Parameter domains for spots and stripes in mechanical models for biological pattern formation

Abstract

Mechanochemical models for biological pattern formation have been applied to the development of a variety of patterning problems, such as feather germ primordia and cartilage formation in the vertebrate limb. Linear analysis has been the main technique for assessing the pattern formation potential of these models to date. In this paper we carry out a nonlinear analysis and numerical simulations of a generic model in two spatial dimensions. With these methods, we obtain conditions for generating specific spatial patterns such as stripes and spots, and divide the parameter space into domains giving rise to distinct types of pattern. We accomplish our goal through a study of model parameter domains by showing how different mechanical forces affect spatial patterning.