Segel equations, with a diffusivity which can become negative if the adhesion coefficient is large. The consequent ill-posedness results in the appearance of spatial oscillations and the development of plateaus in numerical solutions of the underlying discrete model. A global-existence result is obtained for the continuum equations in the case of favourable parameter values and data, and a steady-state analysis, which, amongst other things, accounts for high-adhesion plateaus, is carried out. For ill-posed cases, a singular Stefan-problem formulation of the continuum limit is written down and solved numerically, and the numerical solutions are compared with those of the original discrete model.

ROCK2 Regulates the Expression of Cell Adhesion Molecules and Cell-to-Cell Adhesion in Vascular Endothelial Cells

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 476-P
Author(s):  
YUSUKE TAKEDA ◽  
KEIICHIRO MATOBA ◽  
DAIJI KAWANAMI ◽  
YOSUKE NAGAI ◽  
TOMOYO AKAMINE ◽  
...  
Keyword(s):  
Endothelial Cells ◽  
Cell Adhesion ◽  
Adhesion Molecules ◽  
Cell Adhesion Molecules ◽  
Vascular Endothelial Cells ◽  
Vascular Endothelial ◽  
Cell To Cell Adhesion

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

scholarly journals Integrins: An Important Link between Angiogenesis, Inflammation and Eye Diseases

Cells ◽  
2021 ◽  
Vol 10 (7) ◽  
pp. 1703
Author(s):  
Małgorzata Mrugacz ◽  
Anna Bryl ◽  
Mariusz Falkowski ◽  
Katarzyna Zorena
Keyword(s):  
Cell Adhesion ◽  
Tissue Repair ◽  
Normal Development ◽  
Cell Attachment ◽  
Biological Activities ◽  
Integrin Receptors ◽  
Cytokine Activation ◽  
Eye Disorders ◽  
Membrane Bound ◽  
Cell To Cell Adhesion

Integrins belong to a group of cell adhesion molecules (CAMs) which is a large group of membrane-bound proteins. They are responsible for cell attachment to the extracellular matrix (ECM) and signal transduction from the ECM to the cells. Integrins take part in many other biological activities, such as extravasation, cell-to-cell adhesion, migration, cytokine activation and release, and act as receptors for some viruses, including severe acute respiratory syndrome-related coronavirus 2 (SARS-CoV-2). They play a pivotal role in cell proliferation, migration, apoptosis, tissue repair and are involved in the processes that are crucial to infection, inflammation and angiogenesis. Integrins have an important part in normal development and tissue homeostasis, and also in the development of pathological processes in the eye. This review presents the available evidence from human and animal research into integrin structure, classification, function and their role in inflammation, infection and angiogenesis in ocular diseases. Integrin receptors and ligands are clinically interesting and may be promising as new therapeutic targets in the treatment of some eye disorders.

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