Patterns Formed Through Cell-Cell Interactions: Spontaneous Selection of Dominant Directions
This paper presents an example of patterns formed through the direct interactions of cells. After a brief review of classical ideas from pattern formation, we introduce the idea that the selection of a dominant direction in an initially isotropic medium is analogous to a type of pattern formation, not in physical space, but rather in angle-space. The pattern forms on a unit circle, i. e. on a range of angles 0 < θ < 2π. It is shown that as a result of cell-cell interactions, uniform angular distributions of cells are unstable and that peaks in these distributions form spontaneously. These peaks represent dominant directions that arise in the cell population as a result of clustering and alignment of cells with one another. (See Figure 19.1). The paper will concentrate on alignment of populations of fibroblasts in vitro, and on analysis of typical equations that arise in modelling angular distributions. Applications of similar models to formation of preferred orientations in populations of organisms and in macromolecular networks will be discussed.
KeywordsAngular Distribution Pattern Formation Lateral Inhibition Free Cell Parallel Array
Unable to display preview. Download preview PDF.
- Civelekoglu, G. 1992. Actin alignment mediated by actin binding proteins. Ph.D. thesis, UBC, Vancouver.Google Scholar
- Edelstein-Keshet, L. 1992. Trail following as an adaptable mechanism for population behaviour. In 3D Animal Aggregations. (Submitted).Google Scholar
- Ermentrout, G. B., Campbell, J., & Oster, G. 1986. A model for shell patterns based on neural activity. Veliger, 28, 369–388.Google Scholar
- Meinhardt, H. 1982. Models of biological pattern formation. New York: Academic Press.Google Scholar
- Murray, J. D. 1981a. On pattern formation mechanisms for lepidopteran wing patterns and mammalian coat markings. Phil Trans. Roy. Soc. (London), B295, 473–496.Google Scholar
- Murray, J. D. 1989. Mathematical biology. New York: Springer Verlag.Google Scholar
- Othmer, H. G. 1969. Interactions of reaction and diffusion in open systems. Ph.D. thesis, Chemical Engineering Dept., Univ. of Minnesota.Google Scholar
- Raignier, A., & van Boven, J. 1955. étude taxonomique, biologique, et biometrique des Dorylusdu sous-genre Anomma(hymenoptera: Formicidae) Annals du Musee Royal du Congo Belge n.s. 4. sciences zoologiques, 2, 1–359.Google Scholar
- Turing, A. M. 1952. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. Lond., B237, 37–72.Google Scholar