scholarly journals A mathematical model of collective cell motility and pattern formation

2008 ◽  
Vol 22 (S1) ◽  
Author(s):  
Andras Szabo ◽  
Andras Czirok
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Cell Motility

scholarly journals The Role of Cell Motility in Metastatic Cell Dominance Phenomenon: Analysis by a Mathematical Model

2000 ◽  
Vol 3 (1) ◽  
pp. 63-77 ◽  
Author(s):  
A. V. Kolobov ◽  
A. A. Polezhaev ◽  
G. I. Solyanik
Keyword(s):  
Mathematical Model ◽  
Cell Motility ◽  
Threshold Value ◽  
Experimental Investigations ◽  
Metastatic Cell ◽  
Metastatic Cells ◽  
Motile Cells ◽  
Cell Subpopulations ◽  
Cell Motion ◽  
Slow Growing

Metastasis is the outcome of several selective sequential steps where one of the first and necessary steps is the progressive overgrowth or dominance of a small number of metastatic cells in a tumour. In spite of numerous experimental investigations concerning the growth advantage of metastatic cells, the mechanisms resulting in their dominance are still unknown. Metastatic cell overgrowth occurs even if doubling time of the metastatic subpopulation is shorter than that of all others subpopulations in a heterogeneous tumour. In order to examine the hypothesis that under conditions of competition of cell subpopulations for common substrata cell motility of the slow-growing subpopulation can result in its dominance in a heterogeneous tumour, a mathematical model of heterogeneous tumour growth is suggested. The model describes two cell subpopulations which can grow with different rates and transform into the resting state depending on the concentration of the substrate consumed by both subpopulations. The slow-growing subpopulation is assumed to be motile. In numerical simulations it is shown that this subpopulation is able to overgrow the other one. The dominance phenomenon (resulting from random cell motion) depends on the motility coefficient in a threshold manner: in a heterogeneous tumour the slow-dividing motile subpopulation is able to overgrow its non-motile counterparts if its motility coefficient exceeds a certain threshold value. Computations demonstrate independence of the motile cells overgrowth from the initial tumour composition.

scholarly journals Microbe Profile: Dictyostelium discoideum: model system for development, chemotaxis and biomedical research

Microbiology ◽  
2021 ◽  
Author(s):  
Catherine J. Pears ◽  
Julian D. Gross
Keyword(s):  
Pattern Formation ◽  
Cell Motility ◽  
Dictyostelium Discoideum ◽  
Biomedical Research ◽  
Model System ◽  
Developmental Pattern ◽  
Social Amoeba ◽  
The Social ◽  
Host Pathogen ◽  
Soil Amoeba

The social amoeba Dictyostelium discoideum is a versatile organism that is unusual in alternating between single-celled and multi-celled forms. It possesses highly-developed systems for cell motility and chemotaxis, phagocytosis, and developmental pattern formation. As a soil amoeba growing on microorganisms, it is exposed to many potential pathogens; it thus provides fruitful ways of investigating host-pathogen interactions and is emerging as an influential model for biomedical research.

A mathematical model of self-organized pattern formation on the combs of honeybee colonies

1990 ◽  
Vol 147 (4) ◽  
pp. 553-571 ◽  
Author(s):  
Scott Camazine ◽  
James Sneyd ◽  
Michael J. Jenkins ◽  
J.D. Murray
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Self Organized

A model for the longitudinal patterns shaped by water on erodible rocks

2020 ◽  
Author(s):  
Matteo Bernard Bertagni ◽  
Carlo Camporeale
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Laminar Flow ◽  
Spatial Scales ◽  
Concentration Field ◽  
Water Film ◽  
Time And Space ◽  
Longitudinal Patterns ◽  
Flow Intensity ◽  
Alpine Environments

<p>The interactions between water and rocks create an extensive variety of marvelous patterns, which span on several classes of time and space scales. In this work, we provide a mathematical model for the formation of longitudinal erosive patterns commonly found in karst and alpine environments. The model couples the hydrodynamics of a laminar flow of water (Orr-Somerfield equation) to the concentration field of the eroded-rock chemistry. Results show that an instability of the plane rock wetted by the water film leads to a longitudinal channelization responsible for the pattern formation. The spatial scales predicted by the model span over different orders of magnitude depending on the flow intensity and this may explain why similar patterns of different sizes are observed in nature (millimetric microrills, centimetric rillenkarren, decametric solution runnels).</p>

scholarly journals Pattern Formation by Lateral Inhibition with Feedback: a Mathematical Model of Delta-Notch Intercellular Signalling

1996 ◽  
Vol 183 (4) ◽  
pp. 429-446 ◽  
Author(s):  
Joanne R. Collier ◽  
Nicholas A.M. Monk ◽  
Philip K. Maini ◽  
Julian H. Lewis
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Lateral Inhibition ◽  
Intercellular Signalling

A Multiscale Computational Model of Chemotactic Axon Guidance

2011 ◽  
pp. 628-645
Author(s):  
Giacomo Aletti ◽  
Paola Causin ◽  
Giovanni Naldi ◽  
Matteo Semplice
Keyword(s):  
Mathematical Model ◽  
Nervous System ◽  
Cell Motility ◽  
Growth Cone ◽  
Ligand Concentration ◽  
Transmembrane Receptors ◽  
Axonal Projections ◽  
Long Time ◽  
Tight Connection ◽  
Cytoskeleton Rearrangement

In the development of the nervous system, the migration of neurons driven by chemotactic cues has been known since a long time to play a key role. In this mechanism, the axonal projections of neurons detect very small differences in extracellular ligand concentration across the tiny section of their distal part, the growth cone. The internal transduction of the signal performed by the growth cone leads to cytoskeleton rearrangement and biased cell motility. A mathematical model of neuron migration provides hints of the nature of this process, which is only partially known to biologists and is characterized by a complex coupling of microscopic and macroscopic phenomena. This chapter focuses on the tight connection between growth cone directional sensing as the result of the information collected by several transmembrane receptors, a microscopic phenomenon, and its motility, a macroscopic outcome. The biophysical hypothesis investigated is the role played by the biased re-localization of ligand-bound receptors on the membrane, actively convected by growing microtubules. The results of the numerical simulations quantify the positive feedback exerted by the receptor redistribution, assessing its importance in the neural guidance mechanism.

A Mathematical Model of Pattern Formation by Swimming Microorganisms*

1975 ◽  
Vol 22 (2) ◽  
pp. 296-306 ◽  
Author(s):  
M. LEVANDOWSKY ◽  
W. S. CHILDRESS ◽  
E. A. SPIEGEL ◽  
S. H. HUTNER
Keyword(s):  
Mathematical Model ◽  
Pattern Formation ◽  
Swimming Microorganisms
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