Orientation of Turing-like Patterns by Morphogen Gradients and Tissue Anisotropies

Abstract

Patterning of periodic stripes during development requires mechanisms to control both stripe spacing and orientation. A number of models can explain how stripe spacing is controlled, including molecular mechanisms, such as Turing's reaction-diffusion model, as well as cell-based and mechanical mechanisms. However, how stripe orientation is controlled in each of these cases is poorly understood. Here, we model stripe orientation using a simple, yet generic model of periodic patterning, with the aim of finding qualitative features of stripe orientation that are mechanism-independent. Our model predicts three qualitatively distinct classes of orientation mechanism: gradients in production rates, gradients in model parameters, and anisotropies (e.g. in diffusion or growth). We provide evidence that the results from our minimal model may also apply to more specific and complex models, revealing features of stripe orientation that may be common to a variety of biological systems.