ArticleJournal of mathematical biology1996
Selecting a common direction. II. Peak-like solutions representing total alignment of cell clusters.
Article in Journal of mathematical biology, 1996. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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The abstract states no effect estimate the extractor could read, or names no intervention and outcome on the map, so this paper lights no cell and moves no belief. It is still indexed, cited and linked below.
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Who cites it
3 citing papers in PubMed.
- Dynamic formation of oriented patches in chondrocyte cell cultures.Journal of mathematical biology · 2011Article
- Microfilament orientation constrains vesicle flow and spatial distribution in growing pollen tubes.Biophysical journal · 2009Article
- Modelling cell migration strategies in the extracellular matrix.Journal of mathematical biology · 2009Article
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Authors and funding
3 authors.
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Abstract
The problem of alignment of cells (or other objects) that interact in an angle-dependent way was described in Mogilner and Edelstein-Keshet (1995). In this sequel we consider in detail a special limiting case of nearly complete alignment. This occurs when the rotational diffusion of individual objects becomes very slow. In this case, the motion of the objects is essentially deterministic, and the individuals or objects tend to gather in clusters at various orientations. (Numerical solutions show that the angular distribution develops sharp peaks at various discrete orientations.) To understand the behaviour of the deterministic models with analytic tools, we represent the distribution as a number of delta-like peaks. This approximation of a true solution by a set of (infinitely sharp) peaks will be referred to as the peak ansatz. For weak but nonzero angular diffusion, the peaks are smoothed out. The analysis of this case leads to a singular perturbation problem which we investigate. We briefly discuss other applications of similar techniques.
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