Patterns Formed Through Cell-Cell Interactions: Spontaneous Selection of Dominant Directions

Abstract

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.